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Population Dynamics of the Amazonian Palm Mauritia flexuosa

Permanent Link: http://ufdc.ufl.edu/UFE0021479/00001

Material Information

Title: Population Dynamics of the Amazonian Palm Mauritia flexuosa Model Development and Simulation Analysis
Physical Description: 1 online resource (97 p.)
Language: english
Creator: Holm, Jennifer A
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: harvesting, matrix, models, optimization, palm, tropical
Interdisciplinary Ecology -- Dissertations, Academic -- UF
Genre: Interdisciplinary Ecology thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The tropical palm Mauritia flexuosa has high ecological and economic value, but some wild populations are harvested excessively by cutting the stem to retrieve the fruit. It is likely that M. flexuosa harvesting in the Amazon will continue to increase over time. I investigated the population dynamics of this important palm, the effects of harvesting, and suggested sustainable harvesting regimes. Data were collected from populations in the Ecuadorian Amazon that were assumed to be stable. I used a matrix population model to calculate the density independent asymptotic population growth rate (lambda = 1.046) and to evaluate harvesting scenarios. Elasticity analysis showed that survival (particularly in the second and fifth size class) contributes more to the population growth rate than does growth and fecundity. In order to simulate a stable population at carrying capacity, density dependence was incorporated and applied to the seedling survival and growth parameters in the transition matrix. Harvesting scenarios were simulated with the density dependent population models to predict sustainable harvesting regimes for the dioecious palm. I simulated the removal of only female palms and showed how both sexes are affected with harvest intensities between 15 and 75% and harvest intervals of 1 to 15 years. By assuming a minimum female threshold, I demonstrated a continuum of sustainable harvesting schedules for various intensities and frequencies for 100 years of harvest. Furthermore, by setting the population model?s lambda = 1.00, I found that a harvest of 22.45 percent on a 20 year frequency for the M. flexuosa population in Ecuador is consistent with a sustainable, viable population over time. Demographic parameters of long-lived plants are difficult to accurately estimate with short duration studies. Genetic algorithm (GA) optimizations have been used to calibrate the matrix population model from populations sampled in Ecuador. Assuming that the observed population was stable at carrying capacity, sampling error could explain that the estimated demographic parameters (transition probabilities) do not project equilibrium population values that match the observed size class distribution. GA optimization of seedling parameters somewhat improved the match to the observed size class distribution, but the optimal parameters were from a range of local optima. GA optimization of non-seedling demographic parameters for the Ecuador population produced a close fit to the observed population size class distribution. It was found that the technique of constrained GA optimization produced models that closely matched the observed size class distribution and were consistent with plot measurements. This study also compared the palm size class distributions and demographic characteristics between Peru and Ecuador populations. Unlike in Ecuador, palm populations in Peru are heavily harvested, with reduced numbers of adult females and an uneven sex-specific size class distribution. Finally, I explored GA as a tool to reconstruct plausible harvesting histories by assuming that a harvested population in Peru started with the same population structure as the Ecuador population. Harvest regime variables included harvest intensity (fraction removed), harvest frequency (return time) and the time span with harvesting. No parameter combinations for regular uniform harvest regimes were found that closely matched the observed Peru size class distribution.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jennifer A Holm.
Thesis: Thesis (M.S.)--University of Florida, 2007.
Local: Adviser: Cropper, Wendell P.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021479:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021479/00001

Material Information

Title: Population Dynamics of the Amazonian Palm Mauritia flexuosa Model Development and Simulation Analysis
Physical Description: 1 online resource (97 p.)
Language: english
Creator: Holm, Jennifer A
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: harvesting, matrix, models, optimization, palm, tropical
Interdisciplinary Ecology -- Dissertations, Academic -- UF
Genre: Interdisciplinary Ecology thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The tropical palm Mauritia flexuosa has high ecological and economic value, but some wild populations are harvested excessively by cutting the stem to retrieve the fruit. It is likely that M. flexuosa harvesting in the Amazon will continue to increase over time. I investigated the population dynamics of this important palm, the effects of harvesting, and suggested sustainable harvesting regimes. Data were collected from populations in the Ecuadorian Amazon that were assumed to be stable. I used a matrix population model to calculate the density independent asymptotic population growth rate (lambda = 1.046) and to evaluate harvesting scenarios. Elasticity analysis showed that survival (particularly in the second and fifth size class) contributes more to the population growth rate than does growth and fecundity. In order to simulate a stable population at carrying capacity, density dependence was incorporated and applied to the seedling survival and growth parameters in the transition matrix. Harvesting scenarios were simulated with the density dependent population models to predict sustainable harvesting regimes for the dioecious palm. I simulated the removal of only female palms and showed how both sexes are affected with harvest intensities between 15 and 75% and harvest intervals of 1 to 15 years. By assuming a minimum female threshold, I demonstrated a continuum of sustainable harvesting schedules for various intensities and frequencies for 100 years of harvest. Furthermore, by setting the population model?s lambda = 1.00, I found that a harvest of 22.45 percent on a 20 year frequency for the M. flexuosa population in Ecuador is consistent with a sustainable, viable population over time. Demographic parameters of long-lived plants are difficult to accurately estimate with short duration studies. Genetic algorithm (GA) optimizations have been used to calibrate the matrix population model from populations sampled in Ecuador. Assuming that the observed population was stable at carrying capacity, sampling error could explain that the estimated demographic parameters (transition probabilities) do not project equilibrium population values that match the observed size class distribution. GA optimization of seedling parameters somewhat improved the match to the observed size class distribution, but the optimal parameters were from a range of local optima. GA optimization of non-seedling demographic parameters for the Ecuador population produced a close fit to the observed population size class distribution. It was found that the technique of constrained GA optimization produced models that closely matched the observed size class distribution and were consistent with plot measurements. This study also compared the palm size class distributions and demographic characteristics between Peru and Ecuador populations. Unlike in Ecuador, palm populations in Peru are heavily harvested, with reduced numbers of adult females and an uneven sex-specific size class distribution. Finally, I explored GA as a tool to reconstruct plausible harvesting histories by assuming that a harvested population in Peru started with the same population structure as the Ecuador population. Harvest regime variables included harvest intensity (fraction removed), harvest frequency (return time) and the time span with harvesting. No parameter combinations for regular uniform harvest regimes were found that closely matched the observed Peru size class distribution.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jennifer A Holm.
Thesis: Thesis (M.S.)--University of Florida, 2007.
Local: Adviser: Cropper, Wendell P.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021479:00001


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09dbd331703923fcaf3c24d0adae4a45
96c1a52c70b9dcdbfa8e9e0639f7fea4b717284c







POPULATION DYNAMICS OF THE AMAZONIAN PALM Mauritiaflexuosa: MODEL
DEVELOPMENT AND SIMULATION ANALYSIS




















By

JENNIFER A. HOLM


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2007

































2007 Jennifer A. Holm

































To my family who encouraged me at a young age, to keep striving for academic knowledge, and
to my friends









ACKNOWLEDGMENTS

I gratefully thank my supervisory committee, Dr. Kainer and Dr. Bruna, and most

importantly my committee chair, Dr. Wendell P. Cropper Jr. for their time and effort. I

acknowledge the School of Natural Resources and Conservation, the School of Forest Resources

and Conservation, and the Tropical Conservation and Development Program, the United States

Forest Service, and the Fulbright Scholar Program for funding and guidance. Data collection in

Ecuador was conducted with the help from Dr. Christopher Miller, Drs. Eduardo Asanza and

Ana Cristina Sosa, Joaquin Salazar, and all the Siona people of Cuyabeno Faunal Reserve. Data

collected in Peru was conducted with the help from Weninger Pinedo Flores, Exiles Guerra,

Gerardo Bertiz, Dr. Jim Penn, and with the generosity of Paul and Dolly Beaver of the Tahuayo

Lodge. Lastly, I would like to thank my parents for their support through my education

experience, Heather, Chris, friends, and fellow graduate students.









TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ..............................................................................................................4

L IST O F T A B L E S ................................................................................................... . 7

L IST O F FIG U R E S ............................................................................... 8

ABSTRACT ........................................... .. ......... ........... 10

CHAPTER

1 IN T R O D U C T IO N ....................................................................................... .................... 12

2 POPULATION DYNAMICS OF THE DIOECIOUS AMAZONIAN PALM Mauritia
flexuosa: SIMULATION ANALYSIS OF SUSTAINABLE HARVESTING...................14

2 .1 Introdu action ...................................... .................................................. 14
2 .2 M e th o d s ................................................................................................................... 1 7
2 .2 .1 S tu d y S ite ................................................................. .................................1 7
2.2.2 Study Species ......................................... ................... .... ....... 17
2.2.3 D ata Collection .............. .......................................... ...... ................ ......18
2.2.4 Matrix Model Development and Parameter Estimation............................... 19
2 .3 R e su lts .................. .................................................................................................. 2 2
2 .3 .1 D en sity D ependence............................................................... .....................22
2.3.2 Sustainable H arvest Scenarios ........................................ ....... ............... 23
2 .4 D iscu ssio n .............................................................................................................. 2 5
2.4.1 Sustainable H arvest Scenarios ........................................ ....... ............... 25
2.4.2 Implications for M anagem ent .................................. ............... ............... 26

3 GENETIC ALGORIHTM OPTIMIZATION FOR DEMOGRAPHIC PARAMETER
CALIBRATION AND POPULATION TRAITS OF A HARVESTED TROPICAL
P A L M ................................................................................... .. 4 1

3.1 Introduction ......... ........ .... .... ... ........... ... ..... ...............41
3.1.1 South American Palms and Consequences of Wild Harvesting ....................41
3.1.2 Matrix Modeling and Population Dynamics...............................................42
3.1.3 Param eter Calibration............................................................ 43
3.1.4 Introduction to Genetic Algorithm s ...................................... ............... 44
3 .1.5 O bjectiv es ...................................... ............................................. 4 5
3.2 M ethods........................................................ 45
3.2.1 Study Site: E cuador............ .... ........................................... .. .... ............... 45
3 .2 .2 Stu dy Site: P eru ............. ........................................................ .. .... ..... .. 4 6
3.2.3 Study Species R ole in Peru ................................................ ............... .... 47
3.2.4 Palm Distribution and Matrix Model Development: ..................................48
3.2.5 G A M ethod D escription......................................................... ............... 48









3 .3 R esu lts ..................................................................................................................... 5 1
3 .3 .1 G enetic A lgorithm s .................................................................................. .... 5 1
3.3.2 Peru Size Class Distribution and Demographic Characteristics ....................54
3.3.3 Genetic Algorithm: Harvest History for Peru M. flexuosa Palm Population....55
3 .4 D iscu ssio n ..............................................................................5 7
3.4.1 G enetic A lgorithm s ............................................................... ....................... 57
3.4.2 Peru Size Class Distribution and Demographic Characteristics ....................59
3.4.3 Genetic Algorithm: Peru M. flexuosa Palm Population............................... 60
3 .5 C on clu sion s ................................60.............................

4 SU M M A R Y ............. .............................................................................................. 84

4.1 A applicability ........................................... 84
4.2 Future for M flexuosa ............... ................................................ ......... ...........84
4.3 Future Research................................... .. ... ..... ....... .......85

APPENDIX: PERU GARDEN DATA FOR Mauritiaflexuosa ....................................... 86

L IST O F R E F E R E N C E S ...................................................................................... ...................89

B IO G R A PH IC A L SK E T C H .............................................................................. .....................96









LIST OF TABLES


Table page

2-1 Observed size class distribution (based on height) ofM. flexuosa...............................29

2-2 M flexuosa (Ecuador) transition matrix ........................................ ........................ 30

2-3 Size class distribution for density independent (DI) and density dependent (DD)
m models after 100 yr. ..................................................................... ... 3 1

2-4 Adult (stage 5 & 6) M. flexuosa transition probabilities............................... ...............32

3-1 M. flexuosa population size class distribution in Ecuador and Peru..............................62

3-2 Optimal Ecuador seedling parameters and carrying capacity using observed
dem graphic param eters.. ........................................................................ ....................63

3-3 Observed range of the 13 non-seedling demographic transition probabilities. ................64

3-4 Observed and optimal Ecuador transition matrices. .................................. .................65

3-5 Optimal Ecuador seedling parameters and carrying capacity using optimal
dem graphic param eters. ......................................................................... ....................66

3-6 Demographic traits for the Peru population in size classes 3-6 (palms that have
developed trunks) ................. .......... .... ........... ......................... 67

3-7 GA estimates of harvest regimes consistent with the observed size class distribution. ....68

3-8 Peru's harvesting history found using separate GAs which uses the Ecuador optimal
demographic parameters to reach Peru's observed population distribution....................69









LIST OF FIGURES


Figure pe

2-1 Elasticity for the M. flexuosa matrix population model.................................................33

2-2 Density dependent model for M. flexuosa simulated over 500 yr ................. ...............34

2-3 Four simulated harvesting scenarios with various harvest frequencies and intensities
for M flexuosa. ................................... .................................. ........... 35

2-4 The average number of female palms the year before harvesting over a 100 yr
harvest regime e. ............................................................................ 38

2-5 Harvesting 22.45 percent at a frequency of every 20 yr ..................................................39

2-6 Two harvest scenarios (both 75 percent at a frequency of every 10 yr) with density
independence (DI) and density dependence (DD). ...................................................40

3-1 M ap of study site in Ecuador. ................................................ ................................ 71

3-2 M ap of study site in P eru. ........................................................................ ....................72

3-3 Ecuador Genetic Algorithm (GA) size class distribution and observed size class
distribution after running a GA to find optimal seedling parameters (stasis and
growth) and carrying capacity. Fitness score for this GA is 46.67................................73

3-4 Ecuador GA size class distribution and observed size class distribution after running
a GA using the observed transition parameters and evaluating how well it matches
the observed population distribution. Fitness score for this GA is 67.03........................74

3-5 Genetic algorithm simulated and observed size class distribution of the Ecuador palm
population for unconstrained, all values (UCAV) GA optimization. Fitness score for
this G A is 14 .14 ........................................................ ................. 75

3-6 Genetic algorithm simulated and observed size class distribution of the Ecuador palm
population for unconstrained, no two-size class transitions (UCNT) GA optimization.
Fitness score for this G A is 5.07 ............................................... ............................. 76

3-7 Stasis and growth demographic points generated from a GA optimization for (A) an
UCAV (unconstrianed, all value), and (B) an UCNT (unconstrained, no two size-
cla ss tran sitio n s) ......................................... .. .......................... ................ 7 7

3-8 Stasis and growth demographic points generated from CAV (constrained, all values)
G A optim ization ..................................................... ................ 7 8

3-9 Stasis and growth demographic points generated from a CNT (constrained, no two-
size class transitions) GA optimization...................... ..... ............................ 79









3-10 Genetic algorithm simulated and observed size class distribution of the Ecuador palm
population for CAV (constrained, all values) GA optimization. Fitness score for this
G A is 6 .2 9 ................................................................................8 0

3-11 Genetic algorithm simulated and observed size class distribution of the Ecuador palm
population for CNT (constrained, no two-size class transitions) GA optimization.
Fitness score for this G A is 7.69 ............................................... ............................. 81

3-12 M. flexuosa population distribution for palm populations in a Iha area in Peru and
E cuador ......................................................................................... 82

3-13 Distribution of male vs. female palms and estimated, averaged fecundity values from
Peru and Ecuador. ........................................... ........................... 83

A-i Average height(m) for M. flexuosa palms sampled in Peru (wild and gardens).

A-2 Comparison of average palm height and average number of petioles, for juvenile M
flexuosa located in gardens and wild populations (in Peru).

A-3 M. flexuosa palms in Peru homegardens. (A) Picture of juvenile (pre-reproductive)
M. flexuosa palms in a homegardens. (B) Picture of dwarf, reproductive female palm
in Peru.









Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

POPULATION DYNAMICS OF THE AMAZIONIAN PALM Mauritiaflexuosa: MODEL
DEVELOPMENT AND SIMULATION ANALYSIS

By

Jennifer A. Holm

December 2007

Chair: Wendell P. Cropper Jr.
Major: Interdisciplinary Ecology

The tropical palm Mauritiaflexuosa has high ecological and economic value, but some

wild populations are harvested excessively by cutting the stem to retrieve the fruit. It is likely

that M. flexuosa harvesting in the Amazon will continue to increase over time. I investigated the

population dynamics of this important palm, the effects of harvesting, and suggested sustainable

harvesting regimes. Data were collected from populations in the Ecuadorian Amazon that were

assumed to be stable. I used a matrix population model to calculate the density independent

asymptotic population growth rate (X = 1.046) and to evaluate harvesting scenarios. Elasticity

analysis showed that survival (particularly in the second and fifth size class) contributes more to

the population growth rate than does growth and fecundity. In order to simulate a stable

population at carrying capacity, density dependence was incorporated and applied to the seedling

survival and growth parameters in the transition matrix. Harvesting scenarios were simulated

with the density dependent population models to predict sustainable harvesting regimes for the

dioecious palm. I simulated the removal of only female palms and showed how both sexes are

affected with harvest intensities between 15 and 75% and harvest intervals of 1 to 15 years. By

assuming a minimum female threshold, I demonstrated a continuum of sustainable harvesting

schedules for various intensities and frequencies for 100 years of harvest. Furthermore, by









setting the population model's X = 1.00, I found that a harvest of 22.45 percent on a 20 year

frequency for the M. flexuosa population in Ecuador is consistent with a sustainable, viable

population over time.

Demographic parameters of long-lived plants are difficult to accurately estimate with short

duration studies. Genetic algorithm (GA) optimizations have been used to calibrate the matrix

population model from populations sampled in Ecuador. Assuming that the observed population

was stable at carrying capacity, sampling error could explain that the estimated demographic

parameters (transition probabilities) do not project equilibrium population values that match the

observed size class distribution.

GA optimization of seedling parameters somewhat improved the match to the observed

size class distribution, but the optimal parameters were from a range of local optima. GA

optimization of non-seedling demographic parameters for the Ecuador population produced a

close fit to the observed population size class distribution. It was found that the technique of

constrained GA optimization produced models that closely matched the observed size class

distribution and were consistent with plot measurements. This study also compared the palm

size class distributions and demographic characteristics between Peru and Ecuador populations.

Unlike in Ecuador, palm populations in Peru are heavily harvested, with reduced numbers of

adult females and an uneven sex-specific size class distribution. Finally, I explored GA as a tool

to reconstruct plausible harvesting histories by assuming that a harvested population in Peru

started with the same population structure as the Ecuador population. Harvest regime variables

included harvest intensity (fraction removed), harvest frequency (return time) and the time span

with harvesting. No parameter combinations for regular uniform harvest regimes were found

that closely matched the observed Peru size class distribution.









CHAPTER 1
INTRODUCTION

In general terms, population ecology entails analyzing the demography of a population

through estimating its vital rates (survival, growth, fecundity, mortality), and assessing change in

numbers over time. In particular, understanding population dynamics is important for evaluating

how a population density changes in response to external and/or internal influences. Modeling

population dynamics is useful for developing and evaluating hypotheses in population ecology.

