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Optimal management of Bolivian tropical dry forests

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Optimal management of Bolivian tropical dry forests
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Boltz, Frederick
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ix, 103 p. : ill. ; 29 cm.

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Fees ( jstor )
Forest growth ( jstor )
Forest management ( jstor )
Forests ( jstor )
Logging ( jstor )
Sustainable forest management ( jstor )
Timber ( jstor )
Trees ( jstor )
Tropical forests ( jstor )
Wildlife management ( jstor )
Arid regions forestry -- Bolivia ( lcsh )
Dissertations, Academic -- Forest Resources and Conservation -- UF ( lcsh )
Forest Resources and Conservation thesis, Ph.D ( lcsh )
Forest conservation -- Bolivia ( lcsh )
Sustainable forestry -- Bolivia ( lcsh )
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theses ( marcgt )
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Thesis (Ph.D.)--University of Florida, 2003.
Bibliography:
Includes bibliographical references.
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Printout.
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Vita.
Statement of Responsibility:
by Frederick Boltz.

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OPTIMAL MANAGEMENT OF BOLIVIAN TROPICAL DRY FORESTS


By

FREDERICK BOLTZ

















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2003































Copyright 2003

by

Frederick Boltz















ACKNOWLEDGMENTS

I am deeply indebted to my advisor, Dr. Douglas R. Carter, for his skilled

mentoring and enthusiastic support throughout my graduate studies. Likewise, I am

grateful for the valuable tutelage and dear friendship offered to me over the years by the

members of my supervisory committee, Drs. Janaki LR.R Alavalapati, Thomas P. Holmes,

Clyde F. Kiker, and Francis E. "Jack" Putz. This research was partially financed by

Proyecto BOLFOR, a USAID-funded sustainable forest management project in Bolivia

through an agreement among Chemonics International, Inc., The Forest Management

Trust, and the University of Florida. Colleagues of Proyecto BOLFOR provided

excellent technical support and guidance (notably, Freddy Contreras, Todd Fredericksen,

Joaquin Justiniano, Claudio Leafio, Juan Carlos Licona, Froilan Merlo, John Nittler, and

Marisol Toledo). I am beholden to Roberto Quevedo S., Roberto Sainz V., Alberto Arce

and William Rojas for their honest and enthusiastic responses to my cost surveys. My

sincere gratitude is also due to the competent team of professors and professional staff of

the School of Forest Resources and Conservation (SFRC), who greatly enriched my

graduate career. Lastly, my gratitude is extended to the Graduate School of the

University of Florida, the Institute of Food and Agricultural Sciences, and the SFRC for

their award of the E.T. York Presidential Fellowship, which provided important financial

and institutional support for this research.
















TABLE OF CONTENTS


ACKNOWLEDGMENTS .................................................................. iii

LIST OF TABLES..................................................................... ................................. vi

LIST OF FIGURES ............................................................................................... viii

A B STRA CT ................................... .............................................................................. ix

CHAPTER

1 INTRODUCTION 1

2 MULTINOMIAL LOGIT ESTIMATION OF A MATRIX GROWTH MODEL
FOR TROPICAL DRY FORESTS OF EASTERN BOLIVIA .............................4

Introduction ............................ ..... .............................................................. 4
Study Site ........................................ ............................................................... 8
M ethods......... ... ........ ..................... .. ..... ..... ......... ........ ......... ............ 9
Results and Discussion................................ ................................................. 15
Growth Model Estimation..................................... .......................15
Recruitm ent............................................ ............................................ 20
Static, Deterministic Modeling........................... ........................ 21
Static, Stochastic Modeling ................................... .......................23
Dynamic M odeling .................... .......... ............... ... ..................... 23
An Application....................... ............ ............................25
Conclusions .............................................. ............. ................26

3 OPTIMAL MANAGEMENT OF A CHIQUITANO TROPICAL
DRY FOREST..................................... ................... .............................27

Introduction ............................ ..... .................... ............................. 27
M ethods........................................... ...................................................................30
Forest Growth M odel............................................. ............................30
Economic Data.......................... ........ ............................31
Optimization Models ................................ ..................35
Residual Stand State Indices........ ........... ................. ..........................40
Results and Discussion..................................................... ............................43
Optimal Harvest per Management Alternative.......................................43









Profitability of Management...................................................... 48
Stand State and Forest Value Measures...............................................49
Conclusions .......................................................... ....... ............................ 54

4 REGULATORY POLICY EFFICIENCY IN PROMOTING SUSTAINABLE
TIMBER MANAGEMENT FOR A BOLIVIAN TROPICAL DRY FOREST......57

Introduction ........................... .................... ...... ...... ........ ..............57
M ethods.............................................. ........... .... ........... ............... 58
Forest Growth and Optimization Models ....................................... .............58
Regulatory Policies..... ....... .... ................................62
Results and Discussion............ ...... .. .......................68
Harvesting Behavior and Forest Condition................................68
Profitability and Rent Distribution ................................ ........73
Conclusions ..... .............. .............................74

5 CONCLUSIONS....................................................................... 77

APPENDIX

A GUILD CLASSIFICATION OF LOMERIO TREE SPECIES.......................82

B FOREST HARVESTING COSTS PER COMPONENT..................................86

C MARKET VALUE OF MERCHANTABLE TIMBER SPECIES........................ 88

D DEFINITION OF OPTIMIZATION VARIABLES............. .......................... 89

E MATHEMATICAL DESCRIPTION OF MANAGEMENT ALTERNATIVES ...91

F MATHEMATICAL DESCRIPTION OF OPTIMIZATION SCENARIOS
WITH REGULATORY MECHANISMS..........................................................94

LIST OF REFERENCES.......................................................97

BIOGRAPHICAL SKETCH ................................... ............ .........103















LIST OF TABLES
Table Rge

2-1. Maximum likelihood estimates (MLE) of transition model parameters.................. 16

2-2. Marginal effects of attributes xi on transition probabilities ...................................17

2-3. Comparison of predicted and observed mean transition probabilities
for all size classes by guild................................. ....................................... 18

2-4. Ordinary least squares (OLS) estimate of recruitment model................................21

2-5. Deterministic prediction of forest evolution, aggregate population.........................21

3-1. Market values and merchantable proportions of stems per guild............................33

3-2. Mean volume of stem extracted in harvest per size class and guild (Vy,.)............... 34

3-3. Net value (vj) of an extracted stem per size class and guild..................................35

3-4. Mean ordinal market (Mk) and wildlife (Wk) values per sub-guild ........................42

3-5. Harvest level in absolute terms and in proportion of the available
merchantable volume in Year 0 per management alternative................................44

3-6. Comparison ofpre-harvest population (yo) and sustained-yield (STY)
distribution (y*) per guild ............................. ...............................................45

3-7. Comparison ofpre-harvest population (yo) and sustained-yield (SFM)
distribution (y**) per guild ......................... ............................................... 46

3-8. Net present value and opportunity costs of management alternatives ..................48

3-9. Discount rate effects on the NPV of harvest returns for a 40-year horizon .............49

3.10. State of the aggregate residual stand population per management alternative.........51

3-11. Residual merchantable species population per management alternative ...............51

3-12. Wildlife and diversity indices per management alternative ...................................53







vii


4-1. Residual distribution of merchantable stock (trees >40 cm dbh per ha)
per regulatory policy, Year 40.................................. ......................69

4-2. Profitability and rent distribution per regulatory policy...................................73















LIST OF FIGURES
Figure e

2-1. Observed and predicted stability probabilities per dbh class for Guild 5 ...............20

2-2. Static, deterministic prediction of forest evolution with observed (G)
and MNL estimated (GMNL) transition matrices....................................................22

2-3. Stochastic, stationary estimation of the forest population (all guilds)
25 years after the observed harvest ................................ ....... ..... 23

2-4. Comparison of static and dynamic model estimates of tree population
distribution 25 years after harvesting 40% of merchantable stems.....................24

2-5. Undisturbed, steady-state equilibrium condition (y") estimated with
observed and MNL-estimated transition probability matrices...........................26

3-1. Aggregate merchantable and non-merchantable residual population
structure under management alternatives and climax condition............................50

3-2. Residual merchantable population structure under management
alternatives and climax condition...............................................................52

4-1. Distribution of merchantable population per regulatory policy, Year 40 ...............70

4-2. Distribution of merchantable stems of Guild 1 per regulatory
policy, Y ear 40 ............................................................... .......... .... .............70

4-3. Distribution of merchantable stems of Guild 5 per regulatory
policy, Year 40 ............................ ....... .................. ... ...... ............................71

4-4. Percent compliance (p) with the STY condition and NPV of returns
from management ($/ha) relative to performance bond level ()............................ 72















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

OPTIMAL MANAGEMENT OF BOLIVIAN TROPICAL DRY FORESTS

By

Frederick Boltz

May 2003

Chair: Douglas R. Carter
Major Department: School of Forest Resources and Conservation

The prospect of sustainable management of natural tropical forests for their timber

and non-timber benefits faces important biological and technical challenges of defining

the conditions necessary for sustainability, as well as economic impediments concerning

opportunity costs and appropriate incentive mechanisms. In this study, an optimization

model of forest management is employed to examine the conditions necessary for

sustainable management of a Bolivian tropical dry forest. Integration of a forest growth

model in the optimization enables an examination of harvesting impacts on forest

structure and composition in addition to the economic returns to management. Results of

the optimization analyses are then employed to examine the efficiency of alternative

fiscal regulatory mechanisms in promoting more sustainable logging behavior.

Simulation results indicate that sustainable management for timber production is both

feasible and profitable in the dry forest site. Alternative regulatory policies may achieve

sustainability goals more efficiently than current Bolivian forest policy, but compromises

between the efficiency and practicality of regulatory approaches are warranted.

ix














CHAPTER 1
INTRODUCTION

The success of initiatives promoting sustainable forest management (SFM) in

natural tropical forests will depend on demonstration that it is not only technically

feasible, but also equally decisive, that it is economically viable. Critical to the effective

conservation of tropical forest ecosystems managed for timber will be tangible incentives

for improved, sustainable management by forest landowners and the logging industry.

The management of natural tropical forests for timber is a complex and contentious issue.

Its complexity derives from the nature of the mixed-species, uneven-aged tropical forests

themselves, which confound attempts to estimate the conditions necessary for

sustainable, productive management. Its contentiousness derives from the extraordinary

nonmarket value of the biodiversity and ecological service flows conserved by tropical

forests, the increasing scarcity of tropical forests, and the deleterious consequences of

their mismanagement.

Although the technical challenges to defining and implementing sustainable forest

management (SFM) are imposing, most authors agree that the principal impediment to its

greater adoption is SFM's financial inferiority relative to conventional logging practices,

and alternative land uses (Verissimo et al. 1992, Kishor and Constantino 1993, Rice et al.

1997, Pearce et al. 2003). Given this conclusion, and the desirability of a sustainable

solution to unabated demands for the harvest of tropical timbers, there is urgent need for

empirically rigorous examination of the marginal costs of more sustainable management,

and the trade-offs that may be optimal to achieve both production and conservation goals.

1









Recent studies of Dipterocarp forests in peninsular Malaysia examined such trade-offs

between the financial and ecological benefits of natural forest management (Boscolo and

Buongiorno 1997, Ingram and Buongiomo 1997, and Boscolo and Vincent 2000). The

present research contributes to earlier work by examining the conditions necessary for,

and the biological consequences and economic costs of sustainability, of a forest in the

eastern Bolivian lowlands.

The Bolivian forestry law was revised in 1996 (Ley 1700) to more effectively

promote sustainable management of the nation's forest resources, which are allocated in

renewable concessions to the logging industry (Art. #1). The present study offers a

contribution to the analysis of whether or not new forestry legislation is likely to achieve

these sustainability goals. The study offers an economic comparison of management

alternatives under current and alternative regulatory constraints, and a robust analysis of

the biological impact of such alternatives for stands representative of the Chiquitano

tropical dry forests of eastern Bolivia.

The study focuses on 800 hectares (ha) of seasonally dry forest located near the Las

Trancas community (1613'S, 61050'W) in the Lomerio region south of Concepci6n,

Santa Cruz, Bolivia. The forest is representative of the Chiquitano tropical dry forest

ecosystem, which lies in a transition zone between the humid forests of the Amazon

Basin and the thorn scrub of the Gran Chaco (Killeen et al. 1998). Numerous timber

concessions have been awarded in the Chiquitano forests, which are valued for their

stocks of tropical hardwood species such as Spanish cedar (Cedrelafissilis), Spanish oak

(Amburana cearensis), and "morado" (Machaerium scleroxylon).









Objectives of the study are to portray the optimal behavior of a forest

concessionaire, whose goal is to maximize the financial returns from logging and whose

management actions are circumscribed by biological, market, and regulatory constraints.

The study aims, moreover, to determine the conditions necessary to maximize the returns

from logging while meeting the goals of sustained timber yield and maintenance of

desired forest conditions. The study comprises three principal elements, each of which is

fully developed in the ensuing chapters. These elements include:

* Estimation of a forest growth and yield model as a basis for establishing the
biological conditions by which management is constrained

* An economic optimization comparing the profitability and forest impacts of
alternative management regimes

An analysis of regulatory policies as means of providing incentives to
concessionaires for more sustainable forest management behavior

Together these components respond to fundamental issues of sustainable forest

management, notably: what are the biological conditions necessary for sustainability,

what are the costs of achieving this goal, and what are appropriate regulatory mechanisms

for inducing sustainable behavior. For reasons of tractability, numerous assumptions are

made in developing the biological and economic models. Consequently, although the

models are derived in rigorous empirical analysis, the simulation results are indicative,

not definitive. It is hoped, nonetheless, that the results of this study will inform

management and policy formulation for the Chiquitano forests and enrich important

research concerning the biological and economic requirements for the sustainable

management of tropical forests.
















CHAPTER 2
MULTINOMIAL LOGIT ESTIMATION OF A MATRIX GROWTH MODEL FOR
TROPICAL DRY FORESTS OF EASTERN BOLIVIA

Introduction

The development of growth and yield models for tropical forests is often a daunting

task because of the complexity of these rich, diverse ecosystems, and the paucity of data

enabling robust model estimation. The difficulties of representing the dynamics of

species interaction, recruitment, and response to disturbance are compounded when the

model is intended to serve goals of management planning, in addition to scientific

simulation. In the present study, I develop a matrix model of forest growth and yield for

tropical dry forests of eastern Bolivia, the product of several years of tree growth

measurements conducted by members of the Bolivian forest management project

(BOLFOR). The model was developed to respond to the need for meticulous estimation

of timber returns and forest impacts from polycyclic harvesting. The study contributes to

forest growth modeling science through its novel use of multinomial logistic regression

methods to estimate a five-guild matrix growth model for a Chiquitano tropical dry

forest.

Matrix models were first formulated by Leslie (1945) for animal populations and

later modified by Usher (1966, 1969) for managed forests. Buongiomo and Michie

(1980) extended this work by introducing density-dependent recruitment to solve the









problem of exponential growth of the tree population in the Leslie and Usher models.

Their model formulation provided the basis for a large number of later studies by

Buongioro and colleagues that integrated species stratification, forest regulation, and

economic and ecological criteria with economic optimization models founded upon

density-dependent matrix growth model estimation (e.g., Buongiomo and Lu 1990, Lu

and Buongiomo 1993, Buongiorno et al. 1994, Ingram and Buongioro 1996, Boscolo

and Buongiomo 1997).

Matrix models are based on projections of whole stands, as opposed to individual

trees. Trees are commonly aggregated according to their size class and perhaps species

group so that the entire stand may be represented by a vector (or several vectors) of tree

population per class at a given time. Matrix models are based on a system of linear

difference equations, describing the change in tree populations per size class over discrete

time periods. Accordingly, for any given population value in a size class (yi) at time

t= 0, where the function describes the change of y, over a discrete time period for all

periods {y,, =it, yi-,.), t = 1, 2, 3... T}, there exists a uniquely determined function y,, that

is a solution of the equation and has the given value for t = 0 (Sydsaeter and Hammond

1995).

An important advantage of the matrix formulation is its relative simplicity and ease

of integration into linear programming optimization models (Buongiomo and Michie

1980). Classifying the growing stock relative to only a few parameters greatly simplifies

the modeling of complex uneven-aged, multi-species stands. The linear form of the

model and stand classification into size/species groups with consistent behavior greatly









simplifies model calibration and inferences concerning forest evolution (Lu and

Buongiomo 1993).

Transition probabilities are commonly estimated by simple mean proportions of

movement calculated from observations of the animal or tree populations (Leslie 1945,

Usher 1966, Buongiomo and Michie 1980). Logistic regression to predict the probability

that an individual tree will be 'successful' in an event with a binary outcome has been

used to predict mortality (Hamilton and Edwards 1976, Buchman et al. 1983),

regeneration (Johnson 1984, Ferguson et al. 1986), and diameter increment (Lowell and

Mitchell 1987, Vanclay 1991). The logistic function constrains probability predictions to

the interval (0,1), provides a binomial distribution of errors, and allows the use of

individual tree data rather than class means for tree size and other explanatory variables

(Vanclay 1994). Moreover, the logistic equation is robust in the presence of outliers and

decrements in the data (Vanclay 1991).

In the present study, I employ multinomial logistic (MNL) regression to estimate

the transition probabilities of a matrix growth model for a dry forest of the eastern

Bolivian lowlands. The MNL estimates of transition probabilities are derived from tree

and stand attributes influencing growth and mortality. Lowell and Mitchell (1987)

developed a logistic model that estimated growth and mortality simultaneously, though

these were portrayed as binary choices; specific growth proportions were applied to the

"successful" population in a subsequent model step. Rather than estimating the

probability of "success" for a binary outcome, such as mortality or survival, the

multinomial formulation allows estimation of the probability of one of three events

occurring for a size-class and species group of trees during a given growth interval:









* Mortality
* Remaining in the same size class or "stability"
* Moving up one size class or upgrowthh"

This approach differs from previous work in its use of tree and forest characteristics

to simultaneously estimate the probability of these three outcomes. The approach is

advantageous in allowing deterministic, stochastic, and dynamic prediction of forest

evolution, while preserving the simple linear form of matrix models that permits their

straightforward integration into optimization studies. Moreover, it is expected that the

transition probabilities resulting from MNL estimation are more smoothly distributed

across size classes relative to those resulting from simple proportional estimation from

observed forest populations, which are likely to be much more erratically distributed

given limited population samples and time spans of observations.

The MNL transition model allows stochastic simulation of transition probabilities

while preserving the stationarity of a deterministic model form. The model may thus

incorporate the biological uncertainty inherent in forest growth estimation and may allow

for a more robust statistical comparison of results. Compatible deterministic and

stochastic forms permit more robust statistical analyses, while preserving the efficiency

of a deterministic model (Vanclay 1991).

An important limitation of the transition matrix models developed by Leslie (1945),

Usher (1966, 1969), and Buongiomo and colleagues (e.g., Buongiomo and Michie 1980)

is the assumption of stationarity-- that the transition probabilities for a given size/species

class remain constant over time. Estimations of steady-state stocking and harvest levels

are feasible; and with stationarity, a unique solution for sustainable harvesting and

growing stock levels can be found (Buongiomo and Michie 1980). The stationarity









assumption that upgrowth and mortality probabilities remain constant over time may be

violated in managed stands, however (Johnson et al. 1991, Favrichon 1998). Forest

succession is likely a non-stationary process. Thus, probabilities of growth may be better

represented in a functional rather than constant form (Usher 1979). The impacts of

harvesting and of inter-harvest silvicultural treatments on established tree growth

therefore cannot be simulated, given the stationarity assumption. Stationarity may not

well describe actual stand behavior if, for instance, the growth of larger trees responds to

structural changes caused by harvesting, as observed in humid tropical forests of

Suriname and Brazil (Graaf 1986, Jonkers 1987, Silva 1989).

The MNL model estimation enables dynamic projections of forest growth by

reestimating transition probabilities at each time interval, thus overcoming the

stationarity limitation of traditional matrix models. The MNL model thus allows for

simulation of forest development dynamics, with transitions influenced by changing

stand characteristics. Decisions concerning harvesting and other silvicultural treatments,

as well as the evolution of stand structure and density, may be considered in iterative

projections of stand development at different time intervals. Stochastic estimation may

also be employed in the dynamic model form.

Study Site

The matrix model is estimated from permanent sample plot (PSP) data collected in

two 400 hectare (ha) forest blocks near the community of Las Trancas (16013'S,

61050'W) in the Lomerio region south of Concepci6n, Santa Cruz, Bolivia. The

seasonally dry tropical forests of Lomerio lie in a transition zone between the humid

forests of the southern rim of the Amazon basin and the thorn scrub of the Gran Chaco on

the southwestern edge of the Brazilian shield (Killeen et al. 1998). The forests are typical









of the Chiquitano dry forests of eastern Bolivia. Seasonal mean temperature in the region

is 24.3C with a mean annual precipitation of about 1100 mm and an acute dry season

from May to October. Soils of the region are primarily Inceptisols (shallow) and Oxisols

(deep), found in four distinct mapping units: hilltops, upper slopes, lower slopes, and

valley bottoms (Iporre 1996). The natural vegetation is classified as tropical dry forest

(Holdridge 1967). The undulating topography is dominated by low hills composed of

granite, gneiss, and metamorphic rocks of Precambrian origin (Geobold 1981). Elevation

varies between 400 m and 600 m asl.

Three distinct habitats constitute the Lomerio forests: upland forest; riparian or

valley-bottom forest; and granitic outcrops (inselbergs). Mature upland and riparian

forest canopies range from 12 18 m tall and are dominated by trees of the Leguminosae,

Bignoniaceae, Anacardiaceae, and Bombacaceae (Killeen et al. 1998). Understory trees

are mostly Sapindaceae and Myrtaceae (Kennard et al. 2002). The spiny ground

bromeliad Pseudananas sagenarius is distributed over approximately 80% of the forest

(MacDonald et al. 1998) and regenerates vigorously in upland forest clearings. Light

selective logging for Spanish cedar (Cedrelafissilis), Spanish oak (Amburana cearensis),

and "morado" (Machaerium scleroxylon) occurred at undetermined intervals in the past

(Fredericksen et al. 2001).

Methods

BOLFOR researchers arranged 180 PSPs of 20 x 50 m in a stratified random design

in the two 400 ha forest blocks in 1994 (LT94, Claros and Licona 1995) and 1995 (LT95,

Killeen et al. 1998). The PSP cover a total forest area of 18 ha: 8 ha in plot LT94 and 10

ha in LT95. Measurements of diameter at breast height (dbh), crown and stem quality,

crown position, liana infestation, damage, and mortality were conducted bi-annually.









Final PSP measurements for this study were conducted in July 2001. The forest blocks

were lightly logged 1 year after their installation. Mean harvesting intensities in the PSPs

were 2.72 trees per ha or a basal area of approximately 0.68 m2/ha.

The density of trees > 10 cm dbh was estimated at 418 stems/ha in the initial PSP

inventories of LT94 and 437 stems/ha in LT95, indicating that the Lomerio forest canopy

is relatively open (Killeen et al. 1998). Of 6005 trees 2 10 cm dbh initially inventoried

and monitored for growth in the PSPs, 5273 (87.8%) were retained for growth modeling.

The remaining trees were purged from the data set because of irregular stem form (8.2%),

apparent measurement error (3.6%), or unknown species (0.4%). Trees of irregular form

included species of Arecaceae and Cactaceae, as well as species that change stem form

with growth (Acosmiun cardenasii, Aspidosperma spp., Chorisia speciosa, and Ficus

gomelleira). The discarded trees were included in estimates of plot BA employed in

model regressions. Growth increments were recorded for trees 10 to 122 cm dbh.

Adjusted for season of measurement, the PSP growth data cover 82 months (LT94) and

68 months (LT95). Annual growth rates ranged from 0.00-1.83 cm/y.

Given the heterogeneity of species attributes and of forest habitats, a grouping of

tree species into ecological guilds was conducted to enable more precise modeling of

growth, recruitment, and mortality (Appendix A). Ninety-three tree species were

grouped into five guilds defined by forest habitat and shade tolerance of regeneration

(Pinard et al. 1999). Shade tolerance of regeneration is expected to be a robust measure

of differences between guilds (Grubb 1977). For cases in which the shade tolerance of

regeneration was not classified, mature tree shade tolerance was employed in guild










grouping. The five guilds retained for development of growth and yield models for

Lomerio are defined as follows:

* Guild 1: riparian species, shade tolerant

* Guild 2: riparian species, shade intolerant

* Guild 3: early successional and granitic outcrop species, shade intolerant

* Guild 4: mature upland forest canopy species and generalists, shade intolerant

* Guild 5: mature upland canopy species and generalists, shade tolerant


The growth model for Lomerio forests is founded upon a characterization of the

tree population by structure and composition. Classification of trees by diameter class is

utilized to describe forest structure and a grouping of species by ecological guild is

conducted both to portray floristic composition and to enable more precise modeling of

regeneration and disturbance events. Diameter classes are defined in five-centimeter

intervals from 10 cm to 85+ cm dbh and the growth interval 6 is defined as a five-year

period. The growth model is specified as


yr+= G(y, h,)+ r, (2-1)


where


,G ,

G= G2 .

G.,


y,= [yiy2, Y2, .. Y,]'
ht = [hi,, h2t, ... hmr]' and
r = [rli, r2t ..... rm '










Trees in the stand are divided into a finite number of diameter classes (n) and

guilds (m) with y, the number of trees prior to harvest in the th diameter class of guildj

at time t. The total density of guildj at time t is defined as the column vector

yi,= [yit ].

The number of trees harvested per diameter class (i in a given guild (/) is described

by the column vector hit = [Ih,].

The probabilities of upgrowth or movement from one diameter class to the next

during a 5-year growth interval (0) are expressed as a matrix (G) of transition sub-

matrices, and used to predict change for a specific time interval (O0).

a,,
b1, a21
Gj b21 a3

bn-lj a



The matrix Gj is composed of transition probabilities for trees of guildj, which

define the movement of trees into size classes (i) during the period 0 as follows:

ay is the probability that a tree in size class i will remain alive and in size
class i, or stability;

by is the probability that a tree in size class i-1 will remain alive and grow
into i from size class i-1, or upgrowth;

cj is the probability that a tree in size class i will die during the period, or
mortality.

The probabilities are related by the following equations:

ay+by+cy+=1 fori
ay +c= 1 fori=n









The MNL growth model estimates the probability of an individual tree observing

one of these three transition alternatives during a five-year growth interval. Mortality

includes both natural death and harvest-induced death, which is observed for those trees

immediately killed during harvest operations and those damaged during harvesting that

later die. Transition probabilities are estimated as a function of tree attributes and stand

characteristics, described as follows:

* DBH tree size class (dbh in 5 cm increments)

* RD/BA tree relative diameter (tree dbh/mean dbh of stand) divided by total
post-harvest basal area per hectare (m2/ha)

* TPH total number of trees per hectare prior to harvest

* HBA harvest basal area per ha (m'/ha)

* Gj dummy variable representing guildj, j= 2...5

* GI*DBH guild dummy variable multiplied by size class


Size class and relative diameter variables portray the relative dominance of each

tree in its immediate forest environment. Tree population, harvest basal area and post-

harvest basal area describe the density and competition specific to each plot. The dummy

variables G, and Gj*DBH describe behavioral differences among ecological guilds,

attributable to their sensitivity to light and habitat. Gj are intercept shifters, while

G,*DBH change the slope of the growth curve relative to guild and size class variables.

The dummy variables have the effect of increasing upgrowth probabilities for shade

intolerant Guilds 2, 3, and 4 and of decreasing the upgrowth probabilities for shade

intolerant Guild 5. The dummy variables adjust transition probabilities for Guilds 2-5

relative to Guild 1.









Transition probabilities for each guild are estimated according to Greene (2000, p.

858). The probability that tree i will transition to state is


Prob(Tree, = = j) forj = 0, 1, 2; (2-2)



where,
0 = mortality, 1= stability, 2 = upgrowth


It is assumed for analytical convenience that the data conform to the Independence

of Irrelevant Alternatives (IIA) property. This property stipulates that "the ratio of the

probabilities of choosing any two alternatives is independent of the attributes of any other

alternative in the choice set" (Hausman and McFadden 1984, p.1221). More simply

stated, IIA requires that the equation errors are independent across states or choice

alternatives.

The marginal effect of attribute x, on the transition probability to state is a

function of the beta vector for other states. Following Greene (2000, p. 861), the

marginal effect ofx, is defined as


P = P, s- Z Pkfl, (2-3)


Recruitment (the number of live trees that grow into the smallest diameter class

during a 5-year interval t to t+0) is expressed as a function of the total tree population

after harvest. A negative relationship is expected between recruitment and residual tree

population. The recruitment function is of the form

5 n
r, = d+ee (y, -h,) (2-4)
j-l i =1









where rt is the number of recruits into the 10 cm size class and d and e are regression

parameters to be estimated. Recruitment is estimated for the aggregate tree population,

as data did not permit the estimation of statistically significant recruitment models for

each guild. Recruitment levels for each guild are allocated proportionately, according to

the guild proportion of the total stand population observed prior to harvest. This method

is imprecise, but an unfortunate imposition of limited recruitment data.

The population per guild at time t+O is determined by the situation at time t, the

harvest during the growth interval (0), and the recruitment during this interval by

equations for each of the n guilds

yljt = rj + aI(yv- hyr)

y2,t+, = b2(yjy, hyj ) + a+(y2, h2j,)

Y3-I+o = b3(y2jt- h2j,)+ a3j(y3j,- h3j,)



Yjl+o = by(y.-yl,- h.,yj,) + a,(yjt- ht)

Growth may be assumed stationary, and long-term projections of stand growth

from initial conditions (yo) made deterministically as

r-I
y = G'yo + Gkr, (2-5)
k=O
for y growth periods of length 0 (Buongiomo and Michie 1980). Alternately, multiple

growth intervals (yO) may be estimated iteratively to more closely reflect the dynamics of

forest growth, with reestimation of the transition probabilities at each 5-year interval.

Results and Discussion

Growth Model Estimation

Multinomial logit (MNL) estimation resulted in a significant matrix model









(P < 0.001) from 5273 observations (Table 2-1). The marginal effects of tree and stand

attributes (x,) on the transition probabilities are estimated at the mean of x (Table 2-2).

Table 2-1. Maximum likelihood estimates (MLE) of transition model parameters b
MLE Parameter
Variable Stability Upgrowth
DBH 0.11899 0.05704
(0.01126) (0.01285)
DBH2 -0.00074 -0.00011*
(0.00016) (0.00017)
RD/BA -9.92015 -8.03101
(2.58866) (2.99525)
TPH -0.00009' -0.00096
(0.00021) (0.00025)
HBA -0.09417 -0.06784
(0.01693) (0.01966)
G2 0.30933' 0.75517'
(0.77065) (0.82540)
G3 0.87904 0.77800t
(0.40223) (0.46470)
G4 0.87814 1.89981
(0.27010) (0.28991)
Gs 0.76966 0.88485
(0.19444) (0.22188)
G2* DBH -0.00239' -0.00334'
(0.02934) (0.03114)
G3* DBH -0.03752 -0.03436
(0.01509) (0.01660)
G4* DBH -0.05345 -0.06214
(0.01047) (0.01137)
G5*DBH -0.03654 -0.03347
(0.00957) (0.01072)
X2 (18d.f.) 281.3135
In L -4590.429
Notes: a. Asymptotic standard errors in parentheses
b. Parameters for mortality are set to zero in MNL estimation
t Significant to P< 0.10
Not significant









Table 2-2. Marginal effects of attributes x, on transition probabilities] "
Marginal Effect


Variable
DBH


DBH2

RD/BA

TPH

HBA

G2

G3


Gs

G2* DBH

G3* DBH

G4* DBH

Gs*DBH


Mortality
-0.01205
(0.00123)
0.00007
(0.00002)
1.10026
(0.28906)
0.00004'
(0.00002)
0.01020
(0.00188)
-0.04911'
(0.08785)
-0.09944
(0.04540)
-0.13225
(0.03000)
-0.09304
(0.02184)
0.00031'
(0.00338)
0.00428
(0.00171)
0.00648
(0.00117)
0.00417
(0.00108)


Upgrowth


Notes: a. Asymptotic standard errors in parentheses
t Significant toP<0.10
Not significant

The MNL estimated transition probabilities are not significantly different

(P < 0.05) from the observed probabilities derived from Lomerio PSP data by calculation

of simple mean proportions of movement per size class and guild (Table 2-3).


Stability
0.01911
(0.00181)
-0.00015
(0.00002)
-1.13126
(0.45397)
0.00012
(0.00004)
-0.01192
(0.00315)
-0.03591'
(0.10680)
0.09088'
(0.06616)
-0.06753'
(0.04113)
0.050851
(0.03068)
-0.0007'
(0.00369)
-0.00372t
(0.00220)
-0.00343
(0.00145)
-0.00362
(0.00133)


-0.00706
(0.00155)
0.00009
(0.00002)
0.03100'
(0.39240)
-0.00015
(0.00003)
0.00173*
(0.00273)
0.08501'
(0.08313)
0.00856*
(0.05712)
0.19978
(0.03297)
0.04218'
(0.02626)
-0.00023'
(0.00275)
-0.00056'
(0.00179)
-0.00305
(0.00116)
-0.00055'
(0.00111)










Table 2-3. Comparison of predicted and observed mean transition probabilities for all size classes by guild
Guild 1 Guild 2 Guild 3 Guild 4 Guild 5
M S U M S U M S U M S U M S U
Predicted 0.07 0.75 0.18 0.07 0.70 0.23 0.13 0.70 0.17 0.23 0.54 0.23 0.13 0.68 0.19
Observed 0.12 0.73 0.15 0.09 0.73 0.18 0.15 0.65 0.20 0.19 0.55 0.26 0.16 0.70 0.14
t Stat 0.83 0.42 0.76 0.51 0.47 0.81 0.37 0.86 0.77 0.92 0.21 0.87 0.53 0.27 2.05










0.580 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.25 0.63 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0.22 0.66 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0.20 0.70 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0.18 0.72 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0.17 0.74 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0.16 0.75 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0.16 0.75 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0.16 0.74 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0.16 0.73 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0.160.71 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0.170.69 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0.19 0.65 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0.21 0.61 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0.23 0.55 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.26 0.

0.57 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.27 0.69 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0.14 0.74 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0.16 0.68 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0.16 0.78 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0.14 0.73 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0.19 0.70 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0.180.680 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0.22 0.71 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0.10 0.82 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0.12 0.64 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0.18 0.73 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0.27 1.00 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0.001.00 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0.00 0.00 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000.0


As an example, the resulting MNL transition matrix (Gs5mL) estimated for stand

conditions after the observed harvest and the transition matrix generated by simple









proportional estimation (G5) for Guild 5 with a five-year interval and 5 cm dbh classes is

described below. Guild 5 is selected for comparison of observed and predicted transition

matrices because it had the highest number of observations (2762).

As hypothesized, the MNL transition matrix results in a smoother distribution of

transition probabilities across size classes relative to that generated by simple

proportional estimation (Figure 2-1). The MNL estimation corrects for variance in the

forest data and for sample error effects on matrix elements (Usher 1976), such as the

elevated probabilities of movement in large size classes generated by proportional

estimation from a very small sample of large trees.

1.20

1.00 .*

0.80

S0.60 -

0.40

0.20 ------ Observed Predicted

0.00 .
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
DBH class (cm)
Figure 2-1. Observed and predicted stability probabilities per dbh class for Guild 5

Recruitment

The OLS estimated recruitment function (r) observes the expected negative

relationship between recruitment and total trees per hectare (TPH) (Table 2-4). Although

the fit is quite poor, the variables and the model are all significant to P < 0.05.