This research employed simulation modeling to develop matrix population models for evaluating

the population behavior of a tropical palm, Mauritiaflexuosa. Constructing matrix population

models, including density dependence, simulating sustainable harvesting scenarios, and

developing methods to calibrate poorly sampled model parameters was the main goals of this

research. This research is not recommended to be used directly for management purposes. The

simulated sustainable harvest regimes identified in this study represent testable hypotheses; and

rigorous testing should be done before any implementation.

The tropical palm Mauritiaflexuosa is found in the Amazon Basin and often forms

monodominant stands. Destructive harvesting is occurring in parts of the Amazon to retrieve the

palm fruits, which are then sold in local markets. Demographic population modeling was used to

estimate the population's current behavior, as well as estimate the population's response to

assumed harvesting scenarios. This thesis is organized as two separate journal papers (chapter 2

and chapter 3). Chapter 2 describes the model structure, data and methods used for model

development, and results of harvest scenario analysis. One of the principal uncertainties of this

work is associated with the relatively short period of data collection (2 years). Chapter 3

describes the use of genetic algorithms for simultaneous estimation of up to 13 model









parameters. This technique provides a test of the consistency of parameter estimates and the

observed size class distribution.









CHAPTER 2
POPULATION DYNAMICS OF THE DIOECIOUS AMAZONIAN PALM MAURITIA
FLEXUOSA: SIMULATION ANALYSIS OF SUSTAINABLE HARVESTING

2.1 Introduction

There is growing concern for conserving and sustaining tropical forests (Houghton et al.

1991, Sioli 1991, Olmsted & Alvarez-Buylla 1995). Many tropical tree species provide

ecological as well as economic benefits. These benefits include valuable resource production or

important functions associated with tropical biodiversity and conservation. Managing these

critical species requires an understanding of their population dynamics by practitioners and

communities (Olmsted & Alvarez-Buylla 1995). Palms make up a large portion of the

economically useful tropical trees and are utilized for a wide range of products (Balick & Beck

1990, Anderson et al. 1991, Kahn 1991, Kahn & de Granville 1992, Henderson et al. 1995). The

palm Mauritiaflexuosa L.f, also called canangucho or morete in the Ecuadorian Amazon, was

the focus species of this study, used in the development of matrix population models.

Mauritiaflexuosa is found in tropical, flooded, swamps (Kahn & Mejia 1990, Kalliola et

al. 1991, Cardoso et al. 2002) throughout the Amazonia Basin and northern South America

(Henderson 1995, Ponce et al. 2000). Mauritiaflexuosa has significant, but underdeveloped

potential as a multifunctional, non-timber forest resource of great economic value (Denevan &

Treacy 1987, Carrera 2000, Peters et al. 1989a, 1989b, Ponce et al. 2000). The fruit of the palm

is currently its most economically useful product (Padoch 1988). Oil fractions extracted from M

flexuosa fruit have high concentrations of vitamins, carotene, and lipids (de Franca et al. 1999).

Mauritiaflexuosa is one of the most commonly found palms in the Amazon, and forest

dwellers currently invest substantial effort in gathering fruits from these palms to generate

income (Kahn 1988, Peters 1992, Coomes et al. 2004). These products are not processed on an

industrial scale, but they do provide income and employment for many people in Iquitos and









other Amazonian communities, with the fruit being sold in many forms (Padoch 1988). There

has been an increasing shift to growing M. flexuosa in small homegardens, also known as

chacras. Until recently, however most M. flexuosa fruit has been harvested from wild stands. In

dense, monodominant, flooded natural stands, the mature palm trees are typically greater than

20m in height making the fruit difficult to harvest. As a result, in many Amazonia locations the

fruit-bearing female palms are cut down leading to nonviable populations (Peters et al. 1989a,

Vasquez & Gentry 1989), which makes M. flexuosa a good candidate for non-timber forest

product (NTFP) management.

A goal of my research was to identify potential sustainable harvest regimes for M

flexuosa. Because fruit harvest for this particular species results in tree mortality, matrix

population models are appropriate tools to simulate monodominant stands of M flexuosa. If

markets continue to flourish with M. flexuosa products then in time formerly low levels of

harvesting will likely intensify in Ecuadorian forests as it has in other Amazon Basin locations

(Peters et al. 1989a, Vasquez & Gentry 1989). Many studies have looked at the 1) implications

of harvesting palm parts (NTFPs) as well as 2) identifying useful palms needing conservation

(Johnson 1988, Fonseca 1999, Mendoza and Oyama 1999, Endress et al. 2004a, Ticktin 2004).

Ticktin et al. (2002) used matrix models to assess the effects of harvesting on a NTFP bromeliad

in Mexico. Endress et al. (2004b) as well as Olmsted and Alvarez-Buylla (1995) used matrix

models to evaluate harvesting techniques for tropical palms (Chamaedorea radicalis, Thrinax

radiata, and Coccothrinax readii). Likewise, matrix models have been used on the tropical palm

Iriartea deltoidea to evaluate stem harvesting, population stability, and conservation (Pinard

1993, Anderson & Putz 2002). Matrix models have also been coupled with habitat

fragmentation analysis to assess changes in plant population dynamics in tropical environments









(Bruna 2003). Improper harvesting of palm products has been demonstrated to have a negative

effect at the population level (O'Brien & Kinnaird 1996, Clay 1997).

Lefkovitch matrix models (1965), a generalization of matrix population models proposed

by Leslie (1945), typically simulate the population in sized-based stages as opposed to the age

classification of a Leslie model. In many tree populations, the demographic parameters (survival

probability, growth rate, and fecundity) are a function of tree size and not of tree age (Caswell

2001, Vandermeer & Goldberg 2003). The standard matrix population model will project

exponential growth if the dominant eigenvalue (X) of matrix is greater than 1 (implying no

resource limitations or competition) or decline exponentially if k is less than 1. Matrix

population models have been used to aid management and conservation of many species (Crouse

et al. 1987, Wootton & Bell 1992, Silvertown et al. 1996).

The role of density dependence is important in some tropical palm populations (Cropper &

Anderson 2004), but data are limited. A study of the tropical palm Euterpe edulis showed that

there was a clear effect of density on the population structure and demography (Matos et al.

1999). A second study of the same palm showed that density dependence, as well as timing of

harvest, must be considered for accurate assessment of population responses to harvesting

(Freckleton et al. 2003). Little is known about density dependence in tropical tree systems that

are harvested, but previous work suggests that density often has its strongest effect on seedlings

of tropical palms and other tree species (Augspurger & Kelly 1984, Sarukhan et al. 1985,

Martinez-Ramos et al. 1988, Matos et al. 1999). I hypothesize similar demographic patterns in

monodominant stands of M. flexuosa.

An important characteristic ofM. flexuosa for harvest management is that the palm is

dioecious; only females bear the economically useful fruit. One study has looked at









demographic consequences of harvesting of an understory dioecious palm, finding that leaf

harvest can reduce female fecundity (Berry & Gorchov 2007). I know of no studies using matrix

models to simulate sustainable harvest regimes in a tropical species with only female removals.

Specifically, my objectives were: (1) to determine how density dependence affects the

population dynamics and harvesting; (2) to estimate sustainable harvests with an assortment of

different harvesting intensities and frequencies ofM. flexuosa, specifically looking at how

harvesting a dioecious species affects the population; and (3) to estimate a sustainable harvest

while maintaining a stable population (k equal to 1.00).

2.2 Methods

2.2.1 Study Site

Data were collected in the Ecuadorian Amazon from the Cuyabeno Faunal Reserve, a

655,781 ha reserve located between the San Miguel and Aguarico river basins and managed by

Siona and Secoya indigenous groups. All field components were conducted near the Cuyabeno

Field Station (07'N, 761 1'W), located in a tropical rainforest with an elevation of 200m.

Cuyabeno is characterized by a series of oligotrophic lakes, connected to M. flexuosa swamps

(morichales) that ultimately drain into the Cuyabeno River. Water levels in M. flexuosa swamps

fluctuate depending on the season and rainfall level, which averages 3400 mm/yr. Three distinct

seasons are evident: dry (mid-December to March), wet (April to July), and transitional (August

to December) (Asanza 1985).

2.2.2 Study Species

Mauritiaflexuosa is a long-lived, dioecious, canopy dominant palm, found throughout the

Amazon basin at elevations below 500m, but sometimes reaching 900m (Henderson et al. 1995).

Juveniles initially have only leaves above-ground, and then begin to form a trunk covered by

persistent petiole bases. As a palm matures, the petioles fall off exposing a permanent trunk.









Mature palms have 8 20 leaves with leaf blades 2.5m long and 4.5m wide, and split into

approximately 200 stiff or pendulous leaflets (Kahn & de Granville 1992, Henderson et al.

1995). The inflorescences are 2m or more in length with 25 40 flowering branches. Fruits are

oblong drupes, 5 x 7cm on average, and are covered with a brick-red epicarp of scale texture.

The only edible part of the fruit for humans is its yellow mesocarp, but the seed is useful to

artisans who produce small carvings. Padoch (1988) describes a number ofM. flexuosa products

found in the Iquitos market, including the ripe fruit and a pulp mash, a drink, popsicles, and ice

cream. Previously studied permanently flooded forests, inhabited by M. flexuosa, are seen to

have soil composed of decomposed organic matter for several meters saturated with acidic water

(Kahn 1991).

In the Ecuadorian Amazon these flooded forests that are mostly dominated by M. flexuosa

(called morichales) are found along river edges. In others parts of the Amazon, this palm is

intensely harvested from these wild stands. Wild harvesting of M. flexuosa has historically

occurred in Ecuador, but at low levels. M. flexuosa can be considered a keystone species

because of large number of other species that feed on the fruit and seed. These include agouties

(Dasyprocta leporina aguti), spider monkeys (Ateles geoffroyi), red and green macaws (Ara

chloroptera), lowland tapirs (Tapirus terrestris), red and gray brocket deer (Mazama americana

and Mazama gouazoubira respectively), white-lipped and collared peccaries (Tayassu pecari and

Tayassu tajacu respectively), and fish (Goulding 1989, Bodmer 1990, Bodmer 1991, Henderson

et al. 1995, Fragoso 1999, Zona 1999).

2.2.3 Data Collection

I used a demographic data set that was collected previously by a research collaborator (C.

Miller) from five plots (20m x 100m) in old growth natural stands in Ecuador (morichales).

Demographic data were collected from 1994-1996. I do not know the exact criteria for selecting









the five plots. All five plots were within a half a day's travel or less from each other. I assumed

that minimal female harvesting had occurred on the five plots (based on evidence from the size

distribution ratio of adult males to females and remnant trunks of harvested female individuals).

Harvest intensity prior to the study, however is unknown. In the first year demographic data was

collected for each palm individual over all five 20m x 100m plots. Palms were tagged with

numbered, metal tags. Data collection consisted of:

1) Palm height for all size classes (actual for palms that could be reached, and estimated
with a clinometer for taller palms).
2) Leaf counts on seedlings and most juveniles.
3) Recording of sex for adults.
4) Leaf scars on palms that had developed trunks.
5) Raceme counts on females.

In the second year, the number of seedlings was based on ten 5m x 5m subplots (randomly

selected) within the 20m x 100m plots. Otherwise, the same data collection was repeated in the

second year. In the third year only seedling data was recorded in the previously marked ten

subplots.

2.2.4 Matrix Model Development and Parameter Estimation

Distribution of palms in each of the five plots was variable. For population analysis and

stage-based matrix modeling, I aggregated the population into a 1-ha pooled data group (Table 2-

1). The population was classified into seven size classes based on height. Only a limited

number of adult growth transitions (size class 5) were observed, leading to potentially poor

estimates of the vital rates. Growth rates were estimated for each size class in the pooled data

set. To estimate survival and growth transitions, I assumed that the observed size class

distribution was stable and that the average growth rates per size class applied to all individuals

within that class. Mean size class specific growth rates were estimated (0.4159 m/yr, 0.3902

m/yr, 0.8107 m/yr, 1.08 m/yr, and 0.4333 m/yr) for size class 1 through 5 respectively. The








matrix parameters (survival, si and growth, gij) that did not have a limited number of

observations were estimated by following the state vs. fate of the palms over time. Fecundity

(fij) parameter estimates were based on equation 2-1:

( fx)(no (t+l))
2
f ij--- 2- --

N. (2-1)


where f(x) is the seedling survival probability, no(t+l) is the average number of established

seedlings at the next time interval, and Ni is the number of reproductive individuals. The term in

the numerator is divided by two, assuming a 1:1 sex ratio. The matrix model was simulated with

the equation 2-2:

n(t+) = A n(t) (2-2)

where n(t) represents the population vector at time t, and A represents the 7 x 7 transition matrix

containing the probabilities for individual palms to remain in the same stage or move to another

stage and their fecundity probabilities (Table 2-2). Elasticity analysis is often used to

demonstrate the sensitivity of the dominant eigenvalue to variations in matrix elements (survival,

growth, fecundity). Unlike absolute sensitivity, elasticity analysis shows the relative

contribution of each vital rate to the population growth rate, X (Caswell 2001, Morris & Doak

2002).

Density dependence was simulated using the monotonic decreasing Ricker function:

ao (N) = a max* e (-p (2-3)

Density dependence was applied to the two seedling parameters (survival and growth) in

the transition matrix, because density has been observed to influence seedlings of tropical palms

(Matos et al. 1999). The first seedling parameter is seedling survival, the probability that a









seedling will survive and remain in the same size class. The second seedling parameter is

seedling growth, the probability that a seedling will survive and grow into the next size class. In

the Ricker function, aij(N) is the probability that a seedling will survive or grow as a function of

the total M. flexuosa population (N, the sum of n population vector). Seedling survival and

growth decreases as density of the entire palm population increases. aijmax represents the matrix

probabilities for the seedling parameters a00 and al 0 in the original transition matrix with no

density limitation. 3 was found by using the bisection method (Cropper and DiResta 1999) to

estimate the seedling parameter values for a stable (k = 1) population and equation 2-4:


in a
a, max
-K = (2-4)


where K is the carrying capacity including all seedling and non-seedling individuals and

aj' represents the matrix probability when k, the dominant eigenvalue of the A matrix, equals

1.00 (the population is stable with a density equal to the carrying capacity). A 39.77 percent

reduction in seedling vital rates was consistent with an equilibrium population at K. Separate

density dependent models were simulated for males and females with identical parameters,

except that male fecundity values were set to zero. Male seedling recruits were assumed to equal

the number of female seedling recruits and were added directly to the male population vector.

I developed scenarios to estimate a sustainable harvest regime based on two options. The

first (1) setting a minimum female threshold (MFT) (20 individuals) to maintain a sustainable

population; and (2) finding the adult survival and growth probabilities that produce a stable, thus

sustainable, intrinsic population growth rate (X = 1.00), using the bisection method. With the

first option I then: (la) varied the intensity of harvests scenarios; (2a) varied the frequency of

harvest, from annual to periodic harvests to find a continuum of harvest scenarios that produced









a sustainable population. In both harvesting scenarios separate population vectors were

simulated for males and females, since M. flexuosa is dioecious and only female palms are felled

during harvest. Harvesting scenarios are initiated after a 600 year density dependent simulation

to avoid transient dynamics associated with a possible non-equilibrium size class distribution.

There are short-lived transients associated with simulations started at the observed stage class

distribution, but they typically damp out rapidly. I assumed that the population has not been

recently harvested, and that the equilibrium size class distribution provides a good estimate of

the expected distribution used as a uniform basis for comparison. Evaluations of harvest

simulations for sustainability are not sensitive to this assumption.

2.3 Results

Elasticity analysis of the density independent M. flexuosa matrix showed that the stasis

probabilities (the elements in the main diagonal) contribute the most to X sensitivity (Figure 2-1,

A). Specifically, the survival and stasis parameter in the second juvenile stage (size 3.0m -

6.0m), and the survival and stasis of the first adult stage (size 20.0m 28.0m) were sensitive

parameters (Figure 2-1, B). The M. flexuosa transition matrix (Table 2-2) produced an

asymptotic population growth rate of = 1.046, which shows that the population has the

potential for rapid increase.

2.3.1 Density Dependence

With density dependence, the population growth rate slows as N approaches the carrying

capacity. I assume that for seedlings, transition rates depend on the number of individuals in

their own size class and all other size classes. The simulated density dependent model shows

that the M. flexuosa population at equilibrium (K) is large (Figure 2-2), but most of the

individuals are in the seedling class (Table 2-3). There was a large difference in the size class









distribution between the density independent model and the density dependent model at 100 yr

simulation (Table 2-3). At approximately 100 to 150 years, the simulated palm population began

to reach equilibrium. The full density dependent simulation was run for 500 years (Figure 2-2).

At equilibrium (after 500 yr) the model predicted an adult size class distribution of

approximately 120 individuals per ha for each sex. The number of adults that were measured in

the study site was approximately 45 per ha for each sex. After equilibrium was reached in the

density dependent simulation, the following harvesting scenarios were initiated.

2.3.2 Sustainable Harvest Scenarios

Multiple harvesting options (Figure 2-3) are consistent with sustainable management ofM.

flexuosa. Harvesting at intensities of 15 percent, 20 percent, 30 percent, 50 percent, and 75

percent removal of adult females are seen in Figure 2-3 (A-C). Harvest frequency, or return

time, is directly coupled with the total number of palms that can be harvested. Periodic

harvesting frequencies were simulated for return times of 5 yr, 10 yr, and 15 yr. I also simulated

an annual harvest regime (Figure 2-3, D), although harvesting is rarely that frequent from natural

M. flexuosa stands because local people understand the threat to these palms survival if

harvesting is done each year. Simulations at a range of intensities (Figure 2-3, D) support the

conventional wisdom that annual harvests are not sustainable in the long-term. With adequate

recovery time, the M. flexuosa population can be dynamically stable following periodic

harvesting (Figure 2-3, A-C). After each periodic harvest, there was a sharp decrease in adult

palm density, followed by an increase in population density (recovery), which is faster in the

years immediately after harvest then slows with increasing density. Recovery is defined as the

number of females that grow into the adult size class 5 from the juvenile size class 4. For all

harvesting intensities (15%-75%), female recovery was greatest with 15 yr harvest intervals

(Figure 2-3, C). Average number of female palms at simulated time of harvest ranged from 37 -









115 depending on harvest intensity and frequency (Figure 2-4). Larger female numbers available

for harvest are associated with longer harvest intervals and lower harvest intensities. Although a

less intense harvesting regime would increase biological sustainability, this may not be adequate

for supplying household income needs.

I have set a sustainable harvest rate for this palm through two different methods. The first

is by assuming 20 adult females per hectare as the MFT needed to sustain population viability.

With 20 adult females set as the threshold, Figure 2-3 shows that the following can be

sustainable; a 30 percent harvest every 5 yr, a 50 percent harvest every 10 yr, and a 50 percent -

75 percent harvest every 15 yr. Only these harvesting intensities are consistent with a viable

population for 100 years, because they maintain the number of female palms above the MFT.

These harvest options can only be done for a hundred year time span. After 100 years if the

harvest intensity remains constant, the population will fall below a minimum sustainable

threshold level. The second method I used to find a sustainable harvest rate allows for

harvesting over an indefinite time period, assuming that population parameters do not change.