Table 2-4. Ordinary least squares (OLS) estimate of recruitment model
Variable Parameter Std. Error
Intercept 152.775 27.213
TPH -0.117 0.054
Adj R2 0.021 -
F test 4.583 -


Static, Deterministic Modeling

In static, deterministic form, transition probabilities estimated per guild at the initial

stand state are maintained throughout the projection horizon. The MNL model of forest

evolution after harvest shows an increase in total tree population and a leveling of the

population distribution across size classes with increasing age (Table 2-5).

Table 2-5. Deterministic prediction of forest evolution, aggregate population
DBH Class Post-harvest Projected (trees/ha)
(cm) (trees/ha) year 25 year 50 year 100
10 170.2 191.3 189.6 187.7
15 141.2 129.4 129.3 127.7
20 82.7 88.6 90.0 88.8
25 47.7 57.9 61.9 62.0
30 33.3 36.1 40.5 42.8
35 26.5 23.2 25.3 28.7
40 19.7 16.2 15.8 18.3
45 11.8 11.2 10.2 11.2
50 8.6 7.3 6.6 6.8
55 4.6 4.3 4.1 4.1
60 3.3 2.6 2.5 2.5
65 1.9 1.6 1.5 1.6
70 1.3 1.0 0.9 1.0
75 0.5 0.6 0.6 0.6
80 0.7 0.3 0.4 0.4
85 0.9 0.3 0.3 0.3
Total 554.8 571.7 579.3 584.6


Comparison of model projections using the observed transition probabilities (G)

and the MNL estimated probabilities (GMNL) reveals important differences in the









resulting stand distribution estimates (Figure 2-2). Whereas the MNL estimated matrix

model predicts a leveling population distribution with increasing age, the matrix model

derived from observed transition probabilities predicts a distribution similar to that

observed after the initial harvest and a greater decline in stems of merchantable size (> 40

cm dbh). The MNL model predicts a greater number of trees in the merchantable 20 to

40 cm dbh classes relative to the observed prediction due to the "smoothing" effect of the

regression on transition probabilities across size classes. While the observed matrix

model exhibits considerable variance in transition probabilities, especially in those guilds

with limited samples (Guilds 2 and 3), the MNL model corrects for sample variance. The

MNL model predicts greater stability of stems in the 20 to 40 cm range and greater

upgrowth of smaller stems into these size classes relative to the observed model, with less

variance of these transition probabilities among similar size classes.

200 Initial distribution


160 -. Year 100, MNL model

a -- Year 100, observed
120 -
Stransition probabilities

S80


40



10 20 30 40 50 60 70 80
DBH class (cm)


Figure 2-2. Static, deterministic prediction of forest evolution with observed (Go) and
MNL estimated (G ) transition matrices









Static, Stochastic Modeling

The MNL estimation of transition probabilities permits stochastic simulation of

stand evolution, drawing upon the standard errors of regression parameters. The

stochastic approach considers biological uncertainty in projections of stand growth,

providing a confidence interval of expected population values for a future stand state.

Stochastic simulation has the benefit of enabling more rigorous statistical comparison of

results from alternative simulations and permitting sensitivity analyses. The stochastic

element can be introduced into static projections, for which the initial transition

probability estimates are maintained throughout the projection horizon (Figure 2-3) or in

dynamic, iterative projections.

250
95th pere
200 M +SD

Mean


100 -


so



10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
DBH class (cm)

Figure 2-3. Stochastic, stationary estimation of the forest population (all guilds) 25 years
after the observed harvest (SD = standard deviation, pere = percentile)

Dynamic Modeling

Changes in the growth dynamics of the forest over time may be considered by

iterative estimation of forest evolution with the re-estimation of transition probabilities at









each 5-year growth interval. Forest response and recovery trajectories following

disturbances caused in harvesting or silviculture may be more precisely estimated in

dynamic form. As an example, estimated stand populations and their distribution twenty-

five years after a simulated harvest of 40% of all merchantable stems (> 40 cm dbh;

Guilds 1, 2, 4,and 5) are quite distinct in static and dynamic model forms (Figure 2-4).

The 25-year growth horizon simulated in this example was selected merely for

demonstration purposes. Changes in the stand population, basal area, and harvest

variables over time result in modest changes in the transition probability estimates

generated by the MNL model, which may more precisely reflect forest dynamics and

disturbance effects.

200
-- Year 0

160- Static model, year25

.... -. Dynamic model, year 25
S120-

S80

40


0
10 20 30 40 50 60 70 80
DBH class (cm)
Figure 2-4. Comparison of static and dynamic model estimates of tree population
distribution 25 years after harvesting 40% of merchantable stems

That the dynamic model predicts more stems in 10-40 cm dbh classes relative to

static model (Figure 2-4) reveals an important advantage of the dynamic prediction form.

In the static model, the transition probabilities estimated for the initial harvest are









maintained throughout the 25-year projection period. Consequently, the high mortality

probabilities estimated after a 40%0 proportional harvest are retained at each 5-year

growth interval in the static model, reducing the residual population at each interval. The

dynamic model avoids this modeling limitation by recalculating transition probabilities at

each growth interval, according to the state of the stand at these 5-year intervals.

Accordingly, the high mortality probabilities estimated immediately after the simulated

40% harvest, are not maintained throughout the projection. Instead, mortality

probabilities decline with increasing time after this harvest, as the stand returns to

relatively stable conditions compared to the disturbed state created by harvesting.

An Application

The benefits of the MNL model form relative to a matrix model generated from

observed transition probabilities are best revealed in model application. Following

Buongiomo and Michie (1980), the undisturbed, steady-state or "climax" equilibrium

(y) may be calculated for a matrix growth model as

y- (I-G)'r (2-6)

Expectations for the undisturbed steady-state are that the tree population converge to a

negative exponential distribution, typical of uneven-aged, mixed species forests and that

with greater length between disturbances this distribution gradually even out across size

classes. The MNL steady-state demonstrates precisely this result (Fig. 2-5). The steady-

state generated by the matrix model derived from observed transition probabilities

suggests a relative decline of large stems with increasing age. Moreover, an anomalous

"bump" in the population distribution for trees of size class 70 cm dbh results from model

estimation errors imposed by the limited sample of trees in large stem classes.










200
S- Observed matrix model
160-
MNL matrix model
120-


| 80


40



10 20 30 40 50 60 70 80
Dbh class (cm)

Figure 2-5. Undisturbed, steady-state equilibrium condition (y) estimated with observed
and MNL-estimated transition probability matrices

Conclusions

Multinomial logistic (MNL) estimation of the transition probabilities in matrix

models of forest growth offers important benefits relative to matrices derived from

proportional, static estimates derived from forest plot observation means. The MNL

model results in a smoother distribution of transition probabilities across size classes,

correcting for variance in the data and model estimation errors imposed by limited

samples. The MNL form also allows for deterministic and stochastic projection in both

static and dynamic model forms. Stochastic simulation enables more rigorous testing of

hypotheses concerning stand growth by accounting for fundamental biological

uncertainties. The static model form allows greater ease of integration in optimization

studies, while dynamic forms enable more meticulous simulation of stand evolution

dynamics and the effects of disturbance events.














CHAPTER 3
OPTIMAL MANAGEMENT OF A CHIQUITANO TROPICAL DRY FOREST

Introduction

Sustainable forest management has drawn great attention in the debate over

appropriate strategies to achieve often competing, but necessarily compatible objectives

of environmental conservation and sustainable economic development in developing

nations with large tropical forest reserves (Kishor and Constantino 1994, Dickinson et al.

1996, Rice et al. 1997, Frumhoff and Losos 1998, Rice et al. 2001, Pearce et al. 2003).

Despite conclusions concerning the viability or appropriateness of sustainable

management initiatives within this polemic debate, the conditions necessary for

sustainable management and, consequently, rigorous analyses of the costs and benefits of

these strategies relative to alternative tropical forestry options have been conducted in

only a few noteworthy studies (Howard et al. 1996, Howard and Valerio 1996, Ingram

and Buongiomo 1996, Boscolo and Buongiorno 1997, Boscolo and Vincent 2000). This

deficiency is primarily attributable to the paucity of statistically robust models of the

growth and yield of mixed-species tropical forests. This paucity, in turn, is due to the

common inadequacy of tropical forest growth data, particularly that offering evidence of

forest responses to harvest interventions. Furthermore, a precise definition of what

constitutes SFM remains elusive, but commonly sustainability is defined by one of two

management objectives:

* Maintaining timber yield over an indefinite harvest horizon or sustained-yield
timber management (STY)









* Maintaining non-declining timber yields; and sustaining other forest benefits (non-
timber products, ecological services, and biodiversity)

The latter may be more strictly defined as SFM; a possible distinction being that STY

may generate a less sustainable flow of non-timber products relative to SFM (Pearce et

al. 2003).

Financial analyses comparing returns from more environmentally benign, or

hypothetically sustainable, harvest prescriptions with those from conventional logging

practices in tropical forests, reveal in some instances that improved forest management,

such as reduced-impact logging, is financially and ecologically superior, though the

conditions required for sustainability are not precisely identified (Barreto et al. 1998,

Armstrong 2000, Holmes et al. 2002). Other studies estimating the reduced harvest

levels and conservation easements necessary for SFM in natural tropical forests conclude

that the opportunity costs of more sustainable harvest regimes relative to conventional

logging or other land uses are excessively high (Kishor and Constantino 1993, Howard

and Valerio 1996, Hout 1999, Tay 1999, Healey et al. 2000, Pinard et al. 2000). Still,

suitably indicative estimates of the financial costs and ecological benefits of STY, let

alone SFM, remain elusive due to the inadequacy of dependable growth models and rare

attempts to integrate these models into an appropriate form for rigorous economic

analysis of forest management alternatives.

The present study aims to make a modest contribution to resolving this inadequacy

by producing a statistically robust economic comparison of management alternatives for

forests representative of the Chiquitano tropical dry forests of eastern Bolivia. The

analysis draws upon a matrix model of forest growth and yield and an economic

optimization model, integrated to enable the estimation of conditions necessary for









sustained timber yield and a comparison of this optimum with optimal harvest solutions

for alternative forest management regimes. The optimization study concerns the

management by large timber firms of Chiquitano forest concessions and derives from

economic and forest data collected in the Chiquitano region and the provincial capital,

Santa Cruz, Bolivia. Alternative management scenarios examined in the study include

unregulated or unconstrained harvest (U), management under constraints imposed by the

Bolivian forestry law (BFL), sustained timber yield management (STY), and

management constrained by objectives of sustaining timber yield and maintaining the

structure and composition of a theoretical "climax equilibrium" forest (SFM). The

harvest horizon for all scenarios is set at 40 years to allow for comparison of the net

present value of returns. The actual harvest horizons for all scenarios are longer, those of

the sustainable scenarios STY and SFM being infinite, however the harvest horizon was

limited to 40 years due to poor fit of the recruitment function in the growth model, which

would significantly affect stocking and harvest levels for longer horizons. Forty years

was selected since it is the legal concession period under the Bolivian forestry law.

Harvesting is selective, its selectivity defined by the value and merchantability of trees

and constraints on their extraction.

The SFM scenario does not derive from mathematical conditions describing

sustained production of non-timber products or ecological benefit flows, but rather that of

attaining a residual forest condition approximating the structure and composition of an

undisturbed forest, as defined by the growth model. The theoretical "climax" condition

(y') or undisturbed equilibrium distribution is defined mathematically

ya= (I-G)"-r (3-1)









where

* I is the identify matrix

* G is a matrix of transition probabilities defining the movement of trees from one
size class to the next during a 5-year growth interval

* r is a recruitment function defining the number of trees entering the smallest size
class during a 5-year growth interval.

These and all other variables used in the present study are defined in Appendix D. The

climax condition is defined solely by the growth model and does not assume that the

forest condition prior to harvesting is in this undisturbed equilibrium.'

Conserving forest vegetative structure and composition is assumed an appropriate

proxy for the maintenance of non-timber and ecological benefit flows (cf., Terborgh

1986, Hunter 1990). The SFM regime thus hypothetically achieves the objectives of

SFM defined above, though empirical evidence of the maintenance of non-timber

benefits is not presented. Results of the present study are at best indicative, given the

assumptions required for modeling; however, they provide important insight into the

conditions required for sustainability and the costs and benefits of sustainable

prescriptions relative to alternative harvest possibilities.

Methods

Forest Growth Model

The optimization study employs a five-guild matrix model of forest growth, which

was estimated by multinomial logit (MNL) regression of permanent sample plot (PSP)

data collected in two 400 hectare (ha) forest blocks near the community of Las Trancas

(16013'S, 6150'W) in the Lomerio region south of Concepci6n (cf., Chapter 2). The

The theoretical climax condition should arguably be presented in quotations or italics, given its
debatable nature. For reading ease, however, such formatting will not be employed throughout the text
Climax is understood to refer to the theoretical forest condition defined mathematically as y= (I-G)-'r.








MNL matrix growth model projects the probabilities of upgrowth, stability, or mortality

of trees in each of five ecological guilds during a 5-year growth period and predicts

recruitment of trees into the smallest size class (10 cm dbh) for each guild. The linear

form of the MNL model and the assumption of stationarity for the transition probabilities

throughout the harvest horizon enable its straightforward integration into the present

linear optimization study. The Las Trancas sites are typical of the Chiquitano dry forests,

and thus provide a representative stand for the examination of management alternatives in

Chiquitano concessions. Light selective logging for Spanish Cedar (Cedrelafissilis),

Spanish Oak (Amburana cearensis), and "morado" (Machaerium scleroxylon) occurred at

undetermined intervals in the past (Fredericksen et al. 2001), so they are not in an

undisturbed, climax state.

Economic Data

The Bolivian forestry law was revised in 1996 (Ley 1700) to more effectively

promote sustainable management of the nations forest resources (Art. #1). The law set

aside areas for conservation and protection purposes, and permits logging only in other

forest areas. Logging concessions are allocated for a 40-year duration upon formal

application to, and approval by, Bolivia's forest service (Superintendencia Forestal).

The law requires forest management plans for all concessions and for forest

authorizations in private lands. Concessions also can be traded and inherited and are

renewable upon validation of the concessionaire's observance of sustainable forest

management plans.

Forest management costs are drawn from surveys of four industrial forestry firms

based in Santa Cruz and possessing logging concessions in Chiquitano dry forests.

Structured surveys were conducted in November 2000 and validated in follow-up









interview with each of the firms in July 2001. All costs and timber prices are reported in

2001 $US and are assumed constant throughout the management horizon (Appendix B).

Management costs FOB forest mill are classified as one of three types:

* Variable costs (C) in $/m3 for felling, skidding and log deck operations incurred
relative to the level of harvest intensity

* Fixed costs (F) in $/ha incurred regardless of harvest intensity at each cutting-cycle
entry for planning and capital costs including depreciation

* Annual costs (A) in $/ha paid throughout the harvesting horizon regardless of
harvest intensity, which include an area fee of $1/ha for the concession (patente)
and inscription fees to government agencies and trade associations

Variable costs are estimated at $12.11/m3, fixed costs at $62.51/ha and annual costs

at $1.55/ha. Variable costs are estimated relative to the efficiency of felling and skidding

(m3/hr) and the hourly costs of labor and machinery used in these operations. Felling

efficiency of 3.48 m3/hr is the statistical mode for data collected in Chiquitano forest

concessions of two-person felling teams in both planned and unplanned harvesting

operations (Cavero 1998, Menacho 1999) and fit to a gamma distribution. Skidding

efficiency of 3.68 m3/hr is the statistical mode for data collected in studies of operations

using rubber-tired skidders in three forest concessions in Chiquitania (Alarc6n 1997,

Patiflo 1997, Crespo 1999) and fit to a gamma distribution.

A discount rate of 18.75 % is assumed for the analysis. This is the mean real

interest rate on loans for 2001 reported by Bolivia's Central Bank (Banco Central de

Bolivia 2002). Market prices for merchantable stems per guild delivered to concession-

based timber mills (FOB mill) are drawn from surveys of timber consultants and lumber

yards in Santa Cruz, and from market surveys of Chiquitania conducted in 2001 by

BOLFOR researchers (Appendix C). Timber species demanded in Santa Cruz

lumberyards in 2001 are assumed to comprise the merchantable stock. Market value per









guild (p,) is estimated as the weighted mean price for merchantable stems of Guildj

(Table 3-1). This assumption greatly simplifies market value calculations for multiple-

species harvest. However, greater precision in calculating the market value of timber was

necessarily sacrificed for increased tractability of the optimization model.

Guild populations comprise merchantable and non-merchantable stems. Harvest is

necessarily constrained by the merchantability of the timber stock, as loggers will only

harvest those stems that are of merchantable species and form. It is assumed that

harvesting is restricted to logs appropriate for saw-timber milling, i.e. stems of 40 cm dbh

and greater. The merchantable proportion of stems per guild (co) is estimated as the

product of the proportion of merchantable species (sj) per guild and the proportion of

stems of merchantable form (ff) in that guild, based upon PSP data for the sample forest

blocks (Table 3-1). Trees of Guild 3, those growing in inselberg habitats, are not

merchantable.

Table 3-1. Market values and merchantable proportions of stems per guild
Market value (pj) Merchantable proportion
Guild ($US/m3) Species (s,) Form (nf) Stems (o,)
1 41.28 0.52 0.78 0.41
2 62.50 0.90 0.96 0.87
3 0.00 0.00 0.88 0.00
4 57.03 0.69 0.87 0.60
5 104.53 0.26 0.84 0.22


If the forest structure at time t is represented by the vector y, = [y;,, y2, ..., y.]',

forest volume is obtained by pre-multiplying y, by the square matrix















where j = [ g], i = 1 ...,n; j = l...,m; is the mean extracted volume of a tree in

diameter class i and guildj. The mean volume extracted in harvesting is estimated as

85% of the mean volume per dbh class and guild, assuming 15% of merchantable volume

lost in logging waste (Table 3-2). The 15% waste proportion is slightly higher than the

12.3% reported in production forests of Brazil for high stumps, split logs, and bucking

waste (Holmes et al. 2002).

Table 3-2. Mean volume of stem extracted in harvest per size class and guild (yi)
Mean extracted volume per stem (m3/stem)
Dbh class Guild 1 Guild 2 Guild 3 Guild 4 Guild 5
40 0.65 0.71 0.71 0.74 0.62
45 0.88 0.91 0.92 0.97 0.83
50 1.15 1.14 1.16 1.24 1.08
55 1.47 1.40 1.44 1.54 1.37
60 1.85 1.68 1.75 1.89 1.70
65 2.28 2.00 2.09 2.29 2.09
70 2.78 2.35 2.48 2.73 2.52
75 3.34 2.74 2.91 3.22 3.01
80 3.97 3.16 3.37 3.76 3.56
85+ 4.67 3.61 3.88 4.36 4.17

The net value (v#) of an extracted stem of size i in guildj in 2001 $US/m3

(Table 3-3) is thus calculated as the product of the mean price per guild (pj) less variable

harvesting costs (C) of $12.1 1/m3 and the mean extracted volume per stem of a given size

class and guild (V), assuming no economies of scale in harvesting. The net value of

stems in Guild 3 is negative as species have no market value, thus harvesting would

strictly impose costs.









Table 3-3. Net value (vi,) of an extracted stem per size class and guild
Net value ($/stem)
Dbh class Guild 1 Guild 2 Guild 3 Guild 4 Guild 5
40 22.33 41.96 -10.11 39.17 67.76
45 30.11 53.86 -13.10 51.25 90.34
50 39.46 67.44 -16.54 65.33 117.18
55 50.52 82.74 -20.47 81.54 148.63
60 63.41 99.82 -24.89 100.01 185.02
65 78.28 118.75 -29.84 120.86 226.70
70 95.27 139.56 -35.33 144.21 274.00
75 114.50 162.33 -41.39 170.18 327.26
80 136.13 187.11 -48.04 198.91 386.82
85+ 160.28 213.95 -55.30 230.50 453.02

Optimization Models

The optimization model prescribes maximization of the net present value (NPV) of

polycyclic harvesting (Z) subject to biological, market, policy, and sustainability

constraints. The objective function does not consider the costs of investment in the

growing stock described by the economic stocking rule for selection harvest (Duerr and

Bond 1952) or soil expectation value (SEV) used in similar optimization studies

(Buongiomo and Michie 1980, Boscolo and Buongiorno 1997, Bach 1999, Kant 1999).

These costs are opportunity costs of not harvesting merchantable stems in the initial

harvest entry in order to maintain the timber growing stock. The decision to exclude the

opportunity costs of maintaining the growing stock from the calculation of net returns is

based upon the nature of the forest property. As these forests are allocated in concessions

to private industry under government ownership, the opportunity costs of conserving the

residual stock are public rather than private costs. These opportunity costs are revealed

in the difference between unconstrained and constrained harvest cases described below.









The management problems are posed as linear programs and, as such, stationarity

is assumed for the transition probabilities of the matrix growth model to permit a global

optimum solution to each problem. The transition probabilities estimated for the PSP

following their harvest in 1995 and 1996 are selected as the stationary probabilities in the

guild growth matrices, as these estimates are expected to most closely approximate

growth in these forests. Four forest management alternatives are considered in the

optimization, notably:

* Unconstrained harvesting at 40-year intervals (U)
* Harvesting under Bolivian forestry law constraints at 40-year intervals (BFL)
* Sustained timber yield management at 5-year intervals (STY)
* Sustainable forest management at 5-year intervals (SFM)

A full mathematical description of each alternative is presented in Appendix E.

The cutting-cycle between harvesting under regimes U and BFL is set at 40-years,

the minimum interval required for profitable harvest (NPVt > 0), while that of the STY

and SFM scenarios is 5 years, selected to maximize the NPV of returns from these less

intensive harvesting systems. Financial returns from the sustainable scenarios (STY and

SFM) do not include any returns from regulation harvests, which would be undertaken to

convert the initial stand to steady-state, sustained-yield conditions. The harvest horizon

for all scenarios was set at 40 years to allow for comparison of the NPV of returns.

The objective function for U, BFL and STY cases prescribes maximization of the

NPV of returns from polycyclic harvesting, Z(% y), calculated as the present value of a

terminating series at discount rate 3, with harvest horizon T= 40 years and cutting-cycle

length t = y0, with period y0 being the number of intervals (y) of 5-year growth periods

(0) in a cutting-cycle. Cutting-cycles are 40 years (t = 40, y = 8) for U and BFL and 5

years for STY and SFM (t= 5, y =1). The objective function is defined mathematically









v'h F 1-(1+ 3)- )
max Z(,= =A (3-2)
,.o (1 +) ) o )
All management alternatives are constrained by the forest growth model, which

defines growth and recruitment in the residual forest between harvest intervals. All cases

are also constrained by absolute harvest restrictions, requiring that the harvest level not

exceed the growing stock (yt h, > 0) and non-negativity constraints (yt, hl > 0).

Forest growth constraint for cases U and BFL require that the sum of the harvest

and growing stock at time t equal the residual stocking at time t-1 plus any growth and

recruitment in this growing stock between these cutting-cycles (Eq. 3-3). This forest

growth constraint is defined as follows

7-1
h,+ y, -G'(y,_, -h,_,)= G'r (3-3)
k-0
Merchantability restrictions require that the proportion of trees harvested per size

class i and guildj at time t be equal or inferior to the merchantable stock (wo,) present in

the stand. The constraint is expressed

ho, co, (y,, + h,,) < 0 (3-4)
where o, is the merchantable proportion per guild.

For subsequent cutting-cycles of cases U and BFL, the merchantable proportion is

expected to decrease, as merchantable volume is removed and upgrowth during the

cutting-cycle interval does not replenish the merchantable stock to initial levels. Thus,

while equation 3-4 is applied as a constraint to the initial harvest of U and BFL,

subsequent merchantable stock constraints are comprised of the growing stock of residual

merchantable stems remaining after harvest (yI"i) plus any upgrowth into this









merchantable stock during the cutting-cycle interval. This constraint is described

mathematically


h, ,G'r,, 5 0 (3-5)
k-0
In addition, merchantability standards require that trees equal or exceed 40cm dbh, or

35
Y- =0 (3-6)
4-0
The Bolivian forestry law constrained management alternative (BFL) employs the

same objective function (Eq. 3-2) and is constrained by the same forest growth (Eq. 3-3)

and merchantability (Eq. 3-4, 3-5) restrictions as the unconstrained alternative (U). The

BFL case is constrained by the technical standards established by the government of

Bolivia for all concessions and private forests > 200 ha (Ministerio de Desarollo

Sostenible y Planificaci6n 1998). The standards stipulate a minimum 20-year cutting-

cycle, a maximum 80% allowable cut of the merchantable stock per species, and a

minimum dbh limit for harvested stems. The 20-year cutting-cycle restriction is not

binding for the present analysis, given that the minimum cutting-cycle for positive NPV

was estimated at 40 years and this interval assumed for the BFL scenario.

The minimum dbh limit standard is not uniform for all species of the Chiquitano

dry forest. Stems that are more valuable generally have higher dbh limits, such as

Cedrela fissilis (60 cm) and Amburana cearensis (50 cm), while the absolute minimum

for other stems is 40 cm dbh. The guild grouping employed in this present model does

not allow for precise application of this diversity of dbh limits. Rather, a minimum dbh

of 45 cm is assumed for all merchantable stems as a BFL constraint (Eq. 3-7). Similarly,

the 80% allowable cut restriction is applied per guild and not per species (Eq. 3-8, 3-9).









These assumptions decrease the precision of model projections, but are necessary for

tractability.

40
hA,, =0 (3-7)
-=0
85 85
h, 0.s8 ay,, O 0 (3-8)
1-45 1s45
85 85 85 y-
Eh, -0.8 Gy',-, 0.8 oG r,,, (3-9)
J-45 1=45 -=45 k-0

The STY objective function (Eq. 3-2) is calculated as the NPV of a terminating

periodic series of harvest revenues with harvest horizon T = 40 years and cutting-cycle

r = 5 years, which is the most profitable interval for low-intensity, sustained harvesting

given the effects of discounting. Higher NPV is achieved at shorter cutting-cycles for

STY and SFM, given the important effects of an 18.75% discount rate. Comparisons of

returns from harvesting at longer cutting-cycles were conducted in preliminary analyses

to confirm the validity of this expectation. The sustainable harvest level increases, but

the present value of net returns decreases markedly with increases in cutting-cycle length.

Forest growth serves as the sustained-yield constraint for the STY case, as it

requires a constant periodic harvest (h, = h+o =h*) and maintenance of a specified stand

structure (y, =yt+~e =y*). Definition of the sustained-yield constraints follows that of

Buongiomo and Michie (1980), who described the fundamental mathematical expression

of the sustained-yield linear optimization problem


Grh' + l-G')y = ZG'r (3-10)
k=O0
The STY regime is further subject to constraints defining merchantable proportion (Eq.

3-4) and size (Eq. 3-6).









The sustainable forest management alternative (SFM) has as its objective to

achieve a sustained-yield, steady-state forest as "close" as possible in structure and

composition to the undisturbed climax condition. The objective function is defined as

minimizing the sum of the absolute differences between the number of trees per size class

and guild in the climax forest (yC) and in the SFM residual stand (y**). Mathematically,

the objective function is expressed

min D(h. y.,d-,d) = Z (d,-B, + dB,) (3-11)
i J
where [dy] and [dy] are vectors of the absolute deviations of the number of trees of size

i and guildj in the growing stocky** and the climax state y' (Buongiorno et al. 1995)

and B,y is the mean basal area per size class (i) and guild (,), employed to place more

weight on large trees.

The SFM alternative observes the same constraints as the STY case, notably

sustained-yield forest growth (Eq. 3-10) and merchantability restrictions (Eq. 3-4, 3-6),

and is further constrained to meet the minimum economic goals of obtaining a non-

negative NPV in perpetual periodic harvest (Eq. 3-12).

v'h" -F A
_> 0 (3-12)
(1+ r)" r

Residual Stand State Indices

Stand state, forest value and diversity criteria are employed to examine changes in

the managed stand under alternative regimes. The criteria allow for a comparison of

residual, managed stands under optimal solutions to the four management alternatives

examined and comparison of these states relative to the climax condition defined by the

growth model (yV). Stand basal area (BA) is a fundamental measure of change in stand









density (m2/ha), which reveals both the level of harvest intensity and the "openness" of

the residual stand in terms of soil occupancy by trees. Changes in structure are examined

by graphically comparing the residual distribution of trees by size class and by estimating

the proximity of residual stand structure and composition to the climax state. The

proximity to climax index (PCI) introduced by Boscolo and Vincent (2000) is employed

to examine the deviation in structure and composition of managed stands from the climax

equilibrium. Proximity to climax structure and density at time t is defined



L(YB,)(313)
PCI=- BI )2

PCI measures the proximity of the residual stand population at time (yyt) to the climax

distribution (y ~). The mean basal area per size class and guild (By) is used to place more

weight on the large trees that are associated with climax forest conditions and high

endemic biodiversity (cf., Boscolo and Vincent 2000).

In addition to the PCI measure of deviation from climax structure and density, the

PCI form is used to examine two other characteristics, proximity to climax market value

(PCM) and proximity to climax wildlife value (PCW). Structural differences are

captured in PCI and thus are not repeated in these indices; instead, the residual density of

stems per sub-guild (yBk) is compared to the climax condition (ykB). Sub-guilds (k)

are derived from Guilds (/) by differentiation of merchantable and non-merchantable

species, except for Guild 3 that contains no merchantable species. Proximity to climax

market value at time t (PCM,) is defined

(y"BM.k yrBkM,)
PCM, =I- V B (3-14)
Y(ykBkMA )2
k









where MA is the mean ordinal market value of sub-guild k (Table 3-4), derived from a

ranking of tree species per market value (0 = no value, 3 = high), which is a refinement of

initial rankings by Pinard et al. (1999) conducted by the author and BOLFOR specialists

(Appendix A). The PCM measures the commercial timber stock value of residual forest

states (y,) relative to that of the climax forest (y").

Similarly, proximity to climax wildlife value (PCW) is defined

(y"k BkW, y BWk )2
PCW,=I- (y*BW,)2 (3-15)


where Wk is the mean ordinal wildlife value of sub-guild k (Table 3-4), derived from the

ranking of tree species per wildlife value (1 = low, 3 = high) by Pinard et al. (1999) and

updated with BOLFOR specialists (Appendix A). Wildlife values are ranked by the

importance of tree species for vertebrate frugivores, based on interviews with local

hunters and stomach contents of wild game (Guinart 1997, Pinard et al. 1999). PCW

permits the interpretation of alternative residual stand states as forest habitat for resident

wildlife.

Table 3-4. Mean ordinal market and wildlife values per sub-guild
Sub-guild Market value (Mk) Wildlife value (Wk)
Guild 1, merchantable 1.00 1.50
Guild 1, non-merchantable 0.00 2.16
Guild 2, merchantable 1.60 2.40
Guild 2, non-merchantable 0.00 2.33
Guild 3, non-merchantable 0.00 1.68
Guild 4, merchantable 2.33 1.00
Guild 4, non-merchantable 0.00 1.57
Guild 5, merchantable 1.60 1.40
Guild 5, non-merchantable 0.00 1.77









The Shannon-Wiener index (H), with natural logarithms (Whittaker 1975), is also

used to examine species and structural diversity as a measure of residual stand state,

defined as follows:


H,, = p, Il ,) (3-16)
i=1 J=1
where py is the proportion of trees in the size class i and guildj. For the Shannon-Wiener

diversity analysis, trees are grouped two ways: (1) for guild diversity, the five guild

groupings, and (2) for guild and structural diversity, 80 groups defined by guild and size

class (dbh). His a measure of evenness, which is maximized if trees are equally

distributed by size class and guild. H has a minimum value of zero for a homogeneous

stand and maximum value of In(n+m) for a perfectly heterogeneous stand; consequently,

the ranges of possible values for the diversity criteria described above are 0 < H5 < 1.61

for guild diversity and 0 < H80 4.38 for guild and structural diversity.

Lastly, the absolute difference between the number of trees per size class and guild

in the climax forest (yv) and in the residual stand (y) defined as the objective function of

the SFM case (Eq. 3-11) is used to examine differences in alternative managed stands

relative to the climax condition.

Results and Discussion

Optimal Harvest per Management Alternative

Given the high discount rates applicable to capital investments in Bolivia and the

low rate of value growth of timber species, which is estimated at a maximum of 1.23%

assuming constant prices, the optimal solution for an unconstrained harvest scenario (U)

is to harvest all the merchantable timber and invest the returns from harvest in more

lucrative activities. Consequently, any retention of merchantable timber would result in a









decrease in the profitability of management. This prescription for liquidation of the

merchantable timber stock is found to be the optimal solution for scenario U, in which

harvest is solely constrained by the merchantability limits established in local timber

markets. Consequently, harvest level is highest under unconstrained management (Table

3-5) and forest impacts are greatest.

Table 3-5. Harvest level in absolute terms and in proportion of the available
merchantable volume in Year 0 per management alternative
Harvest level (stems/ha) Harvest volume (m3/ha)
Year 0 Year 40, Year 0 Year 0 Year 40,
Case proportion cumulative proportion cumulative
U 25.67 100% 35.53 35.86 100% 45.61
BFL 13.36 52% 19.91 24.71 69% 33.75
STY 4.08 16% 36.76 4.18 12% 37.63
SFM 0.51 2% 4.57 1.63 5% 14.67

Harvest constrained by the Bolivian forestry law has a similar optimal solution, notably

that of removing all merchantable timber allowed by legal and merchantable limits. The

lower harvest level and inferior net returns of BFL relative to the unconstrained case are

imposed by dbh limits and the allowable cut restriction, which requires retention of 20%

of the merchantable timber. The reduction in net revenues for the BFL scenario

attributable to the 45 cm dbh limit and 80% allowable cut constraints on the initial

harvest entry are $145.45/ha and $191.60/ha, respectively. The optimal harvest solution

for BFL prescribes progressive depletion of the merchantable stock, subject to these legal

restrictions.

The optimal sustained-yield (STY) solution requires a substantial decrease in

harvest level for the initial entry relative to U and BFL, but the total cumulative volume

harvested over a 40-year management horizon is greater than the BFL alternative (Table

3-5). This is attributable to the fact that STY is not constrained to meet dbh limit or








proportional harvest restrictions as is BFL and to the expectation that the STY system

better conserves the merchantable growing stock over the harvest horizon. The STY

management for a 5-year cutting-cycle stipulates intensive harvesting of stems of

merchantable size in Guilds 4 and 5, the upland forest species and highly selective

harvesting of the riparian species of Guilds 1 and 2 (Table 3-6). The optimal STY

solution is determined by three factors: (1) biological constraints of forest growth and

recruitment and model; (2) cutting-cycle length; and, (3) timber merchantability.

Changes in management costs and discount rates have no effect on the STY solution.