By using the bisection method, I found that the adult survival and growth probabilities necessary

for k = 1.00 are less than the observed probabilities (Table 2-4). I found that harvesting 22.45

percent of the females every 20 yr creates a sustainable harvest (Figure 2-5).

The biologically plausible assumption of density dependence leads to very different

harvest projections than that of the standard density independent matrix population model

(Figure 2-6). The simulated harvest scenario without a density dependence function shows a

large increasing female population. The same scenario modeled with density dependence drops

below MFT and does not provide a sustainable harvest.









2.4 Discussion

This study effectively examines impacts of harvesting a dioecious palm and, is among the

first to provide multiple sustainable, simulated harvesting scenarios for one species. While

population modeling may be a useful tool to project management scenarios, uncertainties in

demographic parameters and difficulties in social and economic planning are likely to preclude

precise harvest planning. A typical assumption in matrix population models is that the

populations are not limited by density. Using the standard density independent model, with

parameters estimated in the field, the M. flexuosa population examined increases by a factor of

1.046 each year (at the stable stage distribution). Given limitations on space and other resources,

it is clearly unrealistic that this population will increase indefinitely (Lack 1947, Milne 1957,

Weiner 1986). A population that is growing (X = 1.046) would produce many more harvestable

palms than one limited by competition. At the limit, an exponentially growing population could

produce any desired harvest, given adequate time. I suggest that simulation of density

dependence in monodominant harvested populations is necessary to properly constrain the rate of

population recovery following harvest.

2.4.1 Sustainable Harvest Scenarios

The challenge for NTFPs is finding the harvest level that will supply enough income to

forest dwellers while at the same time maintaining population viability of harvested species. I

have shown that harvesting the specific M. flexuosa population examined at 22.45 percent every

20 yr could be a sustainable harvesting regime (Figure 2-5), but higher intensities or frequencies

of harvest could send the population into a decline.

Frequency/intensity of harvesting is hard to control and is a response to multiple issues,

such as market demand, fluctuating subsistence needs, accessibility, and morichal fruit

production rate. For these reasons, different harvesting scenarios can be chosen, all maintaining









a sustainable harvest rate for the span of 100 years (Figure 2-3). I have shown a tradeoff

between harvest frequency and intensity. Higher rates of removal will require longer recovery

times between harvests (Figure 2-3). This population's MFT is assumed to be 20 individuals per

hectare. It is reasonable to select a conservative value for MFT, based on the Precautionary

Principle, but other M. flexuosa populations could have a different k and a different minimum

female threshold. It can be misleading to evaluate harvesting regimes based on the number of

females to recover in only one year instead of the entire harvest period recovery. In the first

years following a harvest, initially a higher number of palms recover than in remaining years

after a harvest. A harvesting regime with a longer time interval between harvests will allow

more palms to recover into the adult size classes.

Understanding the implications of harvesting a dioecious species is one goal of this paper.

The current practice, selecting and removing female palms, results in recruitment limitation over

time. Females are directly affected by harvesting, and the male population is affected by

changing adult density and by reduced seedling recruitment. Initially, the male population

remains high, but after a lag time the male population begins to decline along with the females.

Over time, if heavy harvesting is maintained, it is predicted recruitment and regeneration ofM.

flexuosa palms will decline.

2.4.2 Implications for Management

While population modeling may be a useful tool to project management scenarios,

uncertainties in demographic parameters and difficulties in social and economic planning are

likely to preclude precise harvest planning. With the market demand increasing for the M.

flexuosa fruit, many forest dwellers are beginning to cultivate the palm in small homegardens.

Research organizations and non-governmental organizations (NGOs), such as the Rainforest









Conservation Fund, are helping Amazonian mestizos to convert old swidden fields into M.

flexuosa gardens. These gardens can take 10 12 yr to become productive, but after trees grow

to maturity fruit can be harvested repeatedly from managed, easily accessible gardens. Wild

individuals may take an estimated 30 or more years to mature and become productive, based on

leaf and infructescence scars counts (pers. observation). Palms grow faster and mature more

quickly under high light conditions, such as those found in agroforestry gardens (Penn 1999).

Palms that mature more quickly will produce fruit at a shorter height, making harvesting easier.

While harvesting in natural, flooded swamp stands can be done at a sustainable level, if market

demand increases then M. flexuosa production gardens, as opposed to extracted natural stands,

may become a better option.

Many forest dwelling Amazonians understand the important economic role of M flexuosa.

They also understand that natural palm densities are decreasing, but few written management

plans have been implemented to protect this resource. Our simulations demonstrate that

sustainable harvesting scenarios for a species can be found, but the precise nature of a

sustainable harvesting regime depends on accurate representation of the population demography.

Long-term palm survival, growth, and fecundity monitoring should be used to provide a sound

basis for developing harvest strategies for wild populations. Better understanding of density

dependence in monodominant M flexuosa stands is also needed. In summary, the sustainable

harvest scenarios found in this study consist of a range of harvesting regimes for 100 years of

harvest, and an option for a continuous sustainable harvest over time. Management planning

should include community input and participation to generate community specific harvesting

management plans. Analyzing the population dynamics of Mauritiaflexuosa can be used as one









component in management of its role as a NTFP, while conserving the natural Amazonian palm

stands it inhabits.












Table 2-1. Observed size class distribution (based on height) ofM. flexuosa in five plots (plot 1-5
100x20m), and pooled plot 1-ha.

Size
Class Stage Height (m) Plot 1 Plot 2 Plot 3 Plot 4 Plot 5 Pooled Plot
0 Seedling <1.0 45 62 59 42 52 260
1 Juvenile 1.0-3.0 2 14 32 29 10 87
2 Juvenile 3.0-6.0 13 18 25 23 22 101
3 Juvenile 6.0-10.0 6 8 6 7 0 27
4 Juvenile 10.0-20.0 12 7 2 9 2 32
5 Adult 20.0-28.0 9 11 8 10 9 47
6 Adult >28.0 13 5 8 13 3 42










Table 2-2. Transition matrix for M. flexuosa for pooled plot, from five flooded swamp sites in
Ecuador. The dominant eigenvalue, lambda (X) shows the growth rate. X = 1 indicates
a stable population, k < 1 a decreasing population, and X > 1 an increasing
population.
Size Classes
<1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m
0.4923 0.0 0.0 0.0 0.0 16.8 16.8 Pooled Plot
0.0115 0.7471 0.0 0.0 0.0 0.0 0.0 L = 1.046
0.0 0.2184 0.8911 0.0 0.0 0.0 0.0
0.0 0.0115 0.0990 0.7778 0.0 0.0 0.0
0.0 0.0 0.0099 0.2222 0.7813 0.0 0.0
0.0 0.0 0.0 0.0 0.1875 0.8723 0.0
0.0 0.0 0.0 0.0 0.0 0.0851 0.8810












Table 2-3. Size class distribution for density independent (DI) and density dependent (DD)
models after 100 yr.
Size Class Number of palms: DI Model Number of palms: DD Model
0 45729.6 4224.32
1 2888.3 189.26
2 3388.1 271.36
3 832.5 70.60
4 1028.4 104.84
5 964.7 113.14
6 526.9 77.80










Table 2-4. Adult (stage 5 & 6) transition probabilities. Matrix element a55 and a66 are adult
survival and element a65 is adult growth transition. Average of the death due to
harvest produces the adult harvest percent for the second harvesting scenario.


Original survival/growth
probability
0.8723
0.0851
0.8810


Death due to
natural causes
0.128
NA
0.119


Survival/growth
for =1.0
0.6489
0.0633
0.6554


Average
death due to
harvest
0.2234
0.0218
0.2256
0.2245


Matrix
element
a55
a65
a66
Average




















2 -0.1

0.05

-.i

2 3 4 5

Size Classes 6



A




0.25

0.2 as, Fecundity
0 -Stasis
0.15
0.1 --Growth
0.1

0.05

0
0 1 2 3 4 5 6
Size Classes


B

Figure 2-1. Elasticity for the M. flexuosa matrix population model. (A) the 7 x 7 transition
matrix, and (B) the three main vital rates (growth, stasis, fecundity).









3000Mauritia Palm Model
3000

2500

,2000

S1500

1000

500


0 100 200 300 400 500
Years

Figure 2-2. Density dependent model forM. flexuosa simulated over 500 yr. The population
illustrates an asymptotic growth rate as it reaches the carrying capacity (K).










Harvest
140 Intensity
i F-15%
120 F-20%
too100 F-30%

N 80 i-- F-50%
-- F-75%
60
E3 M-15%
40 -- M-20%
20 M-30%
-- M-50%
S--M-75%

Years

A

Figure 2-3. Four harvesting scenarios with various harvest frequencies and intensities. (A) five
different harvesting intensities at a frequency of every 5 yr, (B) five different
harvesting intensities at a frequency of every 10 yr, and (C) five different harvesting
intensities at a frequency of every 15 yr. (D) six different harvest intensities (only
females shown) with annual harvest.











140

120

100

80
N
60

40

20

0


82 91 10


Harvest
Intensity

- F-15%
- F-20%
F-30%
- F-50%
SF-75%
-- M-15%
- M-20%
M-30%
-- M-50%
-- M-75%


Years


Harvest
Intensity
- F-15%
-- F-20%
F-30%
-- F-50%
-- F-75%
-- M-15%
--M-20%
M-30%
S--M-50%
-e- M-75%


Years


C

Figure 2-3. Continued


19 28 37 46 55 64 73


1 10


140

120

100

N 80

60

40

20

0


. ....................
-d

;x
All










140
120
100
80
N 60

40
20
0


- l N f l)N Il


Years
D
Figure 2-3. Continued


Harvest
Intensity


-m-15%
--20%
25%
30%
- 40%
-- 50%


t



















140
120
100
80
N
60
40
20
0


Harvest Percents (Intensities)



Figure 2-4. The average number of female palms the year before harvesting over a 100 yr harvest
regime.


t15 Yr kreq.
~10 y r kreq.
~5 yr kreq.













125
120
115
110
CL 105
100
S95
90
85
80
1 501 1001 1501 -Mae
Male Palms
Years Female Palms


Figure 2-5. Harvesting 22.45 percent at a frequency of every 20 yr.


























E

o80

-0
E
z60



40



20
10 20 30 40 50 60 70 80
Year


Figure 2-6. Two harvest scenarios (both 75 percent at a frequency of every 10 yr) with density
independence (DI) and density dependence (DD).









CHAPTER 3
GENETIC ALGORIHTM OPTIMIZATION FOR DEMOGRAPHIC PARAMETER
CALIBRATION AND POPULATION TRAITS OF A HARVESTED TROPICAL
PALM

3.1 Introduction

3.1.1 South American Palms and Consequences of Wild Harvesting

Tropical palms are important for many values such as, maintaining ecological

diversity, providing economic gains and subsistence products, and for aesthetic value

(Bates 1988, Mejia 1988, Boom 1988, Anderson et al. 1991, Henderson 1994, Henderson

et al. 1995, Johnson 1999). South American tropical palms in particular are widely used

in local environments and exported to outside markets (Balick 1988, Parodi 1988, Kahn

& de Granville 1992, Campos and Ehringhaus 2003). The South American palm,

Mauritiaflexuosa, one of the most important palm species, has been widely studied

(Denevan & Treacy 1987, Kahn 1988, Padoch 1988, Bodmer et al. 1997, Carrera 2000,

Ponce et al. 2002, Coomes et al. 2004). This paper adds to the knowledge on theM.

flexuosa species. Simulation models are often used for managing harvested populations,

but calibration data are often quite limited. It is also difficult to fully understand the

dynamics of harvested palm populations based on short-term studies. I believe that

Genetic Algorithms can be used to improve the quality of calibration for harvested

populations such as those of Mauritiaflexuosa.

Some wild palm populations in the tropics are being destroyed and/or degraded due

to overly high economic utilization (Balick 1988, Johnson 1988, Peters et al. 1989a).

There has been a switch to domestication and cultivation, but for certain palm species,

including M. flexuosa, this switch is slow, poorly understood, or involves species-specific

difficulties. It is important to first understand the population dynamics of palm









populations that are being over-harvested in wild settings. Wild palm extraction is one of

the main process threatening local populations. Extraction is occurring throughout

Amazonia, but is observed to be high around the Iquitos and surrounding regions of Peru

specifically for the palm M. flexuosa (Padoch 1988, Vasquez & Gentry 1989). It is

important to understand the impact of harvesting fruit of M. flexuosa, a dioecious species,

in the Peruvian lowlands, which is destructively harvested by felling adult female trees.

A high level of wild leaf extraction is seen to unfavorably affect a dioecious understory

palm (Berry and Gorchov 2007). Commercial palms (Chamaedorea and Astrocaryum)

are exploited for products like seeds and leaves (biologically important components),

leading to unsustainable harvesting of local populations (Fonseca 1999, Mendoza and

Oyama 1999, Endress et al. 2004, Seibert 2004). Current simulation models of non-

timber forest product harvesting do not adequately represent population dynamics in the

context of multiple use forest management (Valle et al. 2007).

3.1.2 Matrix Modeling and Population Dynamics

Matrix population models have often been used for studying single species

populations (e.g., Crouse et al. 1987, Wootton & Bell 1992, Vantienderen 1995,

Silvertown 1996, Kaye and Pyke 2003). These models typically follow a stage-based

size class model (Lefkovitch 1965) or Leslie's age class model (1945), and have been

further developed in many studies (Caswell 1989, Morris & Doak 2002, Vandermeer &

Goldberg 2003). Many properties of tropical tree populations are difficult to accurately

measure (growth rates, response to density, regeneration rates) but important to

understand, especially in threatened or harvested species (i.e., M. flexuosa). Effective

management and conservation plans for a harvested palm depends on understanding

population dynamics and response to disturbances. Therefore, demographic parameters,









which make up population matrix models, must be understood in detail and accurately

represented. In chapter two of this thesis a study was performed using density dependent

matrix population models to simulate population dynamics ofM. flexuosa from a site in

Ecuador. Several sustainable harvesting scenarios were identified, which may be used as

a component in management plans for the exploited palm. Using simulation models as a

management tool clearly requires the best possible parameter estimates. This study is a

continuum of the previous population modeling chapter on M. flexuosa.

3.1.3 Parameter Calibration

It is difficult to estimate demographic parameters of many tropical species (Wood

1994, Hunter et al. 2000); particularly long lived tropical trees (Alvarez-Buylla et al.

1996). Past studies have focused on demographic stochasticity (Shaffer 1987, Durant and

Hardwood 1992) and environmental stochasticity (Lacy 1993, Kendall 1998, Caswell

2001). Sampling error can also affect the accuracy of projections and the simulated

changes in demographic process over time (Parysow and Tazik 2002, Picard et al. 2007).

Accurate estimation of parameters could even be a matter of concern in a population with

no significant demographic or environmental stochasticity. Examples of likely data

problems include short data collection time frames, poor identification methods, and

measurement error, some of which are found in this study. Although model parameters

typically have varying degrees of influence on model results (Hamby 1994, Janssen

1994), the entire set of demographic parameters interact to produce population dynamics.

Carefully calibrating only the most sensitive parameters may miss other parameters that

were very badly sampled, as well as higher dimension parameter interactions. Genetic

Algorithms are well suited to problems of high dimension optimization.









3.1.4 Introduction to Genetic Algorithms

Evolutionary programming has been used since the 1950's and 1960's, but John

Holland of University of Michigan popularized the genetic algorithm in 1975. Genetic

algorithms (GA) are now used in many disciplines, such as engineering, computer

science, biology and ecology. GAs are modeled after the biological paradigm of natural

selection and survival of the fitness in generations over time. GA's can be used as an

optimization algorithm that seeks to find solutions to multi-dimensional problems where

"fitness" is defined as a measure of closeness to the desired solution (Holland 1975, Koza

1992, Wang 1997, Mitchell and Taylor 1999). GA's are also considered global

algorithms because they search within a population, and then use biological frameworks

of gene passing, mutation, selection, and crossover. The use and development of

evolutionary programming is practical in solving a wide range of problems, including

ecosystem and biological applications (Cropper and Comerford 2005, Yao et al. 2006,

Liu et al. 2006, Termansen et al. 2006, Dreyfus-Leon and Chen 2007).

Using genetic algorithms to understand tropical forest dynamics is an emerging

technique. For example, parameterization with genetic algorithms has been used in a

simplified, aggregated forest model to understand logging cycles across a range of

tropical forest types and forest dynamics (Tietjen and Huth, 2006), and a genetic

algorithm has been used to estimate fecundity, carrying capacity, and seedling

demographic parameters for the palm Iriartea deltoidea (Cropper and Anderson 2004).

The key assumptions of our approach to parameter estimation with genetic algorithms are

that, 1) the observed size class distribution of the Ecuador population represents an

equilibrium population at carrying capacity with no history of harvest, 2) measurements

of palm height (the basis of size classification) are more accurate than estimates of









transition rates (which depend on height measurements), and 3) the local population is

mono-dominant with no significant competition from other plant species.

3.1.5 Objectives

In this study, I proposed;

1 To use genetic algorithms for parameter calibration of a population model of the M.
flexuosa palm. Calibrated parameters for the Ecuador palm population included;
A) seedling survival and growth parameters, B) the carrying capacity on a 1 hectare
plot of land, and C) the non-seedling demographic parameters (survival and
growth).

2 To compare the population distributions and demographic characteristics between a
harvested population (Peru) and a location where harvesting is minimal to none
(Ecuador).

3 To test the hypothesis that a plausible harvest history of the Peruvian palm
population can be found through the use of genetic algorithms. Optimization
parameters include harvest intensity, harvest frequency, length that harvest has
occurred, and carrying capacity for the Peru population.

3.2 Methods

3.2.1 Study Site: Ecuador

Data were collected in Ecuadorian Amazon from the Cuyabeno Faunal Reserve

(Figure 3-1). The reserve is managed by indigenous groups (mostly Siona and Secoya).

This 655,781-ha reserve is located between the San Miguel and Aguarico river basins.

Palm demographic data were collected over the span of two years from five plots (each

20m x 100m) located in seasonally flooded forests. In the first year of sampling all palms

in the five plots (seedlings and non-seedlings) were recorded for demographic data. In

the second year of sampling the same procedure was used, except seedling data were

recorded within ten subplots (5m x 5m) within each of the larger plots. The data

collection in Peru follows the same methods of data collection from the Ecuador study

site, and will be discussed in further detail.









3.2.2 Study Site: Peru

Mauritiaflexuosa demographic data were collected from sites in the lowland

forests of the Peruvian Amazon, in the department of Loreto, Peru during the summer of

2006. The field sites are approximately a 2-hour boat ride south of Iquitos, Peru on the

Amazon River and Tahuayo River (app. 90 miles). Specifically, field locations are

adjacent to the Tamshiyacu-Tahuayo Community Reserve (Figure 3-2). The

Tamshiyacu-Tahuayo Reserve is a 322,500ha protect area created by the Peruvian

government in 1991.

Palm data were collected from five plots in tropical forest swamps dominated by

M. flexuosa palms. Mauritiaflexuosa is the monodominant species in these oligarchic

forests called Aguajales. Three out of the five plots were in close proximity to rivers and

seasonally flooded, while the remaining two plots were in low lying locations that

remained partially flooded through out the year and surrounded by terra firme.