Table 3-6. Comparison of pre-harvest population (yo) and sustained-yield (STY)
distribution (y*) per guild
Dbh class Pre-harvest population, vn (trees/ha) STY distribution, v* (trees/ha)
(cm) Guild 1 2 3 4 5 1 2 3 4 5
10 47.1 2.7 6.2 23.0 91.2 38.8 4.6 6.6 35.1 109.5
15 28.3 2.6 5.0 22.2 83.1 21.4 3.4 4.2 29.3 73.8
20 12.3 1.8 1.3 17.2 50.2 12.9 2.7 2.7 23.7 49.7
25 5.8 2.0 0.5 13.3 26.2 8.4 2.2 1.7 18.2 33.2
30 4.6 0.9 0.2 10.9 16.8 5.8 1.8 1.1 13.3 21.9
35 3.1 0.9 0.4 11.2 10.8 4.2 1.5 0.7 9.1 14.2
40 2.8 0.9 0.5 9.4 6.2 3.1 1.3 0.4 2.1 4.9
45 2.2 0.8 0.2 5.4 3.7 2.3 1.1 0.2 0.0 1.2
50 1.6 0.3 0.3 5.1 1.9 1.8 1.0 0.1 0.0 0.3
55 0.7 0.4 0.1 3.2 1.0 1.4 0.8 0.1 0.0 0.1
60 1.0 0.2 0.1 1.6 0.7 1.1 0.7 0.0 0.0 0.0
65 0.4 0.2 0.2 0.6 0.7 0.8 0.6 0.0 0.0 0.0
70 0.3 0.1 0.2 0.5 0.2 0.6 0.5 0.0 0.0 0.0
75 0.1 0.0 0.1 0.2 0.1 0.5 0.4 0.0 0.0 0.0
80 0.2 0.0 0.1 0.4 0.0 0.1 0.3 0.0 0.0 0.0
85 0.2 0.1 0.6 0.1 0.1 0.0 0.1 0.0 0.0 0.0

A dramatic change in the forest structure is prescribed for the STY condition

relative to the initial stand state, especially for upland species of Guilds 4 and 5 (Table 3-

6). With frequent harvest entries, STY prescribes maintaining a small growing stock to

generate timber just sufficient to meet sustained-yield goals and generate modest profits.









Comparison with the pre-harvest stand state reveals that the STY condition may not be

assumed from Year 0, rather a period of regulation harvest is required to convert the

stand to the STY steady-state. The duration of the regulation period and the returns to

management aimed at achieving the STY condition are unknown. Estimating the returns

to regulation harvest is not as simple as subtracting the STY or SFM populations from the

initial population and estimating the value of the implied harvest. Rather, it is expected

that regulation would require harvesting both merchantable and non-merchantable stems

and active management toward the desired STY or SFM conditions relative to growth

and regeneration responses to silvicultural interventions. Thus, while it may be expected

that the returns to STY or SFM would be increased from an initial harvest intended to

convert the stand to desirable conditions, the nature and value of these returns are

uncertain.

Table 3-7. Comparison of pre-harvest population (yo) and sustained-yield (SFM)
distribution (y**) per guild
Dbh class Pre-harvest population. V~ (trees/ha) SFM distribution, v** (trees/ha)
(cm) Guild 1 2 3 4 5 1 2 3 4 5
10 47.1 2.7 6.2 23.0 91.2 38.8 4.6 6.6 35.1 109.5
15 28.3 2.6 5.0 22.2 83.1 21.4 3.4 4.2 29.3 73.8
20 12.3 1.8 1.3 17.2 50.2 12.9 2.7 2.7 23.7 49.7
25 5.8 2.0 0.5 13.3 26.2 8.4 2.2 1.7 182 33.2
30 4.6 0.9 0.2 10.9 16.8 5.8 1.8 1.1 13.3 21.9
35 3.1 0.9 0.4 11.2 10.8 4.2 1.5 0.7 9.1 14.2
40 2.8 0.9 0.5 9.4 6.2 3.1 1.3 0.4 5.7 9.0
45 2.2 0.8 0.2 5.4 3.7 2.3 1.1 0.2 3.4 5.6
50 1.6 0.3 0.3 5.1 1.9 1.8 1.0 0.1 1.8 3.3
55 0.7 0.4 0.1 3.2 1.0 1.4 0.8 0.1 0.8 2.0
60 1.0 0.2 0.1 1.6 0.7 1.1 0.7 0.0 0.1 1.1
65 0.4 0.2 0.2 0.6 0.7 0.8 0.6 0.0 0.0 0.4
70 0.3 0.1 0.2 0.5 0.2 0.6 0.5 0.0 0.0 0.1
75 0.1 0.0 0.1 0.2 0.1 0.5 0.4 0.0 0.0 0.0
80 0.2 0.0 0.1 0.4 0.0 0.4 0.3 0.0 0.0 0.0
85 0.2 0.1 0.6 0.1 0.1 0.1 0.1 0.0 0.0 0.0










The SFM condition prescribes maintenance of the negative exponential distribution

typical of uneven-aged, mixed species forests, with more modest reduction in the pre-

harvest growing stock relative to STY (Table 3-7). The SFM condition is defined by the

biological needs of meeting sustained timber yield constraints and minimal deviation

from the theoretical climax structure. Some substitution of species of lower market value

for those of higher value may occur in satisfying the minimum deviation objective, due to

inadequacies of the SFM optimization model. Evidence of substitution for large stems of

Guild 4, those of highest value, is inconclusive given the important stocking levels

observed (Table 3-7).

The sustained-yield scenarios are advantageous in that the harvest horizons are

infinite, thus profitable timber extraction may be concentrated in a permanent production

forest estate. Optimal unconstrained management (U) depletes the merchantable stock in

the initial entry (Year 0). The BFL alternative only retains sufficient merchantable stock

to meet legal constraints, implying that only a proportion of those stems growing into size

classes > 45 cm during a cutting-cycle may be harvested in subsequent entries. This

result implies that after the initial concession period (40 years), U and BFL would require

a growing interval longer than 40 years for the forest to produce adequate timber for

profitable harvesting. Removing the stand from production for several decades to allow

for sufficient restocking of merchantable timbers after U and BFL harvesting creates a

short-term need for the expansion of harvesting into other forests to meet production

goals, which defeats the purpose of establishing permanent production forests.








Profitability of Management

Economic returns from the alternative management scenarios indicate, as expected,

a considerable decrease in the NPV of sustained-yield harvesting relative to

unconstrained harvesting (Table 3-8). The opportunity costs of the sustained-yield

alternatives (STY, SFM) are likewise very high, exceeding $1000 per hectare for both

scenarios relative to unconstrained liquidation of the available merchantable timber stock,

assuming accuracy of the cost assumptions. The comparative analysis of financial

returns furthermore assumes that there is no period of regulation harvesting, thus no costs

or financial benefits derived from converting the forest from its initial state (yo) to the

STY (y*) or SFM (y**) conditions.

The great disparity in returns from sustained-yield and unconstrained alternatives is

attributable to the opportunity costs of leaving merchantable stems in initial harvest

entries, given the high discount rate (18.75%). High opportunity costs of sustained-yield

management would occur at even lower discount rates, however, given the low value

growth rate of the tropical hardwoods in this Chiquitano forest.

Table 3-8. Net present value and opportunity costs of management alternatives
NPV Opportunity
Case ($/ha) costs ($/ha)
U 1380.54 0.00
BFL 914.89 465.64
STY 257.18 1123.36
SFM 11.25 1369.29

The sustained-yield scenario (STY) yields profits of $257.18/ha despite the high

discount rate. The more conservative SFM harvest scenario also yields profits

($11.25/ha) while more closely approaching the climax condition. Optimal management

under constraints imposed by Bolivia's Forestry Law (BFL) yields superior financial









returns relative to the sustained-yield alternatives, but has important opportunity costs

relative to unconstrained harvesting ($465.64/ha). These opportunity costs derive from

merchantable stems not harvested in Year 0 in order to meet dbh and allowable-cut

limits.

The discount rate affects the profitability of management under those alternatives

whose objective function is to maximize this output (U, BFL, STY), but does not change

the optimal solution. The optimal solution is constrained by biological and

merchantability restrictions and cutting-cycle length. At lower discount rates, STY

becomes more competitive with the U and BFL options (Table 3-9), exceeding the

profitability of BFL under 1% discounting. The SFM optimal harvest solution changes

with the discount rate as less deviation from the climax condition is allowed at lower

discount rates, while satisfying the binding constraint of non-negative NPV for a

perpetual harvest horizon. Consequently, the NPV of SFM harvesting for a 40-year

horizon decreases with decreases in the discount rate.

Table 3-9. Discount rate effects on the NPV of harvest returns for a 40-year horizon
NPV ($/ha)
Case\ Discount rate: 18.75% 12.00% 6.00% 1.00%
U 1380.54 1379.72 1402.11 1593.29
BFL 914.89 913.55 931.31 1091.75
STY 257.18 338.98 538.41 1087.67
SFM 11.25 9.84 8.73 7.90


Stand State and Forest Value Measures

Comparison of the structure of aggregate merchantable and non-merchantable

residual populations under the alternative management regimes and that projected for the

undisturbed climax reveals minor differences in stand impact among management options

(Fig. 3-1). As expected, the unconstrained scenario has the greatest impact on residual









stand structure, as the merchantable timber stock is progressively liquidated. Also as

anticipated, the SFM regime closely approximates the climax structure, meeting its

defined objective of minimizing deviation from this undisturbed, equilibrium state.




60 U, 40 yrs
60 -
-- BFL, 40 yrs
S----- STY condition
SFM condition
"40- -- --Climax




20 -




0 -
25 30 35 40 45 50 55 60 65 70 75 80 85
Dbh class (cm)
Figure 3-1. Aggregate merchantable and non-merchantable residual population structure
under management alternatives and climax condition

Aggregate residual population structures do not differ greatly under U and STY

management regimes, however, and the BFL constraints appear to achieve greater

proximity to climax stand structure than the STY alternative. Proximity to climax

structure and composition of the aggregate residual populations (PCI) confirms that the

BFL alternative results in greater proximity to this undisturbed forest equilibrium than U

and STY, as indicated in the comparison of aggregate population structure (Table 3-10).

This finding is unexpected, but may be explained by the fact that the aggregate

population may be effectively maintained under BFL, while the stand is impoverished.









This finding is unexpected, but may be explained by the fact that the aggregate

population may be effectively maintained under BFL, while the stand is impoverished.

Table 3-10. State of the aggregate residual stand population per management alternative
Managementalternative Climax
Index U BFL STY SFM condition
BA 19.72 20.76 21.72 26.19 26.90
PCI 0.73 0.78 0.68 0.97 1.00
D 7.50 6.46 5.18 0.56 0.00


This hypothesis is confirmed in closer examination of the impacts of harvest on the

merchantable stock (Table 3-11).

Table 3-11. Residual merchantable species population per management alternative
Management alternative Climax
Index U BFL STY SFM condition
BA (all merch. species) 5.42 6.46 8.55 9.83 12.48
BA (merch. species > 40 cm dbh) 0.00 1.04 2.64 3.92 5.57
PCInmr 0.42 0.53 0.57 0.76 1.00
PCM 0.62 0.70 0.83 0.86 1.00
Note: PCI,,h is defined as PCI, but calculated solely for merchantable species.


Residual stand basal area (BA) measures reveal greater differences between the U

and STY alternatives relative to comparisons of the aggregate residual populations,

though the differences of these states and BFL are less important (Table 3-10). Under

timber management objectives of U, BFL and STY, residual stand density is expected to

be 19% to 27% lower than the climax forest. Harvesting impacts on the merchantable

stock are more revealing of differences between the management alternatives, as

suggested by the proximity to climax market value (PCM) index (Table 3-11). The PCM

of residual stands is considerably lower under U and BFL regimes, than under STY,

given the effective liquidation of merchantable stems stipulated by these scenarios









prescribes maintenance of a growing stock of merchantable stems for future harvest (Fig.

3-2).

Impacts of the alternative harvest regimes on the merchantable species stock are

further elucidated in examination of residual basal area (BA), proximity to climax

merchantable stocking (PCImeh), and proximity to climax market value (PCM) of the

residual stands (Table 3-11). These indices reveal much greater impacts of U and BFL

regimes over the concession agreement (40 years). The basal area comprised by

merchantable species of all size classes under unconstrained harvesting is reduced to less

30
-- U, 40 yrs

BFL, 40 yrs
-. -STY condition
20 \\ SFM condition

and clix c nlimax



10 "





0 .
25 30 35 40 45 50 55 60 65 70 75 80 85
Dbh class (cm)
Figure 3-2. Residual merchantable population structure under management alternatives
and climax condition

than half that of the climax forest and to just over half of the climax merchantable

stocking under BFL constraints.









than half that of the climax forest and to just over half of the climax merchantable

stocking under BFL constraints.

The basal area of merchantable stems is depleted under U and reduced to less than

1/5 of that in the climax forest under BFL. In contrast, the STY and SFM regimes

maintain important stocking levels of merchantable stems throughout the harvest horizon.

Moreover, significant differences are observed in the proximity to climax structure and

composition indices (PCImech) under scenarios constrained to sustained timber yield

(STY, SFM) and those not biologically constrained to meet sustainability objectives

(U, BFL). The PCM measures confirm the depletion of stand market value under the U

and BFL relative to the sustained-yield alternatives.

Wildlife values of the residual stands are less affected by the alternative

management scenarios (Table 3-12), indeed all scenarios result in residual stands that

deviate little from the climax stand in their value to vertebrate frugivores. This result is

expected, as non-merchantable species are as important as merchantable species for

wildlife, if not more so (Table 3-4). Accordingly, depletion of the merchantable stock

has little impact on the value of the forest for wildlife, as measured in this study. Greater

precision on the relative value of tree species to wildlife other than vertebrate frugivores

may be more revealing of the impacts of alternative management scenarios in terms of

forest value for biodiversity.

Table 3-12. Wildlife and diversity indices per management alternative
Management alternative Climax
Index U BFL STY SFM condition
PCW 0.98 0.99 0.96 0.98 1.00
H5 1.17 1.17 1.21 1.20 1.20
HBO 2.93 2.97 2.98 3.04 3.11









Shannon-Wiener measures of stand diversity also reveal little difference among

management alternatives (Table 3-12). The SFM results in slightly greater evenness

across guilds and size classes than would be expected in under more intensive harvest

scenarios (U, BFL, STY), as harvesting results in a decrease in merchantable stems. The

Shannon-Wiener diversity indices reveal little about differences among these timber-

focused management alternatives.

Conclusions

Management of the Chiquitano dry tropical forests of eastern Bolivia for sustained-

timber yield is shown to be feasible and profitable, given certain simplifying assumptions

of the forest growth model. Moreover, the present study demonstrates that sustained-

yield management with greater conservation of forest structure and composition may be

profitably implemented. The optimal trade-offbetween STY and SFM conditions is not

clearly defined and will depend upon further information concerning the marginal

ecological impacts of deviation from the theoretical climax forest condition. The optimal

sustained timber yield (STY) condition, defined as one that maximizes the returns to

harvest given sustained production constraints, is determined by biological criteria for

sustainability, cutting-cycle length and timber merchantability constraints. Harvesting

costs and discount rates have no effect on the optimal STY solution, unless costs increase

to the point of rendering harvest unprofitable, which would eliminate consideration of

logging activities. Marginal changes in costs and discount rates have not effect on the

optimum given the important constraints posed by the biological requirements for

sustainability.

Forest management under STY and SFM steady-state conditions is assumed

possible in Year 0 to allow for comparative analysis of these theoretical forest









management ideals with conventional harvest options (U and BFL). This presumes that

the regulation harvest necessary to convert the forest to sustained-yield conditions is

feasible. Moreover, the assumption of steady-state conditions implies that the duration

and magnitude of regulation harvest do not influence the returns to management. This

assumption is untenable for management of the Las Trancas forests from their current

state; however, strict comparison of returns to the theoretical STY and SFM regimes with

conventional alternatives remains useful and informative of the financial and ecological

implications of management under sustainable equilibria. While it may be expected that

the returns to STY or SFM would be increased from an initial harvest intended to convert

the stand to desirable conditions, the nature and value of these returns are uncertain.

Estimating the management requirements and duration of regulation harvest will be an

important extension of the present work.

The comparison of optimal harvesting behavior with and without constraints aimed

at maintaining the productivity, structure and composition of Chiquitano dry forests

indicates, as anticipated, that the opportunity costs of more sustainable management

relative to unconstrained harvesting are considerably high, assuming modest increases in

profitability from conversion to the STY and SFM conditions. The magnitude of the

decline in harvest profitability of sustained timber yield (STY) relative to unconstrained

(U) management may be largely attributed to the effects of excessively high discount

rates applicable to capital investments in Bolivia. Nonetheless, given the low value

growth rates of tropical hardwoods harvested in the Chiquitano forests, the requirement

for leaving merchantable timber in the forest imposed by both the STY and SFM regimes









implies that these options will consistently generate inferior returns from unconstrained

liquidation of merchantable timber in initial harvest entries.

Examination of the economic and biological impacts of an optimal management

regime constrained by the Bolivian forestry law indicates that although financial returns

from management under BFL are robust, harvesting constraints are not likely to achieve

goals of sustainable timber production or ecosystem maintenance. This conclusion

cannot be drawn without caveats, given the simplifying assumptions required for

modeling the BFL scenario with the available growth and yield. Greater precision in

modeling diameter limits and allowable cut restrictions for individual species and in

projecting forest growth and regeneration may indicate that optimal BFL management

results in forest conditions more closely approximating a sustained-yield state than is

possible to project in this study. However, the simplified model used in the present

analysis indicates that tree diameter and allowable cut restrictions lead to the depletion of

large stems of high value, which is not likely to result in the maintenance of forest

structure and composition necessary to achieve sustained timber yield.

Results indicate that management regimes are possible that achieve sustained

timber yield, while generating profitable returns. Moreover, it is shown that maintaining

forest structure and composition can be compatible with producing sustained timber yield

to meet economic objectives in management of the Chiquitano dry forests, as shown by

the SFM scenario. For the particular case of Chiquitania, goals of sustainable timber

production appear compatible with the maintenance of forest wildlife values, though

more information on the values of timber species for other taxa would allow for a more

conclusive assertion of this apparent compatibility.














CHAPTER 4
REGULATORY POLICY EFFICIENCY IN PROMOTING SUSTAINABLE TIMBER
MANAGEMENT FOR A BOLIVIAN TROPICAL DRY FOREST

Introduction

Regulatory policies are intended to provide a corrective influence on the private use

of forestland to properly defend public goods, both in maintaining desirable benefit flows

from natural resources and in mitigating negative externalities. Fiscal regulatory

instruments, such as royalty systems, have also been identified as a critical determinant of

the manner and magnitude of tropical forest degradation by providing incentives for

logging practices such as high-grading and conversion to alternative land uses (Repetto

and Gillis 1988, Vincent 1990, Hyde and Sedjo 1992, Van Kooten and Bulte 2000).

Despite the important influence of government policies on tropical forest use, few

rigorous comparisons exist of the impact of alternative regulatory mechanisms on private

revenues, government rent capture, and forest condition. Important exceptions include

recent studies by Boscolo and Vincent (2000) and by Amacher et al. (2001) for natural

tropical forests of Malaysia. Boscolo and Vincent (2000) examined concession length,

renewability and performance bonds as mechanisms to promote the adoption of better

logging practices, while Amacher et al. (2001) used a model of policy choice to compare

royalty systems relative to government revenue generation and high-grading behavior.

Although forest degradation has often been attributed to poor regulatory policy, there is

little empirical work examining how selective harvesting behavior and the allocation of

rent between private concessionaires and government is influenced by regulatory









structure, Amacher et al. (2001) being the exception. The present study aims to

contribute to such empirical analyses by considering the impacts of existing regulatory

policy and alternative incentive mechanisms upon optimal harvesting behavior for a

tropical dry forest of eastern Bolivia. The study expands upon this recent work by

examining the influence of fiscal regulatory mechanisms on the logging behavior of

concessionaires, the private returns to logging and government rent capture. A harvest

optimization model is used to conduct a comparative analysis of the efficiency of

alternative policies in fostering forest management compatible with sustained timber

yield (STY) objectives.

Methods

Forest Growth and Optimization Models

The seasonally dry tropical forests of the Lomerio region (1613'S, 61050'W) lie in

a transition zone between the humid forests of the southern rim of the Amazon basin and

the thom scrub of the Gran Chaco on the southwestern edge of the Brazilian shield

(Killeen et al. 1998). The forests are typical of the Chiquitano dry forests of eastern

Bolivia. Forest growth and yield is projected with a five-guild matrix growth model

estimated by multinomial logistic (MNL) regression of permanent sample plot data

collected in two 400 ha forest blocks near the Las Trancas community (Claros and Licona

1995, Killeen et al. 1998). The MNL matrix growth model projects the probabilities of

upgrowth, stability, or mortality of trees in each of five ecological guilds during a 5-year

growth period and predicts recruitment of trees into the smallest size class (10 cm dbh)

for each guild (cf., Chapter 2). The linear form of the MNL model and the assumption of

stationarity of transition probabilities throughout the harvest horizon enable its

straightforward integration into this linear optimization study.









The Bolivian forestry law was revised in 1996 (Ley 1700) to more effectively

promote sustainable management of the nation's forest resources, which are allocated in

renewable concessions to the logging industry (Art. #1). Logging concessions are

awarded for a harvest period of 40 years upon formal application to and approval by

Bolivia's forest service (Superintendencia Forestal). The forestry law requires forest

management plans for all concessions and for forest authorizations in private lands.

Concessions also can be traded and inherited and are renewable upon validation of the

concessionaire's observance of sustainable forest management plans.

Forest management costs for industrial firms of the region and market prices for

roundwood timber delivered to the forest mill derive from surveys conducted in Santa

Cruz and in Chiquitania in 2000 and 2001 (Appendix B). Prices are reported in 2001

$US and are assumed constant throughout the harvest horizon (Appendix C).

Management costs in 2001 $US are classified as one of three types:

* Variable costs (C) in $/m3 for felling, skidding and log deck operations incurred
relative to harvest intensity

* Fixed costs (F) in $/ha incurred regardless of harvest intensity at each cutting-cycle
entry for planning and capital costs

* Annual costs (A) in S/ha paid throughout the harvesting horizon regardless of
harvest intensity, which include an area fee of $1/ha for the concession (Bolivia's
patente) and inscription fees to government and market institutions

These and all other variables used in the present study are defined in Appendix D.

The optimization model prescribes maximization of net present value (NPV) of

polycyclic harvesting (Z) subject to biological, market, and regulatory constraints. The

objective function does not consider the costs of investment in the growing stock

described by the economic stocking rule for selection harvest (Duerr and Bond 1952) or

soil expectation value (SEV) used in similar optimization studies (Buongiorno and








Michie 1980, Boscolo and Buongioro 1997, Bach 1999, Kant 1999). These costs are

opportunity costs of not harvesting merchantable stems in the initial harvest entry in

order to maintain the timber growing stock. The decision to exclude the opportunity

costs of maintaining the growing stock from the calculation of net returns is based upon

the nature of the forest property. As these forests are allocated in concessions to private

industry under government ownership, the opportunity costs of conserving the residual

stock are public rather than private costs.

The objective function (Z(h, y)) of the forest management problem is to maximize

the NPV of returns to harvesting over a 40-year concession period calculated as the

present value of a terminating series at discount rate 8, with harvest horizon T= 40 years

and cutting cycle length I = y6, with period y0 being the number of intervals (y) of 5-year

growth periods (0) in a cutting-cycle. For the present analysis, the cutting cycle (t) is 40

years and y = 8. The cutting-cycle is set equal to the length of the concession period

because the returns from unconstrained, profit maximizing harvesting (U) are negative

for shorter cutting-cycles and the unconstrained optimization is used as the basis for

modeling the impact of regulatory policies (Chapter 3). It is assumed that harvest is

allowed in Year 40, before the end of the concession agreement. The objective function

is defined mathematically


maxZ,, = C i -C h,-F 1--( 1+ )-T (4-1)
i 1.0 (1+6)' 65 )
The net value of an extracted stem of size class i in Guildj in 2001 $US/m3 (Table

3-3) is calculated as the product of the mean price per guild (p,) less the variable costs of

harvesting (C) and the mean extracted volume per size class and guild (V,). Harvesting

from each guild (h1,) is measured in stems per ha. The tree population (y,) and harvest









intensities (hi) are not steady-state variables, as the regulatory solutions are not assumed

to achieve sustained-yield conditions. The real discount rate (S) of 18.75 % is the mean

real interest rate for 2001 reported by Bolivia's Central Bank (Banco Central de Bolivia

2002).

The optimization is constrained by the forest growth model (Eq. 4-2), which

defines growth and recruitment in the residual forest between harvest intervals. The

forest growth constraint requires that the sum of the harvest and growing stock at time t

equal the residual stocking at time t-1 plus any growth and recruitment in this growing

stock between these cutting-cycles.


h + y, Gr(y,_, -h_,)= G'r (4-2)
k=0
The profit maximization objective is further constrained by merchantability criteria

for harvested stems. Merchantability restrictions require that the proportion of trees

harvested per Size Class i and Guildj at Time t be equal or less than the proportion of

merchantable stock (co) present in the stand. The merchantability constraint for the

initial harvest (Year 0) is defined

h,, -mwy, 5 0 (4-3)
where coi is the merchantable proportion per guild. For all ensuing cutting-cycles under

U and BFL, the merchantable proportion is expected to decrease as merchantable volume

is removed. Thus while equation 4-3 is applied as a constraint to the initial harvest,

subsequent merchantable stock constraints are defined by the growing stock of residual

merchantable stems remaining after harvest (y"1-i) and any merchantable upgrowth into

this stock during the cutting-cycle interval. This constraint is described mathematically









"-1
h, -G'ryy,- i ,Gk r,, _0 (4-4)
k--O
In addition, merchantability standards require that trees equal or exceed 40 cm dbh:


h, =0 (4-5)
'-0
Lastly, the optimization is subject to absolute harvest restrictions, requiring that the

harvest intensity not exceed the growing stock (y ht 2 0) and non-negativity constraints

(yt, ht 2 0).

Regulatory Policies

The six regulatory policies examined are as follows:

* Bolivian forestry law (BFL)
* Area fee
S Per-tree royalty
S Volume-based royalty
* Ad valorem royalty
S Performance bond

The level of fee levied for each policy other than BFL was determined iteratively,

based upon the target of achieving a residual merchantable population approaching that

defined for the STY condition (207 trees/ha of all size classes and guilds). This criterion

was selected as a mechanism for examining behavioral change relative to the selective

harvest of timber species, with the objective of comparing the efficiency of alternative

regulations in fostering the maintenance of residual forest conditions compatible with the

structure and composition necessary for sustained-yield harvesting (STY). It is assumed

that the administrative costs of alternative regulatory mechanisms are equal. Relaxing

this assumption is expected to affect government revenues but not the concessionaire's

optimal harvest behavior or profits (cf., Amacher et al. 2001). Mathematical descriptions









of the optimization models for the six regulatory policies and for the STY model are

provided in Appendix F.

A more exhaustive analysis of alternative fee levels per regulatory mechanism

would enable determination of the optimal fee schedule appropriate to achieve both

profitability, rent capture, and sustainability goals. This analytical approach is not fully

developed in the present study. Instead, fee levels required to compel the logger to

maintain a residual merchantable population most closely approaching that required for

STY were selected by iterative estimation in preliminary model simulations. The

alternative regulatory mechanisms are then examined at the selected fee levels to more

closely examine behavioral impacts and effects on financial returns from logging of the

policies, without detailed examination of the marginal effect of alternative fee levels per

policy. A more rigorous examination of the optimal fee levels per regulatory mechanism

would be a valuable extension on this work, though the present analysis provides a useful

comparison of policy impacts.

Sustainable timber management (STY). The regulatory goal of this analysis is

the maintenance of forest conditions necessary for STY; to wit, maintaining the

productivity of the forest such that a constant harvest yield is extracted at each cutting-

cycle entry. The conditions necessary for STY are derived from a static optimization

analysis using the MNL growth model of the Las Trancas forest for a cutting-cycle of 5

years (cf., Chapter 3). The STY harvest intensity is estimated at approximately 4.2 m'/ha

per 5-year cutting-cycle.

An important caveat is necessary regarding the definition of the forest condition

necessary for STY. The STY condition is derived from optimization analysis using the









MNL forest growth model described in Chapter 2. The optimal STY condition is largely

dependent upon the biological constraints imposed by this growth model, by

merchantability constraints for timber species of this Chiquitano forest site, and by the

cutting-cycle length used in the STY analysis (Chapter 3). Alternate STY conditions are

possible with changes in these fundamental constraints. The present study assumes that

the STY condition estimated in Chapter 3 is a desired forest condition and is a

sufficiently accurate definition of the conditions required for sustainability. This latter

assumption may be violated for long-term modeling of sustainability due to the poor fit of

the model of forest recruitment (Chapter 2), which determines long-term changes in

forest composition. Therefore, the precise conditions necessary for STY may not be

conclusively asserted in the present study. Despite this important weakness, the

comparative analysis of the effect of alternative policy mechanisms on logger behavior

remains valid. Its validity derives from the fact that the influence of regulatory

mechanisms is not dependent upon precise definition of the STY condition.

Bolivian forestry law (BFL). The Bolivian forestry law (Ley 1700) and the

technical standards for forest management in concessions and private forests greater than

200 ha (Normas Tecnicas) established normative prescriptions intended to promote the

maintenance of sustained economic, ecological, and social benefits of production forests.

Under this legislation, harvesting is restricted to the following standards: a minimum 20-

year cutting-cycle; a maximum 80%0 allowable cut of the merchantable stock per species;

and, a minimum dbh limit for harvested stems. These regulatory constraints are imposed

upon the optimization model to examine the profitability and impact of expected

management behavior under the Bolivian forestry law in the "BFL" scenario. Under the









BFL case, a minimum diameter of 45 cm is required for merchantable stems (Eq. 4-6)

and an 80% allowable cut restriction is applied per guild (Eq. 4-7).

40
Sh0, = 0 (4-6)
-=0
85 85
-ho, -0.82>yo, 0 (4-7)
-:45 t.45
An annual area fee (patente) of $1/ha is paid on all logged concession lands under

terms of the forest law. Concessionaires may set aside up to 30% of the forest concession

from logging and be exempted from paying the patent on these lands. This fee is

represented in the objective function of the BFL optimization by a $1/ha increase in the

annual costs of management (A).

Area fee. An area fee of (r S/ha), levied each cutting-cycle on harvested lands,

changes the profit maximization objective function to:


map Z,,, =(4-8)
JG (1+(3)' 6
An area fee of $250/ha is used in the present analysis. An area fee facilitates government

rent capture relative to tree or volume royalties, though it is not expected to affect

harvesting behavior on economic forestlands. Rather, those forest areas with timber

values less than the area fee are expected to be taken out of production.

Per-tree royalty. A per-tree royalty of (r $/stem) changes the concessionaire's

objective function to


maxZ( = ~ -C-, 1-F A (4-9)
-=o (1+6) 3
The per-tree royalty is set at $70/tree. This and the other royalties are expected to reduce

the concessionaire's profit margin on individual trees and thus may lead to "high-








grading", or logging of only those stems of superior value and stem size (e.g., Repetto

and Gillis 1988, Boscolo and Vincent 2000).

Volume-based royalty. Concession fees derived from a volume-based royalty

(r $/m3) would change the objective function to

(-r-C ,h, -F 1( (1+6)
maZ (1+)' -A (4-10)

The volume-based royalty is set at $40/m3 for the present analysis.

Ad valorem royalty. An ad valorem royalty is derived as a percentage of the log

price (r % log price) and changes the logger's objective function to

maxZ", = ( -p, -Cyh, -F ( (4-11)
m Zo (1+6)' (4-11)

The ad valorem royalty is set at 71% of the log price of harvested stems.

Performance bond (PB). Although uncommon as regulatory instruments for

forest management, performance bonds may provide a useful incentive mechanism for

logger compliance with desired management practices. For the present study the

performance bond is levied prior to management, and then a proportion equivalent to

logger compliance is refunded to the logger immediately after harvest. The performance

bond (r $/ha) changes the objective function to

T (p -C0h) -F-r+pr _-(1+_)_
maxZ(, = (+h, A 6 (4-12)
I t=o (1+6)' 6
Compliance with the performance bond requires that the residual merchantable

stock population and basal area of the managed forest equal or exceed the residual

merchantable stock of the STY equilibrium (Eq. 4-13, 4-14). Any decrease in the

residual stock implies a proportional decrease in compliance with this standard and thus a

proportional reduction in the performance bond refunded to the concessionaire. The









objective function is accordingly modified to reflect that profit maximization is defined

by the intensity of harvest of merchantable stems and the level of compliance with

performance standards (Eq. 4-12). In addition to the forest growth, merchantability,

absolute harvest, and non-negativity constraints, the performance bond optimization is

constrained by criteria for compliance with sustainability standards (Eq. 4-13, 4-14).

Percent compliance is constrained to the interval (0,1) (Eq. 4-15).

85 T
(y;-p )0 (4-13)
-40 J r-0
85 T
0EY(By,,- pB yr)0 (4-14)
1-40 j =0
p 0, p where

yi = Number of merchantable stems (trees/ha) in size class i and guildj at time t

ym = Number of merchantable stems (trees/ha) in size class i and guildj in the
sustained-yield (SY) distribution

p = % compliance with SY restriction

By= Mean basal area (m2) of Size Class i and Guildj

Determining the appropriate fee level for the performance bond is difficult, as setting the

bond too low will have little effect on management behavior, while setting it too high will

discourage private investment in logging government-allocated concessions (Richards

2000). Nonetheless, for the logger to have the incentive to comply with management

standards and receive a full refund, the bond must be set sufficiently high. Trade offs

between compliance and harvest are expected at lower performance bond levels. The

present PB optimization model allows for an examination of "trade-off solutions", as the

decision variables include both level of compliance as well as harvest intensities per guild









and size class. The performance bond level is set at $750/ha to illustrate one such trade-

off solution compatible with sustained-yield objectives.

Results and Discussion

Alternative regulatory mechanisms result in changes in both optimal harvesting

behavior and in the distribution of timber rents between private concessionaires and the

government relative to BFL policies. The relative efficiency of regulatory mechanisms is

revealed by inspection of the forest condition, profitability, and allocation of stumpage

between the concessionaire and the government. As noted above, the relative efficiency

of alternative policies is conditional on the fee levels selected to meet the criterion of

maintaining a residual merchantable timber stock approaching that of the STY condition.

Harvesting Behavior and Forest Condition

Current Bolivian regulatory policy (BFL) comprises both technical management

standards (minimum diameter limit and 80% allowable cut) and an annual area fee paid

for all forestland subject to logging. The annual area fee has a negligible effect on

harvest behavior for forestland with a timber value exceeding $5.44/ha, the NPV of

$1/ha/yr paid over a 40-year concession contract at a discount rate of 18.75% per annum.

At best, the annual area fee provides an incentive to set aside forestland with marginal

timber value, which consists largely of the inselberg habitats with species of no market

value (Guild 3). The management standards have the desirable effect of maintaining

merchantable stems of smaller size classes (< 45 cm dbh) and maintaining 20% of the

growing stock of merchantable stems of 45 cm dbh and greater. The residual distribution

of merchantable stems under BFL deviates considerably from the STY condition,

however, as the optimal harvest solution is to extract all stems more than 50 cm dbh and









leave stems of the 45 cm dbh class adequate to constitute 20% of the growing stock

(Table 4-1, Fig. 4-1).

The area fee alternative, which requires payment of $250/ha at each cutting-cycle

for the area harvested, does not change optimal harvesting behavior from the liquidation

harvest that would be optimal under unregulated management. The area fee is paid

regardless of harvest intensity, thus the concessionaire's optimal strategy for maximizing

profits would be to extract all merchantable timber at each entry. As modeled, the area

fee would result in depletion of the merchantable stock over the 40-year concession

period (Table 4-1, Fig. 4-1).