Demographic data were collected for each non-seedling palm in all five plots (20m x

100m). In plot 1 seedling counts were low, allowing for data to be recorded for each

seedling. In plots 2-5 seedling counts were high and subplots were created to estimate

seedling data. Seedling data were recorded within eight subplots (5m x 5m) within the

larger 20m x 100m plots. In each of the plots the demographic data collected consisted

of height measurements (actual for palms that could be reached, and estimated with a

clinometer for taller palms), leaf counts on seedlings and most juveniles, sex, leaf scars,

diameter breast height (DBH), and raceme counts on females. Spatial distance was also

measured between each palm to help construct a layout of the plots and location of palms

from each other.









3.2.3 Study Species Role in Peru

Mauritiaflexuosa is an economically and ecological important non-timber species

in the Peruvian Amazon (Padoch 1988, Peters et al. 1989b). The fruit ofM. flexuosa has

been an important product in the Iquitos market as far back as the mid-1980s, selling

approximately 300 sacks per day and experiencing "extreme rise" in the cost per sack

during times of fruit scarcity (Padoch 1988). The largest numbers of fruit are harvested

from the large oligarchic palm swamps along the Maranon, Ucayali, and Chambira rivers

(Peters et al. 1989a), making M. flexuosa one of the highest exploited fruit tree species in

Peru. While income from harvesting these palms can average to high amounts, the

female trees are cut down to retrieve the fruit from the tall palm, ending the production of

fruit from harvested palms. Since, over half the total fruit sold in Iquitos is from wild

harvested species (Vasquez and Gentry 1989), destructive harvesting methods are a

matter of concern.

The rise in "Aguajale" palm swamps dominated by males following harvest, leads

to a need for better management and conservation, possibly through increased knowledge

of population dynamics in palm swamps. It has been suggested that a switch to growing

M. flexuosa in agroforestry or homegardens plots is beneficial for wild stand management

(Vasquez and Gentry 1989, Bodmer et al. 1997). It is hypothesized, growing M. flexuosa

in agricultural settings will reduce use of destructive harvesting techniques, maintain

palm populations, and allow wildlife to continue foraging on palm fruits. The following

wildlife all consume M. flexuosa from most frequent consumption to least, lowland tapir

(Tapirus terrestris), white-lipped peccary (Tayassupecari), collared peccary (Tayassu

tajacu), gray brocket deer (Mazama gouazoubira), and red brocket deer (Mazama

americana) (Bodmer et al. 1989).









3.2.4 Palm Distribution and Matrix Model Development:

Stage-based matrix population models were used in the study. The development of

the matrix models for the Ecuador palm population was described in chapter two of this

research. The matrix models from Ecuador will be used as a basis for further analysis in

this chapter. The matrix model for palms populations in Ecuador consisted of 7

biological stages, based on size classes. Palms from Peru study sites were classified into

the same seven size classes based on height (Table 3-1) to be consistent with Ecuador

methods. Stages consist of 1 seedling, 4 juveniles, and 2 adult stages. The fecundity (fj)

for the Peru population was estimated with the same fecundity values used in Ecuador

(i.e. seedling survival value) due to lack of data. The established number of seedlings in

Peru at t+1 is also unknown; therefore the number of seedlings at tO was used as an

assumption to provide estimated values of fecundity.

3.2.5 GA Method Description

A genetic algorithm is a method that finds optimal solutions by mimicking the

process of evolution. A population of individuals evolves over time in order to reach a

desired goal or fitness function by the following procedure. 1) An initial population is

created by randomly assigning "genes" from a defined range. 2) A reproductive

generation cycle is run from the initial population with selective reproduction (offspring

being chosen), mutation, and crossover occurring in the generation cycle. 3) The

population of individuals is evaluated for "fitness". Individual solutions are represented

in the next generation proportionally to their fitness. 4) Iteration of generation cycle until

maximum fitness is met or until maximum iteration number is reached. During each

generation the genetic algorithm contains components for a fixed population size,

crossover and mutation rates, an acceptance or rejection criteria for optimal solution, and









time of iteration cutoff. This study defined fitness as the absolute deviation of the target

size-class distribution from the simulated size class distribution. The perfect solution

would have a fitness value of zero, indicating that each simulated size class was exactly

equal to the target number.

In this study problem-specific genetic algorithms were generated to find optimal

sets ofM. flexuosa demographic parameters and plausible harvesting scenarios.

Following Cropper and Anderson (2004), the first GA optimization was designed to

calibrate seedling parameters and estimate carrying capacity. The initial population was

created by randomly selecting seedling survival (stasis) probability from range 0.1 0.8

and carrying capacity from range 100.0 2000.0 palms hal-. The seedling growth

parameter was set using equation 3-1:

seedling growth = (1- stasis probability) x (3-1)

where x is a random value from 0.0-1.0. This equation was used because the sum

of the seedling growth and stasis probabilities cannot be greater than one. These two

seedling parameters along with a carry capacity parameter are assigned to

"chromosomes" in each individual in the population. The size of the population in this

GA was 500. The program was run for 25 generations with selection occurring in each

generation. This program's fitness goal was to match the observed Ecuador M. flexuosa

female distribution. The calibrated parameters were put into the new transition matrix

and produced a new simulated population distribution. Equation 3-2 evaluated the fitness

score for all GA optimizations in this study:

Fitness = X(abs(Ntargeti Nsimulatedi)) (3-2)









where Ntargeti are the size-specific palm numbers that are the goal for calibration

and Nsimulatedi are the size-specific palm numbers produced by the individual's

parameter set. A smaller difference is desired and indicates stronger population fitness.

The remaining GA optimizations used in the study were similar to the seedling and

carrying capacity optimization. The following GA was used to calibrate the observed

non-seedling demographic parameters (growth and survival) that make up the transition

matrix found in chapter one. There are thirteen non-seedling demographic parameters in

the palm population transition matrix. This optimization program created an initial

population by assigning random uniform parameters needed for calibration between zero

and one, for all thirteen demographic parameters. The demographic parameters for each

size class were normalized, if necessary, to prevent transition probabilities summing to

greater than one. Another set of calibrations used only eleven out of the thirteen values

(all six stasis values and all five 1-size class growth values) assuming that the rare 2-size

class transitions (only 2 observed) don't occur. If the sum of these three values is greater

than one then the parameters were normalized by dividing each parameter by the sum of

all parameters. Mortality is implicit and does not need to be normalized. For each size

class (1-6) only the stasis and growth parameters (or genes) were assigned to

"chromosomes". The size of the GA population is 1750 and ran for 75 generations. This

program's fitness goal was also to reach the observed Ecuador M. flexuosa female

distribution.

The last GA optimization focused on the Peru M. flexuosa population. The goal of

this GA was to find a plausible past harvest history on the Peru M. flexuosa palm

population, a location of intense female harvesting. I assumed that the unharvested









Ecuador population is the starting point for a harvesting regime that leads to the size class

distribution observed in Peru (the GA target distribution). The optimization initiated by

using the values in the observed Ecuador transition matrix as initial parameters. The GA

population was created with the following parameters to be optimized: harvest intensity

percent, harvest frequency in years, length of harvesting (years), and carrying capacity.

The value for the harvest intensity was randomly picked from 0.0-100.0%. The harvest

frequency was randomly selected from two separate ranges 1-40 yrs and 1-80 yrs. The

length of harvesting was randomly selected from two ranges 50-300 yrs, 100-500 yrs

respectively correlating with the two harvest frequencies. The carrying capacity for the

Peru population was randomly selected from multiple ranges 200-900, 300-1000, and

400-1000 non-seedling individuals per ha. The size of the GA population in this program

was 500 and ran for 25 generations A second round of GA optimizations to find the past

harvesting history of the Peru palm forests was ran using the optimal Ecuador

demographic parameters found in this study, in place of the observed demographic

parameters.

3.3 Results

3.3.1 Genetic Algorithms

The genetic algorithm (GA) used to calibrate the seedling survival and growth

parameters had an average fitness (difference between observed and simulated size class

distributions) of 46.67 (Figure 3-3). GAs cannot be guaranteed to find the global

optimum. The stochastic elements of initial parameter selection, mutation, and crossover

are needed to reduce the computer time needed to exhaustively evaluate the parameter

space. Multiple GA runs were used to evaluate the robustness of the solution; each run

scored approximately 46. The probabilities for seedling survival (matrix position AOO)









and seedling growth (matrix position A10) varied over a wide range (Table 3-2). The

values for carrying capacity in a Iha area were found to range between 346 and 374 non-

seedling palms (Table 3-2).

I found that the observed demographic parameters do not closely match the

observed size class distribution. The matrix population model using the observed

demographic data from the study sites in Ecuador simulated a size class distribution

equivalent to a fitness score of 67.03 (Figure 3-4). The transition probabilities (also

called demographic parameters) of the Ecuador and seedling GA results were not

consistent with the observed size class distribution. I next explored calibration of all

stasis and growth parameters (mortality is implicit) for each non-seedling size class.

These GA optimizations are unconstrained, except for the requirement that the sum of

size class probabilities cannot exceed one. The result for the unconstrained GA that

found a set of 13 optimal demographic parameters has a fitness score of 14.14, producing

a lambda of 1.007 (Figure 3-5). The unconstrained GA with 11 demographic parameters

(excluding the 2-size class growth parameters) has a fitness score of 5.07, producing a

lambda of 1.039 (Figure 3-6). Some of the optimal parameter values fell outside the

range of plot variation (Figure 3-7). The danger of optimizing a large set of unknowns is

finding values that match the target, but do not have biologically plausibility.

Optimization with values constrained to the observed range (Table 3-3) was used to

address this issue.

Six separate GA runs used the constrained parameter ranges. Three GA runs

optimized all 13 parameters, and three others did not include 2-size class growth

transition parameters. The three runs for optimizing all 13 demographic parameters have









fitness scores of 6.29, 9.07, and 7.19 (Figure 3-8). The three runs for optimizing

demographic parameters without the 2-size class growth transitions have scores of 7.69,

12.03, and 13.96 (Figure 3-9). In figure 3-7, 3-8 and 3-9 the "combined data" is the

values for the observed Ecuador stasis and growth parameters of the transition matrix

created in chapter one of this thesis. These data were based on pooling all of the

individual plot data. The best scoring run (Figure 3-10) optimizing all 13 demographic

parameters has a score of 6.29 and a lambda of 1.040. The best scoring run (Figure 3-11)

with no 2-size class growth parameters is 7.69, which has a lambda of 1.038. In figure 3-

10 and 3-11, I found that size class three and four have the largest differences between

the observed and simulated size class distributions. Figure 3-8 and 3-9 shows that size

class three and four also have the largest difference observed and simulated demographic

parameters.

The new transition parameters from the two best constrained GA optimizations

were compared to the empirical transition parameters (Table 3-4). The CAV6.29

(constrained, all values) GA parameter set produced stasis parameters (except size class

1) that are lower then the empirical stasis parameters. The same GA optimization also

shows that the growth parameters are generally greater than the empirical growth

parameters (except size class 1 and both size class 2 growth transitions). Similar results

are seen for the optimal parameters in the matrix with CNT 7.69 (constrained, no two-

size class transitions). In the CNT 7.69, the optimal demographic parameters have a

larger difference from the empirical demographic parameters, then the optimal

parameters in the CAV6.29 run.









Optimization of seedling parameters and carrying capacity was conducted a second

time using the new optimal demographic parameters from both unconstrained and

constrained GA versions. Four separate replicates were run in each of the four GA

versions to assist in accessing variation. Table 3-5 shows the new results of the optimal

seedling survival, seedling growth, and carrying capacity for the Ecuador population. All

of the replicates in the two unconstrained GA versions (score 14.14 and 5.07) as well as

in the two constrained GA versions (score 6.29 and 7.69) show seedling parameter values

which vary over a wide range. In each of the four GA versions, the four separate

replicates all produce a very similar fitness score to each other, showing that the seedling

parameters are insensitive to contributing to the number of individuals in the non-

seedling size classes. While all the new fitness scores are preferable, seedling

demographic values vary and show inconsistency in each of the four replicates in all four

GA versions, and seedling parameters are insensitive during GA optimization. There

should be little confidence that the GA is a useful tool for seedling parameter

optimization based when each run finds a greatly different local optimum.

3.3.2 Peru Size Class Distribution and Demographic Characteristics

At the Peruvian study site 198 non-seedling individuals were present in the Iha

area (seedling size class = 2342). The distribution of individuals shows the largest

amount of palms in size class 1, followed by size class 5, with the lowest amount of

palms in size class 2, 3, 4, and 6 (Table 3-1 and Figure 3-12). The total number of non-

seedling individuals in the Ecuador study site is 336 (seedling number were 260 and 1460

respectively during two years of sampling). The number of adult male and adult female

palms per ha area sampled in Peru is 54 and 23 respectively (Figure 3-13). The number

of adult male and adult female palms in Ecuador, where harvesting palms in minimal, is









54 and 35 respectively. The estimated average fecundity for females in the Peruvian

palm population is 18.2, with 5.2 for size class five and 31.2 for size class six. Size class

six has fewer reproductive females compared to size class five (3 to 18 respectively,

Table 3-1). The taller female palms in size class six are more likely to be felled for

retrieval of the M. flexuosa fruit. Further results of the Ecuador palm population

dynamics can be found in chapter 2.

Peru palm demographic data on number of leaf scars, DBH, and trunk height for

palm individuals in size class 3, 4, 5, and 6 can be found in table 6. Demographic data

were recorded for palms in all size classes, and in the juvenile and adult size classes

(three through six); data related to palm trunks is available. At size class three some

palms transitioned from multiple petioles to beginning to form a trunk. Palms in the

increasing size classes (4-6) have trunks formed. The number of leaf scars was highest

for palms in size class 5 (20-28m), with an average of 61.5 scars present on the trunk.

The tree diameter at breast height was largest for palms in size class 6 (>28m), with an

average of 99.2 cm. Palms are originally assigned into size classes based on their total

height (trunk height and leaf height). The average height of only trunks (not total height)

for pre-reproductive palms in size class three was 2.6m and in size class four was 9.0m

(Table 3-6). Between each size class there was approximately 6.5 7.5m difference in

average trunk height.

3.3.3 Genetic Algorithm: Harvest History for Peru M. flexuosa Palm Population

GA optimizations have been run to find plausible harvesting histories that could

lead from a population distribution observed in Ecuador to the distribution that is

currently seen in Peru. Although this technique cannot reconstruct actual harvest

histories, it may illustrate harvest regimes of realistic magnitude. The transition matrix









from the study site in Ecuador produced a lambda of 1.046 (a growing population

projection) and 336 non-seedling individuals per ha. It is assumed that Ecuador's

population demographic parameters and distribution of individuals are at a somewhat

stable, healthy state. The lambda for the population in Peru in unknown at this point, but

as reported there are 198 non-seedling individuals per ha. Six GA runs using the

observed Ecuador demographic parameters had fitness scores ranging from 62.8 to 135.4

(Table 3-7) and varying parameter results (harvesting percent, harvesting frequency,

harvest length, and fitness scores). In all six runs the carrying capacity value showed a

trend of reaching the lowest value allowed in the range. Harvest lengths were highly

variable and tended to be extreme values within the range. These optima represented

poor fits to the target and do not represent plausible harvesting regimes for transition

from the Ecuador to Peru size class distribution.

The GA-based optimal demographic parameters were used in a second round of

GA optimizations to find plausible harvest histories in Peru, using the same parameter

inputs. Each of the four optimal demographic parameter results (two unconstrained

trails: score 14.14 and 5.07, and two constrained trails: score 6.29 and 7.69) had six

separate GA runs for a total of 24 harvesting optimizations, which produced fitness

scores varying from 41.4 to 74.7 (Table 3-8). Harvest percent and harvest frequency

were the most variable; changing in each of the 24 runs. Typically the optimal carrying

capacity was found at the lowest end of the range possible, except for the six versions in

the GA with all 13 unconstrained demographic parameters. Another trend was that the

length of harvest is typically found at the highest end of the range, except for the six

versions in the GA with all 13 unconstrained demographic parameters.









3.4 Discussion


3.4.1 Genetic Algorithms

The first GA approach was to calibrate seedling survival and growth in the

transition matrix and carrying capacity for a palm population from Ecuador. As noted

earlier in this study, Cropper and Anderson (2004) successfully found the seedling

survival and growth parameters for the palm Iriartea deltoidea. Our study did not find

seedling survival and growth parameters that closely matched the observed Ecuador

population distribution. The seedling parameters found by the GA created a simulated

size class distribution that had a difference of 46.62 individuals from the observed

population. Furthermore, an assortment of seedling survival and growth transition values

repeatedly produced a similar population distribution for each size class. Seedling

parameters found by the GA were insensitive to matching non-seedling size classes with

the observed size classes. This led us to believe that other demographic parameters might

be poorly estimated. The carrying capacity found by the GA is similar to the observed

Ecuador carrying capacity.

Assuming that the Ecuador size class distribution was measured with less error than

the transition rates, GA optimization should lead to improved parameter estimates.

Separate runs of GAs were able to generate optimal non-seedling demographic

parameters that did match the observed population distribution. It was first found that the

empirical demographic parameters from the pooled data in the Ecuador study plots did a

relatively poor job of matching the observed Ecuador population distribution (a

difference of 67.03 individuals). Poorly estimated demographic parameters are most

likely a result of sampling error in this study. All four GAs that estimated optimal

demographic parameters produced a good fit to the fitness goal, the observed population









distribution. Interestingly, the unconstrained GA (with a difference of 14.14 individuals)

had an optimum matrix, which was not similar to the observed transition matrix, even

though the simulated and observed size class distributions were similar. The consistent

deviations of GA estimates of size classes three and four parameters from the observed

data may implicate these data as poorly sampled. In the observed data there were rare 2-

size class growth transition probabilities in size class 1 and 2. Only one palm in each size

class makes this rare 2-size class growth transition. The next GA assumes that there are

never these rare 2-size class growths. This GA produced demographic parameters that

had the best fitness (a summed difference of 5.07 individuals).

Optimal demographic parameters from the two previous GAs were a good fit to the

observed size class distribution, but optimal stasis and growth parameters fell outside the

observed range of demographic parameters. By constraining the optimal parameters to

within the range of observed parameters, more realistic parameters can be found which

still have a strong fitness score. Usually it is not beneficial to constrain initial parameters

in a GA, but results from the unconstrained GAs produced stasis and growth parameters

in size class 1, 3, and 4 that were unlikely. Both constrained GAs create good fits to the

observed distribution, with similar fitness scores (6.29 and 7.69). Abandoning the 2-size

class growth transition does not notably affect the GA optimizations. Multiple runs of

the same GA are recommended because GA optimizations can get "stuck" in a local

parameters space minimum.

Since the GA technique was able to calibrate the non-seedling demographic

parameters, it was beneficial to use these new parameters to re-estimate the seedling

survival and growth parameters. Using the optimal demographic parameters did find









seedling parameters that produced a size class distribution that matched the observed

population distribution, but as seen before the seedling parameters varied over a wide

range in each separate trial. It would be premature to conclude that seedling survival is

of little demographic importance in these populations, but variation in seedling survival

and growth may not contribute significantly to the size class distribution of larger palms.