Table 4-1. Residual distribution of merchantable stock (trees > 40 cm dbh per ha) per
regulatory policy, Year 40
Regulatory mechanism
Dbh class Ad
(cm) STY BFL Area Per-tree Volume valorem PB
40 3.2 6.3 0.0 6.3 3.9 1.0 4.6
45 2.1 1.6 0.0 3.5 2.9 0.8 3.2
50 1.6 0.0 0.0 2.6 2.0 0.7 2.0
55 1.3 0.0 0.0 1.3 1.3 0.5 1.1
60 1.1 0.0 0.0 0.3 0.8 0.3 0.3
65 0.9 0.0 0.0 0.2 0.5 0.2 0.3
70 0.7 0.0 0.0 0.0 0.3 0.2 0.2
75 0.6 0.0 0.0 0.0 0.1 0.1 0.1
80 0.3 0.0 0.0 0.0 0.1 0.1 0.1
85+ 0.0 0.0 0.0 0.0 0.1 0.1 0.1


The per-tree royalty creates the incentive to leave smaller stems of lesser value,

notably those stems whose net value do not exceed the $70 per-tree fee, such as the

species of Guild 1, which have the lowest market value (Fig. 4-2). The per-tree royalty

results in modest improvements toward achieving the STY condition relative to the area










-- STY
-- Area
.- Per tree
- Volume
- Ad valorem
-- PB
--BFL


0 -I--- --,-., IF -I* z
35 40 45 50 55 60 65 70 75 80 85+

Dbh class (cm)


Figure 4-1. Distribution of merchantable population per regulatory policy, Year 40

2
STY

Area

------ Per-tree

S-*- Volume, Ad valorem, PB

1 ---BFL


35 40 45 50 55 60 65 70 75 80 85
Dbh class (cm)

Figure 4-2. Distribution of merchantable stems of Guild 1 per regulatory policy, Year 40









fee (Table 4-1, Fig. 4-1), but maintains the incentive to high-grade the forest concession

and thus, as modeled, is not an efficient mechanism for attaining STY goals.

The optimal harvesting strategy under regulation by the volume-based royalty

would be to leave stems of low value, notably those of Guilds 1 and 4. The merchantable

stock of lesser-valued species would be maintained (Fig. 4-1, 4-2), but species whose

values exceed the volume fee ($40/m3) would be depleted (Fig. 4-3). The effect of the

volume fee is similar to a reduction in the price of timber. The consequence would be

more selective high-grading.


-- STY

-- Area, Volume, Ad
3 valorem, PB
----. Per-tree

2 ---BFL
2-








35 40 45 50 55 60 65 70 75 80 85
Dbh class (cm)

Figure 4-3. Distribution of merchantable stems of Guild 5 per regulatory policy, Year 40

The performance bond mechanism creates an incentive for partial to full

compliance, according to the bond level (Fig. 4-4). At the $750/ha bond level examined,

the concessionaire's optimal strategy would be for approximately 80% compliance with

the standard of maintaining a residual stock equal to that of the STY condition (11.7









stems/ha) at each cutting-cycle. In other words, the optimal harvest intensity is that

which results in a residual merchantable population approximately 20% lower

(8.2 stems/ha) than that necessary for STY. Given the incentive for compliance, the

performance bond results in a forest condition more closely approximating the STY

condition than the alternative regulatory options examined (Table 4-1, Fig. 4-1). As

defined, however, the PB mechanism permits high-grading of the stand and satisfaction

of performance criteria by leaving lesser-valued stems (Fig. 4-2, 4-3). In terms of

efficiency, a PB regulatory policy is preferable to the alternative undifferentiated

mechanisms, but would be even more effective with greater precision in the definition of

performance standards. Criteria for maintaining residual stocking per guild and size class

groupings would promote closer compliance with the maintenance of forest structure and

composition required for STY, as defined by the forest growth and optimization models.

1.00 $738.99/ba


0.80


g 0.60


.0.40


0.20 $1035.50/ha $790.70/ha
0.0 $899.16/ha

0.00
350 400 450 500 550 600 650 700 750 800

Performance bond (T $/ha)
Figure 4-4. Percent compliance (p) with the STY condition and NPV of returns from
management (S/ha) relative to performance bond level (r)









Marginal increases in compliance (p) relative to performance bond fee (r) are low

up to a fee level of $650/ha, at which point compliance increases dramatically with

increases in bond level (Figure 4-4). The behavior of this compliance curve suggests that

the optimal performance bond fee lies between $640/ha and $800/ha, the precise level

defined by a trade-off between profitability and proximity to STY conditions. If the

marginal benefit curve for production of timber and non-timber benefits under STY were

known, the optimal fee level could be more precisely estimated as that point at which the

marginal cost of an increase in fees equals to marginal benefit of greater compliance.

The estimation of optimal fee levels for performance bond mechanism would be a

valuable extension of this work.

Profitability and Rent Distribution

With the exception of the area fee mechanism, which has no impact on harvesting

behavior, regulatory alternatives to the existing Bolivian forestry law result in lower

concessionaire profits and greater government rent capture (Table 4-2).

Table 4-2. Profitability and rent distribution per regulatory policy
Rent capture (NPV $/ha)
Regulatory policy Concessionaire Government
Sustained timber yield (STY) 257.18 8.26
Bolivian forestry law (BFL) 914.89 5.33
Area fee 1135.61 250.26
Per-tree royalty 129.37 356.32
Volume-based royalty 83.21 292.13
Ad valorem royalty 93.98 1345.17
Performance bond (PB) 740.13 148.46


The magnitude of the area fee has no impact on harvesting behavior; it simply

influences the net private and governmental returns to management. Certainly, if the area

fee dissipates all profits to management, the concessionaire is unlikely to log. As long as









the concessionaire can expect profitable returns to management, however, the

concessionaire's previous optimal strategy of maximizing profits in liquidating the

merchantable stock is unchanged; the net profits are just lower.

The royalty systems result in substantially lower private returns for modest

improvements toward the STY condition relative to BFL or, in the ad valorem case,

further depletion of the forest stock. All alternative mechanisms would result in greater

government rent capture relative to current BFL conditions.

The performance bond option reduces concessionaire profits the least, while

increasing government rent capture and resulting in greater proximity to the STY

condition relative to current and alternative regulatory mechanisms. The challenges of

defining appropriate performance criteria and enforcing logger compliance under a

performance bond are imposing. Moreover, high performance bond fees are required to

induce favorable levels of compliance with desired forest management standards.

Excessive fees will discourage private investment in logging government-allocated

concessions. The incentive for compliance created by a performance bond mechanism is

particularly compelling, though the complexity of its application may be limiting.

Conclusions

Alternatives to current Bolivian regulatory policy for forest concessions may

provide more effective fiscal incentives for sustainable forestry, while improving

government rent capture. The goal of changing logger behavior toward greater

compliance with STY standards may be achieved by alternative royalty systems or a

performance bond mechanism, given appropriate fee levels. An area fee, unless

complemented by technical standards for management such as the Normas Tecnicas, is

unlikely to change the concessionaire's incentive to liquidate all merchantable timber in









initial harvest entries. For all alternative regulatory mechanism forms examined in this

study, optimal concessionaire behavior is to high-grade the forest, as revealed in

examination of the residual stock of stems of the highest value, which constitute Guild 5

(Fig. 4-3). This optimal "high-grading" behavior may be modified with differentiation of

regulatory fees (Amacher et al. 2001), such as higher per-tree and volume royalties for

more valuable relative to lesser-valued species and more precise STY compliance

standards for the PB mechanism. Presently, the policy alternatives are defined as

undifferentiated mechanisms, meaning that all stems are subjected to the same level of

fiscal regulation. This regulatory approach is considerably more straightforward to

implement, but does not result in the differential harvesting behavior that would be

necessary to compel loggers to conserve the growing stock of more valuable species.

Examining better differentiated forms of the performance bond and royalty mechanisms

would be a valuable extension of this research.

Establishing straightforward and meaningful standards by which the appropriate fee

levels may be estimated and concessionaire management performance may be evaluated

is problematic because of the complexity of mixed tropical forests and the difficulty of

estimating forest conditions necessary for sustained timber productivity. Appropriate

regulatory mechanisms must balance efficiency gains of improved compliance with STY

standards and desirable distribution of resource rents with the practical aspects of

implementation. Regulatory mechanisms that are too complex will likely be poorly

implemented and are unlikely to achieve the theoretical efficiency gains for which they

are designed.






76

Moreover, the design of fiscal regulatory policies has implications across a broader

landscape of land uses. While higher forest fees seem necessary to counter incentives for

high-grading and to constrain optimal behavior to the conditions necessary for

sustainability, increasing forest fees lowers the profits of forest management for timber.

A decrease in the profitability of logging implies that natural forests of marginal

economic value will drop out of timber production. Higher taxation reduces the incentive

for maintaining forestland in timber production for all but the most highly valued species

and creates greater incentive to convert natural forests to plantations or non-forest uses.

The optimal regulatory policy is likely a compromise between efficient fiscal

mechanisms and modest fee increases, complemented by the enforcement of appropriate

technical standards, or best management practices.














CHAPTER 5
CONCLUSIONS

The present study of optimal management regimes for a Chiquitano tropical dry

forest offers an indication of the biological and economic requirements for sustained

timber yield (STY) and sustainable forest management (SFM), given a land use objective

of profit maximization in logging and the biological, market and regulatory constraints on

its achievement. Results generated by the forest growth model and optimization analyses

are conditional on the modeling assumptions required for a tractable analysis. The

accuracy of these bioeconomic models fundamentally determines the validity of estimates

concerning the conditions required for sustainable management and simulations of

management impacts on the natural forests. Constraining the harvest horizon to a 40-year

concession period lends greater integrity to the analysis of logging behavior, but does not

resolve all issues caused by data limitations and restrictive modeling assumptions.

These limitations notwithstanding, the study offers several useful contributions to

research on the biological and economic requirements for sustainable forest management.

The novel application of the multinomial logit (MNL) regression method for estimating

matrix transition models demonstrates important benefits relative to previous techniques

employed in matrix model estimation. The MNL method corrects for variance in the data

and model estimation errors imposed by limited samples. Moreover, the MNL form

offers compatible simulation alternatives, including deterministic and stochastic

projection in both static and dynamic model forms. The study demonstrates that

sustaining the productive capacity of the Chiquitano forest for timber can be compatible









with generating positive financial returns from management and with improved

ecosystem conservation. The integrated bioeconomic optimization model reveals the

governing influence of forest growth, cutting-cycle length, and timber merchantability on

the sustainable management solutions. Finally, the analysis of regulatory policies

demonstrates the effects and relative efficiencies of alternative fiscal regulatory

instruments as means of inducing logger compliance with desirable forest management

practices.

The extraordinary discount rate of 18.75% applied in this study and the slow

growth rates of merchantable timber species suggest that short cutting-cycles and

measured, selective harvesting promise the highest financial returns to sustainable

management of the Chiquitano forest This high discount rate also substantially inflates

the opportunity costs of more sustainable management relative to unconstrained

harvesting. Given the low value growth rate of tropical hardwoods, however, the

requirement for leaving merchantable timber in the forest imposed by both the

sustainable forestry scenarios (STY and SFM) implies that these options will consistently

generate inferior returns to unconstrained liquidation of merchantable timber in initial

harvest entries.

Results of the SFM optimization indicate that maintaining forest structure and

composition can be compatible with producing sustained timber yield to meet the

economic objective of generating profitable returns from management. Moreover, for the

particular case of Chiquitano tropical dry forests, both STY and SFM goals appear

compatible with the maintenance of forest wildlife values. More information on the









values of timber species for wildlife taxa other than vertebrate frugivores would allow for

a more conclusive assertion of this apparent compatibility.

The finding that the opportunity costs of sustainable management alternatives are

high, relative to unsustainable logging methods, should not imply that the pursuit of

sustainability is an unworthy, or impractical, objective. The private opportunity costs of

sustainable management may be high, but the public opportunity costs of the progressive

depletion of natural forest timber stocks and concomitant degradation of non-timber

benefits produced by natural forests that are expected to occur under conventional,

unsustainable logging are arguably much higher. The critical issues for this and similar

research on sustainable tropical forestry are whether sustainable management for timber

and non-timber benefits is biologically feasible and economically viable. If so, the goal

of establishing permanent production forests to meet demands for tropical hardwoods is

both a worthy and practical alternative to extensive high-grading and degradation of

natural forests for short-term timber production.

Examination of the economic and biological impacts of optimal management under

constraints imposed by current Bolivian forestry regulations (BFL) indicates that,

although the financial returns to management are appreciable, BFL standards are not

likely to achieve sustainability goals. This conclusion cannot be drawn without caveats,

given the simplifying assumptions accepted in analyzing the BFL scenario with the

available forest growth and optimization models. Optimization results indicate that tree

diameter and allowable cut restrictions of BFL provide the logger with an incentive to

deplete large stems of high value, a practice unlikely to result in the maintenance of forest









structure and composition necessary to achieve sustained timber yield by present model

estimates.

Alternatives to current Bolivian regulatory policy for forest concessions may

provide more effective fiscal incentives for sustainable forestry, while improving

government rent capture. The goal of compelling logger behavior toward greater

compliance with sustainability standards may be more efficiently achieved by alternative

royalty systems, or a performance bond mechanism, given appropriate fee levels. High-

grading is expected to result from greater fiscal regulation, however, if such regulations

are undifferentiated across timber value classes. Examining more precise, differentiated

forms of performance bond, and royalty mechanisms, would be a valuable extension of

this research. Still, establishing meaningful standards by which management

performance may be evaluated is problematic because of the complexity of mixed

tropical forests and the difficulty of estimating forest conditions necessary for sustained

timber productivity. Appropriate regulatory mechanisms must balance efficiency gains

of improved compliance with sustainability standards and of a more desirable distribution

of resource rents with the practical aspects of their implementation and enforcement.

Numerous interesting extensions of this work are possible. The assumption of

stationarity for transition probabilities of the matrix model limits the examination of

forest dynamics. An inspection of forest impacts and sustainability conditions under

dynamic modeling would make better use of the research potential of the MNL model.

Recalculation of transition probabilities per harvest episode and silvicultural treatment

may offer greater insight into the expected forest response to management and parameters

for optimal harvest. The optimal path of regulated harvest necessary to maximize profits









while converting the forest to a sustained-yield state is another compelling extension.

The period of regulation required to establish STY conditions and the financial

implications of this regulation may offer important insights into the management needs

for establishing a regulated forest. The integrated optimization model enables an

examination of conservation and management alternatives proposed in recent conceptual

studies. Examples include the "log and protect model" suggested by Rice et al. (2001),

the effects of a price premium for certified timber with and without effective harvest

regulation, and the effects of a market for carbon sequestration.

Results of the present research offer a modest, but hopefully useful, contribution to

scientific understanding of the complex and contentious issue of sustainable forestry.

Improving the precision and dynamics of the modeling tools developed in this study will

enable further and more practical contributions to management, economic analysis, and

policy design.














APPENDIX A
GUILD CLASSIFICATION OF LOMERIO TREE SPECIES

Forest Regen.shadeMature shade Timber Wildlife
Scientific name Guild habitat* tol. (1-3) tol. (0,1) value (0-3) value (1-3)
Allophylus edulis 1 6 3 1 0 1
Ampelocera ruizii 1 7 3 1 0 2
Aspidosperma cylindrocarpon 1 7 2 1 1 1
Aspidosperma pyrifolium 1 7 2 1 1 1
Attaleaphalerata 1 8 2 1 0 3
Bougainvillea sp. 1 5 2 1 0 1
Bouganvillea modest 1 5 2 1 0 1
Calyptranthes sp. 1 6 3 1 0 2
Campomanesia aromatic 1 7 2 1 0 3
Capparis prisca 1 7 3 1 0 3
Cariniana ianeirensis 1 7 2 1 1 2
Chrysophyllun gonocarpum 1 7 3 1 0 3
Dalbergia riparia 1 8 2 1 0 1
Duguettia guitarensis 1 8 3 1 0 3
Erythroxylum sp. 1 6 3 1 0 1
Esenbeckia almawillea 1 6 3 1 0 1
Galipea trifoliata 1 6 3 1 0 1
Gallesia integrifolia 1 5 3 1 1 1
Genipa americana 1 7 2 1 0 3
Inga marginata 1 7 2 1 0 3
Lonchocarpus guillemineanus 1 7 2 0 1 1
Myrciaria cauliflora 1 8 3 1 0 3
Myrtaceae sp. 1 7 2 1 0 3
Neea hermaphrodita 1 6 3 1 0 2
Phyllostylon rhamnoides 1 7 3 1 0 1
Piper alboreum 1 8 3 1 0 2
Qualea acuminata 1 7 2 1 0 1
Rhamnidium elaeocarpum 1 7 2 1 0 3
Rheedia acuminata 1 8 3 2 0 3
Salacia elliptica 1 8 3 1 0 3
Sorocea saxicola 1 7 3 1 1 3
Syagrus sancona 1 8 3 1 0 3









Forest Regen.shadeMature shade Timber Wildlife
Scientific name Guild habitat* tol. (1-3) tol. (0,1) value (0-3) value (1-3)
Talisia esculenta 1 7 3 1 0 3
Trichiliapalliata 1 6 3 2 0 1
Triplaris americana 1 8 2 1 0 1
Vitex cymosa 1 7 3 1 0 3
Ximenia americana 1 8 2 1 0 3
Cariniana domestic 2 7 1 0 2 2
Cecropia concolor 2 8 1 0 0 3
Cyclolobium blanchetianum 2 7 1 0 0 1
Ficus gomelleira 2 7 1 0 0 3
Guazuma ulmifolia 2 8 1 1 1 3
Hymenea courbaril 2 7 1 0 2 3
Samanea tubulosa 2 8 1 1 0 3
Sapindus saponaria 2 8 1 1 0 3
Sapium longifolium 2 8 1 1 0 1
Tabebuia serratifolia 2 7 1 0 2 2
Zeyheria turberculosa 2 7 1 0 1 2
Agonanda brasilensis 3 3 1 0 2
Bauhinia ungulata 3 2 1 0 0 1
Celtis iguanea 3 2 1 1 0 3
Celtis spinosa 3 2 1 0 0 3
Cereusspp. 3 3 2 0 0 3
Cochlospermum vitifolium 3 2 1 0 0 1
Eriotheca roseorum 3 3 1 0 0 2
Heliocarpus americanus 3 1 1 1 0 1
Jacaranda cuspidifolia 3 3 1 0 0 1
Lueheapeniculata 3 3 2 1 0 1
Pseudobombax marginatum 3 3 1 0 0 2
Scheffiera morototoni 3 2 1 0 0 3
Sebastiana brasiliensis 3 1 3 1 0 1
Stryphnodendron guianense 3 3 1 0 0 1
Tabernaemontana sp. 3 4 2 1 0 1
Trigonia boliviana 3 2 3 0 0 1
Urera baccifera 3 1 1 0 0 3
Vochysia mapirensis 3 2 1 0 0 1
Amburana cearensis 4 5 1 0 3 1
Anadenanthera colubrina 4 5 1 0 2 1
Astronium urundeuva 4 5 1 0 2 1
Cedrelafissilis 4 5 1 0 3 1
Ceiba samauma 4 5 1 0 0 2










Forest Regen.shadeMature shade Timber Wildlife
Scientific name Guild habitat* tol. (1-3) tol.(0,1) value (0-3) value (1-3)
Centrolobium microchaete 4 4 1 0 2 1
Chorisia speciosa 4 5 1 0 0 2
Cordia glabrata 4 5 1 0 3 1
Mimosa sp. 4 4 1 0 0 1
Physocalymma scaberrimum 4 5 2 0 0 1
Piptadenia viridifolia 4 5 2 0 0 1
Platymiscium ulei 4 5 1 0 0 1
Pterogyne nitens 4 5 1 0 2 1
Schinopsis brasilensis 4 5 1 0 3 1
Spondias mombin 4 5 2 0 0 3
Terminalia oblonga 4 5 1 0 1 1
Acacia albocorticata 5 5 1 0 0 2
Acosmiun cardenasii 5 5 3 1 0 1
Aspidosperma nobile 5 5 2 0 1 1
Aspidosperma rigidum 5 5 2 0 2 1
Caesalpinia paraguarensis 5 4 1 0 0 1
Caesalpiniapluviosa 5 5 2 0 0 2
Capparis retusa 5 4 3 1 0 3
Casearia gossipiosperma 5 4 3 1 0 3
Combretum leprosum 5 5 2 1 0 1
Copaifera sp. 5 5 3 1 0 2
Dictyolomaperuviana 5 5 1 0 0 1
Enterolobium contortisiliquum 5 5 1 0 0 3
Guibourtia chodatiana 5 5 3 1 1 3
Jatropha minuscule 5 5 1 0 0 1
Machaerium acutifolium 5 5 3 1 0 1
Machaerium hirtum 5 5 1 0 0 1
Machaeriumjacarandifolium 5 4 3 0 0 1
Machaerium scleroxylon 5 5 3 0 3 1
Maclura tinctoria 5 5 1 0 0 2
Opuntia brasiliensis 5 5 3 0 0 3
Pereskia sacharosa 5 5 2 0 0 1
Platypodium elegans 5 5 3 0 1 1
Pogonopus tubulosus 5 5 3 1 0 1
Rollinia emarginata 5 4 3 1 0 3
Simira rubescens 5 5 3 0 0 1
Swartziajorori 5 4 3 1 0 3
Zanthoxylum sp. 5 5 1 0 0 2









* Lomerio forest habitats (T. Fredericksen, personal comment)
1: Short-lived (3-4 years), early successional
2: Long-lived colonizers of disturbed sites
3: Borders of rock outcrops
4: Generalists
5: Mature upland forest canopy
6: Mature upland forest understory
7: Riparian forest canopy
8: Riparian forest understory














APPENDIX B
FOREST HARVESTING COSTS PER COMPONENT

Direct costs SUS/ba $US/m3
Road construction and maintenance 18.81 3.33
Management plan (compounded 2 yrs @18.75%) 0.91 0.26
Inventory 0.31 0.06
Plan (data analysis, mapping, write-up) 0.36 0.09
Census of merchantable stems 10.04 2.49
(compounded 1 year @18.75%)
Annual Operating Plan 0.86 0.10
(compounded 1 year @18.75%)
Felling & bucking
Labor (sawyer + assistant) 2.57 0.49
Chainsaw (Stihl 070)
Depreciation 0.24 0.05
Chains 0.20 0.04
Blades 0.14 0.03
Pinions 0.03 0.01
Files 0.03 0.00
Spark plugs 0.01 0.00
Filters 0.02 0.00
Fuel 0.16 0.02
Motor oil 0.06 0.01
Safety equipment 0.01 0.00
Skidding
Labor (skidder operator + assistant) 3.08 0.59
Skidder (CAT 518)
Depreciation 4.74 0.96
Cables 0.33 0.06
Tires 0.34 0.08
Filters 0.03 0.00
Annual maintenance 1.01 0.19
Fuel 2.61 0.48
Motor oil 0.35 0.05
Hydrolic fluid 0.06 0.01
Safety equipment 0.01 0.00









Measuring and bucking at log landing
Labor (sawyer + technician) 6.21 1.18
Radio 0.08 0.01
Fuel 2.61 0.48
Motor oil 0.35 0.05
Loading
Labor (loader + assistant) 2.91 0.55
Loader (CAT 950B)
Depreciation 8.18 1.12
Tires 0.54 0.07
Filters 0.03 0.00
Annual maintenance 1.26 0.17
Fuel 3.89 0.53
Motor oil 0.23 0.03
Hydrolic fluid 0.49 0.07
Supervision of harvest operations 9.76 1.85
(activities of forest engineer and site manager)
Transport (forest to Concepci6n mill, -30 km.) 33.70 5.72
Indirect costs $US/ha $US/m3
Taxes and fees
Area fee (Patente) 1.00 6.35
Registration: Camara Forestal (CF) 0.10 0.02
Registration: Superintendencia Forestal 0.29 0.04
Registration: Export Chamber 0.15 0.02
Forest Origin Certificate (CFO) 1.46 0.28
Aggregate Valor Tax (IVA) 0.27 0.04
Training 1.24 0.20
Overhead (10% of direct costs) 11.69 2.11
Employee benefits (included in labor cost calculation)
Pension fund (AFP) 2.5%
Medical insurance 10.0%
Vacation (days/yr) 17.50
Bonus (extra month pay) 1.00
Total costs $US/ha $US/m3
Variable Costs 12.11
Fixed Costs 62.51
Annual Costs 1.55













APPENDIX C
MARKET VALUE OF MERCHANTABLE TIMBER SPECIES

Mean sawnwood price Mean roundwood priceab
(FOB Santa Cruz) (FOB Forest Mill)
Scientific name Bs/bf $US/bf Bs/m3 $US/m3
Amburana cearensis 3.50 0.52 601.44 89.90
Anadenanthera colubrina 2.40 0.36 344.92 51.56
Aspidosperma nobile 2.75 0.41 426.54 63.76
Aspidosperma spp. 2.65 0.40 403.22 60.27
Astronium urundeuva 2.65 0.40 403.22 60.27
Cariniana domestic 2.00 0.30 251.64 37.61
Cariniana ianeirensis 1.75 0.26 193.34 28.90
Cedrelafissilis 4.00 0.60 718.04 107.33
Centrolobium microchaete 3.00 0.45 484.84 72.47
Cordia glabrata, C. alliodora 3.80 0.57 671.40 100.36
Gallesia integrifolia 1.55 0.23 146.70 21.93
Guibourtia chodatiana 3.00 0.45 484.84 72.47
Hymenea courbaril 2.90 0.43 461.52 68.99
Lonchocarpus guillemineanus 1.30 0.19 88.40 13.21
Machaerium scleroxylon 10.51 1.57 2237.01 334.38
Phyllostylon rhamnoides 2.40 0.36 344.92 51.56
Schinopsis brasilensis 3.75 0.56 659.74 98.62
Sorocea saxicola 2.40 0.36 344.92 51.56
Sweetiafruticosa 2.90 0.43 461.52 68.99
Tabebuia serratifolia 2.75 0.41 426.54 63.76
Terminalia oblonga 2.65 0.40 403.22 60.27
a. Less transport (0.36 Bs/bf) and milling costs (19.38 Bs/m)
b. 233.2 bf/m3 roundwood














APPENDIX D
DEFINITION OF OPTIMIZATION VARIABLES

y, [yLv], number of trees in size class i, guildj at time t

ya [Yjt], undisturbed steady-state or "climax" equilibrium distribution of trees

ym, [ yi,'], number of trees in size class i, guildj at time t

y' [y'*], number of trees in size class i, guildj in the STY steady-state

y* [yg"], number of trees in size i, guildj in the SFM steady-state

hi [hqi], number of stems harvested in size class i, guildj at time t

h [ho,], number of stems harvested in size class i, guildj in the STY steady-state

h" [hy*], number of stems harvested in size class i, guildj in the SFM steady-state

Gj Matrix of transition probabilities for trees of guildj, which define the movement
of trees into size classes (i) during a 5-year growth period (0)

r, [rjt], number of recruits into the 10 cm size class of guildj during the 5-year
growth interval t to t+O

Z Objective function of the optimization

t = yO Cutting-cycle length, defined as the number (y) of 5-year growth periods (0)

T Harvest horizon

6 Discount rate

By Mean basal area (m2) of a stem in size class i and guildj

(oj Merchantable proportion of stems in guildj

sj Proportion of merchantable species in guildj

fj Proportion of stems of merchantable form in guildj

pi Market value of merchantable species ($/m3) in guildj

89








Vy (pj C)i#, net value of an extracted stem of size i in guildj in 2001 $US/m3

C Variable costs ($/m3) of felling, skidding and log deck operations

F Fixed costs ($/ha) of planning and capital costs including depreciation

A Annual costs ($/ha) including an area fee of $1/ha for the concession and
inscription fees to government agencies and trade associations

yei Mean extracted volume of a tree, estimated as 85% of mean volume per size class
(i) and guild (/), assuming 15% of merchantable volume lost in logging waste

vy Net value ($/m) of an extracted stem of size i in guildj

9 Annual concession fee or "patente" ($1/ha) per Bolivian forestry law

t Regulatory fee defines per fiscal instrument (see Appendix F)

p % compliance with STY restriction measured for the performance bond

< [dyj], vector of negative deviations of the number of trees of size i and guildj in
the Yt from the climax state y", expressed as an absolute value

td [dj], vector of positive deviations of the number of trees of size i and guildj in Yt
from the climax state y'













APPENDIX E
MATHEMATICAL DESCRIPTION OF MANAGEMENT ALTERNATIVES

Unconstrained Harvest (U)

T v'h,-F 1 -(1+( )-')
maxZ,,, = s.t.
t--o (1+0) 6 )

r-1
h+y, -G'(y, -h,_) = G'r Forest growth
k=0

h,,, y,, < 0 Merchantable stock, initial cutting-
cycle (CC)
y-I
h,, Gry",,-1 aGk'r,,, < 0 Merchantable stock, all ensuing CC
k-0


h = 0
0


y,-h, >0

h, >O,yt0O


Merchantable dbh limit


Absolute harvest level

Non-negativity


Bolivian Forestry Law (BFL)

-v'h,-F l-(1+)-"
max Z(,,Y) = A ('-(+ s.t.
1.0 (1+6)' .t.



k=0

h, co, y < 0 Merchantable stock, initial CC

y-I
h,, G'y ,-i co,G k_, _< 0 Merchantable stock, all ensuing CC
k=0




Full Text
2
Recent studies of Dipterocarp forests in peninsular Malaysia examined such trade-offs
between the financial and ecological benefits of natural forest management (Boscolo and
Buongiomo 1997, Ingram and Buongiomo 1997, and Boscolo and Vincent 2000). The
present research contributes to earlier work by examining the conditions necessary for,
and the biological consequences and economic costs of sustainability, of a forest in the
eastern Bolivian lowlands.
The Bolivian forestry law was revised in 1996 (Ley 1700) to more effectively
promote sustainable management of the nations forest resources, which are allocated in
renewable concessions to the logging industry (Art. #1). The present study offers a
contribution to the analysis of whether or not new forestry legislation is likely to achieve
these sustainability goals. The study offers an economic comparison of management
alternatives under current and alternative regulatory constraints, and a robust analysis of
the biological impact of such alternatives for stands representative of the Chiquitano
tropical dry forests of eastern Bolivia.
The study focuses on 800 hectares (ha) of seasonally dry forest located near the Las
Trancas community (1613S, 6150W) in the Lomero region south of Concepcin,
Santa Cruz, Bolivia The forest is representative of the Chiquitano tropical dry forest
ecosystem, which lies in a transition zone between the humid forests of the Amazon
Basin and the thorn scrub of the Gran Chaco (Killeen et al. 1998). Numerous timber
concessions have been awarded in the Chiquitano forests, which are valued for their
stocks of tropical hardwood species such as Spanish cedar (Cedrela Jissilis), Spanish oak
(Amburana cearensis), and morado (Machaerium scleroxylori).


24
each 5-year growth interval. Forest response and recovery trajectories following
disturbances caused in harvesting or silviculture may be more precisely estimated in
dynamic form. As an example, estimated stand populations and their distribution twenty-
five years after a simulated harvest of 40% of all merchantable stems (> 40 cm dbh;
Guilds 1,2,4,and 5) are quite distinct in static and dynamic model forms (Figure 2-4).
The 25-year growth horizon simulated in this example was selected merely for
demonstration purposes. Changes in the stand population, basal area, and harvest
variables over time result in modest changes in the transition probability estimates
generated by the MNL model, which may more precisely reflect forest dynamics and
disturbance effects.
Figure 2-4. Comparison of static and dynamic model estimates of tree population
distribution 25 years after harvesting 40% of merchantable stems
That the dynamic model predicts more stems in 10-40 cm dbh classes relative to
static model (Figure 2-4) reveals an important advantage of the dynamic prediction form.
In the static model, the transition probabilities estimated for the initial harvest are


49
returns relative to the sustained-yield alternatives, but has important opportunity costs
relative to unconstrained harvesting ($465.64/ha). These opportunity costs derive from
merchantable stems not harvested in Year 0 in order to meet dbh and allowable-cut
limits.
The discount rate affects the profitability of management under those alternatives
whose objective function is to maximize this output (U, BFL, STY), but does not change
the optimal solution. The optimal solution is constrained by biological and
merchantability restrictions and cutting-cycle length. At lower discount rates, STY
becomes more competitive with the U and BFL options (Table 3-9), exceeding the
profitability of BFL under 1% discounting. The SFM optimal harvest solution changes
with the discount rate as less deviation from the climax condition is allowed at lower
discount rates, while satisfying the binding constraint of non-negative NPV for a
perpetual harvest horizon. Consequently, the NPV of SFM harvesting for a 40-year
horizon decreases with decreases in the discount rate.
Table 3-9. Discount rate effects on the NPV of harvest returns for a 40-year horizon
NPV ($/ha)
Case\ Discount rate:
18.75%
12.00%
6.00%
1.00%
U
1380.54
1379.72
1402.11
1593.29
BFL
914.89
913.55
931.31
1091.75
STY
257.18
338.98
538.41
1087.67
SFM
11.25
9.84
8.73
7.90
Stand State and Forest Value Measures
Comparison of the structure of aggregate merchantable and non-merchantable
residual populations under the alternative management regimes and that projected for the
undisturbed climax reveals minor differences in stand impact among management options
(Fig. 3-1). As expected, the unconstrained scenario has the greatest impact on residual


I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope^ad quality, as a
dissertation for the degree of Doctor of Philosophy"
Douglas R. Carter, Chair
Associate Professor of Forest Resources and
Conservation
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Janaki R.R. Alavalapati
Assistant Professor of Forest Resources and
Conservation
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope an^quality, as a
dissertation for the degree of Doctor of Philosophy.
Clyde F. Kiker
Professor of Food and Resource Economics
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully ^dequa^e, in scope apd-quqlity, as a
dissertation for the degree of Doctor of Philos
fancis E. Putz
Professor of Botany
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
bomas P. Holmes, Research Forester
USDA Forest Service
Research Triangle Park, North Carolina


33
guild ipj) is estimated as the weighted mean price for merchantable stems of Guild j
(Table 3-1). This assumption greatly simplifies market value calculations for multiple-
species harvest. However, greater precision in calculating the market value of timber was
necessarily sacrificed for increased tractability of the optimization model.
Guild populations comprise merchantable and non-merchantable stems. Harvest is
necessarily constrained by the merchantability of the timber stock, as loggers will only
harvest those stems that are of merchantable species and form. It is assumed that
harvesting is restricted to logs appropriate for saw-timber milling, i.e. stems of 40 cm dbh
and greater. The merchantable proportion of stems per guild (mj) is estimated as the
product of the proportion of merchantable species (sj) per guild and the proportion of
stems of merchantable form (fj) in that guild, based upon PSP data for the sample forest
blocks (Table 3-1). Trees of Guild 3, those growing in inselberg habitats, are not
merchantable.
Table 3-1. Market values and merchantable proportions of stems per guild
Guild
Market value (pi)
Merchantable proportion
($US/m3)
Species (s,)
Form (f¡)
Stems ( 1
41.28
0.52
0.78
0.41
2
62.50
0.90
0.96
0.87
3
0.00
0.00
0.88
0.00
4
57.03
0.69
0.87
0.60
5
104.53
0.26
0.84
0.22
If the forest structure at time I is represented by the vector y, = [y;,, yn,..., ym(]',
forest volume is obtained by pre-multiplying y, by the square matrix


Per-Tree Royalty (t $/stem)
maxZ
(*,rt _
[pl-C-r)i/ljhJt-F
(1 + S)
Volume-Based Royalty (x $/m3)
maxZ(n.,)
yyy(Pt T F
o+i)'
Ad valorem Royalty (x % log price):
, (tpj c\/jhj-F l-(l + >yr
max2(*J.)=ZZZ- n.,
I j 1=0 (l + t>)
Performance Bond (x $/ha)
lit0' zSk^lfL.i^iIL
I J 1-0 U + o)
,s.t.
constraints for Area Fee (above) and
III
(40 j /=0
III (Bvy;-pB0y;')>o
(=40 j 1=0
p<\
p> 0
where, y",y, = number of merchantable stems (trees/ha) in size class i
and guild j at time t
fj = number of merchantable stems (trees/ha) in size class i
and guild j in the STY distribution
p % compliance with STY restriction
B,j= mean basal area (m2)of a stem in size class i and guild j
96


69
leave stems of the 45 cm dbh class adequate to constitute 20% of the growing stock
(Table 4-1, Fig. 4-1).
The area fee alternative, which requires payment of $250/ha at each cutting-cycle
for the area harvested, does not change optimal harvesting behavior from the liquidation
harvest that would be optimal under unregulated management. The area fee is paid
regardless of harvest intensity, thus the concessionaires optimal strategy for maximizing
profits would be to extract all merchantable timber at each entry. As modeled, the area
fee would result in depletion of the merchantable stock over the 40-year concession
period (Table 4-1, Fig. 4-1).
Table 4-1. Residual distribution of merchantable stock (trees > 40 cm dbh per ha) per
regulatory policy, Year 40
Regulatory mechanism
Dbh class Ad
(cm)
STY
BFL
Area
Per-tree
Volume
valorem
PB
40
3.2
6.3
0.0
6.3
3.9
1.0
4.6
45
2.1
1.6
0.0
3.5
2.9
0.8
3.2
50
1.6
0.0
0.0
2.6
2.0
0.7
2.0
55
1.3
0.0
0.0
1.3
1.3
0.5
1.1
60
1.1
0.0
0.0
0.3
0.8
0.3
0.3
65
0.9
0.0
0.0
0.2
0.5
0.2
0.3
70
0.7
0.0
0.0
0.0
0.3
0.2
0.2
75
0.6
0.0
0.0
0.0
0.1
0.1
0.1
80
0.3
0.0
0.0
0.0
0.1
0.1
0.1
85+
0.0
0.0
0.0
0.0
0.1
0.1
0.1
The per-tree royalty creates the incentive to leave smaller stems of lesser value,
notably those stems whose net value do not exceed the $70 per-tree fee, such as the
species of Guild 1, which have the lowest market value (Fig. 4-2). The per-tree royalty
results in modest improvements toward achieving the STY condition relative to the area


3
Objectives of the study are to portray the optimal behavior of a forest
concessionaire, whose goal is to maximize the financial returns from logging and whose
management actions are circumscribed by biological, market, and regulatory constraints.
The study aims, moreover, to determine the conditions necessary to maximize the returns
from logging while meeting the goals of sustained timber yield and maintenance of
desired forest conditions. The study comprises three principal elements, each of which is
fully developed in the ensuing chapters. These elements include:
Estimation of a forest growth and yield model as a basis for establishing the
biological conditions by which management is constrained
An economic optimization comparing the profitability and forest impacts of
alternative management regimes
An analysis of regulatory policies as means of providing incentives to
concessionaires for more sustainable forest management behavior
Together these components respond to fundamental issues of sustainable forest
management, notably: what are the biological conditions necessary for sustainability,
what are the costs of achieving this goal, and what are appropriate regulatory mechanisms
for inducing sustainable behavior. For reasons of tractability, numerous assumptions are
made in developing the biological and economic models. Consequently, although the
models are derived in rigorous empirical analysis, the simulation results are indicative,
not definitive. It is hoped, nonetheless, that the results of this study will inform
management and policy formulation for the Chiquitano forests and enrich important
research concerning the biological and economic requirements for the sustainable
management of tropical forests.