3.4.2 Peru Size Class Distribution and Demographic Characteristics

The ratio of adult males to female palms in Peru implies that removal of female

palms has been occurring. The main target of female palm removal is size class six,

which contains the tallest palms and is assumed to be the most difficult to climb. This

removal of adult female palms can alter the seedling regeneration, density dependence,

and interactions with other species. Comparing the distribution of M flexuosa palms in

Ecuador and Peru displays the impact of harvesting in Peru and consequently the

eradicate number of individuals in each size class. This study has shown there is

difficulty in estimating demographic transition values in Ecuador, leading to the use of a

GA to calibrate parameters, it is also predicted that the difficulty will be just as

challenging if not more for the Peru population.

Leaf scars on palms are one method to estimate the rate at which palms are

growing, as well as the length in time palms have been growing. It is predicted that the

palms in the larger size class six are growing at a fast rate, presumably to reach the

canopy and become emergent. Size class six M. flexuosa have on average fewer leaf

scars than size class five M. flexuosa palms, and may indicate growing at a faster rate

than shorter M flexuosa palms. It is also interesting to look into the difference in trunk

height between size classes. The large increase in trunk height from size class three to

size class four, (as well as into size class five), might suggest that palm growth is rapid in









late juvenile and possibly early reproductive stages. This coincides with data collected

on palms in Ecuador (see second chapter). The Ecuador transition matrix shows a high

growth probability in size class three (although GA parameter estimates indicate that the

observed rate could be an overestimate). The relatively low numbers in size classes three

and four may also indicate a rapid growth to the adult sizes.

3.4.3 Genetic Algorithm: Peru M. flexuosa Palm Population

Estimating the harvesting history and carrying capacity of the Peruvian palm

population was challenging. Our study did not find harvesting values that closely

matched the observed Peru size class distribution. There are many combinations of

harvesting parameters that could have occurred in the past to produce the observed

population distribution. Consequently, the GA technique was not able to provide

plausible levels of prior palm removal in Peru. Reasons might include: 1) the Peru

population has different demography (survival, growth, fecundity) than Ecuador's

population and 2) the actual history of harvest was not regular and uniform. Estimating

the optimal carrying capacity was also a challenge, but it is possible that the carrying

capacity in Peru is lower than observed in other M. flexuosa populations, because the GA

generally converges on lowest carrying capacity possible. Through communication with

local Peruvians and knowledge of past area history, we know that female palm harvesting

has occurred in our area of data collection.

3.5 Conclusions

Genetic algorithms may be useful for calibrating demographic parameters in a

matrix model. Constraining the demographic parameters to be chosen within a realistic

range resulted in the best procedure. Usually GA initial search parameters are limited

when they are constrained, providing lower fitness results than unconstrained GAs, but









that was not the case in this study. The demographic data showed that this particular

palm population has rare transitions (two individuals grew two size classes in one time

step). I found that excluding the rare, two size class growth transitions did not strongly

affect the GA optimizations. These large, rare transitions and other vital rates might have

been incorrectly recorded due to sampling error. Sampling error is a common problem in

population data collection. This study found that sampling error (specifically in

estimating stasis parameters) could affect the accuracy of transition matrix models, while

rare growth transitions do not have an effect.

While a previous GA has estimated seedling survival and growth parameters for a

tropical palm, this study was unable to estimate consistent seedling parameters that

matched the non-seedling population distribution. In this study, the value of seedling

survival and growth parameters for the Ecuador palm population is insensitive to

optimization. The recorded palm data from Peru does show that the population is

experiencing loss of females due to harvesting. This study was also unable to accurately

estimate the harvesting trends that have occurred in the past to produce the observed Peru

study site distribution. Palm removals in wild locations in Peru are likely to continue in

the future, until there is a full switch to agricultural gardens ofM. flexuosa. Accurately

understanding demographic parameters through the use of parameter calibration is greatly

needed for management of harvesting or species recovery and restoration efforts.











Table 3-1. M. flexuosa population distribution, for palms in a Iha area, from Peru and
Ecuador, as well as the number of male and female palms in each size class
from both locations. (Palms generally become reproductive at size class 5, but
in Peru some palms were seen to become reproductive in size class 4).
Peru Peru Peru Ecuador Ecuador Ecuador
Size Classes N(t) 2006 Males Females N Males Females
0 <1.0 2342.0 1171.0 1171.0 260.0 130.0 130.0
1 1.01-3.0 72.0 36.0 36.0 87.0 43.5 43.5
2 3.01-6.0 22.0 11.0 11.0 101.0 50.5 50.5
3 6.01-10.0 10.0 5.0 5.0 27.0 13.5 13.5
4 10.01-20.0 20.0 10.0 10.0 32.0 16.0 16.0
5 20.01-28.0 60.0 41.0 18.0 47.0 29.0 18.0
6 >28.01 14.0 11.0 3.0 42.0 25.0 17.0

Total 198.0 54.0a 23.0a 336.0 54.0a 35.0a
a Total number of only reproductive individuals.










Table 3-2. Optimal values for two seedling parameters (seedling stasis probability
(matrix position AOO), seedling growth probability (matrix position A10)),
and for Ecuador's carrying capacity (K) in a Iha area, using observed
demographic data.
Seedling and K runs with observed data
K AOO A10 Opt Score
348 0.5899 0.0050 46.766
346 0.1734 0.7178 46.624
374 0.0257 0.0056 46.617










Table 3-3. Observed range of the 13 non-seedling demographic transition probabilities,
found from data collected at 5 separate study plots in Ecuador.
Ecuador Plot Observations
Matrix
position Low range High range
1 All 0.50 0.9290
2 A21 0.07 0.5000
3 A22 0.62 0.9600
4 A31 0.00 0.0115
5 A32 0.04 0.3800
6 A33 0.66 0.8500
7 A42 0.00 0.0099
8 A43 0.14 0.3300
9 A44 0.50 0.8800
10 A54 0.00 0.5000
11 A55 0.67 1.0000
12 A65 0.00 0.3300
13 A66 0.67 0.9230










Table 3-4. Transition matrices for 1) the observed pooled data in Ecuador, 2) GA
optimization for all 13 demographic parameters, with constraints on
parameters, and 3) GA optimization for all demographic parameters expect 2
size class growth transitions, with constraints on parameters.
Observed transition values
Seedlings Young Juveniles Old Juveniles Adult
<1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m
0.4923 0.0 0.0 0.0 0.0 16.8 16.8
0.0115 0.7471 0.0 0.0 0.0 0.0 0.0
0.0 0.2184 0.8911 0.0 0.0 0.0 0.0
0.0 0.0115 0.0990 0.7778 0.0 0.0 0.0
0.0 0.0 0.0099 0.2222 0.7813 0.0 0.0
0.0 0.0 0.0 0.0 0.1875 0.8723 0.0
0.0 0.0 0.0 0.0 0.0 0.0851 0.8810



Score 6.29 Optimal GA values all demographic parameters
Seedlings Young Juveniles Old Juveniles Adult
<1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m
0.4923 0.0 0.0 0.0 0.0 16.8 16.8
0.0115 0.8204 0.0 0.0 0.0 0.0 0.0
0.0 0.1700 0.8536 0.0 0.0 0.0 0.0
0.0 0.0077 0.1276 0.6440 0.0 0.0 0.0
0.0 0.0 0.0059 0.3171 0.6040 0.000 0.0
0.0 0.0 0.0 0.0 0.3450 0.8150 0.0
0.0 0.0 0.0 0.0 0.0 0.1310 0.8460



Score 7.69 Optimal GA values no 2 size class transition parameters
Seedlings Young Juveniles Old Juveniles Adult
<1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m
0.4923 0.0 0.0 0.0 0.0 16.8 16.8
0.0115 0.8210 0.0 0.0 0.0 0.0 0.0
0.0 0.1590 0.8602 0.0 0.0 0.0 0.0
0.0 0.0 0.1389 0.6234 0.0 0.0 0.0
0.0 0.0 0.0 0.3098 0.6457 0.000 0.0
0.0 0.0 0.0 0.0 0.3295 0.8250 0.0
0.0 0.0 0.0 0.0 0.0 0.1698 0.7800










Table 3-5. Optimal values for two seedling parameters, seedling stasis probability (matrix
position AOO), seedling growth probability (matrix position A10), and for
Ecuador's carrying capacity (K) in a Iha area.


Results from using unconstrained parameters
All Transitions (14.14)
K AOO A10 Opt Score
380 0.03061 0.77135 14.193
380 0.13129 0.82250 14.193
1660 0.53000 0.00971 13.870
379 0.11627 0.51079 14.252


Results from using constrained parameters
All Transitions (6.29)
K AOO A10 Opt Score
368 0.16995 0.19438 6.225
475 0.76935 0.00201 6.362
369 0.23126 0.00898 6.212
370 0.31195 0.00676 6.210


No 2-size Class Transitions (5.07)
K AOO A10
350 0.4341 0.00507
350 0.4931 0.00463
348 0.1786 0.00814
430 0.7700 0.00173


No 2-size Class Transitions (7.69)
K AOO A10
361 0.64787 0.13415
362 0.63258 0.00407
361 0.10501 0.89291
361 0.17342 0.80883


Opt Score
5.008
5.008
5.214
4.958


Opt Score
7.674
7.683
7.674
7.674











Table 3-6. Demographic traits for the Peru population in size classes 3-6 (palms that have
developed trunks).


Pre-reproductive Juveniles
Size Class 3 Size Class 4


Reproductive Adults
Size Class 5 Size Class 6


Avg. # of Leaf Scars na 29.4 61.5 60.4
Avg. DBH (cm) na 84.2 86.6 99.2
Avg. Trk. Height (m) 2.6 9.0 16.5 24.2












Table 3-7. GA estimates of harvest regimes consistent with the observed size class distribution.
RESULTS USING OBSERVED DEMOGRAPHIC PARAMETERS


harvest
percent
0.0-100.0
0.0-100.0


Parameter Inputs
harvest
frequency harvest
(yr) length (yr)
1.0-41.0 50-301
1.0-81.0 100-501


0.0-100.0 1.0-41.0 50-301
0.0-100.0 1.0-81.0 100-501

0.0-100.0 1.0-41.0 50-301
0.0-100.0 1.0-81.0 100-501


carrying
capacity
400-1000
400-1000

300-1000
300-1000


200-900
200-900


harvest
percent
0.74
0.42


0.49
0.01

0.70
0.27


Parameter Outputs
harvest
frequency harves
(vr) length (y


31.0
21.0


t
T)


50.0
101.0

300.0
500.0


6.0 300.0


79.0


482.0


carrying
capacity
400.0
400.0

300.0
300.0


opt
score
130.8
135.4

99.7
99.7


200.0
200.0


62.8
62.8












Table 3-8. Peru's harvesting history found using separate GAs which uses the four sets of Ecuador optimal demographic parameters
to reach Peru's observed population distribution. Optimization found harvest percent, harvest frequency, length harvesting
has occurred, and carrying capacity.
RESULTS USING CAV 6.29 (CONSTRAINED, ALL VALUES) OPTIMAL DEMOGRAPHIC PARAMETERS
Parameter Inputs Parameter Outputs
harvest harvest
harvest frequency harvest carrying harvest frequency harvest carrying opt
percent (yr) length (yr) capacity percent (yr) length (yr) capacity score
0.0-100.0 1.0-41.0 50-301 400-1000 0.71 27.0 300.0 400.0 59.9
0.0-100.0 1.0-81.0 100-501 400-1000 0.61 1.0 414.0 400.0 59.9

0.0-100.0 1.0-41.0 50-301 300-1000 0.56 23.0 300.0 300.0 48.1
0.0-100.0 1.0-81.0 100-501 300-1000 0.14 54.0 429.0 300.0 48.1

0.0-100.0 1.0-41.0 50-301 200-900 0.42 37.0 300.0 200.0 47.0
0.0-100.0 1.0-81.0 100-501 200-900 0.46 45.0 451.0 200.0 47.0



RESULTS USING CNT 7.69 (CONSTRAINED, NO TWO SIZE-CLASS TRANSITIONS) OPTIMAL DEMOGRAPHIC PARAMETERS
Parameter Inputs Parameter Outputs
harvest harvest
harvest frequency harvest carrying harvest frequency harvest carrying opt
percent (yr) length (yr) capacity percent (yr) length (yr) capacity score
0.0-100.0 1.0-41.0 50-301 400-1000 0.39 18.0 300.0 400.0 55.8
0.0-100.0 1.0-81.0 100-501 400-1000 0.29 36.0 462.0 400.0 55.8

0.0-100.0 1.0-41.0 50-301 300-1000 0.77 19.0 300.0 300.0 45.8
0.0-100.0 1.0-81.0 100-501 300-1000 0.61 56.0 444.0 300.0 45.8

0.0-100.0 1.0-41.0 50-301 200-900 0.65 36.0 297.0 200.0 45.5
0.0-100.0 1.0-81.0 100-501 200-900 0.14 72.0 459.0 200.0 45.5













Table 3-8. Continued


RESULTS USING UCNT 5.07 (UNCONSTRAINED, NO TWO SIZE-CLASS TRANSITIONS) OPTIMAL DEMOGRAPHIC PARAMETERS
Parameter Inputs Parameter Outputs
harvest harvest
harvest frequency harvest carrying harvest frequency harvest carrying opt
percent (yr) length (yr) capacity percent (yr) length (yr) capacity score
0.0-100.0 1.0-41.0 50-301 400-1000 0.86 34.0 300.0 400.0 74.7
0.0-100.0 1.0-81.0 100-501 400-1000 0.63 1.0 469.0 400.0 74.7

0.0-100.0 1.0-41.0 50-301 300-1000 0.59 17.0 300.0 300.0 48.5
0.0-100.0 1.0-81.0 100-501 300-1000 0.44 80.0 491.0 300.0 48.5

0.0-100.0 1.0-41.0 50-301 200-900 0.51 11.0 300.0 200.0 46.4
0.0-100.0 1.0-81.0 100-501 200-900 0.51 10.0 499.0 200.0 46.4



RESULTS USING UCAV 14.14 (UNCONSTRAINED, ALL VALUES) OPTIMAL DEMOGRAPHIC PARAMETERS
Parameter Inputs Parameter Outputs
harvest harvest
harvest frequency harvest carrying harvest frequency harvest carrying opt
percent (yr) length (yr) capacity percent (yr) length (yr) capacity score
0.0-100.0 1.0-41.0 50-301 400-1000 0.36 23.0 50.0 999.0 41.4
0.0-100.0 1.0-81.0 100-501 400-1000 0.8 56.0 100.0 999.0 45.0

0.0-100.0 1.0-41.0 50-301 300-1000 0.38 35.0 50.0 999.0 41.4
0.0-100.0 1.0-81.0 100-501 300-1000 0.29 69.0 101.0 998.0 45.1

0.0-100.0 1.0-41.0 50-301 200-900 0.72 34.0 50.0 896.0 42.3
0.0-100.0 1.0-81.0 100-501 200-900 0.25 57.0 102.0 897.0 45.9






















S--- -



~~ci
*- / -- :4 "

.. .t -





Flj.,n
.. 2. "7 -- -,--
,-. K.I ,,,r ECUADOR

.. ....r.
." ,. .. _.. ..-








i.. 4 -- -,


,, "" n) i 'i'D g .ni r" --"
.-- tt, I *O ,- .i,-. t,,- .


:I :4
... iu"* .- .1 -_
*f 1 ,[ ./ -t .\ *,, k : -







,,. ...... I *-, _. -.
; "rrt A. !
41," ;-, 7. ..,J ~-,f3~ --tc ,
-r 1 2500000 ,<


-.a '11 / */ fe'' S&


... .. *.t 1 -

r,
/^i .". .<, *'} & \ S
1/ i- ss
*e ".,. ', ca. Jna
'~ swe


:i
1
t
4,
/


a


O~an


, .


Figure 3-1. Map of study site in Ecuador. Cuyabeno Faunal Reserve is located in the

north-eastern section of Ecuador in the highlighted area. (Source:

http://www.ecuaworld.com/map_of ecuador.htm, last accessed July 25,

2007).


L.pn~oys~t
(r~ULnr~nrm


M


rx


hi

In


jm" .,-I












Study site along Tahuayo River,
adjacent to Tamshiyacu-
Tahuayo Communal Reserve.


Figure 3-2. Map of study site in Peru. (Source:
http://www.micktravels.com/peru/images/perumap.jpg, last accessed July 22,
2007).












60


50


40


Z 30


Simulated
SObserved


3 4
Size Class


Figure 3-3. Genetic algorithm simulated (red bars) and observed distribution (blue bars) for the
Ecuador palm population after running a GA to find optimal seedling survival and
growth parameters using the observed transition parameters. Fitness score for this GA
is 46.67, found by ((X(abs(observed distribution simulated distribution)).






































Size Class
Size Class


Figure 3-4. Genetic algorithm simulated and observed distribution for the Ecuador palm
population after running a GA using the observed transition parameters and
evaluating how well it matches the observed population distribution. Fitness score for
this GA is 67.03, found by ((X(abs(observed distribution simulated distribution)).


I r


O Simulated
S observed






















z 30


20






1 2 3 4 5 6 7
Size Class

Figure 3-5. Genetic algorithm simulated and observed distribution for the Ecuador palm
population after running an unconstrained GA to optimize all non-seedling
demographic parameters in the transition matrix. Fitness score for this GA is 14.14,
found by ((X(abs(observed distribution simulated distribution)).






























Size Class


Figure 3-6. Genetic algorithm simulated and observed distribution for the Ecuador palm
population after running an unconstrained GA to optimize non-seedling stasis and
growth parameters in the transition matrix (two size class growth transitions not
included). Fitness score for this GA is 5.07, found by ((X(abs(observed distribution
simulated distribution)).
















S


> 1

0.8

S0.6
.o
' 0.4
I0.2
0.2

0


I


Size Classes


Stasis and growth demographic points generated from an unconstrained GA. The red
lines in both figures A and B, are the low and high ranges of possible demographic
points measured from the five plots in Ecuador. (A) Demographic data of stasis
transition parameters for three separate trials, 1) the combined data from the
observed study plots, 2) the unconstrained GA run with all 13 demographic
parameters, and 3) the unconstrained GA run without the 2 size class growth
parameters. (B) Demographic data of growth transition parameters for the same
three separate trials.


1 2 3 4 5 6
Size Classes











*S
N


0.6

S0.5

0.4
I-
S0.3

'V 0.2

- 0.1

0


Figure 3-7.


-Low range

-High Range

Combined data

D GA optimum
14.14
GA optimum
5.07









- Low range

-High range

Combined
data
GA optimum
14.14
GA optimum
5.07














Low range
0.8 High range

Combined
S0.6 data
I-W GA optimum
0.4 -6.29
0 GA optimum
9.07
0.2 -- GA optimum
7.19


1 2 3 4 5 6
Size Class

A
0.6

0.5 -- Low range
0.4 High range

S Combined
S0.3 Data
S. -M- GA optimum
0.2 6.29
-*- GA optimum
9.07
0.1 -*- GA optimum
7.19
0
0 1 2 3 4 5 6
Size Class

B
Figure 3-8. Stasis and growth demographic points generated from a constrained GA. The red
lines in both figures A and B, are the low and high ranges of possible demographic
points measured from the five plots in Ecuador. (A) Demographic data of stasis
transition parameters for the combined data from the observed study plots, and three
separate constrained GA trials that calibrate estimates of all 13 demographic
parameters. (B) Demographic data of growth transition parameters for the combined
data from the observed study plots, and the same three separate trials











1.2

1 Low range
0.8 S High range
SCombined Data
S -0.6 -- GA optimum
0.4 7.69
-- GA optimum
12.03
0.2 --GA optimum
13.96
0
0 ---------------------
1 2 3 4 5 6
Size Class

A

0.6

0.5
0.5- Low range

S0.4 -High range
2 Combined
S03 Data
0 -- GA optimum
0.2 7.69
i-*-- GA optimum
12.03
0.1 -*- GA optimum
13.96


0 1 2 3 4 5 6

Size Class

B
Figure 3-9. Stasis and growth demographic points generated from a constrained GA. The red
lines in both figures A and B, are the low and high ranges of possible demographic
points measured from the five plots in Ecuador. (A) Demographic data of stasis
transition parameters for the combined data from the observed study plots, and three
separate constrained GA trials that calibrate estimates of demographic parameters
without the 2 size class growths. (B) Demographic data of growth transition
parameters for the combined data from the observed study plots, and the same three
separate trials.






























Size Class


Figure 3-10. Simulated output of the best constrained GA run with all 13 demographic
parameters. Simulated and observed distribution for the Ecuador palm population
after running a GA to optimize all non-seedling demographic parameters in the
transition matrix. Fitness score for this GA is 6.29 found by ((X(abs(observed
distribution simulated distribution)).






















z 30


20


10



1 2 3 4 5 6 7
Size Class

Figure 3-11. Simulated output of the best constrained GA run with demographic parameters that
do not include 2 size class growths. Simulated and observed distribution for the
Ecuador palm population after running a GA to optimize all stasis and 1 size class
growth non-seedling demographic parameters in the transition matrix. Fitness score
for this GA is 7.69 found by ((C(abs(observed distribution simulated distribution)).








120
100
80
Z 60
40
20
0


M


Figure 3-12. M. flexuosa population distribution for palm populations in a lha area in Peru and
Ecuador (seedling, size class zero, not included).


Peru
Ecuador


Q/


3 4
Size Class















50

40
U Peru
z 30 U Ecuador

20

10


Male Female AMg. Fecundity


Figure 3-13. Distribution of male vs. female palms and estimated, averaged fecundity values
from Peru and Ecuador.









CHAPTER 4
SUMMARY

4.1 Applicability

This research has potential use for creation of Mauritiaflexuosa management plans that

can be applied to the studied Ecuadorian palm population. Forest-dwelling people who utilize

M. flexuosa can use the results from the harvesting simulations for specifically the examined

Ecuador population. Multiple communities who harvest wild M. flexuosa from the same

populations will need to create collaborative harvesting plans that meet all stakeholders' needs as

well as abide by sustainable harvesting limits proposed in this research. It is the hopes of this

author that these methods can also be applied to M. flexuosa palm populations in all parts of the

Amazon. To do so, specific population dynamics such as transition probabilities and growth rate

will have to be estimated for populations in separate locations. Then similar methods of

development for modeling sustainable harvesting scenarios can be applied. This study is also

applicable to other harvested palm species through the tropics.

The results found from the genetic algorithm (GA) optimization conclude that matrix

model parameters can be calibrated to find optimal demographic parameters. The GA

optimizations in this study have applicability to aid in parameterization of current and future

matrix population models that are developed with sampling error. Accurate matrix population

models can be applied to improvement of population management plans.

4.2 Future for M. flexuosa

It is difficult to predict the exact future for a species, but it is estimated that fruit from M

flexuosa will continue to be a marketable resource. In Peru there is a switch from harvesting

palms in the wild, to growing M. flexuosa in gardens and small agricultural plots. It is predicted

that this palm could become a domesticated crop in other Amazon locations and countries. Data









collected on palms grown in homegardens in Peru show that palms mature at a shorter height and

in a faster time span (Figure A-i). Data collected on juvenile M flexuosa in homegardens also

show that the number of petioles is on average higher than palms located in wild populations

(Figure A-2). Palms that are maintained in gardens with initial weeding, spacing, and some

maintenance can develop into each size class at a faster rate then seen in the wild (Figure A-3).

This data shows that M. flexuosa has the potential to successfully be domesticated.

4.3 Future Research

To fully understand the switch to growing M. flexuosa as a cultivated palm, crop evolution

and genetics should be studied for the species. There is a potential that a genetic selection is

already occurring for choosing dwarf palms. Agricultural research, such as planting season,

intercropping management, plant nutrition, and disease and pest management, should be

considered for this species before it goes into large-scale tropical crop production. Future

research on understanding the population dynamics of this species is still needed. For example,

each size class's role in density dependence should be further understood. Fecundity rates for

female palms during different stages of population equilibrium and non-equilibrium should be

understood in more detail. A prompt future study should use the optimal transition matrices

containing optimal demographic parameters to immediately re-estimate sustainable harvesting

scenarios for Ecuador populations. It is proposed that the demographic parameters found by

GA's in this study should estimate more accurate harvesting regimes.









APPENDIX A
PERU GARDEN DATA FOR MAURITIA FLEXUOSA

Data collected from three separate homegardens in the Peruvian Amazon show the

difference between palms grown in gardens and palms in wild locations. This difference is seen

in palm height, number of petioles, and the size of petiole sheaths. A main difference is that

cultivated palms become mature and reproductive at a shorter height. This is an important

process for harvesting fruit in a non-destructive manner. I believe more data on cultivated M.

flexuosa is needed to understand the difference between palms growing in the wild and palms in

gardens. In Figure A-i the following is the number measured (N) for each category of palms.

Wild population: 76, 12, and 36 for young juveniles, old juveniles, and adults respectively.

Garden population: 104, 26, and 11 for young juveniles, old juveniles, and adults respectively.

Seedlings were not measured in garden locations. In Figure A-2 the following is the number

measured (N) for each category of palms. Smaller juveniles: 34 and 32, respectively for garden

palms and wild palms. Larger juveniles: 70 and 50, respectively for garden palms and wild

palms.












25
20 M WIld population
E 15 M Garden population
i 10 -
5-
0
Seedling Young Juv. Old Juv. Adult
Palm Stages


Figure A-i. Average height (m) forM. flexuosa palms in the seedling stage, young juvenile
stage, old juvenile stage, and adult (reproductive) stage; from palms sampled in wild
population and gardens in Peru.


pu .u
Garden height Wild pop.
(m) height (m)


Garden
petiole count


* Smaller Juveniles

* Larger Juveniles


Wild pop.
petiole count


Figure A-2. Comparison of average palm height and average number of petioles, for juvenile M.
flexuosa located in gardens and wild populations (in Peru).


8.00
* 7.00
o 6.00
- 5.00
o
.2
, 4.00
3.00
S2.00
" 1.00
0.00

















































Figure A-3. M. flexuosa palms in Peru homegardens. (A) Picture of juvenile (pre-reproductive)
M. flexuosa palms in a homegarden. (B) Picture of dwarf, reproductive female palm.
Both pictures were taken by Dr. Jim Penn in 2006.









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BIOGRAPHICAL SKETCH

Jennifer grew up in the wooded area of Douglasville, Georgia, a suburb of Atlanta. Her

parents always encouraged her to play and explore outside, and it was through this

encouragement that she developed a love for the interactions in the forested environment around

her. In her early education she was always excited to read many books and learn about anything

related to science. From a young age she knew that she wanted to get a higher education in the

biological sciences and hopefully become a scientist at some point. Jennifer's father, being a

physicist had a large influence on her. Jennifer graduated high school with a 4.0 GPA and was

valedictorian. Her next stop on her educational path was Emory University in Atlanta, GA in

2000.

At Emory University Jennifer majored in environmental studies and minored in

anthropology. Her classes ranged between many sub-disciplines in environmental education,

including classes in geology, earth systems dynamics, behavioral ecology, and tropical ecology.

The summer before her junior year made the largest impact on her decision for future path of

studies. Jennifer was accepted into the School for Field Studies and traveled to Queensland,

Australia where she took a field course in tropical restoration. During this trip she partially

worked on a 5-year project that focused on tropical corridor construction in the rainforests of

northern Australia. Upon her return to Emory University and Atlanta, she began an internship at

the Atlanta Botanical Gardens working with neo-tropical plants, X 7pe'/he% She wanted to learn

anything she could about tropical plants and tropical ecology. During Jennifer's time at Emory

University she also took a field course that offered a trip to Costa Rica to learn about its

environment. After her four years at Emory University, she next enrolled at University of

Florida in the Interdisciplinary Ecology program in the School of Natural Resources and

Environment.









At University of Florida Jennifer worked under the guidance and leadership of Dr. Wendell

P. Cropper Jr. in the School of Forest Resources and Conservation. She considered her graduate

studies to have two different concentrations, 1) forest ecology and 2) tropical conservation and

development. During her 2 12 years as a masters student at University of Florida, one of her

biggest moments was conducting field research in the Peruvian Amazon. This was a big step for

Jennifer as a researcher and helped her develop field data collection experience. Another large

moment for her was presenting at the 2006 Ecological Society of American annual meeting, and

at various other conferences and meetings. Jennifer's classes and work at University of Florida

have been worthwhile and a good learning experience. After finishing her research and

graduating with a master's degree, she considers herself a tropical forest ecologist who focuses

on population and simulation modeling. It is with the help and guidance of her advisor,

committee, fellow graduate students, and especially her family that she has gotten to where she is

today.





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1 POPULATION DYNAMICS OF THE AMAZONIAN PALM Mauritia flexuosa : MODEL DEVELOPMENT AND SIMULATION ANALYSIS By JENNIFER A. HOLM A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2007

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2 2007 Jennifer A. Holm

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3 To my family who encouraged me at a young ag e, to keep striving for academic knowledge, and to my friends

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4 ACKNOWLEDGMENTS I gratefully thank my supervisory committ ee, Dr. Kainer and Dr. Bruna, and most importantly my committee chair, Dr. Wendell P. Cropper Jr. for their time and effort. I acknowledge the School of Natural Resources and Conservation, the School of Forest Resources and Conservation, and the Tropical Conservation and Development Program, the United States Forest Service, and the Fulbrigh t Scholar Program for funding and guidance. Data collection in Ecuador was conducted with the help from Dr. Christopher Miller, Drs. Eduardo Asanza and Ana Cristina Sosa, Joaquin Salazar, and all the Siona people of Cuyabeno Faunal Reserve. Data collected in Peru was conducted with the help from Weninger Pinedo Fl ores, Exiles Guerra, Gerardo Brtiz, Dr. Jim Penn, and with the genero sity of Paul and Dolly Beaver of the Tahuayo Lodge. Lastly, I would like to thank my pa rents for their suppor t through my education experience, Heather, Chris, friend s, and fellow graduate students.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES................................................................................................................ .........8 ABSTRACT....................................................................................................................... ............10 CHAPTER 1 INTRODUCTION..................................................................................................................12 2 POPULATION DYNAMICS OF THE DIOECIOUS AMAZONIAN PALM Mauritia flexuosa : SIMULATION ANALYSIS OF SUSTAINABLE HARVESTING......................14 2.1 Introduction...................................................................................................................14 2.2 Methods........................................................................................................................ .17 2.2.1 Study Site..........................................................................................................17 2.2.2 Study Species....................................................................................................17 2.2.3 Data Collection.................................................................................................18 2.2.4 Matrix Model Development and Parameter Estimation....................................19 2.3 Results........................................................................................................................ ...22 2.3.1 Density Dependence..........................................................................................22 2.3.2 Sustainable Harvest Scenarios..........................................................................23 2.4 Discussion.....................................................................................................................25 2.4.1 Sustainable Harvest Scenarios..........................................................................25 2.4.2 Implications for Management...........................................................................26 3 GENETIC ALGORIHTM OPTIMIZATI ON FOR DEMOGRAPHIC PARAMETER CALIBRATION AND POPULATION TRAI TS OF A HARVESTED TROPICAL PALM........................................................................................................................... ..........41 3.1 Introduction...................................................................................................................41 3.1.1 South American Palms and Consequences of Wild Harvesting.......................41 3.1.2 Matrix Modeling and Population Dynamics.....................................................42 3.1.3 Parameter Calibration........................................................................................43 3.1.4 Introduction to Genetic Algorithms..................................................................44 3.1.5 Objectives..........................................................................................................45 3.2 Methods........................................................................................................................ .45 3.2.1 Study Site: Ecuador...........................................................................................45 3.2.2 Study Site: Peru.................................................................................................46 3.2.3 Study Species Role in Peru...............................................................................47 3.2.4 Palm Distribution and Matr ix Model Development:........................................48 3.2.5 GA Method Description....................................................................................48

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6 3.3 Results........................................................................................................................ ...51 3.3.1 Genetic Algorithms...........................................................................................51 3.3.2 Peru Size Class Distribution a nd Demographic Characteristics.......................54 3.3.3 Genetic Algorithm: Harvest History for Peru M. flexuosa Palm Population....55 3.4 Discussion.....................................................................................................................57 3.4.1 Genetic Algorithms...........................................................................................57 3.4.2 Peru Size Class Distribution a nd Demographic Characteristics.......................59 3.4.3 Genetic Algorithm: Peru M. flexuosa Palm Population....................................60 3.5 Conclusions...................................................................................................................60 4 SUMMARY........................................................................................................................ ....84 4.1 Applicability..................................................................................................................84 4.2 Future for M. flexuosa ...................................................................................................84 4.3 Future Research.............................................................................................................85 APPENDIX: PERU GARDEN DATA FOR Mauritia flexuosa ...................................................86 LIST OF REFERENCES............................................................................................................. ..89 BIOGRAPHICAL SKETCH.........................................................................................................96

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7 LIST OF TABLES Table page 2-1 Observed size class distri bution (based on height) of M. flexuosa ....................................29 2-2 M. flexuosa (Ecuador) transition matrix............................................................................30 2-3 Size class distribution for density inde pendent (DI) and dens ity dependent (DD) models after 100 yr............................................................................................................31 2-4 Adult (stage 5 & 6) M. flexuosa transition probabilities....................................................32 3-1 M. flexuosa population size class distri bution in Ecuador and Peru..................................62 3-2 Optimal Ecuador seedling parameters and carrying capacity using observed demographic parameters....................................................................................................63 3-3 Observed range of the 13 non-seedli ng demographic transition probabilities..................64 3-4 Observed and optimal Ecuador transition matrices...........................................................65 3-5 Optimal Ecuador seedling parameters and carrying capacity using optimal demographic parameters....................................................................................................66 3-6 Demographic traits for the Peru populat ion in size classes 3-6 (palms that have developed trunks).............................................................................................................. .67 3-7 GA estimates of harvest regimes consistent with the observed si ze class distribution.....68 3-8 Perus harvesting history found using sepa rate GAs which uses the Ecuador optimal demographic parameters to reach Pe rus observed populat ion distribution......................69

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8 LIST OF FIGURES Figure page 2-1 Elasticity for the M. flexuosa matrix population model.....................................................33 2-2 Density dependent model for M. flexuosa simulated over 500 yr.....................................34 2-3 Four simulated harvesting scenarios with various harvest frequencies and intensities for M. flexuosa ...................................................................................................................35 2-4 The average number of female palms the year before harvesting over a 100 yr harvest regime................................................................................................................. ...38 2-5 Harvesting 22.45 percent at a frequency of every 20 yr....................................................39 2-6 Two harvest scenarios (both 75 percent at a frequency of every 10 yr) with density independence (DI) and density dependence (DD).............................................................40 3-1 Map of study site in Ecuador.............................................................................................71 3-2 Map of study site in Peru.................................................................................................. .72 3-3 Ecuador Genetic Algorith m (GA) size class distribution and observed size class distribution after running a GA to find optimal seedling parameters (stasis and growth) and carrying capacity. Fitn ess score for this GA is 46.67....................................73 3-4 Ecuador GA size class dist ribution and observed size cla ss distribution after running a GA using the observed transition parame ters and evaluating how well it matches the observed population dist ribution. Fitness score for this GA is 67.03..........................74 3-5 Genetic algorithm simulated and observed si ze class distribution of the Ecuador palm population for unconstrained, all values (U CAV) GA optimization. Fitness score for this GA is 14.14............................................................................................................... ..75 3-6 Genetic algorithm simulated and observed si ze class distribution of the Ecuador palm population for unconstrained, no two-size class transitions (UCNT) GA optimization. Fitness score for this GA is 5.07........................................................................................76 3-7 Stasis and growth demographic points ge nerated from a GA optimization for (A) an UCAV (unconstrianed, all value), and (B ) an UCNT (unconstrained, no two sizeclass transitions)............................................................................................................. ....77 3-8 Stasis and growth demographic points generated from CAV (constrained, all values) GA optimization................................................................................................................ .78 3-9 Stasis and growth demographic points generated from a CNT (constrained, no twosize class transitions ) GA optimization..............................................................................79

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9 3-10 Genetic algorithm simulated and observed si ze class distribution of the Ecuador palm population for CAV (constrained, all values) GA optimization. Fitness score for this GA is 6.29..................................................................................................................... .....80 3-11 Genetic algorithm simulated and observed si ze class distribution of the Ecuador palm population for CNT (constrained, no two-si ze class transition s) GA optimization. Fitness score for this GA is 7.69........................................................................................81 3-12 M. flexuosa population distribution for palm populat ions in a 1ha area in Peru and Ecuador........................................................................................................................ ......82 3-13 Distribution of male vs. female palms a nd estimated, averaged fecundity values from Peru and Ecuador...............................................................................................................83 A-1 Average height(m) for M. flexuosa palms sampled in Peru (wild and gardens). A-2 Comparison of average palm height and average number of pe tioles, for juvenile M. flexuosa located in gardens and w ild populations (in Peru). A-3 M. flexuosa palms in Peru homegardens. (A) Pi cture of juvenile (pre-reproductive) M. flexuosa palms in a homegardens. (B) Picture of dwarf, reproductive female palm in Peru.