LIST OF FIGURES
Figure page
2-1. Observed and predicted stability probabilities per dbh class for Guild 5 20
2-2. Static, deterministic prediction of forest evolution with observed (G)
and MNL estimated (GMNL) transition matrices 22
2-3. Stochastic, stationary estimation of the forest population (all guilds)
25 years after the observed harvest 23
2-4. Comparison of static and dynamic model estimates of tree population
distribution 25 years after harvesting 40% of merchantable stems 24
2-5. Undisturbed, steady-state equilibrium condition (y) estimated with
observed and MNL-estimated transition probability matrices 26
3-1. Aggregate merchantable and non-merchantable residual population
structure under management alternatives and climax condition 50
3-2. Residual merchantable population structure under management
alternatives and climax condition 52
4-1. Distribution of merchantable population per regulatory policy, Year 40 70
4-2. Distribution of merchantable stems of Guild 1 per regulatory
policy, Year 40 70
4-3. Distribution of merchantable stems of Guild 5 per regulatory
policy, Year 40 71
4-4. Percent compliance (p) with the STY condition and NPV of returns
from management ($/ha) relative to performance bond level (t) 72
viii


54
Shannon-Wiener measures of stand diversity also reveal little difference among
management alternatives (Table 3-12). The SFM results in slightly greater evenness
across guilds and size classes than would be expected in under more intensive harvest
scenarios (U, BFL, STY), as harvesting results in a decrease in merchantable stems. The
Shannon-Wiener diversity indices reveal little about differences among these timber-
focused management alternatives.
Conclusions
Management of the Chiquitano dry tropical forests of eastern Bolivia for sustained-
timber yield is shown to be feasible and profitable, given certain simplifying assumptions
of the forest growth model. Moreover, the present study demonstrates that sustained-
yield management with greater conservation of forest structure and composition may be
profitably implemented. The optimal trade-off between STY and SFM conditions is not
clearly defined and will depend upon further information concerning the marginal
ecological impacts of deviation from the theoretical climax forest condition. The optimal
sustained timber yield (STY) condition, defined as one that maximizes the returns to
harvest given sustained production constraints, is determined by biological criteria for
sustainability, cutting-cycle length and timber merchantability constraints. Harvesting
costs and discount rates have no effect on the optimal STY solution, unless costs increase
to the point of rendering harvest unprofitable, which would eliminate consideration of
logging activities. Marginal changes in costs and discount rates have not effect on the
optimum given the important constraints posed by the biological requirements for
sustainability.
Forest management under STY and SFM steady-state conditions is assumed
possible in Year 0 to allow for comparative analysis of these theoretical forest


CHAPTER 5
CONCLUSIONS
The present study of optimal management regimes for a Chiquitano tropica] dry
forest offers an indication of the biological and economic requirements for sustained
timber yield (STY) and sustainable forest management (SFM), given a land use objective
of profit maximization in logging and the biological, market and regulatory constraints on
its achievement. Results generated by the forest growth model and optimization analyses
are conditional on the modeling assumptions required for a tractable analysis. The
accuracy of these bioeconomic models fundamentally determines the validity of estimates
concerning the conditions required for sustainable management and simulations of
management impacts on the natural forests. Constraining the harvest horizon to a 40-year
concession period lends greater integrity to the analysis of logging behavior, but does not
resolve all issues caused by data limitations and restrictive modeling assumptions.
These limitations notwithstanding, the study offers several useful contributions to
research on the biological and economic requirements for sustainable forest management.
The novel application of the multinomial logit (MNL) regression method for estimating
matrix transition models demonstrates important benefits relative to previous techniques
employed in matrix model estimation. The MNL method corrects for variance in the data
and model estimation errors imposed by limited samples. Moreover, the MNL form
offers compatible simulation alternatives, including deterministic and stochastic
projection in both static and dynamic model forms. The study demonstrates that
sustaining the productive capacity of the Chiquitano forest for timber can be compatible
77


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48
Profitability of Management
Economic returns from the alternative management scenarios indicate, as expected,
a considerable decrease in the NPV of sustained-yield harvesting relative to
unconstrained harvesting (Table 3-8). The opportunity costs of the sustained-yield
alternatives (STY, SFM) are likewise very high, exceeding $1000 per hectare for both
scenarios relative to unconstrained liquidation of the available merchantable timber stock,
assuming accuracy of the cost assumptions. The comparative analysis of financial
returns furthermore assumes that there is no period of regulation harvesting, thus no costs
or financial benefits derived from converting the forest from its initial state (yo) to the
STY (y*) or SFM (y**) conditions.
The great disparity in returns from sustained-yield and unconstrained alternatives is
attributable to the opportunity costs of leaving merchantable stems in initial harvest
entries, given the high discount rate (18.75%). High opportunity costs of sustained-yield
management would occur at even lower discount rates, however, given the low value
growth rate of the tropical hardwoods in this Chiquitano forest.
Table 3-8. Net present value and opportunity costs of management alternatives
Case
NPV
($/ha)
Opportunity
costs ($/ha)
U
1380.54
0.00
BFL
914.89
465.64
STY
257.18
1123.36
SFM
11.25
1369.29
The sustained-yield scenario (STY) yields profits of $257.18/ha despite the high
discount rate. The more conservative SFM harvest scenario also yields profits
($11.25/ha) while more closely approaching the climax condition. Optimal management
under constraints imposed by Bolivias Forestry Law (BFL) yields superior financial


CHAPTER 3
OPTIMAL MANAGEMENT OF A CHIQUITANO TROPICAL DRY FOREST
Introduction
Sustainable forest management has drawn great attention in the debate over
appropriate strategies to achieve often competing, but necessarily compatible objectives
of environmental conservation and sustainable economic development in developing
nations with large tropical forest reserves (Kishor and Constantino 1994, Dickinson et al.
1996, Rice et al. 1997, Frumhoff and Losos 1998, Rice et al. 2001, Pearce et al. 2003).
Despite conclusions concerning the viability or appropriateness of sustainable
management initiatives within this polemic debate, the conditions necessary for
sustainable management and, consequently, rigorous analyses of the costs and benefits of
these strategies relative to alternative tropical forestry options have been conducted in
only a few noteworthy studies (Howard et al. 1996, Howard and Valerio 1996, Ingram
and Buongiomo 1996, Boscolo and Buongiomo 1997, Boscolo and Vincent 2000). This
deficiency is primarily attributable to the paucity of statistically robust models of the
growth and yield of mixed-species tropical forests. This paucity, in turn, is due to the
common inadequacy of tropical forest growth data, particularly that offering evidence of
forest responses to harvest interventions. Furthermore, a precise definition of what
constitutes SFM remains elusive, but commonly sustainability is defined by one of two
management objectives:
Maintaining timber yield over an indefinite harvest horizon or sustained-yield
timber management (STY)
27


41
density (m2/ha), which reveals both the level of harvest intensity and the openness of
the residual stand in terras of soil occupancy by trees. Changes in structure are examined
by graphically comparing the residual distribution of trees by size class and by estimating
the proximity of residual stand structure and composition to the climax state. The
proximity to climax index (PCI) introduced by Boscolo and Vincent (2000) is employed
to examine the deviation in structure and composition of managed stands from the climax
equilibrium. Proximity to climax structure and density at time t is defined
PCI, = 1 -
(3-13)
PCI measures the proximity of the residual stand population at time / (y¡¡,) to the climax
distribution (y ¡j). The mean basal area per size class and guild (By) is used to place more
weight on the large trees that are associated with climax forest conditions and high
endemic biodiversity (cf., Boscolo and Vincent 2000).
In addition to the PCI measure of deviation from climax structure and density, the
PCI form is used to examine two other characteristics, proximity to climax market value
(PCM) and proximity to climax wildlife value (PCW). Structural differences are
captured in PCI and thus are not repeated in these indices; instead, the residual density of
stems per sub-guild (yhBt) is compared to the climax condition (yVi*) Sub-guilds (k)
are derived from Guilds (f) by differentiation of merchantable and non-merchantable
species, except for Guild 3 that contains no merchantable species. Proximity to climax
market value at time I (PCM,) is defined
(3-14)


78
with generating positive financial returns from management and with improved
ecosystem conservation. The integrated bioeconomic optimization model reveals the
governing influence of forest growth, cutting-cycle length, and timber merchantability on
the sustainable management solutions. Finally, the analysis of regulatory policies
demonstrates the effects and relative efficiencies of alternative fiscal regulatory
instruments as means of inducing logger compliance with desirable forest management
practices.
The extraordinary discount rate of 18.75% applied in this study and the slow
growth rates of merchantable timber species suggest that short cutting-cycles and
measured, selective harvesting promise the highest financial returns to sustainable
management of the Chiquitano forest. This high discount rate also substantially inflates
the opportunity costs of more sustainable management relative to unconstrained
harvesting. Given the low value growth rate of tropical hardwoods, however, the
requirement for leaving merchantable timber in the forest imposed by both the
sustainable forestry scenarios (STY and SFM) implies that these options will consistently
generate inferior returns to unconstrained liquidation of merchantable timber in initial
harvest entries.
Results of the SFM optimization indicate that maintaining forest structure and
composition can be compatible with producing sustained timber yield to meet the
economic objective of generating profitable returns from management. Moreover, for the
particular case of Chiquitano tropical dry forests, both STY and SFM goals appear
compatible with the maintenance of forest wildlife values. More information on the


6
simplifies model calibration and inferences concerning forest evolution (Lu and
Buongiomo 1993).
Transition probabilities are commonly estimated by simple mean proportions of
movement calculated from observations of the animal or tree populations (Leslie 1945,
Usher 1966, Buongiomo and Michie 1980). Logistic regression to predict the probability
that an individual tree will be successful in an event with a binary outcome has been
used to predict mortality (Hamilton and Edwards 1976, Buchman et al. 1983),
regeneration (Johnson 1984, Ferguson et al. 1986), and diameter increment (Lowell and
Mitchell 1987, Vanclay 1991). The logistic function constrains probability predictions to
the interval (0,1), provides a binomial distribution of errors, and allows the use of
individual tree data rather than class means for tree size and other explanatory variables
(Vanclay 1994). Moreover, the logistic equation is robust in the presence of outliers and
decrements in the data (Vanclay 1991).
In the present study, I employ multinomial logistic (MNL) regression to estimate
the transition probabilities of a matrix growth model for a dry forest of the eastern
Bolivian lowlands. The MNL estimates of transition probabilities are derived from tree
and stand attributes influencing growth and mortality. Lowell and Mitchell (1987)
developed a logistic model that estimated growth and mortality simultaneously, though
these were portrayed as binary choices; specific growth proportions were applied to the
successful population in a subsequent model step. Rather than estimating the
probability of success for a binary outcome, such as mortality or survival, the
multinomial formulation allows estimation of the probability of one of three events
occurring for a size-class and species group of trees during a given growth interval:


74
the concessionaire can expect profitable returns to management, however, the
concessionaires previous optimal strategy of maximizing profits in liquidating the
merchantable stock is unchanged; the net profits are just lower.
The royalty systems result in substantially lower private returns for modest
improvements toward the STY condition relative to BFL or, in the ad valorem case,
further depletion of the forest stock. All alternative mechanisms would result in greater
government rent capture relative to current BFL conditions.
The performance bond option reduces concessionaire profits the least, while
increasing government rent capture and resulting in greater proximity to the STY
condition relative to current and alternative regulatory mechanisms. The challenges of
defining appropriate performance criteria and enforcing logger compliance under a
performance bond are imposing. Moreover, high performance bond fees are required to
induce favorable levels of compliance with desired forest management standards.
Excessive fees will discourage private investment in logging government-allocated
concessions. The incentive for compliance created by a performance bond mechanism is
particularly compelling, though the complexity of its application may be limiting.
Conclusions
Alternatives to current Bolivian regulatory policy for forest concessions may
provide more effective fiscal incentives for sustainable forestry, while improving
government rent capture. The goal of changing logger behavior toward greater
compliance with STY standards may be achieved by alternative royalty systems or a
performance bond mechanism, given appropriate fee levels. An area fee, unless
complemented by technical standards for management such as the Normas Tcnicas, is
unlikely to change the concessionaires incentive to liquidate all merchantable timber in


LD
1789
20£_L
UNIVERSITY OF FLORIDA
3 1262 08556 6189


Forest Regen.shadeMature shade
Timber
Wildlife
Scientific name
Guild habitat*
tol. (1-3)
tol. (0,1)
value (0-3) value (1-3)
Centrolobium microchaete
4
4
1
0
2
1
Chorisia speciosa
4
5
1
0
0
2
Cordia glabrala
4
5
1
0
3
1
Mimosa sp.
4
4
1
0
0
1
Physocalymma scaberrimum
4
5
2
0
0
1
Piptadenia viridifolia
4
5
2
0
0
1
Platymiscium ulei
4
5
1
0
0
1
Pterogyne nitens
4
5
1
0
2
1
Schinopsis brasilensis
4
5
1
0
3
1
Spondias mombin
4
5
2
0
0
3
Terminalia oblonga
4
5
1
0
1
1
Acacia albocorticata
5
5
1
0
0
2
Acosmiun cardenasii
5
5
3
1
0
1
Aspidosperma nobile
5
5
2
0
1
1
Aspidosperma rigidum
5
5
2
0
2
1
Caesalpinia paraguarensis
5
4
1
0
0
1
Caesalpinia pluviosa
5
5
2
0
0
2
Capparis retusa
5
4
3
1
0
3
Casearia gossipiosperma
5
4
3
1
0
3
Combretum leprosum
5
5
2
1
0
1
Copaifera sp.
5
5
3
1
0
2
Diclyoloma peruviana
5
5
1
0
0
1
Enterolobium contortisiliquum
5
5
1
0
0
3
Guibourtia chodatiana
5
5
3
1
1
3
Jatropha minscula
5
5
1
0
0
1
Machaerium acutifolium
5
5
3
1
0
1
Machaerium hirtum
5
5
1
0
0
1
Machaerium jacarandifolium
5
4
3
0
0
1
Machaerium scleroxylon
5
5
3
0
3
1
Maclura tinctoria
5
5
1
0
0
2
Opuntia brasiliensis
5
5
3
0
0
3
Pereskia sacharosa
5
5
2
0
0
1
Platypodium elegans
5
5
3
0
1
1
Pogonopus tubulosus
5
5
3
1
0
1
Rollinia emarginata
5
4
3
1
0
3
Simira rubescens
5
5
3
0
0
1
Swartzia jorori
5
4
3
1
0
3
Zanthoxylum sp.
5
5
1
0
0
2
84


30
where
I is the identify matrix
G is a matrix of transition probabilities defining the movement of trees from one
size class to the next during a 5-year growth interval
r is a recruitment function defining the number of trees entering the smallest size
class during a 5-year growth interval.
These and all other variables used in the present study are defined in Appendix D. The
climax condition is defined solely by the growth model and does not assume that the
forest condition prior to harvesting is in this undisturbed equilibrium.1
Conserving forest vegetative structure and composition is assumed an appropriate
proxy for the maintenance of non-timber and ecological benefit flows (cf., Terborgh
1986, Hunter 1990). The SFM regime thus hypothetically achieves the objectives of
SFM defined above, though empirical evidence of the maintenance of non-timber
benefits is not presented. Results of the present study are at best indicative, given the
assumptions required for modeling; however, they provide important insight into the
conditions required for sustainability and the costs and benefits of sustainable
prescriptions relative to alternative harvest possibilities.
Methods
Forest Growth Model
The optimization study employs a five-guild matrix model of forest growth, which
was estimated by multinomial logit (MNL) regression of permanent sample plot (PSP)
data collected in two 400 hectare (ha) forest blocks near the community of Las Trancas
(1613S, 6150W) in the Lomero region south of Concepcin (cf., Chapter 2). The
1 The theoretical climax condition should arguably be presented in quotations or italics, given its
debatable nature. For reading ease, however, such formatting will not be employed throughout the text
Climax is understood to refer to the theoretical forest condition defined mathematically as y= (I-C) 'r.


21
Table 2-4. Ordinary least squares (OLS) estimate of recruitment model
Variable
Parameter
Std. Error
Intercept
152.775
27.213
TPH
-0.117
0.054
Adj R2
0.021

F test
4.583

Static, Deterministic Modeling
In static, deterministic form, transition probabilities estimated per guild at the initial
stand state are maintained throughout the projection horizon. The MNL model of forest
evolution after harvest shows an increase in total tree population and a leveling of the
population distribution across size classes with increasing age (Table 2-5).
Table 2-5. Deterministic prediction of forest evolution, aggregate population
DBH Class
(cm)
Post-harvest
Projected (trees/ha)
(trees/ha)
year 25
year 50
year 100
10
170.2
191.3
189.6
187.7
15
141.2
129.4
129.3
127.7
20
82.7
88.6
90.0
88.8
25
47.7
57.9
61.9
62.0
30
33.3
36.1
40.5
42.8
35
26.5
23.2
25.3
28.7
40
19.7
16.2
15.8
18.3
45
11.8
11.2
10.2
11.2
50
8.6
7.3
6.6
6.8
55
4.6
4.3
4.1
4.1
60
3.3
2.6
2.5
2.5
65
1.9
1.6
1.5
1.6
70
1.3
1.0
0.9
1.0
75
0.5
0.6
0.6
0.6
80
0.7
0.3
0.4
0.4
85
0.9
0.3
0.3
0.3
Total
554.8
571.7
579.3
584.6
Comparison of model projections using the observed transition probabilities (G)
and the MNL estimated probabilities (GMNL) reveals important differences in the


O
VI
1
:S>
S'
1
i
Merchantable stock
IV*=0
1.0 J
Merchantable dbh limit
y**-ct + d=)P
Integrity of deviation calculation
y**-h**> 0
Absolute harvest level
h**, y**,ct,d >0
Non-negativity
93


37
(3-2)
All management alternatives are constrained by the forest growth model, which
defines growth and recruitment in the residual forest between harvest intervals. All cases
are also constrained by absolute harvest restrictions, requiring that the harvest level not
exceed the growing stock (yt ht > 0) and non-negativity constraints (yt, hi > 0).
Forest growth constraint for cases U and BFL require that the sum of the harvest
and growing stock at time t equal the residual stocking at time 1-1 plus any growth and
recruitment in this growing stock between these cutting-cycles (Eq. 3-3). This forest
growth constraint is defined as follows
h +y,-Gr O',-1-*-, ) = £or
(3-3)
Merchantability restrictions require that the proportion of trees harvested per size
class i and guild j at time t be equal or inferior to the merchantable stock {a>,) present in
the stand. The constraint is expressed
(3-4)
where w, is the merchantable proportion per guild.
For subsequent cutting-cycles of cases U and BFL, the merchantable proportion is
expected to decrease, as merchantable volume is removed and upgrowth during the
cutting-cycle interval does not replenish the merchantable stock to initial levels. Thus,
while equation 3-4 is applied as a constraint to the initial harvest of U and BFL,
subsequent merchantable stock constraints are comprised of the growing stock of residual
merchantable stems remaining after harvest (ym,./) plus any upgrowth into this


52
prescribes maintenance of a growing stock of merchantable stems for future harvest (Fig.
3-2).
Impacts of the alternative harvest regimes on the merchantable species stock are
further elucidated in examination of residual basal area (BA), proximity to climax
merchantable stocking (PCImerch), and proximity to climax market value (PCM) of the
residual stands (Table 3-11). These indices reveal much greater impacts of U and BFL
regimes over the concession agreement (40 years). The basal area comprised by
merchantable species of all size classes under unconstrained harvesting is reduced to less
Figure 3-2. Residual merchantable population structure under management alternatives
and climax condition
than half that of the climax forest and to just over half of the climax merchantable
stocking under BFL constraints.


63
of the optimization models for the six regulatory policies and for the STY model are
provided in Appendix F.
A more exhaustive analysis of alternative fee levels per regulatory mechanism
would enable determination of the optimal fee schedule appropriate to achieve both
profitability, rent capture, and sustainability goals. This analytical approach is not fully
developed in the present study. Instead, fee levels required to compel the logger to
maintain a residual merchantable population most closely approaching that required for
STY were selected by iterative estimation in preliminary model simulations. The
alternative regulatory mechanisms are then examined at the selected fee levels to more
closely examine behavioral impacts and effects on financial returns from logging of the
policies, without detailed examination of the marginal effect of alternative fee levels per
policy. A more rigorous examination of the optimal fee levels per regulatory mechanism
would be a valuable extension on this work, though the present analysis provides a useful
comparison of policy impacts.
Sustainable timber management (STY). The regulatory goal of this analysis is
the maintenance of forest conditions necessary for STY; to wit, maintaining the
productivity of the forest such that a constant harvest yield is extracted at each cutting-
cycle entry. The conditions necessary for STY are derived from a static optimization
analysis using the MNL growth model of the Las Trancas forest for a cutting-cycle of 5
years (cf., Chapter 3). The STY harvest intensity is estimated at approximately 4.2 m3/ha
per 5-year cutting-cycle.
An important caveat is necessary regarding the definition of the forest condition
necessary for STY. The STY condition is derived from optimization analysis using the


67
objective function is accordingly modified to reflect that profit maximization is defined
by the intensity of harvest of merchantable stems and the level of compliance with
performance standards (Eq. 4-12). In addition to the forest growth, merchantability,
absolute harvest, and non-negativity constraints, the performance bond optimization is
constrained by criteria for compliance with sustainability standards (Eq. 4-13,4-14).
Percent compliance is constrained to the interval (0,1) (Eq. 4-15).
IIEoi-d*0 (4-13)
(=40 j t=0
iziW-pBXW (4 I4)
i-40 j 1=0
p> 0, p< 1 (4-15)
where
ym¡jt = Number of merchantable stems (trees/ha) in size class i and guild j at time t
Number of merchantable stems (trees/ha) in size class i and guild j in the
sustained-yield (SY) distribution
p = % compliance with SY restriction
B¡j= Mean basal area (m2) of Size Class i and Guild j
Determining the appropriate fee level for the performance bond is difficult, as setting the
bond too low will have little effect on management behavior, while setting it too high will
discourage private investment in logging government-allocated concessions (Richards
2000). Nonetheless, for the logger to have the incentive to comply with management
standards and receive a full refund, the bond must be set sufficiently high. Trade offs
between compliance and harvest are expected at lower performance bond levels. The
present PB optimization model allows for an examination of trade-off solutions, as the
decision variables include both level of compliance as well as harvest intensities per guild


25
maintained throughout the 25-year projection period. Consequently, the high mortality
probabilities estimated after a 40% proportional harvest are retained at each 5-year
growth interval in the static model, reducing the residual population at each interval. The
dynamic model avoids this modeling limitation by recalculating transition probabilities at
each growth interval, according to the state of the stand at these 5-year intervals.
Accordingly, the high mortality probabilities estimated immediately after the simulated
40% harvest, are not maintained throughout the projection. Instead, mortality
probabilities decline with increasing time after this harvest, as the stand returns to
relatively stable conditions compared to the disturbed state created by harvesting.
An Application
The benefits of the MNL model form relative to a matrix model generated from
observed transition probabilities are best revealed in model application. Following
Buongiomo and Michie (1980), the undisturbed, steady-state or climax equilibrium
(y) may be calculated for a matrix growth model as
y= (I-G)'V (2-6)
Expectations for the undisturbed steady-state are that the tree population converge to a
negative exponential distribution, typical of uneven-aged, mixed species forests and that
with greater length between disturbances this distribution gradually even out across size
classes. The MNL steady-state demonstrates precisely this result (Fig. 2-5). The steady-
state generated by the matrix model derived from observed transition probabilities
suggests a relative decline of large stems with increasing age. Moreover, an anomalous
bump in the population distribution for trees of size class 70 cm dbh results from model
estimation errors imposed by the limited sample of trees in large stem classes.


61
intensities (h¡) are not steady-state variables, as the regulatory solutions are not assumed
to achieve sustained-yield conditions. The real discount rate (S) of 18.75 % is the mean
real interest rate for 2001 reported by Bolivias Central Bank (Banco Central de Bolivia
2002).
The optimization is constrained by the forest growth model (Eq. 4-2), which
defines growth and recruitment in the residual forest between harvest intervals. The
forest growth constraint requires that the sum of the harvest and growing stock at time t
equal the residual stocking at time i-1 plus any growth and recruitment in this growing
stock between these cutting-cycles.
h,+yl-G'(y,_,-h,_}) = fiGkr (4-2)
*=0
The profit maximization objective is further constrained by merchantability criteria
for harvested stems. Merchantability restrictions require that the proportion of trees
harvested per Size Class i and Guild j at Time t be equal or less than the proportion of
merchantable stock (coj) present in the stand. The merchantability constraint for the
initial harvest (Year 0) is defined
hj,SO (4-3)
where U and BFL, the merchantable proportion is expected to decrease as merchantable volume
is removed. Thus while equation 4-3 is applied as a constraint to the initial harvest,
subsequent merchantable stock constraints are defined by the growing stock of residual
merchantable stems remaining after harvest {fui) and any merchantable upgrowth into
this stock during the cutting-cycle interval. This constraint is described mathematically


OPTIMAL MANAGEMENT OF BOLIVIAN TROPICAL DRY FORESTS
By
FREDERICK BOLTZ
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2003


LIST OF TABLES
Table Ea¡£
2-1. Maximum likelihood estimates (MLE) of transition model parameters 16
2-2. Marginal effects of attributes xi on transition probabilities j 17
2-3. Comparison of predicted and observed mean transition probabilities
for all size classes by guild 18
2-4. Ordinary least squares (OLS) estimate of recruitment model 21
2-5. Deterministic prediction of forest evolution, aggregate population 21
3-1. Market values and merchantable proportions of stems per guild 33
3-2. Mean volume of stem extracted in harvest per size class and guild (i/i¡,.) 34
3-3. Net value (v*,) of an extracted stem per size class and guild 35
3-4. Mean ordinal market (Mk) and wildlife (W) values per sub-guild 42
3-5. Harvest level in absolute terms and in proportion of the available
merchantable volume in Year 0 per management alternative 44
3-6. Comparison of pre-harvest population (y distribution (y*) per guild 45
3-7. Comparison of pre-harvest population (yo) and sustained-yield (SFM)
distribution (y**) per guild 46
3-8. Net present value and opportunity costs of management alternatives 48
3-9. Discount rate effects on the NPV of harvest returns for a 40-year horizon 49
3.10. State of the aggregate residual stand population per management alternative 51
3-11. Residual merchantable species population per management alternative 51
3-12. Wildlife and diversity indices per management alternative 53
vi


CHAPTER 1
INTRODUCTION
The success of initiatives promoting sustainable forest management (SFM) in
natural tropical forests will depend on demonstration that it is not only technically
feasible, but also equally decisive, that it is economically viable. Critical to the effective
conservation of tropical forest ecosystems managed for timber will be tangible incentives
for improved, sustainable management by forest landowners and the logging industry.
The management of natural tropical forests for timber is a complex and contentious issue.
Its complexity derives from the nature of the mixed-species, uneven-aged tropical forests
themselves, which confound attempts to estimate the conditions necessary for
sustainable, productive management. Its contentiousness derives from the extraordinary
nonmarket value of the biodiversity and ecological service flows conserved by tropical
forests, the increasing scarcity of tropical forests, and the deleterious consequences of
their mismanagement.
Although the technical challenges to defining and implementing sustainable forest
management (SFM) are imposing, most authors agree that the principal impediment to its
greater adoption is SFMs financial inferiority relative to conventional logging practices,
and alternative land uses (Verissimo et al. 1992, Kishor and Constantino 1993, Rice et al.
1997, Pearce et al. 2003). Given this conclusion, and the desirability of a sustainable
solution to unabated demands for the harvest of tropical timbers, there is urgent need for
empirically rigorous examination of the marginal costs of more sustainable management,
and the trade-offs that may be optimal to achieve both production and conservation goals.
1


vii
4-1. Residual distribution of merchantable stock (trees >40 cm dbh per ha)
per regulatory policy, Year 40 69
4-2. Profitability and rent distribution per regulatory policy 73


42
where M* is the mean ordinal market value of sub-guild k (Table 3-4), derived from a
ranking of tree species per market value (0 = no value, 3 = high), which is a refinement of
initial rankings by Pinard et al. (1999) conducted by the author and BOLFOR specialists
(Appendix A). The PCM measures the commercial timber stock value of residual forest
states (y<) relative to that of the climax forest (y).
Similarly, proximity to climax wildlife value (PCW) is defined
PCW, =1-
|Z( y*BkWk-yhBkIVk?
(3-15)
1 *
where Wt is the mean ordinal wildlife value of sub-guild k (Table 3-4), derived from the
ranking of tree species per wildlife value (1 = low, 3 = high) by Pinard et al. (1999) and
updated with BOLFOR specialists (Appendix A). Wildlife values are ranked by the
importance of tree species for vertebrate frugivores, based on interviews with local
hunters and stomach contents of wild game (Guinart 1997, Pinard et al. 1999). PCW
permits the interpretation of alternative residual stand states as forest habitat for resident
wildlife.
Table 3-4. Mean ordinal market and wildlife values per sub-guild
Sub-guild
Market value (Aft)
Wildlife value (If*)
Guild 1, merchantable
1.00
1.50
Guild 1, non-merchantable
0.00
2.16
Guild 2, merchantable
1.60
2.40
Guild 2, non-merchantable
0.00
2.33
Guild 3, non-merchantable
0.00
1.68
Guild 4, merchantable
2.33
1.00
Guild 4, non-merchantable
0.00
1.57
Guild 5, merchantable
1.60
1.40
Guild 5, non-merchantable
0.00
1.77


APPENDIX F
MATHEMATICAL DESCRIPTION OF OPTIMIZATION SCENARIOS WITH
REGULATORY MECHANISMS
Sustained Timber Yield Management (STY)
maxZ(M) =LLL
J i-o
0 + i)'
-A
i-o+ , s.t.
/ \
Grti + {l-G,)y =Y,Gr
k=0
LXV=
1.0 j
y*-h*>0
h* > 0, y* >0
Sustained-yield forest growth
Merchantable stock
Merchantable dbh limit
Absolute harvest level
Non-negativity
Bolivian Forestry Law (BFL)
7 jK~f
max2W> =LLL
, j ,.o (l + o)
where, q = annual area fee patente
h,+yl-G'(y,-i-h,J = XGkr
k=0
of($l/ha), s.t.
Forest growth
Merchantable stock, initial cutting-
cycle (CC)
94


81
while converting the forest to a sustained-yield state is another compelling extension.
The period of regulation required to establish STY conditions and the financial
implications of this regulation may offer important insights into the management needs
for establishing a regulated forest. The integrated optimization model enables an
examination of conservation and management alternatives proposed in recent conceptual
studies. Examples include the log and protect model suggested by Rice et al. (2001),
the effects of a price premium for certified timber with and without effective harvest
regulation, and the effects of a market for carbon sequestration.
Results of the present research offer a modest, but hopefully useful, contribution to
scientific understanding of the complex and contentious issue of sustainable forestry.
Improving the precision and dynamics of the modeling tools developed in this study will
enable further and more practical contributions to management, economic analysis, and
policy design.


17
Table 2-2. Marginal effects of attributes x¡ on transition probabilities /a
Marginal Effect
Variable
Mortality
Stability
Upgrowth
DBH
-0.01205
0.01911
-0.00706
(0.00123)
(0.00181)
(0.00155)
DBH2
0.00007
-0.00015
0.00009
(0.00002)
(0.00002)
(0.00002)
RD/BA
1.10026
-1.13126
0.03100
(0.28906)
(0.45397)
(0.39240)
TPH
0.00004
0.00012
-0.00015
(0.00002)
(0.00004)
(0.00003)
HBA
0.01020
-0.01192
0.00173*
(0.00188)
(0.00315)
(0.00273)
o2
-0.04911
-0.03591
0.08501*
(0.08785)
(0.10680)
(0.08313)
g3
-0.09944
0.09088*
0.00856*
(0.04540)
(0.06616)
(0.05712)
g4
-0.13225
-0.06753*
0.19978
(0.03000)
(0.04113)
(0.03297)
g5
-0.09304
o.ososs*
0.04218*
(0.02184)
(0.03068)
(0.02626)
G2* DBH
0.00031
-0.0007'
-0.00023*
(0.00338)
(0.00369)
(0.00275)
G3* DBH
0.00428
-0.00372t
-0.00056*
(0.00171)
(0.00220)
(0.00179)
G4* DBH
0.00648
-0.00343
-0.00305
(0.00117)
(0.00145)
(0.00116)
g5*dbh
0.00417
-0.00362
-0.00055*
(0.00108)
(0.00133)
(0.00111)
Notes: a. Asymptotic standard errors in parentheses
* Significant to P < 0.10
Not significant
The MNL estimated transition probabilities are not significantly different
(P < 0.05) from the observed probabilities derived from Lomero PSP data by calculation
of simple mean proportions of movement per size class and guild (Table 2-3).