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10 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science POPULATION DYNAMICS OF THE AMAZIONIAN PALM Mauritia flexuosa : MODEL DEVELOPMENT AND SIMULATION ANALYSIS By Jennifer A. Holm December 2007 Chair: Wendell P. Cropper Jr. Major: Interdisciplinary Ecology The tropical palm Mauritia flexuosa has high ecological and economic value, but some wild populations are harvested excessi vely by cutting the stem to retr ieve the fruit. It is likely that M. flexuosa harvesting in the Amazon will continue to increase over time. I investigated the population dynamics of this important palm, the effects of harvesting, a nd suggested sustainable harvesting regimes. Data were collected from populations in the Ecuadorian Amazon that were assumed to be stable. I used a matrix populat ion model to calculate the density independent asymptotic population growth rate ( = 1.046) and to evaluate harves ting scenarios. Elasticity analysis showed that survival (p articularly in the second and fifth size class) contri butes more to the population growth rate than does growth and fecundity. In order to simulate a stable population at carrying capacity, density dependence was incorporated and a pplied to the seedling survival and growth parameters in the transition matrix. Harvesting scenarios were simulated with the density dependent population models to predict sustainable harvesting regimes for the dioecious palm. I simulated the removal of onl y female palms and showed how both sexes are affected with harvest intensities between 15 and 75% and harvest intervals of 1 to 15 years. By assuming a minimum female threshold, I demonstr ated a continuum of sustainable harvesting schedules for various intensitie s and frequencies for 100 years of harvest. Furthermore, by

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11 setting the population models = 1.00, I found that a harves t of 22.45 percent on a 20 year frequency for the M. flexuosa population in Ecuador is consiste nt with a sustainable, viable population over time. Demographic parameters of long-lived plants ar e difficult to accurately estimate with short duration studies. Genetic algorithm (GA) optimiza tions have been used to calibrate the matrix population model from populations sampled in Ec uador. Assuming that the observed population was stable at carrying capacit y, sampling error could explain th at the estimated demographic parameters (transition probabil ities) do not project e quilibrium population valu es that match the observed size class distribution. GA optimization of seedling parameters so mewhat improved the match to the observed size class distribution, but the optimal paramete rs were from a range of local optima. GA optimization of non-seedling demographic parame ters for the Ecuador population produced a close fit to the observed populati on size class distribution. It wa s found that the technique of constrained GA optimization produced models that closely matched the observed size class distribution and were consistent with plot measurements. This study also compared the palm size class distributions and demographic character istics between Peru and Ecuador populations. Unlike in Ecuador, palm populations in Peru ar e heavily harvested, with reduced numbers of adult females and an uneven sex-specific size cla ss distribution. Finally, I explored GA as a tool to reconstruct plausible harves ting histories by assuming that a harvested population in Peru started with the same population structure as the Ecuador populat ion. Harvest regime variables included harvest intensity (fraction removed), ha rvest frequency (return time) and the time span with harvesting. No parameter combinations for regular uniform harvest regimes were found that closely matched the observe d Peru size cla ss distribution.

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12 CHAPTER 1 INTRODUCTION In general terms, population ecology entail s analyzing the demography of a population through estimating its vital rates (survival, growth, fecundity, mo rtality), and assessing change in numbers over time. In particular, understandin g population dynamics is important for evaluating how a population density changes in response to ex ternal and/or internal influences. Modeling population dynamics is useful for developing and evaluating hypothese s in population ecology. This research employed simulation modeling to develop matrix population models for evaluating the population behavior of a tropical palm, Mauritia flexuosa Constructing matrix population models, including density dependence, simula ting sustainable harves ting scenarios, and developing methods to calibrate poorly sampled m odel parameters was the main goals of this research. This research is not recommended to be used directly for management purposes. The simulated sustainable harvest regimes identified in this study represent testable hypotheses; and rigorous testing should be done before any implementation. The tropical palm Mauritia flexuosa is found in the Amazon Basin and often forms monodominant stands. Destructive harvesting is occurring in parts of the Amazon to retrieve the palm fruits, which are then sold in local markets. Demographi c population modeling was used to estimate the populations current behavior, as we ll as estimate the populations response to assumed harvesting scenarios. This thesis is orga nized as two separate jo urnal papers (chapter 2 and chapter 3). Chapter 2 describes the model structure, data and methods used for model development, and results of harvest scenario analys is. One of the principal uncertainties of this work is associated with the relatively short pe riod of data collection (2 years). Chapter 3 describes the use of genetic algorithms for simultaneous es timation of up to 13 model

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13 parameters. This technique provides a test of the consistency of parameter estimates and the observed size class distribution.

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14 CHAPTER 2 POPULATION DYNAMICS OF THE DIOECIOUS AMAZONIAN PALM MAURITIA FLEXUOSA: SIMULATION ANALYSIS OF SUSTAINABLE HARVESTING 2.1 Introduction There is growing concern for conserving and sustaining tropical forests (Houghton et al 1991, Sioli 1991, Olmsted & Alvarez-Buylla 19 95). Many tropical tree species provide ecological as well as economic benefits. These be nefits include valuable resource production or important functions associated with tropical biodiversity and conservation. Managing these critical species requires an understanding of their population dynamics by practitioners and communities (Olmsted & Alvare z-Buylla 1995). Palms make up a large portion of the economically useful tropical tree s and are utilized for a wide ra nge of products (Balick & Beck 1990, Anderson et al. 1991, Kahn 1991, Kahn & de Granville 1992, Henderson et al 1995). The palm Mauritia flexuosa L.f., also called canangucho or morete in the Ecuadorian Amazon, was the focus species of this study, used in th e development of matr ix population models. Mauritia flexuosa is found in tropical, flooded, swamps (Kahn & Mejia 1990, Kalliola et al 1991, Cardoso et al 2002) throughout the Amazonia Ba sin and northern South America (Henderson 1995, Ponce et al 2000). Mauritia flexuosa has significant, but underdeveloped potential as a multifunctional, non-timber forest resource of great economic value (Denevan & Treacy 1987, Carrera 2000, Peters et al. 1989a, 1989b, Ponce et al 2000). The fruit of the palm is currently its most economically useful produc t (Padoch 1988). Oil fractions extracted from M. flexuosa fruit have high concentrations of v itamins, carotene, and lipids (de Franca et al 1999). Mauritia flexuosa is one of the most commonly f ound palms in the Amazon, and forest dwellers currently invest substa ntial effort in gathering fruits from these palms to generate income (Kahn 1988, Peters 1992, Coomes et al 2004). These products are not processed on an industrial scale, but th ey do provide income and employme nt for many people in Iquitos and

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15 other Amazonian communities, with the fruit be ing sold in many forms (Padoch 1988). There has been an increasing shift to growing M. flexuosa in small homegardens, also known as chacras Until recently, however most M. flexuosa fruit has been harvested from wild stands. In dense, monodominant, flooded natural stands, the mature palm trees are typically greater than 20m in height making the fruit difficult to harves t. As a result, in many Amazonia locations the fruit-bearing female palms are cut down leading to nonviable populations (Peters et al 1989a, Vasquez & Gentry 1989), which makes M. flexuosa a good candidate for non-timber forest product (NTFP) management. A goal of my research was to identify pot ential sustainable harvest regimes for M. flexuosa Because fruit harvest for this particular species results in tree mortality, matrix population models are appropr iate tools to simulate monodominant stands of M. flexuosa If markets continue to flourish with M. flexuosa products then in time formerly low levels of harvesting will likely intensify in Ecuadorian fo rests as it has in other Amazon Basin locations (Peters et al 1989a, Vasquez & Gentry 1989). Many studies have looked at the 1) implications of harvesting palm parts (NTFPs) as well as 2) identifying useful palm s needing conservation (Johnson 1988, Fonseca 1999, Mendoza and Oyama 1999, Endress et al. 2004a, Ticktin 2004). Ticktin et al (2002) used matrix models to assess th e effects of harvesting on a NTFP bromeliad in Mexico. Endress et al (2004b) as well as Olmsted and Al varez-Buylla (1995) used matrix models to evaluate harvesting techniques for tropical palms ( Chamaedorea radicalis, Thrinax radiata, and Coccothrinax readii ). Likewise, matrix models have been used on the tropical palm Iriartea deltoidea to evaluate stem harvesting, populat ion stability, and conservation (Pinard 1993, Anderson & Putz 2002). Matrix models have also been coupled with habitat fragmentation analysis to asse ss changes in plant popul ation dynamics in tropical environments

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16 (Bruna 2003). Improper harvesting of palm produc ts has been demonstrated to have a negative effect at the population level (OB rien & Kinnaird 1996, Clay 1997). Lefkovitch matrix models (1965), a generalizat ion of matrix populati on models proposed by Leslie (1945), typically simula te the population in sized-based stages as opposed to the age classification of a Leslie model. In many tree populations, the de mographic parameters (survival probability, growth rate, and fec undity) are a function of tree si ze and not of tree age (Caswell 2001, Vandermeer & Goldberg 2003). The standa rd matrix population model will project exponential growth if th e dominant eigenvalue ( ) of matrix is greate r than 1 (implying no resource limitations or compe tition) or decline exponentially if is less than 1. Matrix population models have been used to aid manage ment and conservation of many species (Crouse et al 1987, Wootton & Bell 1992, Silvertown et al. 1996). The role of density dependence is important in some tropical palm populations (Cropper & Anderson 2004), but data are limited. A study of the tropical palm Euterpe edulis showed that there was a clear effect of density on th e population structure and demography (Matos et al 1999). A second study of the same palm showed th at density dependence, as well as timing of harvest, must be considered for accurate as sessment of population responses to harvesting (Freckleton et al 2003). Little is known about density dependence in tropical tree systems that are harvested, but previous work suggests that density often has its strongest effect on seedlings of tropical palms and other tree sp ecies (Augspurger & Kelly 1984, Sarukhan et al. 1985, Martinez-Ramos et al. 1988, Matos et al 1999). I hypothesize simila r demographic patterns in monodominant stands of M. flexuosa An important characteristic of M. flexuosa for harvest management is that the palm is dioecious; only females bear the economica lly useful fruit. One study has looked at

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17 demographic consequences of harvesting of an understory dioecious pa lm, finding that leaf harvest can reduce female fecundity (Berry & Go rchov 2007). I know of no studies using matrix models to simulate sustainable harvest regimes in a tropical species with only female removals. Specifically, my objectives were: (1) to de termine how density dependence affects the population dynamics and harvesting; (2) to estimate sustainable harvests w ith an assortment of different harvesting intensities and frequencies of M. flexuosa specifically looking at how harvesting a dioecious species a ffects the population; and (3) to estimate a sustainable harvest while maintaining a stable population ( equal to 1.00). 2.2 Methods 2.2.1 Study Site Data were collected in the Ecuadorian Am azon from the Cuyabeno Faunal Reserve, a 655,781 ha reserve located between the San Miguel and Aguarico river basins and managed by Siona and Secoya indigenous groups. All fiel d components were conduc ted near the Cuyabeno Field Station (0N, 76W), loca ted in a tropical rainforest with an elevation of 200m. Cuyabeno is characterized by a series of oligotroph ic lakes, connected to M. flexuosa swamps ( morichales ) that ultimately drain into the Cuyabeno River. Water levels in M. flexuosa swamps fluctuate depending on the season and rainfall leve l, which averages 3400 mm/yr. Three distinct seasons are evident: dry (mid-Dece mber to March), wet (April to July), and transitional (August to December) (Asanza 1985). 2.2.2 Study Species Mauritia flexuosa is a long-lived, dioeci ous, canopy dominant pa lm, found throughout the Amazon basin at elevations below 500m, but sometimes reaching 900m (Henderson et al. 1995). Juveniles initially have only leaves above-ground, and then be gin to form a trunk covered by persistent petiole bases. As a palm matures, the petioles fall off exposing a permanent trunk.

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18 Mature palms have 8 20 leaves with leaf blades 2.5m long and 4.5m wide, and split into approximately 200 stiff or pendulous leafle ts (Kahn & de Granville 1992, Henderson et al. 1995). The inflorescences are 2m or more in leng th with 25 40 flowering branches. Fruits are oblong drupes, 5 x 7cm on average, and are covered with a brick-red epicarp of scale texture. The only edible part of the fruit for humans is its yellow mesocarp, but the seed is useful to artisans who produce small carvings. Padoch (1988) describes a number of M. flexuosa products found in the Iquitos market, including the ripe fruit and a pulp mash, a drink, popsicles, and ice cream. Previously studied permanently flooded fo rests, inhabited by M. flexuosa, are seen to have soil composed of decomposed organic matter for several meters saturated with acidic water (Kahn 1991). In the Ecuadorian Amazon these flooded forests that are mostly dominated by M. flexuosa (called morichales ) are found along river edges. In others parts of the Amazon, this palm is intensely harvested from these wild stands. Wild harvesting of M. flexuosa has historically occurred in Ecuador, but at low levels. M. flexuosa can be considered a keystone species because of large number of other species that fe ed on the fruit and seed. These include agouties ( Dasyprocta leporina aguti) spider monkeys ( Ateles geoffroyi ), red and green macaws ( Ara chloroptera ), lowland tapirs ( Tapirus terrestris ), red and gray brocket deer ( Mazama americana and Mazama gouazoubira respectively), white-lipped and collared peccaries ( Tayassu pecari and Tayassu tajacu respectively), and fish (Goulding 1989, Bodmer 1990, Bodmer 1991, Henderson et al. 1995, Fragoso 1999, Zona 1999). 2.2.3 Data Collection I used a demographic data set that was collect ed previously by a re search collaborator (C. Miller) from five plots (20m x 100m) in old growth natural stands in Ecuador ( morichales ). Demographic data were collected from 1994-1996. I do not know th e exact criteria for selecting

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19 the five plots. All five plots were within a half a days travel or less from each other. I assumed that minimal female harvesting had occurred on th e five plots (based on evidence from the size distribution ratio of adult males to females and re mnant trunks of harvested female individuals). Harvest intensity prior to the st udy, however is unknown. In the fi rst year demographic data was collected for each palm individual over all five 20m x 100m plots. Palms were tagged with numbered, metal tags. Data collection consisted of: 1) Palm height for all size classes (actual for palms that could be reached, and estimated with a clinometer for taller palms). 2) Leaf counts on seedlings and most juveniles. 3) Recording of sex for adults. 4) Leaf scars on palms that had developed trunks. 5) Raceme counts on females. In the second year, the number of seedlings was based on ten 5m x 5m subplots (randomly selected) within the 20m x 100m plots. Otherwise, the same data collection was repeated in the second year. In the third year only seedling data was recorded in the previously marked ten subplots. 2.2.4 Matrix Model Development and Parameter Estimation Distribution of palms in each of the five pl ots was variable. For population analysis and stage-based matrix modeling, I aggr egated the population into a 1ha pooled data group (Table 21). The population was classified into seven size classes based on height. Only a limited number of adult growth transi tions (size class 5) were obser ved, leading to potentially poor estimates of the vital rates. Growth rates were estimated for each size class in the pooled data set. To estimate survival and growth transi tions, I assumed that the observed size class distribution was stable and that the average growth rates per size class applied to all individuals within that class. Mean size class specific growth rate s were estimated (0.4159 m/yr, 0.3902 m/yr, 0.8107 m/yr, 1.08 m/yr, and 0.4333 m/yr) for size class 1 th rough 5 respectively. The

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20 matrix parameters (survival, sij and growth, gij) that did not have a limited number of observations were estimated by following the state vs. fate of the palms over time. Fecundity (fij) parameter estimates were based on equation 2-1: i t n f ijN fx2 )) 1 ( )( (0 (2-1) where f(x) is the seedling survival probability, n0(t+1) is the average number of established seedlings at the next time interval, and Ni is the number of reproductive individuals. The term in the numerator is divided by two, assuming a 1:1 sex ratio. The ma trix model was simulated with the equation 2-2: ) () 1 (t n A nt (2-2) where n(t) represents the population vector at time t, and A represents the 7 x 7 transition matrix containing the probabilities for individual palms to remain in the same stage or move to another stage and their fecundity probabilities (Table 2-2). Elastic ity analysis is often used to demonstrate the sensitivity of the dominant eigenvalu e to variations in matrix elements (survival, growth, fecundity). Unlike absolute sensitiv ity, elasticity analysis shows the relative contribution of each vital rate to the population growth rate, (Caswell 2001, Morris & Doak 2002). Density dependence was simulated using th e monotonic decreasing Ricker function: ) (max ) (N ij ije a N a (2-3) Density dependence was applied to the two s eedling parameters (survival and growth) in the transition matrix, because dens ity has been observed to influence seedlings of tropical palms (Matos et al. 1999). The first seedling paramete r is seedling survival, the probability that a

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21 seedling will survive and remain in the same size class. The second seedling parameter is seedling growth, the probability that a seedling will su rvive and grow into the next size class. In the Ricker function, aij(N) is the probability that a seedling will survive or grow as a function of the total M. flexuosa population (N, the sum of n population vector). Seedling survival and growth decreases as density of th e entire palm population increases. aijmax represents the matrix probabilities for the seedling parameters a00 and a10 in the original transition matrix with no density limitation. was found by using the bisection me thod (Cropper and DiResta 1999) to estimate the seedling parameter values for a stable ( = 1) population and equation 2-4: K a aij ijmax ln (2-4) where K is the carrying capacity including al l seedling and non-seedling individuals and aij represents the matrix probability when the dominant eigenvalue of the A matrix, equals 1.00 (the population is stable w ith a density equal to the car rying capacity). A 39.77 percent reduction in seedling vital rates wa s consistent with an equilibr ium population at K. Separate density dependent models were simulated for males and females with identical parameters, except that male fecundity values were set to zer o. Male seedling recruits were assumed to equal the number of female seedling recruits and were added directly to the male population vector. I developed scenarios to estimate a sustainabl e harvest regime based on two options. The first (1) setting a minimum female threshold (M FT) (20 individuals) to maintain a sustainable population; and (2) finding the adult survival and gr owth probabilities that produce a stable, thus sustainable, intrinsic pop ulation growth rate ( = 1.00), using the bisect ion method. With the first option I then: (1a) varied th e intensity of harvests scenarios; (2a) varied the frequency of harvest, from annual to periodic harvests to fi nd a continuum of harves t scenarios that produced

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22 a sustainable population. In both harvesting scenarios separate population vectors were simulated for males and females, since M. flexuosa is dioecious and only female palms are felled during harvest. Harvesting scen arios are initiated after a 600 y ear density dependent simulation to avoid transient dynamics associated with a possible non-equilibrium size class distribution. There are short-lived transients associated with simulations star ted at the observed stage class distribution, but they typically damp out rapidly. I assumed that the population has not been recently harvested, and that the equilibrium si ze class distribution provides a good estimate of the expected distribution used as a uniform basis for comparison. Evaluations of harvest simulations for sustainability are not sensitive to this assumption. 2.3 Results Elasticity analysis of the density independent M. flexuosa matrix showed that the stasis probabilities (the elements in the ma in diagonal) contribute the most to sensitivity (Figure 2-1, A). Specifically, the survival a nd stasis parameter in the seco nd juvenile stage (size 3.0m 6.0m), and the survival and stasis of the firs t adult stage (size 20.0m 28.0m) were sensitive parameters (Figure 2-1, B). The M. flexuosa transition matrix (Tab le 2-2) produced an asymptotic population growth rate of = 1.046, which shows that the population has the potential for rapid increase. 2.3.1 Density Dependence With density dependence, the population growth rate slows as N approaches the carrying capacity. I assume that for seedlings, transiti on rates depend on the number of individuals in their own size class and all othe r size classes. The simulate d density dependent model shows that the M. flexuosa population at equilibrium (K) is large (Figure 2-2), but most of the individuals are in the seedling cl ass (Table 2-3). There was a la rge difference in the size class

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23 distribution between the density independent model and the density dependent model at 100 yr simulation (Table 2-3). At a pproximately 100 to 150 years, the simulated palm population began to reach equilibrium. The full density dependent simulation was run for 500 years (Figure 2-2). At equilibrium (after 500 yr) the model pr edicted an adult size class distribution of approximately 120 individuals per ha for each sex. The number of adults that were measured in the study site was approximately 45 per ha for ea ch sex. After equilibrium was reached in the density dependent simulation, the followi ng harvesting scenario s were initiated. 2.3.2 Sustainable Harvest Scenarios Multiple harvesting options (Figure 2-3) are co nsistent with sustainable management of M. flexuosa Harvesting at intensities of 15 percent, 20 percent, 30 percen t, 50 percent, and 75 percent removal of adult females are seen in Fi gure 2-3 (A-C). Harvest frequency, or return time, is directly coupled with the total numbe r of palms that can be harvested. Periodic harvesting frequencies were simulated for return time s of 5 yr, 10 yr, and 15 yr. I also simulated an annual harvest regime (Figure 23, D), although harvesting is ra rely that frequent from natural M. flexuosa stands because local people understand th e threat to these palms survival if harvesting is done each year. Simulations at a ra nge of intensities (Fi gure 2-3, D) support the conventional wisdom that annual harvests are no t sustainable in the long-term. With adequate recovery time, the M. flexuosa population can be dynamically stable following periodic harvesting (Figure 2-3, A-C). After each periodic harvest, there was a sharp decrease in adult palm density, followed by an increase in populati on density (recovery), which is faster in the years immediately after harvest th en slows with increasing density. Recovery is defined as the number of females that grow into the adult size class 5 from the j uvenile size class 4. For all harvesting intensities (15%-75%), female recove ry was greatest with 15 yr harvest intervals (Figure 2-3, C). Average number of female palm s at simulated time of harvest ranged from 37

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24 115 depending on harvest intensity and frequency (Fi gure 2-4). Larger female numbers available for harvest are associated with longer harvest in tervals and lower harvest intensities. Although a less intense harvesting regime would increase biol ogical sustainability, this may not be adequate for supplying household income needs. I have set a sustainable harves t rate for this palm through tw o different methods. The first is by assuming 20 adult females per hectare as th e MFT needed to sustain population viability. With 20 adult females set as the threshold, Figure 2-3 shows that the following can be sustainable; a 30 percent harves t every 5 yr, a 50 per cent harvest every 10 yr and a 50 percent 75 percent harvest every 15 yr. On ly these harvesting intensities are consistent with a viable population for 100 years, because they maintain the number of female palms above the MFT. These harvest options can only be done for a hundr ed year time span. After 100 years if the harvest intensity remains constant, the popul ation will fall below a minimum sustainable threshold level. The second method I used to find a sustainable harvest rate allows for harvesting over an indefinite time period, assu ming that population parameters do not change. By using the bisection method, I found that the a dult survival and growth probabilities necessary for = 1.00 are less than the observed probabilitie s (Table 2-4). I found that harvesting 22.45 percent of the females every 20 yr create s a sustainable harves t (Figure 2-5). The biologically plausible assumption of de nsity dependence leads to very different harvest projections than that of the standard density independent ma trix population model (Figure 2-6). The simulated harvest scenario without a density depe ndence function shows a large increasing female populati on. The same scenario modeled with density dependence drops below MFT and does not provide a sustainable harvest.