35
Table 3-3. Net value (v¡,) of an extracted stem per size class and guild
^ \
Net value ($/stem)
Dbh class
Guild 1
Guild 2
Guild 3
Guild 4
Guild 5
40
22.33
41.96
-10.11
39.17
67.76
45
30.11
53.86
-13.10
51.25
90.34
50
39.46
67.44
-16.54
65.33
117.18
55
50.52
82.74
-20.47
81.54
148.63
60
63.41
99.82
-24.89
100.01
185.02
65
78.28
118.75
-29.84
120.86
226.70
70
95.27
139.56
-35.33
144.21
274.00
75
114.50
162.33
-41.39
170.18
327.26
80
136.13
187.11
-48.04
198.91
386.82
85+
160.28
213.95
-55.30
230.50
453.02
Optimization Models
The optimization model prescribes maximization of the net present value (NPV) of
polycyclic harvesting (Z) subject to biological, market, policy, and sustainability
constraints. The objective function does not consider the costs of investment in the
growing stock described by the economic stocking rule for selection harvest (Duerr and
Bond 1952) or soil expectation value (SEV) used in similar optimization studies
(Buongiomo and Michie 1980, Boscolo and Buongiomo 1997, Bach 1999, Kant 1999).
These costs are opportunity costs of not harvesting merchantable stems in the initial
harvest entry in order to maintain the timber growing stock. The decision to exclude the
opportunity costs of maintaining the growing stock from the calculation of net returns is
based upon the nature of the forest property. As these forests are allocated in concessions
to private industry under government ownership, the opportunity costs of conserving the
residual stock are public rather than private costs. These opportunity costs are revealed
in the difference between unconstrained and constrained harvest cases described below.


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
OPTIMAL MANAGEMENT OF BOLIVIAN TROPICAL DRY FORESTS
By
Frederick Boltz
May 2003
Chair: Douglas R. Carter
Major Department: School of Forest Resources and Conservation
The prospect of sustainable management of natural tropical forests for their timber
and non-timber benefits faces important biological and technical challenges of defining
the conditions necessary for sustainability, as well as economic impediments concerning
opportunity costs and appropriate incentive mechanisms. In this study, an optimization
model of forest management is employed to examine the conditions necessary for
sustainable management of a Bolivian tropical dry forest. Integration of a forest growth
model in the optimization enables an examination of harvesting impacts on forest
structure and composition in addition to the economic returns to management. Results of
the optimization analyses are then employed to examine the efficiency of alternative
fiscal regulatory mechanisms in promoting more sustainable logging behavior.
Simulation results indicate that sustainable management for timber production is both
feasible and profitable in the dry forest site. Alternative regulatory policies may achieve
sustainability goals more efficiently than current Bolivian forest policy, but compromises
between the efficiency and practicality of regulatory approaches are warranted.
rx


58
structure, Amacher et al. (2001) being the exception. The present study aims to
contribute to such empirical analyses by considering the impacts of existing regulatory
policy and alternative incentive mechanisms upon optimal harvesting behavior for a
tropical dry forest of eastern Bolivia. The study expands upon this recent work by
examining the influence of fiscal regulatory mechanisms on the logging behavior of
concessionaires, the private returns to logging and government rent captare. A harvest
optimization model is used to conduct a comparative analysis of the efficiency of
alternative policies in fostering forest management compatible with sustained timber
yield (STY) objectives.
Methods
Forest Growth and Optimization Models
The seasonally dry tropical forests of the Lomero region (1613S, 6150W) lie in
a transition zone between the humid forests of the southern rim of the Amazon basin and
the thorn scrub of the Gran Chaco on the southwestern edge of the Brazilian shield
(Killeen et al. 1998). The forests are typical of the Chiquitano dry forests of eastern
Bolivia. Forest growth and yield is projected with a five-guild matrix growth model
estimated by multinomial logistic (MNL) regression of permanent sample plot data
collected in two 400 ha forest blocks near the Las Trancas community (Claros and Licona
1995, Killeen et al. 1998). The MNL matrix growth model projects the probabilities of
upgrowth, stability, or mortality of trees in each of five ecological guilds during a 5-year
growth period and predicts recruitment of trees into the smallest size class (10 cm dbh)
for each guild (cf., Chapter 2). The linear form of the MNL model and the assumption of
stationarity of transition probabilities throughout the harvest horizon enable its
straightforward integration into this linear optimization study.


i
Measuring and bucking at log landing
Labor (sawyer + technician)
6.21
1.18
Radio
0.08
0.01
Fuel
2.61
0.48
Motor oil
0.35
0.05
Loading
Labor (loader + assistant)
2.91
0.55
Loader (CAT 950B)
Depreciation
8.18
1.12
Tires
0.54
0.07
Filters
0.03
0.00
Annual maintenance
1.26
0.17
Fuel
3.89
0.53
Motor oil
0.23
0.03
Hydrolic fluid
0.49
0.07
Supervision of harvest operations
9.76
1.85
(activities of forest engineer and site manager)
Transport (forest to Concepcin mill, ~30 km.)
33.70
5.72
Indirect costs
$US/ha
$US/m3
Taxes and fees
Area fee (Patente)
1.00
6.35
Registration: Camara Forestal (CF)
0.10
0.02
Registration: Superintendencia Forestal
0.29
0.04
Registration: Export Chamber
0.15
0.02
Forest Origin Certificate (CFO)
1.46
0.28
Aggregate Valor Tax (IVA)
0.27
0.04
Training
1.24
0.20
Overhead (10% of direct costs)
11.69
2.11
Employee benefits (included in labor cost calculation)
Pension fund (AFP)
2.5%
Medical insurance
10.0%
Vacation (days/yr)
17.50
Bonus (extra month pay)
1.00
Total costs
$US/ha
$US/m3
Variable Costs
12.11
Fixed Costs
62.51
Annual Costs
1.55
87


64
MNL forest growth model described in Chapter 2. The optimal STY condition is largely
dependent upon the biological constraints imposed by this growth model, by
merchantability constraints for timber species of this Chiquitano forest site, and by the
cutting-cycle length used in the STY analysis (Chapter 3). Alternate STY conditions are
possible with changes in these fundamental constraints. The present study assumes that
the STY condition estimated in Chapter 3 is a desired forest condition and is a
sufficiently accurate definition of the conditions required for sustainability. This latter
assumption may be violated for long-term modeling of sustainability due to the poor fit of
the model of forest recruitment (Chapter 2), which determines long-term changes in
forest composition. Therefore, the precise conditions necessary for STY may not be
conclusively asserted in the present study. Despite this important weakness, the
comparative analysis of the effect of alternative policy mechanisms on logger behavior
remains valid. Its validity derives from the fact that the influence of regulatory
mechanisms is not dependent upon precise definition of the STY condition.
Bolivian forestry law (BFL). The Bolivian forestry law (Ley 1700) and the
technical standards for forest management in concessions and private forests greater than
200 ha (Normas Tcnicas) established normative prescriptions intended to promote the
maintenance of sustained economic, ecological, and social benefits of production forests.
Under this legislation, harvesting is restricted to the following standards: a minimum 20-
year cutting-cycle; a maximum 80% allowable cut of the merchantable stock per species;
and, a minimum dbh limit for harvested stems. These regulatory constraints are imposed
upon the optimization model to examine the profitability and impact of expected
management behavior under the Bolivian forestry law in the BFL scenario. Under the


APPENDIX E
MATHEMATICAL DESCRIPTION OF MANAGEMENT ALTERNATIVES
Unconstrained Harvest (U)
max Z(h,y)
fy'h,-F
SO+S)
S.t.
A+X-Gr(X-,-V1) = ZGr
*=0
0
K -Gryrv-' o
*=o
£^=o
?=0
>o
h, > 0, y, > 0
Forest growth
Merchantable stock, initial cutting-
cycle (CC)
Merchantable stock, all ensuing CC
Merchantable dbh limit
Absolute harvest level
Non-negativity
Bolivian Forestry Law (BFL)
i v'h, F f 1 (1 + z"-5oT5H
, S.t.
h, +yt ~Gr(y,_t = 'y'Gtr Forest growth
k-0
h,j, <¡y,jt S 0 Merchantable stock, initial CC
7~ 1
h, Grymji-1 a)pkrlJt_\ < 0 Merchantable stock, all ensuing CC
91


46
Comparison with the pre-harvest stand state reveals that the STY condition may not be
assumed from Year 0, rather a period of regulation harvest is required to convert the
stand to the STY steady-state. The duration of the regulation period and the returns to
management aimed at achieving the STY condition are unknown. Estimating the returns
to regulation harvest is not as simple as subtracting the STY or SFM populations from the
initial population and estimating the value of the implied harvest. Rather, it is expected
that regulation would require harvesting both merchantable and non-merchantable stems
and active management toward the desired STY or SFM conditions relative to growth
and regeneration responses to silvicultural interventions. Thus, while it may be expected
that the returns to STY or SFM would be increased from an initial harvest intended to
convert the stand to desirable conditions, the nature and value of these returns are
uncertain.
Table 3-7. Comparison of pre-harvest population (yo) and sustained-yield (SFM)
distribution (y**) per guild
Dbh class
(cm)
Pre-harvest nonulation. vn ftrees/hal
SFM distribution, y**
ftrees/ha)
Guild 1
2
3
4
5
1
2
3
4
5
10
47.1
2.7
6.2
23.0
91.2
38.8
4.6
6.6
35.1
109.5
15
28.3
2.6
5.0
22.2
83.1
21.4
3.4
4.2
29.3
73.8
20
12.3
1.8
1.3
17.2
50.2
12.9
2.7
2.7
23.7
49.7
25
5.8
2.0
0.5
13.3
26.2
8.4
2.2
1.7
18.2
33.2
30
4.6
0.9
0.2
10.9
16.8
5.8
1.8
1.1
13.3
21.9
35
3.1
0.9
0.4
11.2
10.8
4.2
1.5
0.7
9.1
14.2
40
2.8
0.9
0.5
9.4
6.2
3.1
1.3
0.4
5.7
9.0
45
2.2
0.8
0.2
5.4
3.7
2.3
1.1
0.2
3.4
5.6
50
1.6
0.3
0.3
5.1
1.9
1.8
1.0
0.1
1.8
3.3
55
0.7
0.4
0.1
3.2
1.0
1.4
0.8
0.1
0.8
2.0
60
1.0
0.2
0.1
1.6
0.7
1.1
0.7
0.0
0.1
1.1
65
0.4
0.2
0.2
0.6
0.7
0.8
0.6
0.0
0.0
0.4
70
0.3
0.1
0.2
0.5
0.2
0.6
0.5
0.0
0.0
0.1
75
0.1
0.0
0.1
0.2
0.1
0.5
0.4
0.0
0.0
0.0
80
0.2
0.0
0.1
0.4
0.0
0.4
0.3
0.0
0.0
0.0
85
0.2
0.1
0.6
0.1
0.1
0.1
0.1
0.0
0.0
0.0


26
Figure 2-5. Undisturbed, steady-state equilibrium condition (y) estimated with observed
and MNL-estimated transition probability matrices
Conclusions
Multinomial logistic (MNL) estimation of the transition probabilities in matrix
models of forest growth offers important benefits relative to matrices derived from
proportional, static estimates derived from forest plot observation means. The MNL
model results in a smoother distribution of transition probabilities across size classes,
correcting for variance in the data and model estimation errors imposed by limited
samples. The MNL form also allows for deterministic and stochastic projection in both
static and dynamic model forms. Stochastic simulation enables more rigorous testing of
hypotheses concerning stand growth by accounting for fundamental biological
uncertainties. The static model form allows greater ease of integration in optimization
studies, while dynamic forms enable more meticulous simulation of stand evolution
dynamics and the effects of disturbance events.


14
Transition probabilities for each guild are estimated according to Greene (2000, p.
858). The probability that tree i will transition to state j is
(2-2)
for / = 0,1,2;
Prob(7>ee, = j) =
3
where,
0 = mortality, 1= stability, 2 = upgrowth
It is assumed for analytical convenience that the data conform to the Independence
of Irrelevant Alternatives (IIA) property. This property stipulates that the ratio of the
probabilities of choosing any two alternatives is independent of the attributes of any other
alternative in the choice set (Hausman and McFadden 1984, p.1221). More simply
stated, IIA requires that the equation errors are independent across states or choice
alternatives.
The marginal effect of attribute x¡ on the transition probability to state j is a
function of the beta vector for other states. Following Greene (2000, p. 861), the
marginal effect of x, is defined as
(2-3)
Recruitment (the number of live trees that grow into the smallest diameter class
during a 5-year interval t to t+0) is expressed as a function of the total tree population
after harvest. A negative relationship is expected between recruitment and residual tree
population. The recruitment function is of the form
5
(2-4)


APPENDIX B
FOREST HARVESTING COSTS PER COMPONENT
Direct costs
$US/ha
$US/m3
Road construction and maintenance
18.81
3.33
Management plan (compounded 2 yrs @18.75%)
0.91
0.26
Inventory
0.31
0.06
Plan (data analysis, mapping, write-up)
0.36
0.09
Census of merchantable stems
10.04
2.49
(compounded 1 year @18.75%)
Annual Operating Plan
0.86
0.10
(compounded 1 year @18.75%)
Felling & bucking
Labor (sawyer + assistant)
2.57
0.49
Chainsaw (Stihl 070)
Depreciation
0.24
0.05
Chains
0.20
0.04
Blades
0.14
0.03
Pinions
0.03
0.01
Files
0.03
0.00
Spark plugs
0.01
0.00
Filters
0.02
0.00
Fuel
0.16
0.02
Motor oil
0.06
0.01
Safety equipment
0.01
0.00
Skidding
Labor (skidder operator + assistant)
3.08
0.59
Skidder (CAT 518)
Depreciation
4.74
0.96
Cables
0.33
0.06
Tires
0.34
0.08
Filters
0.03
0.00
Annual maintenance
1.01
0.19
Fuel
2.61
0.48
Motor oil
0.35
0.05
Hydrolic fluid
0.06
0.01
Safety equipment
0.01
0.00
86


ACKNOWLEDGMENTS
I am deeply indebted to my advisor, Dr. Douglas R. Carter, for his skilled
mentoring and enthusiastic support throughout my graduate studies. Likewise, I am
grateful for the valuable tutelage and dear friendship offered to me over the years by the
members of my supervisory committee, Drs. Janaki R.R. Alavalapati, Thomas P. Holmes,
Clyde F. Kiker, and Francis E. Jack Putz. This research was partially financed by
Proyecto BOLFOR, a USAID-funded sustainable forest management project in Bolivia
through an agreement among Chemonics International, Inc., The Forest Management
Trust, and the University of Florida. Colleagues of Proyecto BOLFOR provided
excellent technical support and guidance (notably, Freddy Contreras, Todd Fredericksen,
Joaquin Justiniano, Claudio Leao, Juan Carlos Licona, Frailan Merlo, John Nittler, and
Marisol Toledo). I am beholden to Roberto Quevedo S., Roberto Sainz V., Alberto Arce
and William Rojas for their honest and enthusiastic responses to my cost surveys. My
sincere gratitude is also due to the competent team of professors and professional staff of
the School of Forest Resources and Conservation (SFRC), who greatly enriched my
graduate career. Lastly, my gratitude is extended to the Graduate School of the
University of Florida, the Institute of Food and Agricultural Sciences, and the SFRC for
their award of the E.T. York Presidential Fellowship, which provided important financial
and institutional support for this research.
iii


62
hj< ~Gry"j,-\-Yj (4-4)
In addition, merchantability standards require that trees equal or exceed 40 cm dbh:
(4-5)
i-0
Lastly, the optimization is subject to absolute harvest restrictions, requiring that the
harvest intensity not exceed the growing stock (yt ht > 0) and non-negativity constraints
(y.,h.>0).
Regulatory Policies
The six regulatory policies examined are as follows:
Bolivian forestry law (BFL)
Area fee
Per-tree royalty
Volume-based royalty
Ad valorem royalty
Performance bond
The level of fee levied for each policy other than BFL was determined iteratively,
based upon the target of achieving a residual merchantable population approaching that
defined for the STY condition (207 trees/ha of all size classes and guilds). This criterion
was selected as a mechanism for examining behavioral change relative to the selective
harvest of timber species, with the objective of comparing the efficiency of alternative
regulations in fostering the maintenance of residual forest conditions compatible with the
structure and composition necessary for sustained-yield harvesting (STY). It is assumed
that the administrative costs of alternative regulatory mechanisms are equal. Relaxing
this assumption is expected to affect government revenues but not the concessionaires
optimal harvest behavior or profits (cf., Amacher et al. 2001). Mathematical descriptions


68
and size class. The performance bond level is set at $750/ha to illustrate one such trade
off solution compatible with sustained-yield objectives.
Results and Discussion
Alternative regulatory mechanisms result in changes in both optimal harvesting
behavior and in the distribution of timber rents between private concessionaires and the
government relative to BFL policies. The relative efficiency of regulatory mechanisms is
revealed by inspection of the forest condition, profitability, and allocation of stumpage
between the concessionaire and the government. As noted above, the relative efficiency
of alternative policies is conditional on the fee levels selected to meet the criterion of
maintaining a residual merchantable timber stock approaching that of the STY condition.
Harvesting Behavior and Forest Condition
Current Bolivian regulatory policy (BFL) comprises both technical management
standards (minimum diameter limit and 80% allowable cut) and an annual area fee paid
for all forestland subject to logging. The annual area fee has a negligible effect on
harvest behavior for forestland with a timber value exceeding $5.44/ha, the NPV of
$l/ha/yr paid over a 40-year concession contract at a discount rate of 18.75% per annum.
At best, the annual area fee provides an incentive to set aside forestland with marginal
timber value, which consists largely of the inselberg habitats with species of no market
value (Guild 3). The management standards have the desirable effect of maintaining
merchantable stems of smaller size classes (< 45 cm dbh) and maintaining 20% of the
growing stock of merchantable stems of 45 cm dbh and greater. The residual distribution
of merchantable stems under BFL deviates considerably from the STY condition,
however, as the optimal harvest solution is to extract all stems more than 50 cm dbh and


38
merchantable stock during the cutting-cycle interval. This constraint is described
mathematically
/v-tyyy,so (3-5)
k=0
In addition, merchantability standards require that trees equal or exceed 40cm dbh, or
IX =0 (3-6)
1-0
The Bolivian forestry law constrained management alternative (BFL) employs the
same objective function (Eq. 3-2) and is constrained by the same forest growth (Eq. 3-3)
and merchantability (Eq. 3-4, 3-5) restrictions as the unconstrained alternative (U). The
BFL case is constrained by the technical standards established by the government of
Bolivia for all concessions and private forests > 200 ha (Ministerio de Desarollo
Sostenible y Planificacin 1998). The standards stipulate a minimum 20-year cutting-
cycle, a maximum 80% allowable cut of the merchantable stock per species, and a
minimum dbh limit for harvested stems. The 20-year cutting-cycle restriction is not
binding for the present analysis, given that the minimum cutting-cycle for positive NPV
was estimated at 40 years and this interval assumed for the BFL scenario.
The minimum dbh limit standard is not uniform for all species of the Chiquitano
dry forest. Stems that are more valuable generally have higher dbh limits, such as
Cedrela fissilis (60 cm) and Amburana cearensis (50 cm), while the absolute minimum
for other stems is 40 cm dbh. The guild grouping employed in this present model does
not allow for precise application of this diversity of dbh limits. Rather, a minimum dbh
of 45 cm is assumed for all merchantable stems as a BFL constraint (Eq. 3-7). Similarly,
the 80% allowable cut restriction is applied per guild and not per species (Eq. 3-8,3-9).


8
assumption that upgrowth and mortality probabilities remain constant over time may be
violated in managed stands, however (Johnson et al. 1991, Favrichon 1998). Forest
succession is likely a non-stationary process. Thus, probabilities of growth may be better
represented in a functional rather than constant form (Usher 1979). The impacts of
harvesting and of inter-harvest silvicultural treatments on established tree growth
therefore cannot be simulated, given the stationarity assumption. Stationarity may not
well describe actual stand behavior if, for instance, the growth of larger trees responds to
structural changes caused by harvesting, as observed in humid tropical forests of
Suriname and Brazil (Graaf 1986, Jonkers 1987, Silva 1989).
The MNL model estimation enables dynamic projections of forest growth by
reestimating transition probabilities at each time interval, thus overcoming the
stationarity limitation of traditional matrix models. The MNL model thus allows for
simulation of forest development dynamics, with transitions influenced by changing
stand characteristics. Decisions concerning harvesting and other silvicultural treatments,
as well as the evolution of stand structure and density, may be considered in iterative
projections of stand development at different time intervals. Stochastic estimation may
also be employed in the dynamic model form.
Study Site
The matrix model is estimated from permanent sample plot (PSP) data collected in
two 400 hectare (ha) forest blocks near the community of Las Trancas (1613S,
61 50W) in the Lomero region south of Concepcin, Santa Cruz, Bolivia. The
seasonally dry tropical forests of Lomero lie in a transition zone between the humid
forests of the southern rim of the Amazon basin and the thorn scrub of the Gran Chaco on
the southwestern edge of the Brazilian shield (Killeen et al. 1998). The forests are typical


16
(P < 0.001) from 5273 observations (Table 2-1). The marginal effects of tree and stand
attributes (x,) on the transition probabilities are estimated at the mean ofx, (Table 2-2).
Table 2-1. Maximum likelihood estimates (MLE) of transition model parameters * b
MLE Parameter
Variable
Stability
Upgrowth
DBH
0.11899
0.05704
(0.01126)
(0.01285)
DBH2
-0.00074
-0.00011*
(0.00016)
(0.00017)
RD/BA
-9.92015
-8.03101
(2.58866)
(2.99525)
TPH
-0.00009'
-0.00096
(0.00021)
(0.00025)
HBA
-0.09417
-0.06784
(0.01693)
(0.01966)
g2
0.30933*
0.75517*
(0.77065)
(0.82540)
g3
0.87904
0.77800t
(0.40223)
(0.46470)
g4
0.87814
1.89981
(0.27010)
(0.28991)
g5
0.76966
0.88485
(0.19444)
(0.22188)
G2* DBH
-0.00239*
-0.00334*
(0.02934)
(0.03114)
G3* DBH
-0.03752
-0.03436
(0.01509)
(0.01660)
G4* DBH
-0.05345
-0.06214
(0.01047)
(0.01137)
g5*dbh
-0.03654
-0.03347
(0.00957)
(0.01072)
X2 (18 d.f.)
281.3135

In L
-4590.429

Notes: a. Asymptotic standard errors in parentheses
b. Parameters for mortality are set to zero in MNL estimation
* Significant to P < 0.10
Not significant


Legal dbh limit
40
ZZZ*-
i=0 j t
Legal dbh limit
85 85
'Z.K -0.8eoJYiymJ' O
(=45 i=45
Allowable cut
y,-h, >0
Absolute harvest level
h, >0,yi> 0
Non-negativity
Sustained Timber Yield (STY)
^v'h,-F /l-o+rri
S(l + 5)' l 8 J
|,s.t.
Grh,+(l-G,y=J^Glr
k=0
Sustained-yield forest growth
¡5-
1
J3
Vi
IA
o
Merchantable stock
IZV=
f=0 j
Merchantable dbh limit
y*-h*>0
Absolute harvest level
h* >0, y*> 0
Non-negativity
Sustainable Forest Management (SFM)
min D ^ =ZZK^" + V/)
J
, s.t.
Vh"-F A^q
(1+ Non-negative NPV
GGr+^-G'')/=]TgV
A-0
Sustained-yield forest growth
92


72
stems/ha) at each cutting-cycle. In other words, the optimal harvest intensity is that
which results in a residual merchantable population approximately 20% lower
(8.2 stems/ha) than that necessary for STY. Given the incentive for compliance, the
performance bond results in a forest condition more closely approximating the STY
condition than the alternative regulatory options examined (Table 4-1, Fig. 4-1). As
defined, however, the PB mechanism permits high-grading of the stand and satisfaction
of performance criteria by leaving lesser-valued stems (Fig. 4-2,4-3). In terms of
efficiency, a PB regulatory policy is preferable to the alternative undifferentiated
mechanisms, but would be even more effective with greater precision in the definition of
performance standards. Criteria for maintaining residual stocking per guild and size class
groupings would promote closer compliance with the maintenance of forest structure and
composition required for STY, as defined by the forest growth and optimization models.
Figure 4-4. Percent compliance (p) with the STY condition and NPV of returns from
management (S/ha) relative to performance bond level (x)


66
grading, or logging of only those stems of superior value and stem size (e.g., Repetto
and Gillis 1988, Boscolo and Vincent 2000).
Volume-based royalty. Concession fees derived from a volume-based royalty
(t $/m3) would change the objective function to
'(pj-r-Cy^-F (!-(! + maxZ(*.rt =ZZZ-
l j 1-0
(4-10)
(! + <*)'
The volume-based royalty is set at $40/m3 for the present analysis.
Ad valorem royalty. An ad valorem royalty is derived as a percentage of the log
price (r % log price) and changes the loggers objective function to
maxZ(, C^jh; F -A[X~{X + Sy
M rrh o+ (4-11)
The ad valorem royalty is set at 71% of the log price of harvested stems.
Performance bond (PB). Although uncommon as regulatory instruments for
forest management, performance bonds may provide a useful incentive mechanism for
logger compliance with desired management practices. For the present study the
performance bond is levied prior to management, and then a proportion equivalent to
logger compliance is refunded to the logger immediately after harvest. The performance
bond (r $/ha) changes the objective function to
'(pj-C^jhj'-F-T + pr /l-(l + maxZ(*.,) n Vy
I j 1-0 (l+o)
(4-12)
Compliance with the performance bond requires that the residual merchantable
stock population and basal area of the managed forest equal or exceed the residual
merchantable stock of the STY equilibrium (Eq. 4-13,4-14). Any decrease in the
residual stock implies a proportional decrease in compliance with this standard and thus a
proportional reduction in the performance bond refunded to the concessionaire. The


15
where r, is the number of recruits into the 10 cm size class and d and e are regression
parameters to be estimated. Recruitment is estimated for the aggregate tree population,
as data did not permit the estimation of statistically significant recruitment models for
each guild. Recruitment levels for each guild are allocated proportionately, according to
the guild proportion of the total stand population observed prior to harvest. This method
is imprecise, but an unfortunate imposition of limited recruitment data.
The population per guild at time 1+8 is determined by the situation at time t, the
harvest during the growth interval (8), and the recruitment during this interval by
equations for each of the n guilds
yiji+e -1jt + ayfy \jt~ hi//)
V2jne = hi/yi/i- hiy,) + aifyiji- T>2j()
yyt+e = b3/yy,- h2,,)+ a3y ynjt+8 ^inj(yn-\jt hn-\jt) + h,!/;)
Growth may be assumed stationary, and long-term projections of stand growth
from initial conditions (yo) made deterministically as
GV0 (2-5)
k=0
for y growth periods of length 8 (Buongiomo and Michie 1980). Alternately, multiple
growth intervals (yd) may be estimated iteratively to more closely reflect the dynamics of
forest growth, with reestimation of the transition probabilities at each 5-year interval.
Results and Discussion
Growth Model Estimation
Multinomial logit (MNL) estimation resulted in a significant matrix model


TABLE OF CONTENTS
page
ACKNOWLEDGMENTS iii
LIST OF TABLES vi
LIST OF FIGURES viii
ABSTRACT ix
CEIAPTER
1 INTRODUCTION 1
2 MULTINOMIAL LOGIT ESTIMATION OF A MATRIX GROWTH MODEL
FOR TROPICAL DRY FORESTS OF EASTERN BOLIVIA 4
Introduction 4
Study Site 8
Methods 9
Results and Discussion 15
Growth Model Estimation 15
Recruitment 20
Static, Deterministic Modeling 21
Static, Stochastic Modeling 23
Dynamic Modeling 23
An Application 25
Conclusions 26
3 OPTIMAL MANAGEMENT OF A CHIQUITANO TROPICAL
DRY FOREST 27
Introduction 27
Methods 30
Forest Growth Model 30
Economic Data 31
Optimization Models 35
Residual Stand State Indices 40
Results and Discussion 43
Optimal Harvest per Management Alternative 43
IV


79
values of timber species for wildlife taxa other than vertebrate ffugivores would allow for
a more conclusive assertion of this apparent compatibility.
The finding that the opportunity costs of sustainable management alternatives are
high, relative to unsustainable logging methods, should not imply that the pursuit of
sustainability is an unworthy, or impractical, objective. The private opportunity costs of
sustainable management may be high, but the public opportunity costs of the progressive
depletion of natural forest timber stocks and concomitant degradation of non-timber
benefits produced by natural forests that are expected to occur under conventional,
unsustainable logging are arguably much higher. The critical issues for this and similar
research on sustainable tropical forestry are whether sustainable management for timber
and non-timber benefits is biologically feasible and economically viable. If so, the goal
of establishing permanent production forests to meet demands for tropical hardwoods is
both a worthy and practical alternative to extensive high-grading and degradation of
natural forests for short-term timber production.
Examination of the economic and biological impacts of optimal management under
constraints imposed by current Bolivian forestry regulations (BFL) indicates that,
although the financial returns to management are appreciable, BFL standards are not
likely to achieve sustainability goals. This conclusion cannot be drawn without caveats,
given the simplifying assumptions accepted in analyzing the BFL scenario with the
available forest growth and optimization models. Optimization results indicate that tree
diameter and allowable cut restrictions of BFL provide the logger with an incentive to
deplete large stems of high value, a practice unlikely to result in the maintenance of forest


23
Static, Stochastic Modeling
The MNL estimation of transition probabilities permits stochastic simulation of
stand evolution, drawing upon the standard errors of regression parameters. The
stochastic approach considers biological uncertainty in projections of stand growth,
providing a confidence interval of expected population values for a future stand state.
Stochastic simulation has the benefit of enabling more rigorous statistical comparison of
results from alternative simulations and permitting sensitivity analyses. The stochastic
element can be introduced into static projections, for which the initial transition
probability estimates are maintained throughout the projection horizon (Figure 2-3) or in
dynamic, iterative projections.
DBH class (cm)
Figure 2-3. Stochastic, stationary estimation of the forest population (all guilds) 25 years
after the observed harvest (SD = standard deviation, perc = percentile)
Dynamic Modeling
Changes in the growth dynamics of the forest over time may be considered by
iterative estimation of forest evolution with the re-estimation of transition probabilities at


65
BFL case, a minimum diameter of 45 cm is required for merchantable stems (Eq. 4-6)
and an 80% allowable cut restriction is applied per guild (Eq. 4-7).
40
I> =0 (4-6)
1=0
IX-o.sJX^0 (4-7)
t=45 =45
An annual area fee (patente) of $ 1 /ha is paid on all logged concession lands under
terms of the forest law. Concessionaires may set aside up to 30% of the forest concession
from logging and be exempted from paying the patente on these lands. This fee is
represented in the objective function of the BFL optimization by a $l/ha increase in the
annual costs of management (A).
Area fee. An area fee of (r $/ha), levied each cutting-cycle on harvested lands,
changes the profit maximization objective function to:
maxZ,
(,)-eiF r-4
/ j 1=0
i-(i+r
(4-8)
(! + An area fee of $250/ha is used in the present analysis. An area fee facilitates government
rent capture relative to tree or volume royalties, though it is not expected to affect
harvesting behavior on economic forestlands. Rather, those forest areas with timber
values less than the area fee are expected to be taken out of production.
Per-tree royalty. A per-tree royalty of (r $/stem) changes the concessionaires
objective function to
, j 1,0 (l + o)
(4-9)
The per-tree royalty is set at $70/tree. This and the other royalties are expected to reduce
the concessionaires profit margin on individual trees and thus may lead to high-


28
Maintaining non-declining timber yields; and sustaining other forest benefits (non
timber products, ecological services, and biodiversity)
The latter may be more strictly defined as SFM; a possible distinction being that STY
may generate a less sustainable flow of non-timber products relative to SFM (Pearce et
al. 2003).
Financial analyses comparing returns from more environmentally benign, or
hypothetically sustainable, harvest prescriptions with those from conventional logging
practices in tropical forests, reveal in some instances that improved forest management,
such as reduced-impact logging, is financially and ecologically superior, though the
conditions required for sustainability are not precisely identified (Barreto et al. 1998,
Armstrong 2000, Holmes et al. 2002). Other studies estimating the reduced harvest
levels and conservation easements necessary for SFM in natural tropical forests conclude
that the opportunity costs of more sustainable harvest regimes relative to conventional
logging or other land uses are excessively high (Kishor and Constantino 1993, Howard
and Valerio 1996, Hout 1999, Tay 1999, Healey et al. 2000, Pinard et al. 2000). Still,
suitably indicative estimates of the financial costs and ecological benefits of STY, let
alone SFM, remain elusive due to the inadequacy of dependable growth models and rare
attempts to integrate these models into an appropriate form for rigorous economic
analysis of forest management alternatives.
The present study aims to make a modest contribution to resolving this inadequacy
by producing a statistically robust economic comparison of management alternatives for
forests representative of the Chiquitano tropical dry forests of eastern Bolivia. The
analysis draws upon a matrix model of forest growth and yield and an economic
optimization model, integrated to enable the estimation of conditions necessary for


11
grouping. The five guilds retained for development of growth and yield models for
Lomero are defined as follows:
= Guild 1: riparian species, shade tolerant
Guild 2: riparian species, shade intolerant
Guild 3: early successional and granitic outcrop species, shade intolerant
Guild 4: mature upland forest canopy species and generalists, shade intolerant
Guild 5: mature upland canopy species and generalists, shade tolerant
The growth model for Lomero forests is founded upon a characterization of the
tree population by structure and composition. Classification of trees by diameter class is
utilized to describe forest structure and a grouping of species by ecological guild is
conducted both to portray floristic composition and to enable more precise modeling of
regeneration and disturbance events. Diameter classes are defined in five-centimeter
intervals from 10 cm to 85+ cm dbh and the growth interval 0 is defined as a five-year
period. The growth model is specified as
y/+=G(y,-h,) + r,
(2-1)
where
y<=[yn,y2/,
h,= [h, h2 ..., hm,]' and
r= [ri r2 r]'


Scientific name
Forest Regen.shadeMature shade
Guild habitat* tol. (1-3) tol. (0,1)
Timber
value (0-3)
Wildlife
value (1-3)
Talisia esculenta
1
7
3
1
0
3
Trichilia palliata
1
6
3
2
0
1
Triplaris americana
1
8
2
1
0
1
Vitex cymosa
1
7
3
1
0
3
Ximenia americana
1
8
2
1
0
3
Cariniana domestica
2
7
1
0
2
2
Cecropia concolor
2
8
1
0
0
3
Cyclolobium blanchetianum
2
7
1
0
0
1
Ficus gomelleira
2
7
1
0
0
3
Guazuma ulmifolia
2
8
1
1
1
3
Hymenea courbaril
2
7
1
0
2
3
Samanea tubulosa
2
8
1
1
0
3
Sapindus saponaria
2
8
1
1
0
3
Sapium longifolium
2
8
1
1
0
1
Tabebuia serratifolia
2
7
1
0
2
2
Zeyheria turberculosa
2
7
1
0
1
2
Agonanda brasilensis
3
3
1
0
2
Bauhinia ungulata
3
2
1
0
0
1
Celtis ¡guanea
3
2
1
1
0
3
Celtis spinosa
3
2
1
0
0
3
Cereus spp.
3
3
2
0
0
3
Cochlospermum vilifolium
3
2
1
0
0
1
Eriotheca roseorum
3
3
1
0
0
2
Heliocarpus americanus
3
1
1
1
0
1
Jacaranda cuspidifolia
3
3
1
0
0
1
Luehea peniculata
3
3
2
1
0
1
Pseudobombax marginatum
3
3
1
0
0
2
Schefflera morototoni
3
2
1
0
0
3
Sebastiana brasiliensis
3
1
3
1
0
1
Stryphnodendron guianense
3
3
1
0
0
1
Tabernaemontana sp.
3
4
2
1
0
1
Trigonia boliviana
3
2
3
0
0
1
Urera baccifera
3
1
1
0
0
3
Vochysia mapirensis
3
2
1
0
0
1
Amburana cearensis
4
5
1
0
3
1
Anadenanthera colubrina
4
5
1
0
2
1
Astronium urundeuva
4
5
1
0
2
1
Cedrela fissilis
4
5
1
0
3
1
Ceiba samauma
4
5
1
0
0
2
83


9
of the Chiquitano dry forests of eastern Bolivia. Seasonal mean temperature in the region
is 24.3 C with a mean annual precipitation of about 1100 mm and an acute dry season
from May to October. Soils of the region are primarily Inceptisols (shallow) and Oxisols
(deep), found in four distinct mapping units: hilltops, upper slopes, lower slopes, and
valley bottoms (Iporre 1996). The natural vegetation is classified as tropical dry forest
(Holdridge 1967). The undulating topography is dominated by low hills composed of
granite, gneiss, and metamorphic rocks of Precambrian origin (Geobold 1981). Elevation
varies between 400 m and 600 m asl.
Three distinct habitats constitute the Lomero forests: upland forest; riparian or
valley-bottom forest; and granitic outcrops (inselbergs). Mature upland and riparian
forest canopies range from 12 18 m tall and are dominated by trees of the Leguminosae,
Bignoniaceae, Anacardiaceae, and Bombacaceae (Killeen et al. 1998). Understory trees
are mostly Sapindaceae and Myrtaceae (Kennard et al. 2002). The spiny ground
bromeliad Pseudananas sagenarius is distributed over approximately 80% of the forest
(MacDonald et al. 1998) and regenerates vigorously in upland forest clearings. Light
selective logging for Spanish cedar (Cedrela fissilis), Spanish oak (Amburana cearensis),
and morado (Machaerium scleroxylori) occurred at undetermined intervals in the past
(Fredericksen et al. 2001).
Methods
BOLFOR researchers arranged 180 PSPs of20 x 50 m in a stratified random design
in the two 400 ha forest blocks in 1994 (LT94, Claros and Licona 1995) and 1995 (LT95,
Killeen et al. 1998). The PSP cover a total forest area of 18 ha: 8 ha in plot LT94 and 10
ha in LT95. Measurements of diameter at breast height (dbh), crown and stem quality,
crown position, liana infestation, damage, and mortality were conducted bi-annually.


55
management ideals with conventional harvest options (U and BFL). This presumes that
the regulation harvest necessary to convert the forest to sustained-yield conditions is
feasible. Moreover, the assumption of steady-state conditions implies that the duration
and magnitude of regulation harvest do not influence the returns to management. This
assumption is untenable for management of the Las Trancas forests from their current
state; however, strict comparison of returns to the theoretical STY and SFM regimes with
conventional alternatives remains useful and informative of the financial and ecological
implications of management under sustainable equilibria. While it may be expected that
the returns to STY or SFM would be increased from an initial harvest intended to convert
the stand to desirable conditions, the nature and value of these returns are uncertain.
Estimating the management requirements and duration of regulation harvest will be an
important extension of the present work.
The comparison of optimal harvesting behavior with and without constraints aimed
at maintaining the productivity, structure and composition of Chiquitano dry forests
indicates, as anticipated, that the opportunity costs of more sustainable management
relative to unconstrained harvesting are considerably high, assuming modest increases in
profitability from conversion to the STY and SFM conditions. The magnitude of the
decline in harvest profitability of sustained timber yield (STY) relative to unconstrained
(U) management may be largely attributed to the effects of excessively high discount
rates applicable to capital investments in Bolivia. Nonetheless, given the low value
growth rates of tropical hardwoods harvested in the Chiquitano forests, the requirement
for leaving merchantable timber in the forest imposed by both the STY and SFM regimes


60
Michie 1980, Boscolo and Buongiomo 1997, Bach 1999, Kant 1999). These costs are
opportunity costs of not harvesting merchantable stems in the initial harvest entry in
order to maintain the timber growing stock. The decision to exclude the opportunity
costs of maintaining the growing stock from the calculation of net returns is based upon
the nature of the forest property. As these forests are allocated in concessions to private
industry under government ownership, the opportunity costs of conserving the residual
stock are public rather than private costs.
The objective function (Z(h, y>) of the forest management problem is to maximize
the NPV of returns to harvesting over a 40-year concession period calculated as the
present value of a terminating series at discount rate 5, with harvest horizon T= 40 years
and cutting cycle length / = yd, with period yd being the number of intervals (y) of 5-year
growth periods (0) in a cutting-cycle. For the present analysis, the cutting cycle (/) is 40
years and y = 8. The cutting-cycle is set equal to the length of the concession period
because the returns from unconstrained, profit maximizing harvesting (U) are negative
for shorter cutting-cycles and the unconstrained optimization is used as the basis for
modeling the impact of regulatory policies (Chapter 3). It is assumed that harvest is
allowed in Year 40, before the end of the concession agreement. The objective function
is defined mathematically
(4-1)
The net value of an extracted stem of size class i in Guild j in 2001 $US/m3 (Table
3-3) is calculated as the product of the mean price per guild (pj) less the variable costs of
harvesting (C) and the mean extracted volume per size class and guild (y/j). Harvesting
from each guild (hj,) is measured in stems per ha. The tree population (y,) and harvest


34
where ji¡ * [y^], <= 1 n; j = l,...,m; is the mean extracted volume of a tree in
diameter class i and guild j. The mean volume extracted in harvesting is estimated as
85% of the mean volume per dbh class and guild, assuming 15% of merchantable volume
lost in logging waste (Table 3-2). The 15% waste proportion is slightly higher than the
12.3% reported in production forests of Brazil for high stumps, split logs, and bucking
waste (Holmes et al. 2002).
Table 3-2.
Mean volume of stem extracted in harvest per
size class and guild (y)
Dbh class
Mean extracted volume per stem (m3/stem)
Guild 1
Guild 2
Guild 3
Guild 4
Guild 5
40
0.65
0.71
0.71
0.74
0.62
45
0.88
0.91
0.92
0.97
0.83
50
1.15
1.14
1.16
1.24
1.08
55
1.47
1.40
1.44
1.54
1.37
60
1.85
1.68
1.75
1.89
1.70
65
2.28
2.00
2.09
2.29
2.09
70
2.78
2.35
2.48
2.73
2.52
75
3.34
2.74
2.91
3.22
3.01
80
3.97
3.16
3.37
3.76
3.56
85+
4.67
3.61
3.88
4.36
4.17
The net value (v¡,) of an extracted stem of size i in guild j in 2001 $US/m3
(Table 3-3) is thus calculated as the product of the mean price per guild (pj) less variable
harvesting costs (C) of $12.11/m3 and the mean extracted volume per stem of a given size
class and guild (y9), assuming no economies of scale in harvesting. The net value of
stems in Guild 3 is negative as species have no market value, thus harvesting would
strictly impose costs.


APPENDIX A
GUILD CLASSIFICATION OF LOMERO TREE SPECIES
Forest Regen.shadeMature shade
Scientific name Guild habitat* tol. (1-3) tol. (0,1)
Timber Wildlife
value (0-3) value (1-3)
Allophylus edulis
1 6
3
1
0
1
Ampelocera ruizii
1 7
3
1
0
2
Aspidosperma cylindrocarpon
1 7
2
1
1
1
Aspidosperma pyrifolium
1 7
2
1
1
1
Attalea phalerata
1 8
2
1
0
3
Bougainvillea sp.
1 5
2
1
0
1
Bouganvillea modesta
1 5
2
1
0
1
Calyptranthes sp.
1 6
3
1
0
2
Campomanesia aromtica
1 7
2
1
0
3
Capparis prisca
1 7
3
1
0
3
Gariniana ianeirensis
1 7
2
1
1
2
Chrysophyllun gonocarpum
1 7
3
1
0
3
Dalbergia riparia
1 8
2
1
0
1
Duguettia guitarensis
1 8
3
1
0
3
Erythroxylum sp.
1 6
3
1
0
1
Esenbeckia almawillea
1 6
3
1
0
1
Galipea trifoliata
1 6
3
1
0
1
Gallesia integrifolia
1 5
3
1
1
1
Genipa americana
1 7
2
1
0
3
Inga marginata
1 7
2
1
0
3
Lonchocarpus guillemineanus
1 7
2
0
1
1
Myrciaria cauliflora
1 8
3
1
0
3
Myrtaceae sp.
1 7
2
1
0
3
Neea hermaphrodita
1 6
3
1
0
2
Phyllostylon rhamnoides
1 7
3
1
0
1
Piper alboreum
1 8
3
I
0
2
Qualea acuminata
1 7
2
1
0
1
Rhamnidium elaeocarpum
1 7
2
1
0
3
Rheedia acuminata
1 8
3
2
0
3
Salada elliptica
1 8
3
1
0
3
Sorocea saxcola
1 7
3
1
1
3
Syagrussancona
1 8
3
1
0
3
82


39
These assumptions decrease the precision of model projections, but are necessary for
tractability.
EM
It
O
(3-7)
i=45 (=45
(3-8)
>* -O.sjrG'yV, -0.8gmyGV,
(3-9)
(-45 (45 (-45 *-0
The STY objective function (Eq. 3-2) is calculated as the NPV of a terminating
periodic series of harvest revenues with harvest horizon T = 40 years and cutting-cycle
t = 5 years, which is the most profitable interval for low-intensity, sustained harvesting
given the effects of discounting. Higher NPV is achieved at shorter cutting-cycles for
STY and SFM, given the important effects of an 18.75% discount rate. Comparisons of
returns from harvesting at longer cutting-cycles were conducted in preliminary analyses
to confirm the validity of this expectation. The sustainable harvest level increases, but
the present value of net returns decreases markedly with increases in cutting-cycle length.
Forest growth serves as the sustained-yield constraint for the STY case, as it
requires a constant periodic harvest (h, = h,+re =h* ) and maintenance of a specified stand
structure (y, =yt*je =>*). Definition of the sustained-yield constraints follows that of
Buongiomo and Michie (1980), who described the iundamental mathematical expression
of the sustained-yield linear optimization problem
G'h+(l-Gry = *¡Gtr (3-10)
*=0
The STY regime is further subject to constraints defining merchantable proportion (Eq.
3-4) and size (Eq. 3-6).


5
problem of exponential growth of the tree population in the Leslie and Usher models.
Their model formulation provided the basis for a large number of later studies by
Buongiomo and colleagues that integrated species stratification, forest regulation, and
economic and ecological criteria with economic optimization models founded upon
density-dependent matrix growth model estimation (e.g., Buongiomo and Lu 1990, Lu
and Buongiomo 1993, Buongiomo et al. 1994, Ingram and Buongiomo 1996, Boscolo
and Buongiomo 1997).
Matrix models are based on projections of whole stands, as opposed to individual
trees. Trees are commonly aggregated according to their size class and perhaps species
group so that the entire stand may be represented by a vector (or several vectors) of tree
population per class at a given time. Matrix models are based on a system of linear
difference equations, describing the change in tree populations per size class over discrete
time periods. Accordingly, for any given population value in a size class (y() at time
1 = 0, where the function/describes the change of y, over a discrete time period for all
periods {y =fit, y¡t-i),t= 1,2, 3... T), there exists a uniquely determined function y that
is a solution of the equation and has the given value for t = 0 (Sydsaeter and Hammond
1995).
An important advantage of the matrix formulation is its relative simplicity and ease
of integration into linear programming optimization models (Buongiomo and Michie
1980). Classifying the growing stock relative to only a few parameters greatly simplifies
the modeling of complex uneven-aged, multi-species stands. The linear form of the
model and stand classification into size/species groups with consistent behavior greatly


Copyright 2003
by
Frederick Boltz


45
proportional harvest restrictions as is BFL and to the expectation that the STY system
better conserves the merchantable growing stock over the harvest horizon. The STY
management for a 5-year cutting-cycle stipulates intensive harvesting of stems of
merchantable size in Guilds 4 and 5, the upland forest species and highly selective
harvesting of the riparian species of Guilds 1 and 2 (Table 3-6). The optimal STY
solution is determined by three factors: (1) biological constraints of forest growth and
recruitment and model; (2) cutting-cycle length; and, (3) timber merchantability.
Changes in management costs and discount rates have no effect on the STY solution.
Table 3-6. Comparison of pre-harvest population (yo) and sustained-yield (STY)
distribution (y*) per guild
Dbh class
(cm)
Pre-harvest Donulation. vn ftrees/hat
STY distribution, y*
(trees/ha)
Guild 1
2
3
4
5
1
2
3
4
5
10
47.1
2.7
6.2
23.0
91.2
38.8
4.6
6.6
35.1
109.5
15
28.3
2.6
5.0
22.2
83.1
21.4
3.4
4.2
29.3
73.8
20
12.3
1.8
1.3
17.2
50.2
12.9
2.7
2.7
23.7
49.7
25
5.8
2.0
0.5
13.3
26.2
8.4
2.2
1.7
18.2
33.2
30
4.6
0.9
0.2
10.9
16.8
5.8
1.8
1.1
13.3
21.9
35
3.1
0.9
0.4
11.2
10.8
4.2
1.5
0.7
9.1
14.2
40
2.8
0.9
0.5
9.4
6.2
3.1
1.3
0.4
2.1
4.9
45
2.2
0.8
0.2
5.4
3.7
2.3
1.1
0.2
0.0
1.2
50
1.6
0.3
0.3
5.1
1.9
1.8
1.0
0.1
0.0
0.3
55
0.7
0.4
0.1
3.2
1.0
1.4
0.8
0.1
0.0
0.1
60
1.0
0.2
0.1
1.6
0.7
1.1
0.7
0.0
0.0
0.0
65
0.4
0.2
0.2
0.6
0.7
0.8
0.6
0.0
0.0
0.0
70
0.3
0.1
0.2
0.5
0.2
0.6
0.5
0.0
0.0
0.0
75
0.1
0.0
0.1
0.2
0.1
0.5
0.4
0.0
0.0
0.0
80
0.2
0.0
0.1
0.4
0.0
0.1
0.3
0.0
0.0
0.0
85
0.2
0.1
0.6
0.1
0.1
0.0
0.1
0.0
0.0
0.0
A dramatic change in the forest structure is prescribed for the STY condition
relative to the initial stand state, especially for upland species of Guilds 4 and 5 (Table 3-
6). With frequent harvest entries, STY prescribes maintaining a small growing stock to
generate timber just sufficient to meet sustained-yield goals and generate modest profits.


44
decrease in the profitability of management. This prescription for liquidation of the
merchantable timber stock is found to be the optimal solution for scenario U, in which
harvest is solely constrained by the merchantability limits established in local timber
markets. Consequently, harvest level is highest under unconstrained management (Table
3-5) and forest impacts are greatest.
Table 3-5. Harvest level in absolute terms and in proportion of the available
merchantable volume in Year 0 per management alternative
Harvest level (stems/ha) Harvest volume (m3/ha)
Case
Year 0
YearO
proportion
Year 40,
cumulative
Year 0
YearO
proportion
Year 40,
cumulative
U
25.67
100%
35.53
35.86
100%
45.61
BFL
13.36
52%
19.91
24.71
69%
33.75
STY
4.08
16%
36.76
4.18
12%
37.63
SFM
0.51
2%
4.57
1.63
5%
14.67
Harvest constrained by the Bolivian forestry law has a similar optimal solution, notably
that of removing all merchantable timber allowed by legal and merchantable limits. The
lower harvest level and inferior net returns of BFL relative to the unconstrained case are
imposed by dbh limits and the allowable cut restriction, which requires retention of 20%
of the merchantable timber. The reduction in net revenues for the BFL scenario
attributable to the 45 cm dbh limit and 80% allowable cut constraints on the initial
harvest entry are $145.45/ha and $191.60/ha, respectively. The optimal harvest solution
for BFL prescribes progressive depletion of the merchantable stock, subject to these legal
restrictions.
The optimal sustained-yield (STY) solution requires a substantial decrease in
harvest level for the initial entry relative to U and BFL, but the total cumulative volume
harvested over a 40-year management horizon is greater than the BFL alternative (Table
3-5). This is attributable to the fact that STY is not constrained to meet dbh limit or


32
interview with each of the firms in July 2001. All costs and timber prices are reported in
2001 $US and are assumed constant throughout the management horizon (Appendix B).
Management costs FOB forest mill are classified as one of three types:
Variable costs (C) in $/m3 for felling, skidding and log deck operations incurred
relative to the level of harvest intensity
Fixed costs (F) in $/ha incurred regardless of harvest intensity at each cutting-cycle
entry for planning and capital costs including depreciation
Annual costs (A) in $/ha paid throughout the harvesting horizon regardless of
harvest intensity, which include an area fee of $ 1 /ha for the concession {patente)
and inscription fees to government agencies and trade associations
Variable costs are estimated at $12.11/m3, fixed costs at $62.51/ha and annual costs
at $1.55/ha. Variable costs are estimated relative to the efficiency of felling and skidding
(m3/hr) and the hourly costs of labor and machinery used in these operations. Felling
efficiency of 3.48 m3/hr is the statistical mode for data collected in Chiquitano forest
concessions of two-person felling teams in both planned and unplanned harvesting
operations (Cavero 1998, Menacho 1999) and fit to a gamma distribution. Skidding
efficiency of 3.68 m3/hr is the statistical mode for data collected in studies of operations
using rubber-tired skidders in three forest concessions in Chiquitania (Alarcon 1997,
Patifio 1997, Crespo 1999) and fit to a gamma distribution.
A discount rate of 18.75 % is assumed for the analysis. This is the mean real
interest rate on loans for 2001 reported by Bolivias Central Bank (Banco Central de
Bolivia 2002). Market prices for merchantable stems per guild delivered to concession-
based timber mills (FOB mill) are drawn from surveys of timber consultants and lumber
yards in Santa Cruz, and from market surveys of Chiquitama conducted in 2001 by
BOLFOR researchers (Appendix C). Timber species demanded in Santa Cruz
lumberyards in 2001 are assumed to comprise the merchantable stock. Market value per


56
implies that these options will consistently generate inferior returns from unconstrained
liquidation of merchantable timber in initial harvest entries.
Examination of the economic and biological impacts of an optimal management
regime constrained by the Bolivian forestry law indicates that although financial returns
from management under BFL are robust, harvesting constraints are not likely to achieve
goals of sustainable timber production or ecosystem maintenance. This conclusion
cannot be drawn without caveats, given the simplifying assumptions required for
modeling the BFL scenario with the available growth and yield. Greater precision in
modeling diameter limits and allowable cut restrictions for individual species and in
projecting forest growth and regeneration may indicate that optimal BFL management
results in forest conditions more closely approximating a sustained-yield state than is
possible to project in this study. However, the simplified model used in the present
analysis indicates that tree diameter and allowable cut restrictions lead to the depletion of
large stems of high value, which is not likely to result in the maintenance of forest
structure and composition necessary to achieve sustained timber yield.
Results indicate that management regimes are possible that achieve sustained
timber yield, while generating profitable returns. Moreover, it is shown that maintaining
forest structure and composition can be compatible with producing sustained timber yield
to meet economic objectives in management of the Chiquitano dry forests, as shown by
the SFM scenario. For the particular case of Chiquitania, goals of sustainable timber
production appear compatible with the maintenance of forest wildlife values, though
more information on the values of timber species for other taxa would allow for a more
conclusive assertion of this apparent compatibility.


Merchantable stock, all ensuing CC
V-oyv-1-I 0
k= 0
Merchantable stock, all ensuing CC
40
EZIX. =
/=0 j 1
Legal dbh limit
flhvl~0.ScoJfjy"lj,i0
1=45 1=45
Allowable cut
y,-h, >0
Absolute harvest level
h, >0,yt> 0
Non-negativity
Area Fee (x $/ha)
i j /.o (1 + b)
h,+y,-Gr{y^-h,_]) = £gV
*=o
Forest growth
O
VI
1
Merchantable stock, initial CC
K - Z ajG%-1 ^0
k=0
Merchantable stock, all ensuing CC
II
O
Merchantable dbh limit
o
Al
Absolute harvest level
hi >0,y,>0
Non-negativity
Note: All subsequent regulatory mechanisms are subject to the constraints defined
for the area fee mechanism.
95


36
The management problems are posed as linear programs and, as such, stationarity
is assumed for the transition probabilities of the matrix growth model to permit a global
optimum solution to each problem. The transition probabilities estimated for the PSP
following their harvest in 1995 and 1996 are selected as the stationary probabilities in the
guild growth matrices, as these estimates are expected to most closely approximate
growth in these forests. Four forest management alternatives are considered in the
optimization, notably:
Unconstrained harvesting at 40-year intervals (U)
Harvesting under Bolivian forestry law constraints at 40-year intervals (BFL)
Sustained timber yield management at 5-year intervals (STY)
Sustainable forest management at 5-year intervals (SFM)
A full mathematical description of each alternative is presented in Appendix E.
The cutting-cycle between harvesting under regimes U and BFL is set at 40-years,
the minimum interval required for profitable harvest (NPVt > 0), while that of the STY
and SFM scenarios is 5 years, selected to maximize the NPV of returns from these less
intensive harvesting systems. Financial returns from the sustainable scenarios (STY and
SFM) do not include any returns from regulation harvests, which would be undertaken to
convert the initial stand to steady-state, sustained-yield conditions. The harvest horizon
for all scenarios was set at 40 years to allow for comparison of the NPV of returns.
The objective function for U, BFL and STY cases prescribes maximization of the
NPV of returns from polycyclic harvesting, Z, y), calculated as the present value of a
terminating series at discount rate <5, with harvest horizon T 40 years and cutting-cycle
length t yd, with period yO being the number of intervals (y) of 5-year growth periods
(6) in a cutting-cycle. Cutting-cycles are 40 years (i = 40, y = 8) for U and BFL and 5
years for STY and SFM {t = 5, y =1). The objective function is defined mathematically


76
Moreover, the design of fiscal regulatory policies has implications across a broader
landscape of land uses. While higher forest fees seem necessary to counter incentives for
high-grading and to constrain optimal behavior to the conditions necessary for
sustainability, increasing forest fees lowers the profits of forest management for timber.
A decrease in the profitability of logging implies that natural forests of marginal
economic value will drop out of timber production. Higher taxation reduces the incentive
for maintaining forestland in timber production for all but the most highly valued species
and creates greater incentive to convert natural forests to plantations or non-forest uses.
The optimal regulatory policy is likely a compromise between efficient fiscal
mechanisms and modest fee increases, complemented by the enforcement of appropriate
technical standards, or best management practices.


31
MNL matrix growth model projects the probabilities of upgrowth, stability, or mortality
of trees in each of five ecological guilds during a 5-year growth period and predicts
recruitment of trees into the smallest size class (10 cm dbh) for each guild. The linear
form of the MNL model and the assumption of stationarity for the transition probabilities
throughout the harvest horizon enable its straightforward integration into the present
linear optimization study. The Las Trancas sites are typical of the Chiquitano dry forests,
and thus provide a representative stand for the examination of management alternatives in
Chiquitano concessions. Light selective logging for Spanish Cedar (Cedrela fissilis),
Spanish Oak (Amburana cearensis), and morado (Machaerium scleroxylon) occurred at
undetermined intervals in the past (Fredericksen et al. 2001), so they are not in an
undisturbed, climax state.
Economic Data
The Bolivian forestry law was revised in 1996 (Ley 1700) to more effectively
promote sustainable management of the nations forest resources (Art. #1). The law set
aside areas for conservation and protection purposes, and permits logging only in other
forest areas. Logging concessions are allocated for a 40-year duration upon formal
application to, and approval by, Bolivias forest service (Superintendencia Forestal).
The law requires forest management plans for all concessions and for forest
authorizations in private lands. Concessions also can be traded and inherited and are
renewable upon validation of the concessionaires observance of sustainable forest
management plans.
Forest management costs are drawn from surveys of four industrial forestry firms
based in Santa Cruz and possessing logging concessions in Chiquitano dry forests.
Structured surveys were conducted in November 2000 and validated in follow-up


40
The sustainable forest management alternative (SFM) has as its objective to
achieve a sustained-yield, steady-state forest as close as possible in structure and
composition to the undisturbed climax condition. The objective function is defined as
minimizing the sum of the absolute differences between the number of trees per size class
and guild in the climax forest (y) and in the SFM residual stand (y**). Mathematically,
the objective function is expressed
min (3-*D
i l
where [df\ and [d,/] are vectors of the absolute deviations of the number of trees of size
i and guild/ in the growing stocky** and the climax stateya (Buongiomo et al. 1995)
and By is the mean basal area per size class (i) and guild (,), employed to place more
weight on large trees.
The SFM alternative observes the same constraints as the STY case, notably
sustained-yield forest growth (Eq. 3-10) and merchantability restrictions (Eq. 3-4, 3-6),
and is further constrained to meet the minimum economic goals of obtaining a non
negative NPV in perpetual periodic harvest (Eq. 3-12).
v'h" F
(1 + rf
(3-12)
Residual Stand State Indices
Stand state, forest value and diversity criteria are employed to examine changes in
the managed stand under alternative regimes. The criteria allow for a comparison of
residual, managed stands under optimal solutions to the four management alternatives
examined and comparison of these states relative to the climax condition defined by the
growth model (y). Stand basal area (BA) is a fundamental measure of change in stand


20
proportional estimation (G50) for Guild 5 with a five-year interval and 5 cm dbh classes is
described below. Guild 5 is selected for comparison of observed and predicted transition
matrices because it had the highest number of observations (2762).
As hypothesized, the MNL transition matrix results in a smoother distribution of
transition probabilities across size classes relative to that generated by simple
proportional estimation (Figure 2-1). The MNL estimation corrects for variance in the
forest data and for sample error effects on matrix elements (Usher 1976), such as the
elevated probabilities of movement in large size classes generated by proportional
estimation from a very small sample of large trees.
DBH class (cm)
Figure 2-1. Observed and predicted stability probabilities per dbh class for Guild 5
Recruitment
The OLS estimated recruitment function (r) observes the expected negative
relationship between recruitment and total trees per hectare (TPH) (Table 2-4). Although
the fit is quite poor, the variables and the model are all significant to P < 0.05.


This dissertation was submitted to the Graduate Faculty of the School of Forest
Resources and Conservation in the College of Agricultural and Life Sciences and to the
Graduate School and was accepted as partial fulfillment of the requirements for the
degree of Doctor of Philosophy.
May 2003
Directo^ Forest Resources and Cons
Conservation
Dean, Graduate School


Vanclay, J.K. 1991. Compatible deterministic and stochastic predictions by probabilistic
modelling of individual trees. For. Sci. 37:1656-1663.
Vanclay, J.K. 1994. Modelling forest growth and yield: Applications to mixed tropical
forests. CAB International, Wallingford, UK. 312 p.
Van Kooten, G.C., and E. Bulte. 2000. The economics of nature: Managing biological
assets. Blackwell, Malden, MA. 512 p.
Verissimo, A., P. Barreto, M. Mattos, R. Tarifa., and C. Uhl. 1992. Logging impacts and
prospects for sustainable forest management in an old Amazonian frontier: the case
of Paragominas. For. Ecol. Manage. 55:169-199.
Vincent, J.R. 1990. Rent capture and the feasibility of tropical forest management. Land
Econ. 66:212-233.
Whittaker, R.H. 1975. Communities and ecosystems. New York, Macmillan. 385 p.
102


13
The MNL growth model estimates the probability of an individual tree observing
one of these three transition alternatives during a five-year growth interval. Mortality
includes both natural death and harvest-induced death, which is observed for those trees
immediately killed during harvest operations and those damaged during harvesting that
later die. Transition probabilities are estimated as a function of tree attributes and stand
characteristics, described as follows:
DBH tree size class (dbh in 5 cm increments)
RD/BA tree relative diameter (tree dbh/mean dbh of stand) divided by total
post-harvest basal area per hectare (m2/ha)
TPH total number of trees per hectare prior to harvest
HBA harvest basal area per ha (m2/ha)
Gj dummy variable representing guild j,j = 2...5
G/*DBH guild dummy variable multiplied by size class
Size class and relative diameter variables portray the relative dominance of each
tree in its immediate forest environment. Tree population, harvest basal area and post-
harvest basal area describe the density and competition specific to each plot. The dummy
variables Gy and G/DBH describe behavioral differences among ecological guilds,
attributable to their sensitivity to light and habitat. Gy are intercept shifters, while
Gy*DBH change the slope of the growth curve relative to guild and size class variables.
The dummy variables have the effect of increasing upgrowth probabilities for shade
intolerant Guilds 2,3, and 4 and of decreasing the upgrowth probabilities for shade
intolerant Guild 5. The dummy variables adjust transition probabilities for Guilds 2-5
relative to Guild 1.


Guinart, D. 1997. Los mamferos del bosque semideciduo neotropical de Lomero
(Bolivia): Interaccin indgena. [Ph.D. dissertation] University of Barcelona, Spain.
Hamilton, D.A., and B.M. Edwards. 1976. Modeling the probability of individual tree
mortality. USDA For. Ser. Res. Pap. INT-185.
Hausman, L, and D. McFadden. 1984. Specification tests for the multinomial logit
model. Econometrica 52:1219-1240.
Healey, J.R., C. Price, and J. Tay. 2000. The costs of carbon retention by reduced impact
logging. For. Ecol. Manage. 139:237-255.
Holdridge, L.R. 1967. Life zone ecology. Tropical Science Center, San Jose, Costa Rica.
206 p.
Holmes, T.P., G.M. Blate, J.C. Zweede, R. Perreira Jr., P. Barreto, F. Boltz, and R.
Bauch. 2002. Financial and ecological indicators of reduced impact logging
performance in the eastern Amazon. For. Ecol. Manage. 163:93-110.
Hout, P. van der. 1999. Reduced impact logging in the tropical rain forest of Guyana:
ecological, economic, and silvicultural consequences. Tropenbos-Guyana Series 6.
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Howard, A., R.E. Rice, and R. Gullison. 1996. Simulated financial returns and selected
environmental impacts from four alternative silvicultural prescriptions applied to
the neotropics: a case study of the Chimanes Forest, Bolivia. For. Ecol. Manage.
89:43-57.
Howard, A., and J. Valerio. 1996. Financial returns from sustainable forest management
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49.
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distribution discussion. Land Econ. 68:343-350.
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of mixed lowland dipterocarps in Malaysia. J. Trop. For. Sci. 9:242-270.
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Doc. No. 28, BOLFOR, Santa Cruz, Bolivia.
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99


12
Trees in the stand are divided into a finite number of diameter classes (n) and
guilds (m) with yiJt the number of trees prior to harvest in the Ith diameter class of guild j
at time t. The total density of guild j at time t is defined as the column vector
yJt = \y,ji ]
The number of trees harvested per diameter class (i) in a given guild (j) is described
by the column vector hy, = [h,y,].
The probabilities of upgrowth or movement from one diameter class to the next
during a 5-year growth interval (0) are expressed as a matrix (G) of transition sub
matrices, and used to predict change for a specific time interval (yO).
G, =
V
The matrix Gy is composed of transition probabilities for trees of guild j, which
define the movement of trees into size classes (i) during the period 8 as follows:
a,y is the probability that a tree in size class i will remain alive and in size
class i, or stability;
b/y is the probability that a tree in size class i-1 will remain alive and grow
into i from size class i-1, or upgrowth;
C/y is the probability that a tree in size class i will die during the period, or
mortality.
The probabilities are related by the following equations:
Oj + b,y + c,y =1 for i a,y + C,y = 1
for i = n


Johnson, S.E., I.S. Ferguson, and L. Rong-Wei. 1991. Evaluation of a stochastic diameter
growth model for mountain ash. For. Sci. 37:1671-1681.
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rain forest in Suriname. Agricultural University, Wageningen. 172 p.
Kant, S. 1999. Sustainable management of uneven-aged private forests: A case study
from Ontario, Canada. Ecol. Econ. 30:131-146.
Kennard, D.K., K. Gould, F.E. Putz, T.S. Fredericksen, and F. Morales. 2002. Effect of
disturbance intensity on regeneration mechanisms in a tropical dry forest. For.
Ecol. Manage. 162:197-208.
Killeen, T., A. Jardim, F. Manami, P. Saravia, and N. Rojas. 1998. Diversity,
composition, and structure of a tropical deciduous forest in the Chiquitania region
of Santa Cruz, Bolivia. J Trop. Ecol. 14: 803-827.
Kishor, N., and L. Constantino. 1993. Forest management and competing land uses: an
economic analysis for Costa Rica, LATEN Dissemination Note. World Bank,
Washington DC.
Kishor, N., and L. Constantino. 1994. Sustainable forestry: Can it compete? Finance &
Dev. 31:36-39.
Leslie, P.H. 1945. On the use of matrices in certain population mathematics. Biometrika
33:183-212.
Lowell, K.E., and R.J. Mitchell. 1987. Stand growth projection: Simultaneous estimation
of growth and mortality using a single probabilistic function. Can. J. For. Res.
17:1466-1470.
Lu, H.S., and J. Buongiomo. 1993. Long and short-term effects of alternative cutting
regimes on economic returns and ecological diversity in selection forests. For.
Ecol. Manage. 58:173-192.
Menacho M., E. 1999. Costos y rendimientos de un sistema de corta en fajas de arboles
comerciales en la zona de Lomero [thesis]. Universidad Autnoma Gabriel Rene
Moreno, Santa Cruz, Bolivia. 200 p.
Ministerio de Desarollo Sostenible y Planificacin. 1998. Normas tcnicas para la
elaboracin de instrumentos de manejo forestal. Resolucin Ministerial No. 248/98.
La Paz, Bolivia. 74 p.
Patifto S., E.F. 1997. Efectos del aprovechamiento tradicional: costos y rendimientos en
un bosque seco subtropical (Nueva Esperanza) [thesis]. Universidad Mayor de San
Simn, Santa Cruz, Bolivia. 50 p.
100


71
fee (Table 4-1, Fig. 4-1), but maintains the incentive to high-grade the forest concession
and thus, as modeled, is not an efficient mechanism for attaining STY goals.
The optimal harvesting strategy under regulation by the volume-based royalty
would be to leave stems of low value, notably those of Guilds 1 and 4. The merchantable
stock of lesser-valued species would be maintained (Fig. 4-1,4-2), but species whose
values exceed the volume fee ($40/m3) would be depleted (Fig. 4-3). The effect of the
volume fee is similar to a reduction in the price of timber. The consequence would be
more selective high-grading.
Figure 4-3. Distribution of merchantable stems of Guild 5 per regulatory policy, Year 40
The performance bond mechanism creates an incentive for partial to full
compliance, according to the bond level (Fig. 4-4). At the $750/ha bond level examined,
the concessionaires optimal strategy would be for approximately 80% compliance with
the standard of maintaining a residual stock equal to that of the STY condition (11.7


CHAPTER 4
REGULATORY POLICY EFFICIENCY IN PROMOTING SUSTAINABLE TIMBER
MANAGEMENT FOR A BOLIVIAN TROPICAL DRY FOREST
Introduction
Regulatory policies are intended to provide a corrective influence on the private use
of forestland to properly defend public goods, both in maintaining desirable benefit flows
from natural resources and in mitigating negative externalities. Fiscal regulatory
instruments, such as royalty systems, have also been identified as a critical determinant of
the manner and magnitude of tropical forest degradation by providing incentives for
logging practices such as high-grading and conversion to alternative land uses (Repetto
and Gillis 1988, Vincent 1990, Hyde and Sedjo 1992, Van Kooten and Bulte 2000).
Despite the important influence of government policies on tropical forest use, few
rigorous comparisons exist of the impact of alternative regulatory mechanisms on private
revenues, government rent capture, and forest condition. Important exceptions include
recent studies by Boscolo and Vincent (2000) and by Amacher et al. (2001) for natural
tropical forests of Malaysia. Boscolo and Vincent (2000) examined concession length,
renewability and performance bonds as mechanisms to promote the adoption of better
logging practices, while Amacher et al. (2001) used a model of policy choice to compare
royalty systems relative to government revenue generation and high-grading behavior.
Although forest degradation has often been attributed to poor regulatory policy, there is
little empirical work examining how selective harvesting behavior and the allocation of
rent between private concessionaires and government is influenced by regulatory
57


51
This finding is unexpected, but may be explained by the fact that the aggregate
population may be effectively maintained under BFL, while the stand is impoverished.
Table 3-10. State of the aggregate residual stand population per management alternative
Index
Management alternative
Climax
condition
U
BFL
STY
SFM
BA
19.72
20.76
21.72
26.19
26.90
PCI
0.73
0.78
0.68
0.97
1.00
D
7.50
6.46
5.18
0.56
0.00
This hypothesis is confirmed in closer examination of the impacts of harvest on the
merchantable stock (Table 3-11).
Table 3-11. Residual merchantable species population per management alternative
Management alternative Climax
Index
U
BFL
STY
SFM
condition
BA (all merch. species)
5.42
6.46
8.55
9.83
12.48
BA (merch. species > 40 cm dbh)
0.00
1.04
2.64
3.92
5.57
PCImcfch
0.42
0.53
0.57
0.76
1.00
PCM
0.62
0.70
0.83
0.86
1.00
Note: PCImerch is defined as PCI, but calculated solely for merchantable species.
Residual stand basal area (BA) measures reveal greater differences between the U
and STY alternatives relative to comparisons of the aggregate residual populations,
though the differences of these states and BFL are less important (Table 3-10). Under
timber management objectives of U, BFL and STY, residual stand density is expected to
be 19% to 27% lower than the climax forest. Harvesting impacts on the merchantable
stock are more revealing of differences between the management alternatives, as
suggested by the proximity to climax market value (PCM) index (Table 3-11). The PCM
of residual stands is considerably lower under U and BFL regimes, than under STY,
given the effective liquidation of merchantable stems stipulated by these scenarios


59
The Bolivian forestry law was revised in 1996 (Ley 1700) to more effectively
promote sustainable management of the nations forest resources, which are allocated in
renewable concessions to the logging industry (Art. #1). Logging concessions are
awarded for a harvest period of 40 years upon formal application to and approval by
Bolivias forest service (Superintendencia Forestal). The forestry law requires forest
management plans for all concessions and for forest authorizations in private lands.
Concessions also can be traded and inherited and are renewable upon validation of the
concessionaires observance of sustainable forest management plans.
Forest management costs for industrial firms of the region and market prices for
roundwood timber delivered to the forest mill derive from surveys conducted in Santa
Cruz and in Chiquitania in 2000 and 2001 (Appendix B). Prices are reported in 2001
$US and are assumed constant throughout the harvest horizon (Appendix C).
Management costs in 2001 $US are classified as one of three types:
Variable costs (Q in $/m3 for felling, skidding and log deck operations incurred
relative to harvest intensity
Fixed costs (F) in $/ha incurred regardless of harvest intensity at each cutting-cycle
entry for planning and capital costs
Annual costs (A) in $/ha paid throughout the harvesting horizon regardless of
harvest intensity, which include an area fee of $ 1/ha for the concession (Bolivias
patente) and inscription fees to government and market institutions
These and all other variables used in the present study are defined in Appendix D.
The optimization model prescribes maximization of net present value (NPV) of
polycyclic harvesting (Z) subject to biological, market, and regulatory constraints. The
objective function does not consider the costs of investment in the growing stock
described by the economic stocking rule for selection harvest (Duerr and Bond 1952) or
soil expectation value (SEV) used in similar optimization studies (Buongiomo and



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PAGE 115

/' eB/ 81,9(56,7< 2) )/25,'$


73
Marginal increases in compliance (p) relative to performance bond fee (t) are low
up to a fee level of $650/ha, at which point compliance increases dramatically with
increases in bond level (Figure 4-4). The behavior of this compliance curve suggests that
the optimal performance bond fee lies between $640/ha and $800/ha, the precise level
defined by a trade-off between profitability and proximity to STY conditions. If the
marginal benefit curve for production of timber and non-timber benefits under STY were
known, the optimal fee level could be more precisely estimated as that point at which the
marginal cost of an increase in fees equals to marginal benefit of greater compliance.
The estimation of optimal fee levels for performance bond mechanism would be a
valuable extension of this work.
Profitability and Rent Distribution
With the exception of the area fee mechanism, which has no impact on harvesting
behavior, regulatory alternatives to the existing Bolivian forestry law result in lower
concessionaire profits and greater government rent capture (Table 4-2).
Table 4-2. Profitability and rent distribution per regulatory policy
Regulatory policy
Rent capture (NPV $/ha)
Concessionaire
Government
Sustained timber yield (STY)
257.18
8.26
Bolivian forestry law (BFL)
914.89
5.33
Area fee
1135.61
250.26
Per-tree royalty
129.37
356.32
Volume-based royalty
83.21
292.13
Ad valorem royalty
93.98
1345.17
Performance bond (PB)
740.13
148.46
The magnitude of the area fee has no impact on harvesting behavior; it simply
influences the net private and governmental returns to management. Certainly, if the area
fee dissipates all profits to management, the concessionaire is unlikely to log. As long as


CHAPTER 2
MULTINOMIAL LOGIT ESTIMATION OF A MATRIX GROWTH MODEL FOR
TROPICAL DRY FORESTS OF EASTERN BOLIVIA
Introduction
The development of growth and yield models for tropical forests is often a daunting
task because of the complexity of these rich, diverse ecosystems, and the paucity of data
enabling robust model estimation. The difficulties of representing the dynamics of
species interaction, recruitment, and response to disturbance are compounded when the
model is intended to serve goals of management planning, in addition to scientific
simulation. In the present study, I develop a matrix model of forest growth and yield for
tropical dry forests of eastern Bolivia, the product of several years of tree growth
measurements conducted by members of the Bolivian forest management project
(BOLFOR). The model was developed to respond to the need for meticulous estimation
of timber returns and forest impacts from polycyclic harvesting. The study contributes to
forest growth modeling science through its novel use of multinomial logistic regression
methods to estimate a five-guild matrix growth model for a Chiquitano tropical dry
forest.
Matrix models were first formulated by Leslie (1945) for animal populations and
later modified by Usher (1966, 1969) for managed forests. Buongiomo and Michie
(1980) extended this work by introducing density-dependent recruitment to solve the
4


LIST OF REFERENCES
Alarcn, J.A. 1997. Efectos del aprovechamiento tradicional costos y rendimientos de
dos zonas de estudio concesin Tarum [thesis]. Universidad Mayor de San Simn,
Santa Cruz, Bolivia. 49 p.
Amacher, G.S., R.J. Brazee, and M.Witvliet. 2001. Royalty systems, government
revenues, and forest condition: An application from Malaysia. Land Econ. 77:300-
313.
Armstrong, S. 2000. Report by Edinburgh Center For Tropical Forests (ECTF) on
reduced impact logging research: Activities and outputs for the Barama Company
Limited. ECTF, Edinburgh, UK. 86 p.
Bach, C.F. 1999. Economic incentives for sustainable management: A small optimal
control model for tropical forestry. Ecol. Econ. 30:251-265.
Banco Central de Bolivia. 2002. Tasas de inters reales de 1996 a Junio 2002. La Paz,
Bolivia. (November 18, 2002) http://www.bcb.gov.bo/
Barreto, P., P. Amaral, E. Vidal, and C. Uhl. 1998. Costs and benefits of forest
management for timber production in eastern Amazonia. For. Ecol. Manage. 108:9-
26.
Boscolo, M., and J. Buongiomo. 1997. Managing a tropical rainforest for timber, carbon
storage, and tree diversity. Comm. For. Rev. 76:246-254.
Boscolo, M. and J.R. Vincent. 2000. Promoting better logging practices in tropical
forests: A simulation analysis of alternative regulations. Land Econ. 76:1-14.
Buchman, R.G., S.P. Pederson, and N.R. Walters. 1983. A tree survival model with
application to species of the Great Lakes region. Can. J. For. Res. 13:601-608.
Buongiomo, J., S. Dahir, H. C. Lu, and C.R. Lin. 1994. Tree size diversity and economic
returns in uneven-aged forest stands. For. Sci. 40:83-103.
Buongiomo, J., and H.-C. Lu. 1990. Economic stocking and cutting-cycle in a regulated
selection forest. For. Ecol. Manage. 32:203-216.
Buongiomo, J., and B.R. Michie. 1980. A matrix model of uneven-aged forest
management. For. Sci. 26:609-625.
97


Pearce, D., F.E. Putz, and J.K. Vanclay. 2003. Sustainable forestry in the tropics: Panacea
or folly? For. Ecol. Manage. 172:229-247.
Pinard, M.A., F.E. Putz, D. Rumz, R. Guzmn, and A. Jardim. 1999. Ecological
characterization of tree species for guiding forest management decisions in
seasonally dry forests in Lomero, Bolivia. For. Ecol. Manage. 113:201-213.
Pinard, M.A., F.E. Putz, and J. Tay. 2000. Lessons learned from the implementation of
reduced-impact logging in hilly terrain in Sabah, Malaysia. Int. For. Rev. 2:33-39.
Repetto, R., and Gillis, M. 1988. Public policies and the misuse of forest resources.
Cambridge University Press, Cambridge. 432 p.
Rice, R.E., R. Gullison, and J. Reid. 1997, Can sustainable management save tropical
forests? Sci. Am. 276:34-39.
Rice, R.E., C.A. Sugal, S.M. Ratay, and G.A. Fonseca. 2001. Sustainable forest
management: A review of conventional wisdom. Advances in Applied Biodiversity
Science, No. 3. Conservation International, Washington, DC. 29 p.
Richards, M. 2000. Can sustainable tropical forestry be made profitable? The potential
and limitations of innovative incentive mechanisms. World Dev. 28:1001-1016.
Silva, J.N.M. 1989. The behaviour of the tropical rain forest of the Brazilian Amazon
after logging [Ph.D. dissertation] Oxford University, Oxford, UK. 325 p.
Sydsaeter, K., and P.J. Hammond. 1995. Mathematics for economic analysis. Prentice-
Hall, NJ. 982 p.
Tay, J. 1999. Economic assessment of reduced-impact logging in Sabah, Malaysia.
[Ph.D. dissertation] University of Wales, Bangor, UK. 161 p.
Terborgh, J. 1986. Keystone plant resources in the tropical forest, pp. 330-344. In: Soul,
M.E. (Ed.). Conservation biology: The science of scarcity and diversity. Sinauer,
Sunderland, MA. 584 p.
Usher, M.B. 1966. A matrix approach to the management of renewable resources, with
special reference to selection forests. J. Appl. Ecol. 3:355-367.
Usher, M.B. 1969.A matrix model for forest management. Biometrics 25:309-315.
Usher, M.B. 1976. Extensions to models, used in renewable resource management, which
incorporate an arbitrary structure. J. Environ. Manage. 4:123-140.
Usher, M.B. 1979. Markovian approaches to ecological succession. J. Animal Ecol.
48:413-426.
101


APPENDIX D
DEFINITION OF OPTIMIZATION VARIABLES
y, \yijt], number of trees in size class i, guild j at time 1
y [y?], undisturbed steady-state or climax equilibrium distribution of trees
A [ number of trees in size class i, guild j at time t
y [y,j ], number of trees in size class i, guild j in the STY steady-state
y" [y¡,**], number of trees in size i, guild j in the SFM steady-state
h, number of stems harvested in size class i, guild j at time t
h' number of stems harvested in size class i, guild j in the STY steady-state
h" [hj'\ number of stems harvested in size class i, guild j in the SFM steady-state
Gj Matrix of transition probabilities for trees of guild j, which define the movement
of trees into size classes (i) during a 5-year growth period (0)
r, number of recruits into the 10 cm size class of guild j during the 5-year
growth interval t to t+8
Z Objective function of the optimization
t = yd Cutting-cycle length, defined as the number (y) of 5-year growth periods (0)
T Harvest horizon
5 Discount rate
By Mean basal area (m2) of a stem in size class i and guild j
oij Merchantable proportion of stems in guild./
Sj Proportion of merchantable species in guild j
fj Proportion of stems of merchantable form in guild j
Pj Market value of merchantable species ($/m3) in guild j
89


10
Final PSP measurements for this study were conducted in July 2001. The forest blocks
were lightly logged 1 year after their installation. Mean harvesting intensities in the PSPs
were 2.72 trees per ha or a basal area of approximately 0.68 m2/ha.
The density of trees > 10 cm dbh was estimated at 418 stems/ha in the initial PSP
inventories of LT94 and 437 stems/ha in LT95, indicating that the Lomero forest canopy
is relatively open (Killeen et al. 1998). Of 6005 trees > 10 cm dbh initially inventoried
and monitored for growth in the PSPs, 5273 (87.8%) were retained for growth modeling.
The remaining trees were purged from the data set because of irregular stem form (8.2%),
apparent measurement error (3.6%), or unknown species (0.4%). Trees of irregular form
included species of Arecaceae and Cactaceae, as well as species that change stem form
with growth (Acosmiun cardenasii, Aspidosperma spp., Chorisia speciosa, and Ficus
gomelleira). The discarded trees were included in estimates of plot BA employed in
model regressions. Growth increments were recorded for trees 10 to 122 cm dbh.
Adjusted for season of measurement, the PSP growth data cover 82 months (LT94) and
68 months (LT95). Annual growth rates ranged from 0.00-1.83 cm/y.
Given the heterogeneity of species attributes and of forest habitats, a grouping of
tree species into ecological guilds was conducted to enable more precise modeling of
growth, recruitment, and mortality (Appendix A). Ninety-three tree species were
grouped into five guilds defined by forest habitat and shade tolerance of regeneration
(Pinard et al. 1999). Shade tolerance of regeneration is expected to be a robust measure
of differences between guilds (Grubb 1977). For cases in which the shade tolerance of
regeneration was not classified, mature tree shade tolerance was employed in guild


80
structure and composition necessary to achieve sustained timber yield by present model
estimates.
Alternatives to current Bolivian regulatory policy for forest concessions may
provide more effective fiscal incentives for sustainable forestry, while improving
government rent capture. The goal of compelling logger behavior toward greater
compliance with sustainability standards may be more efficiently achieved by alternative
royalty systems, or a performance bond mechanism, given appropriate fee levels. High-
grading is expected to result from greater fiscal regulation, however, if such regulations
are undifferentiated across timber value classes. Examining more precise, differentiated
forms of performance bond, and royalty mechanisms, would be a valuable extension of
this research. Still, establishing meaningful standards by which management
performance may be evaluated is problematic because of the complexity of mixed
tropical forests and the difficulty of estimating forest conditions necessary for sustained
timber productivity. Appropriate regulatory mechanisms must balance efficiency gains
of improved compliance with sustainability standards and of a more desirable distribution
of resource rents with the practical aspects of their implementation and enforcement.
Numerous interesting extensions of this work are possible. The assumption of
stationarity for transition probabilities of the matrix model limits the examination of
forest dynamics. An inspection of forest impacts and sustainability conditions under
dynamic modeling would make better use of the research potential of the MNL model.
Recalculation of transition probabilities per harvest episode and silvicultural treatment
may offer greater insight into the expected forest response to management and parameters
for optimal harvest. The optimal path of regulated harvest necessary to maximize profits


43
The Shannon-Wiener index (H), with natural logarithms (Whittaker 1975), is also
used to examine species and structural diversity as a measure of residual stand state,
defined as follows:
(3-16)
where p,¡ is the proportion of trees in the size class i and guild j. For the Shannon-Wiener
diversity analysis, trees are grouped two ways: (1) for guild diversity, the five guild
groupings, and (2) for guild and structural diversity, 80 groups defined by guild and size
class (dbh). if is a measure of evenness, which is maximized if trees are equally
distributed by size class and guild. H has a minimum value of zero for a homogeneous
stand and maximum value of ln(n+m) for a perfectly heterogeneous stand; consequently,
the ranges of possible values for the diversity criteria described above are 0 < if < 1.61
for guild diversity and 0 < if80 < 4.38 for guild and structural diversity.
Lastly, the absolute difference between the number of trees per size class and guild
in the climax forest (y) and in the residual stand (y¡) defined as the objective function of
the SFM case (Eq. 3-11) is used to examine differences in alternative managed stands
relative to the climax condition.
Results and Discussion
Optimal Harvest per Management Alternative
Given the high discount rates applicable to capital investments in Bolivia and the
low rate of value growth of timber species, which is estimated at a maximum of 1.23%
assuming constant prices, the optimal solution for an unconstrained harvest scenario (U)
is to harvest all the merchantable timber and invest the returns from harvest in more
lucrative activities. Consequently, any retention of merchantable timber would result in a


75
initial harvest entries. For all alternative regulatory mechanism forms examined in this
study, optimal concessionaire behavior is to high-grade the forest, as revealed in
examination of the residual stock of stems of the highest value, which constitute Guild 5
(Fig. 4-3). This optimal high-grading behavior may be modified with differentiation of
regulatory fees (Amacher et al. 2001), such as higher per-tree and volume royalties for
more valuable relative to lesser-valued species and more precise STY compliance
standards for the PB mechanism. Presently, the policy alternatives are defined as
undifferentiated mechanisms, meaning that all stems are subjected to the same level of
fiscal regulation. This regulatory approach is considerably more straightforward to
implement, but does not result in the differential harvesting behavior that would be
necessary to compel loggers to conserve the growing stock of more valuable species.
Examining better differentiated forms of the performance bond and royalty mechanisms
would be a valuable extension of this research.
Establishing straightforward and meaningful standards by which the appropriate fee
levels may be estimated and concessionaire management performance may be evaluated
is problematic because of the complexity of mixed tropical forests and the difficulty of
estimating forest conditions necessary for sustained timber productivity. Appropriate
regulatory mechanisms must balance efficiency gains of improved compliance with STY
standards and desirable distribution of resource rents with the practical aspects of
implementation. Regulatory mechanisms that are too complex will likely be poorly
implemented and are unlikely to achieve the theoretical efficiency gains for which they
are designed.


v,j (pj C)y,j, net value of an extracted stem of size i in guild j in 2001 $US/m3
C Variable costs ($/m3) of felling, skidding and log deck operations
F Fixed costs ($/ha) of planning and capital costs including depreciation
A Annual costs ($/ha) including an area fee of $1 /ha for the concession and
inscription fees to government agencies and trade associations
\\Ujt Mean extracted volume of a tree, estimated as 85% of mean volume per size class
(t) and guild (J), assuming 15% of merchantable volume lost in logging waste
v,, Net value ($/m3) of an extracted stem of size i in guild j
5 Annual concession fee or patente ($l/ha) per Bolivian forestry law
x Regulatory fee defines per fiscal instrument (see Appendix F)
p % compliance with STY restriction measured for the performance bond
d [d¡¡], vector of negative deviations of the number of trees of size i and guild j in
the yt from the climax state ya, expressed as an absolute value
d [dy], vector of positive deviations of the number of trees of size i and guild j in yt
from the climax state y1
90


18
Table 2-3. Comparison of predicted and observed mean transition probabilities for all size classes by guild
M
Guild 1
S
U
M
Guild 2
S
U
M
Guild 3
S
U
M
Guild 4
S
U
M
Guild 5
S
U
Predicted
0.07
0.75
0.18
0.07
0.70
0.23
0.13
0.70
0.17
0.23
0.54
0.23
0.13
0.68
0.19
Observed
0.12
0.73
0.15
0.09
0.73
0.18
0.15
0.65
0.20
0.19
0.55
0.26
0.16
0.70
0.14
tStat
0.83
0.42
0.76
0.51
0.47
0.81
0.37
0.86
0.77
0.92
0.21
0.87
0.53
0.27
2.05


19
0.58 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 '
0.25 0.63 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.22 0.66 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.20 0.70 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.18 0.72 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.17 0.74 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.16 0.75 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.16 0.75 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.16 0.74 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.16 0.73 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.16 0.71 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.17 0.69 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.19 0.65 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.21 0.61 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.23 0.55 0
o
0
0
0
0
0
0
0
0
0
0
0
0
0
0.26 0.4<
'0.57 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 1
0.27 0.69 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.14 0.74 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.16 0.68 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.16 0.78 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.14 0.73 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.19 0.70 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.18 0.68 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.22 0.71
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.10 0.82 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.12 0.64 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.18 0.73 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.27 1.00 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.00 1.00 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.00 0.00 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.00 0.05
As an example, the resulting MNL transition matrix (G5MNL) estimated for stand
conditions after the observed harvest and the transition matrix generated by simple


Trees per ha 70
4-1. Distribution of merchantable population per regulatory policy, Year 40
Figure 4-2. Distribution of merchantable stems of Guild 1 per regulatory policy, Year 40


50
stand structure, as the merchantable timber stock is progressively liquidated. Also as
anticipated, the SFM regime closely approximates the climax structure, meeting its
defined objective of minimizing deviation from this undisturbed, equilibrium state.
Figure 3-1. Aggregate merchantable and non-merchantable residual population structure
under management alternatives and climax condition
Aggregate residual population structures do not differ greatly under U and STY
management regimes, however, and the BFL constraints appear to achieve greater
proximity to climax stand structure than the STY alternative. Proximity to climax
structure and composition of the aggregate residual populations (PCI) confirms that the
BFL alternative results in greater proximity to this undisturbed forest equilibrium than U
and STY, as indicated in the comparison of aggregate population structure (Table 3-10).
This finding is unexpected, but may be explained by the fact that the aggregate
population may be effectively maintained under BFL, while the stand is impoverished.


BIOGRAPHICAL SKETCH
Frederick Boltz is a forest economist whose most recent research concerns the
management of permanent production forests in Brazil and Bolivia. Fred received his
B.A. from Duke University in 1989, studying Chinese language, modem history, and
cultural anthropology. He spent the last year-and-a-half of his undergraduate work in
China and Taiwan conducting honors research. After graduating, Fred spent 2 years in
northeastern Madagascar where he began his conservation career on a community forest
initiative. This work led him to cross paths with Conservation International in 1992,
when he became project coordinator of a conservation and development project for the
Zahamena Nature Reserve in eastern Madagascar.
In 1996, Fred left the Zahamena project to begin his M.S. studies at the University
of Florida (UF). He earned his M.S. in forest economics at UF in 1999, and that same
year was awarded the E.T. York Presidential Fellowship to pursue a Ph.D. in forest
economics in UFs School of Forest Resources and Conservation.
A native English speaker, Fred has learned five other languages over the years and
speaks most of them well enough to stay in trouble. He is the lead author of articles
derived from his graduate research in the journals Ecological Economics, Journal of
Forest Economics, and Forest Policy and Economics. Fred has returned to Conservation
International, where he is presently serving as the Senior Director of the People and
Protected Areas Department. He enjoys mountain biking and hiking, but one can usually
find him wrapped around the little finger of his 5-year old daughter.
103


29
sustained timber yield and a comparison of this optimum with optimal harvest solutions
for alternative forest management regimes. The optimization study concerns the
management by large timber firms of Chiquitano forest concessions and derives from
economic and forest data collected in the Chiquitano region and the provincial capital,
Santa Cruz, Bolivia. Alternative management scenarios examined in the study include
unregulated or unconstrained harvest (U), management under constraints imposed by the
Bolivian forestry law (BFL), sustained timber yield management (STY), and
management constrained by objectives of sustaining timber yield and maintaining the
structure and composition of a theoretical climax equilibrium forest (SFM). The
harvest horizon for all scenarios is set at 40 years to allow for comparison of the net
present value of returns. The actual harvest horizons for all scenarios are longer, those of
the sustainable scenarios STY and SFM being infinite, however the harvest horizon was
limited to 40 years due to poor fit of the recruitment function in the growth model, which
would significantly affect stocking and harvest levels for longer horizons. Forty years
was selected since it is the legal concession period under the Bolivian forestry law.
Harvesting is selective, its selectivity defined by the value and merchantability of trees
and constraints on their extraction.
The SFM scenario does not derive from mathematical conditions describing
sustained production of non-timber products or ecological benefit flows, but rather that of
attaining a residual forest condition approximating the structure and composition of an
undisturbed forest, as defined by the growth model. The theoretical climax condition
(y) or undisturbed equilibrium distribution is defined mathematically
y= (I-G)-'r
(3-1)


Caveto, M.A.R. 1998. Evaluacin de la operacin de corta con y sin planificacin, sus
impactos, costos y rendimientos caso: propiedad Amazonic, Concepcin, Santa
Cruz [thesis]. Universidad Mayor de San Simn, Santa Cruz, Bolivia. 96 p.
Claros A., A. and J.C. Licona. 1995. Establecimiento de parcelas permanentes de
medicin en la zona de Las Trancas, Lomero. Proyecto BOLFOR, Santa Cruz,
Bolivia. 86 p.
Crespo F J. R. 1999. Evaluacin de la operacin de arrastre: costos, rendimientos e
impactos del aprovechamiento en la propiedad Amazonic, Concepcin, Santa Cruz
[thesis]. Universidad Mayor de San Simn, Santa Cruz, Bolivia. 300 p.
Dickinson, M., J. Dickinson, and F.E. Putz. 1996. Natural forest management as a
conservation tool in the tropics: divergent views on possibilities and alternatives,
Comm. For. Rev. 75:309-315.
Duerr, W.A. and W.E. Bond. 1952. Optimum stocking of a selection forest. J. For. 50:12-
16.
Favrichon, V. 1998. Modeling the dynamics and species composition of a tropical mixed-
species uneven-aged natural forest: Effects of alternative cutting regimes. For. Sci.
44:113-124.
Ferguson, D.E., A.R. Stage, and R.J. Boyd. 1986. Predicting regeneration in the grand fir-
cedar-hemlock ecosystem of the northern rocky mountains. For. Sci. Monog. 26.
Fredericksen, T.S., B. Mostacedo, J. Justiniano, and J. Ledezma. 2001. Seed tree
retention considerations for uneven-age management in Bolivian tropical forests. J.
Trop. For. Sci. 13:352-363.
Frumhoff, P., and E. Losos. 1998. Setting priorities for conserving biological diversity in
tropical timber production forests. Union of Concerned Scientists and Smithsonian
Institution, Washington, DC. 14 p.
Geobold, M. 1981. Mapa geolgico del area de Concepcin (Cuad SE 20-3, con parte de
SE 20-2) Proyecto Precambrico, Servicio Geolgico de Bolivia, Santa Cruz,
Bolivia and Institute of Geological Sciences National Environment Research
Council, UK.
Graaf, N. R. de. 1986. A silvicultural system for natural regeneration of tropical rain
forest in Suriname. Agricultural University, Wageningen. 250 p.
Greene, W.H. 2000. Econometric analysis, 4th Ed. Prentice-Hall, NJ. 1004 p.
Grubb, P.J. 1977. Maintenance of species-richness in plant communities: Importance of
regeneration niche. Bio. Rev. 52:107-145.
98


V
Profitability of Management 48
Stand State and Forest Value Measures 49
Conclusions 54
4 REGULATORY POLICY EFFICIENCY IN PROMOTING SUSTAINABLE
TIMBER MANAGEMENT FOR A BOLIVIAN TROPICAL DRY FOREST 57
Introduction 57
Methods 58
Forest Growth and Optimization Models 58
Regulatory Policies 62
Results and Discussion 68
Harvesting Behavior and Forest Condition 68
Profitability and Rent Distribution 73
Conclusions 74
5 CONCLUSIONS 77
APPENDIX
A GUILD CLASSIFICATION OF LOMERO TREE SPECIES 82
B FOREST HARVESTING COSTS PER COMPONENT 86
C MARKET VALUE OF MERCHANTABLE TIMBER SPECIES 88
D DEFINITION OF OPTIMIZATION VARIABLES 89
E MATHEMATICAL DESCRIPTION OF MANAGEMENT ALTERNATIVES ...91
F MATHEMATICAL DESCRIPTION OF OPTIMIZATION SCENARIOS
WITH REGULATORY MECHANISMS 94
LIST OF REFERENCES 97
BIOGRAPHICAL SKETCH
103


APPENDIX C
MARKET VALUE OF MERCHANTABLE TIMBER SPECIES
Mean sawnwood price Mean roundwood price3,6
(FOB Santa Cruz) (FOB Forest Mill!
Scientific name Bs/bf$US/bf Bs/m3$US/m3
Amburana cearensis
3.50
0.52
601.44
89.90
Anadenanthera colubrina
2.40
0.36
344.92
51.56
Aspidosperma nobile
2.75
0.41
426.54
63.76
Aspidosperma spp.
2.65
0.40
403.22
60.27
Astronium urundeuva
2.65
0.40
403.22
60.27
Cariniana domestica
2.00
0.30
251.64
37.61
Cariniana ianeirensis
1.75
0.26
193.34
28.90
Cedrela fissilis
4.00
0.60
718.04
107.33
Centrolobium microchaete
3.00
0.45
484.84
72.47
Cordia glabrata, C. alliodora
3.80
0.57
671.40
100.36
Gallesia integrifolia
1.55
0.23
146.70
21.93
Guibourtia chodatiana
3.00
0.45
484.84
72.47
Hymenea courbaril
2.90
0.43
461.52
68.99
Lonchocarpus guillemineanus
1.30
0.19
88.40
13.21
Machaerium scleroxylon
10.51
1.57
2237.01
334.38
Phyllostylon rhamnoides
2.40
0.36
344.92
51.56
Schinopsis brasilensis
3.75
0.56
659.74
98.62
Sorocea saxcola
2.40
0.36
344.92
51.56
Sweetia fruticosa
2.90
0.43
461.52
68.99
Tabebuia serratifolia
2.75
0.41
426.54
63.76
Terminalia oblonga
2.65
0.40
403.22
60.27
a. Less transport (0.36 Bsfof) and milling costs (19.38 Bs/mJ)
b. 233.2 bf/m3 round wood
88


* Lomero forest habitats (T. Fredericksen. personal comment)
1: Short-lived (3-4 years), early successional
2: Long-lived colonizers of disturbed sites
3: Borders of rock outcrops
4: Generalists
5: Mature upland forest canopy
6: Mature upland forest understory
7: Riparian forest canopy
8: Riparian forest understory
85


47
The SFM condition prescribes maintenance of the negative exponential distribution
typical of uneven-aged, mixed species forests, with more modest reduction in the pre
harvest growing stock relative to STY (Table 3-7). The SFM condition is defined by the
biological needs of meeting sustained timber yield constraints and minimal deviation
from the theoretical climax structure. Some substitution of species of lower market value
for those of higher value may occur in satisfying the minimum deviation objective, due to
inadequacies of the SFM optimization model. Evidence of substitution for large stems of
Guild 4, those of highest value, is inconclusive given the important stocking levels
observed (Table 3-7).
The sustained-yield scenarios are advantageous in that the harvest horizons are
infinite, thus profitable timber extraction may be concentrated in a permanent production
forest estate. Optimal unconstrained management (U) depletes the merchantable stock in
the initial entry (Year 0). The BFL alternative only retains sufficient merchantable stock
to meet legal constraints, implying that only a proportion of those stems growing into size
classes > 45 cm during a cutting-cycle may be harvested in subsequent entries. This
result implies that after the initial concession period (40 years), U and BFL would require
a growing interval longer than 40 years for the forest to produce adequate timber for
profitable harvesting. Removing the stand from production for several decades to allow
for sufficient restocking of merchantable timbers after U and BFL harvesting creates a
short-term need for the expansion of harvesting into other forests to meet production
goals, which defeats the purpose of establishing permanent production forests.


22
resulting stand distribution estimates (Figure 2-2). Whereas the MNL estimated matrix
model predicts a leveling population distribution with increasing age, the matrix model
derived from observed transition probabilities predicts a distribution similar to that
observed after the initial harvest and a greater decline in stems of merchantable size (> 40
cm dbh). The MNL model predicts a greater number of trees in the merchantable 20 to
40 cm dbh classes relative to the observed prediction due to the smoothing effect of the
regression on transition probabilities across size classes. While the observed matrix
model exhibits considerable variance in transition probabilities, especially in those guilds
with limited samples (Guilds 2 and 3), the MNL model corrects for sample variance. The
MNL model predicts greater stability of stems in the 20 to 40 cm range and greater
upgrowth of smaller stems into these size classes relative to the observed model, with less
variance of these transition probabilities among similar size classes.
Figure 2-2. Static, deterministic prediction of forest evolution with observed (G) and
MNL estimated (GvfNI) transition matrices


7
Mortality
Remaining in the same size class or stability
Moving up one size class or upgrowth
This approach differs from previous work in its use of tree and forest characteristics
to simultaneously estimate the probability of these three outcomes. The approach is
advantageous in allowing deterministic, stochastic, and dynamic prediction of forest
evolution, while preserving the simple linear form of matrix models that permits their
straightforward integration into optimization studies. Moreover, it is expected that the
transition probabilities resulting from MNL estimation are more smoothly distributed
across size classes relative to those resulting from simple proportional estimation from
observed forest populations, which are likely to be much more erratically distributed
given limited population samples and time spans of observations.
The MNL transition model allows stochastic simulation of transition probabilities
while preserving the stationarity of a deterministic model form. The model may thus
incorporate the biological uncertainty inherent in forest growth estimation and may allow
for a more robust statistical comparison of results. Compatible deterministic and
stochastic forms permit more robust statistical analyses, while preserving the efficiency
of a deterministic model (Vanclay 1991).
An important limitation of the transition matrix models developed by Leslie (1945),
Usher (1966, 1969), and Buongiomo and colleagues (e.g., Buongiomo and Michie 1980)
is the assumption of stationarity that the transition probabilities for a given size/species
class remain constant over time. Estimations of steady-state stocking and harvest levels
are feasible; and with stationarity, a unique solution for sustainable harvesting and
growing stock levels can be found (Buongiomo and Michie 1980). The stationarity


53
than half that of the climax forest and to just over half of the climax merchantable
stocking under BFL constraints.
The basal area of merchantable stems is depleted under U and reduced to less than
1/5 of that in the climax forest under BFL. In contrast, the STY and SFM regimes
maintain important stocking levels of merchantable stems throughout the harvest horizon.
Moreover, significant differences are observed in the proximity to climax structure and
composition indices (PCImerCh) under scenarios constrained to sustained timber yield
(STY, SFM) and those not biologically constrained to meet sustainability objectives
(U, BFL). The PCM measures confirm the depletion of stand market value under the U
and BFL relative to the sustained-yield alternatives.
Wildlife values of the residual stands are less affected by the alternative
management scenarios (Table 3-12), indeed all scenarios result in residual stands that
deviate little from the climax stand in their value to vertebrate frugivores. This result is
expected, as non-merchantable species are as important as merchantable species for
wildlife, if not more so (Table 3-4). Accordingly, depletion of the merchantable stock
has little impact on the value of the forest for wildlife, as measured in this study. Greater
precision on the relative value of tree species to wildlife other than vertebrate frugivores
may be more revealing of the impacts of alternative management scenarios in terms of
forest value for biodiversity.
Table 3-12. Wildlife and diversity indices per management alternative
Index
Management alternative
Climax
condition
U
BFL
STY
SFM
PCW
0.98
0.99
0.96
0.98
1.00
H5
1.17
1.17
1.21
1.20
1.20
H80
2.93
2.97
2.98
3.04
3.11