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25 2.4 Discussion This study effectively examines impacts of harvesting a dioecious palm and, is among the first to provide multiple sustainable, simulate d harvesting scenarios for one species. While population modeling may be a useful tool to project management scenarios, uncertainties in demographic parameters and difficulties in soci al and economic planning are likely to preclude precise harvest planning. A t ypical assumption in matrix pop ulation models is that the populations are not limited by dens ity. Using the standard density independent model, with parameters estimated in the field, the M. flexuosa population examined increases by a factor of 1.046 each year (at the stable stage distribution). Given limitations on space and other resources, it is clearly unrealistic that this populati on will increase indefin itely (Lack 1947, Milne 1957, Weiner 1986). A populati on that is growing ( = 1.046) would produce many more harvestable palms than one limited by competition. At the limit, an exponentially growing population could produce any desired harvest, given adequate tim e. I suggest that simulation of density dependence in monodominant harvested populations is necessary to properly constrain the rate of population recovery following harvest. 2.4.1 Sustainable Harvest Scenarios The challenge for NTFPs is finding the harves t level that will supply enough income to forest dwellers while at the same time maintain ing population viability of harvested species. I have shown that harv esting the specific M. flexuosa population examined at 22.45 percent every 20 yr could be a sustainable harvesting regime (F igure 2-5), but higher inte nsities or frequencies of harvest could send the population into a decline. Frequency/intensity of harvesting is hard to control and is a response to multiple issues, such as market demand, fluctuating s ubsistence needs, accessibility, and morichal fruit production rate. For these reasons, different harvesting scenarios can be chosen, all maintaining

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26 a sustainable harvest rate for the span of 100 years (Figure 2-3). I have shown a tradeoff between harvest frequency and intensity. Higher ra tes of removal will require longer recovery times between harvests (Figure 2-3). This popula tions MFT is assumed to be 20 individuals per hectare. It is reasonable to select a conser vative value for MFT, based on the Precautionary Principle, but other M. flexuosa populations could have a different and a different minimum female threshold. It can be misleading to eval uate harvesting regimes based on the number of females to recover in only one year instead of the entire harvest period recovery. In the first years following a harvest, initially a higher numbe r of palms recover than in remaining years after a harvest. A harvesting regime with a l onger time interval between harvests will allow more palms to recover into the adult size classes. Understanding the implications of harvesting a dio ecious species is one goal of this paper. The current practice, selecting and removing female palms, results in recruitment limitation over time. Females are directly affected by harv esting, and the male popul ation is affected by changing adult density and by reduced seedling recruitment. Initially, the male population remains high, but after a lag time the male populati on begins to decline along with the females. Over time, if heavy harvesting is maintained, it is predicted recruitm ent and regeneration of M. flexuosa palms will decline. 2.4.2 Implications for Management While population modeling may be a useful t ool to project management scenarios, uncertainties in demographic parameters and di fficulties in social and economic planning are likely to preclude precise harvest planning. With the market demand increasing for the M. flexuosa fruit, many forest dwellers are beginning to cultivate the palm in small homegardens. Research organizations and non-governmental orga nizations (NGOs), such as the Rainforest

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27 Conservation Fund, are helping Amazonian mes tizos to convert old swidden fields into M. flexuosa gardens. These gardens can take 10 12 yr to become productive, but after trees grow to maturity fruit can be harvested repeatedly from managed, easily acces sible gardens. Wild individuals may take an estimated 30 or more years to mature and become productive, based on leaf and infructescence scars counts (pers. obser vation). Palms grow faster and mature more quickly under high light conditions, such as t hose found in agroforestry gardens (Penn 1999). Palms that mature more quickly will produce fru it at a shorter height, making harvesting easier. While harvesting in natural, flooded swamp stands can be done at a sustaina ble level, if market demand increases then M. flexuosa production gardens, as opposed to extracted natural stands, may become a better option. Many forest dwelling Amazonians understa nd the important economic role of M. flexuosa They also understand that natural palm dens ities are decreasing, but few written management plans have been implemented to protect this resource. Our simulations demonstrate that sustainable harvesting scenarios for a species can be found, but the precise nature of a sustainable harvesting regime depends on accurate representation of the population demography. Long-term palm survival, growth, and fecundity monitoring should be us ed to provide a sound basis for developing harvest strategies for wild populations. Better understanding of density dependence in monodominant M. flexuosa stands is also needed. In summary, the sustainable harvest scenarios found in this study consist of a range of harv esting regimes for 100 years of harvest, and an option for a continuous sustai nable harvest over time. Management planning should include community input and participatio n to generate community specific harvesting management plans. Analyzing the population dynamics of Mauritia flexuosa can be used as one

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28 component in management of its role as a NT FP, while conserving the natural Amazonian palm stands it inhabits.

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29 Table 2-1. Observed size class di stribution (based on height) of M. flexuosa in five plots (plot 1-5 100x20m), and pooled plot 1-ha. Size Class Stage Height (m) Plot 1 Plot 2 Plot 3 Plot 4 Plot 5 Pooled Plot 0 Seedling <1.045 62 59 42 52 260 1 Juvenile 1.0-3.02 14 32 29 10 87 2 Juvenile 3.0-6.013 18 25 23 22 101 3 Juvenile 6.0-10.06 8 6 7 0 27 4 Juvenile 10.0-20.012 7 2 9 2 32 5 Adult 20.0-28.09 11 8 10 9 47 6 Adult >28.013 5 8 13 3 42

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30 Table 2-2. Transition matrix for M. flexuosa for pooled plot, from five flooded swamp sites in Ecuador. The dominant eigenvalue, lambda ( ) shows the growth rate. = 1 indicates a stable population, < 1 a decreasing population, and > 1 an increasing population. Size Classes <1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m 0.4923 0.0 0.0 0.00.016.8 16.8Pooled Plot 0.0115 0.7471 0.0 0.00.00.0 0.0 = 1.046 0.0 0.2184 0.8911 0.00.00.0 0.0 0.0 0.0115 0.0990 0.77780.00.0 0.0 0.0 0.0 0.0099 0.22220.78130.0 0.0 0.0 0.0 0.0 0.00.18750.8723 0.0 0.0 0.0 0.0 0.00.00.0851 0.8810

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31 Table 2-3. Size class distributi on for density independent (DI) and density dependent (DD) models after 100 yr. Size Class Number of palms: DI Model Number of palms: DD Model 0 45729.6 4224.32 1 2888.3 189.26 2 3388.1 271.36 3 832.5 70.60 4 1028.4 104.84 5 964.7 113.14 6 526.9 77.80

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32 Table 2-4. Adult (stage 5 & 6) transition probabi lities. Matrix element a55 and a66 are adult survival and element a65 is adult growth transition. Average of the death due to harvest produces the adu lt harvest percent for the second harvesting scenario. Matrix element Original survival/growth probability Death due to natural causes Survival/growth for =1.0 Average death due to harvest a55 0.87230.1280.64890.2234 a65 0.0851NA0.06330.0218 a66 0.88100.1190.65540.2256 Average 0.2245

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33 0 1 2 3 4 5 6 0 0.05 0.1 0.15 0.2Elasticity % Size Classes A 0 0.05 0.1 0.15 0.2 0.25 0123456 Size Classes Fecundity Stasis Growth B Figure 2-1. Elasticity for the M. flexuosa matrix population model. (A) the 7 x 7 transition matrix, and (B) the three main vital rates (growth, stasis, fecundity).

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34 Figure 2-2. Density dependent model for M. flexuosa simulated over 500 yr. The population illustrates an asymptotic growth rate as it reaches the carrying capacity (K).

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35 A Figure 2-3. Four harvesting scenario s with various harvest frequenc ies and intensities. (A) five different harvesting intensities at a fre quency of every 5 yr, (B) five different harvesting intensities at a frequency of ev ery 10 yr, and (C) five different harvesting intensities at a frequency of every 15 yr. (D) six different harv est intensities (only females shown) with annual harvest. Harvest Intensity Years N 0 20 40 60 80 100 120 1401 1 0 1 9 2 8 3 7 46 55 64 73 82 9 1 1 00 F-15% F-20% F-30% F-50% F-75% M-15% M-20% M-30% M-50% M-75%

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36 B C Figure 2-3. Continued Harvest Intensity Years N Harvest Intensity Years N 0 20 40 60 80 100 120 140 1 10 19 28 37 46 55 64 73 82 91 10 F-15% F-20% F-30% F-50% F-75% M-15% M-20% M-30% M-50% M-75% 0 20 40 60 80 100 120 1401 11 21 31 41 51 61 71 81 91 F-15% F-20% F-30% F-50% F-75% M-15% M-20% M-30% M-50% M-75%

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37 D Figure 2-3. Continued Harvest Intensity N Years 0 20 40 60 80 100 120 1401 9 17 25 33 41 49 57 65 73 81 89 97 15% 20% 25% 30% 40% 50%

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38 0 20 40 60 80 100 120 140 1520305075 Harvest Percents (Intensities) N 15 yr freq. 10 yr freq. 5 yr freq. Figure 2-4. The average number of female palms th e year before harvesting over a 100 yr harvest regime.

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39 80 85 90 95 100 105 110 115 120 125 150110011501 YearsN (adults per ha) Male Palms Female Palms Figure 2-5. Harvesting 22.45 percent at a frequency of every 20 yr.

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40 Figure 2-6. Two harvest scenarios (both 75 percent at a frequency of every 10 yr) with density independence (DI) and density dependence (DD).

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41 CHAPTER 3 GENETIC ALGORIHTM OPTIMIZATI ON FOR DEMOGRAPHIC PARAMETER CALIBRATION AND POPULATION TRAI TS OF A HARVESTED TROPICAL PALM 3.1 Introduction 3.1.1 South American Palms and Conse quences of Wild Harvesting Tropical palms are important for many valu es such as, maintaining ecological diversity, providing economic gains and subs istence products, and for aesthetic value (Bates 1988, Mejia 1988, Boom 1988, Anderson et al. 1991, Henderson 1994, Henderson et al 1995, Johnson 1999). South American tropical palms in particular are widely used in local environments and exported to outside markets (Balick 1988, Parodi 1988, Kahn & de Granville 1992, Campos and Ehringhaus 2003). The South American palm, Mauritia flexuosa, one of the most important palm species, has been widely studied (Denevan & Treacy 1987, Kahn 1988, Padoch 1988, Bodmer et al. 1997, Carrera 2000, Ponce et al 2002, Coomes et al 2004). This paper adds to the knowledge on the M. flexuosa species. Simulation models are often used for managing harvested populations, but calibration data are often qu ite limited. It is also difficult to fully understand the dynamics of harvested palm populations based on short-term studies. I believe that Genetic Algorithms can be used to improve the quality of calibration for harvested populations such as those of Mauritia flexuosa Some wild palm populations in the tropics are being destroyed and/or degraded due to overly high economic utilization (Balick 1988, Johnson 1988, Peters et al 1989a). There has been a switch to domestication a nd cultivation, but for certain palm species, including M. flexuosa this switch is slow, poorly unders tood, or involves species-specific difficulties. It is important to first un derstand the population dynamics of palm

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42 populations that are being over-har vested in wild settings. W ild palm extraction is one of the main process threatening local populat ions. Extraction is occurring throughout Amazonia, but is observed to be high around the Iquitos and surrounding regions of Peru specifically for the palm M. flexuosa (Padoch 1988, Vasquez & Gentry 1989). It is important to understand the imp act of harvesting fruit of M. flexuosa a dioecious species, in the Peruvian lowlands, which is destruc tively harvested by felling adult female trees. A high level of wild leaf extraction is seen to unfavorably affect a dioecious understory palm (Berry and Gorchov 2007). Commercial palms ( Chamaedorea and Astrocaryum ) are exploited for products like seeds and l eaves (biologically important components), leading to unsustainable harvesting of local populations (Fonseca 1999, Mendoza and Oyama 1999, Endress et al. 2004, Seibert 2004). Current simulation models of nontimber forest product harvesting do not adequa tely represent population dynamics in the context of multiple use forest management (Valle et al 2007). 3.1.2 Matrix Modeling and Population Dynamics Matrix population models have often been used for studying single species populations (e.g., Crouse et al 1987, Wootton & Bell 1992, Vantienderen 1995, Silvertown 1996, Kaye and Pyke 2003). These models typically follow a stage-based size class model (Lefkovitch 1965) or Leslies age class model (1945), and have been further developed in many studies (Cas well 1989, Morris & Doak 2002, Vandermeer & Goldberg 2003). Many properties of tropical tree populations are difficult to accurately measure (growth rates, response to densit y, regeneration rates) but important to understand, especially in threatened or harvested species (i.e., M. flexuosa ). Effective management and conservation plans for a harvested palm depends on understanding population dynamics and response to disturbances. Therefor e, demographic parameters,

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43 which make up population matrix models, must be understood in detail and accurately represented. In chapter two of this thesis a study was performed us ing density dependent matrix population models to simulate population dynamics of M. flexuosa from a site in Ecuador. Several sustainable harvesting scenar ios were identified, which may be used as a component in management plans for the exploited palm. Using simulation models as a management tool clearly requires the best possible parameter estimates. This study is a continuum of the previous population modeling chapter on M. flexuosa 3.1.3 Parameter Calibration It is difficult to estimate demographi c parameters of many tropical species (Wood 1994, Hunter et al. 2000); particularly long lived tropical trees (Alvarez-Buylla et al. 1996). Past studies have focused on demogr aphic stochasticity (S haffer 1987, Durant and Hardwood 1992) and environmental stocha sticity (Lacy 1993, Kendall 1998, Caswell 2001). Sampling error can also affect the a ccuracy of projections and the simulated changes in demographic process over time (Parysow and Tazik 2002, Picard et al. 2007). Accurate estimation of parameters could even be a matter of concer n in a population with no significant demographic or environmental stochasticity. Examples of likely data problems include short data collection tim e frames, poor identification methods, and measurement error, some of which are f ound in this study. Although model parameters typically have varying degrees of infl uence on model results (Hamby 1994, Janssen 1994), the entire set of demographic parameters interact to produce population dynamics. Carefully calibrating only the most sensitive parameters may miss other parameters that were very badly sampled, as well as higher dimension parameter interactions. Genetic Algorithms are well suited to problems of high dimension optimization.

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44 3.1.4 Introduction to Genetic Algorithms Evolutionary programming has been us ed since the 1950s and 1960s, but John Holland of University of Michigan populari zed the genetic algorithm in 1975. Genetic algorithms (GA) are now used in many discip lines, such as engineering, computer science, biology and ecology. GAs are modeled after the biological paradigm of natural selection and survival of the fitness in generations over time. GAs can be used as an optimization algorithm that seeks to find so lutions to multi-dimensional problems where fitness is defined as a measure of closen ess to the desired solution (Holland 1975, Koza 1992, Wang 1997, Mitchell and Taylor 1999). GAs are also considered global algorithms because they search within a popul ation, and then use biological frameworks of gene passing, mutation, selection, and cr ossover. The use and development of evolutionary programming is practical in so lving a wide range of problems, including ecosystem and biological applicatio ns (Cropper and Comerford 2005, Yao et al. 2006, Liu et al 2006, Termansen et al. 2006, Dreyfus-Leon and Chen 2007). Using genetic algorithms to understand tr opical forest dynamics is an emerging technique. For example, parameterization wi th genetic algorithms has been used in a simplified, aggregated forest model to unde rstand logging cycles across a range of tropical forest types and forest dynamics (Tietjen and Huth, 2006), and a genetic algorithm has been used to estimate f ecundity, carrying capa city, and seedling demographic parameters for the palm Iriartea deltoidea (Cropper and Anderson 2004). The key assumptions of our approach to para meter estimation with genetic algorithms are that, 1) the observed size class distributi on of the Ecuador population represents an equilibrium population at carrying capacity with no history of harves t, 2) measurements of palm height (the basis of size classification) are more accurate than estimates of

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45 transition rates (which depend on height meas urements), and 3) the local population is mono-dominant with no significant co mpetition from other plant species. 3.1.5 Objectives In this study, I proposed; 1 To use genetic algorithms for parameter calibration of a population model of the M. flexuosa palm. Calibrated parameters for the Ecuador palm population included; A) seedling survival and growth paramete rs, B) the carrying capacity on a 1 hectare plot of land, and C) the non-seedling demographic parameters (survival and growth). 2 To compare the population distributions a nd demographic charac teristics between a harvested population (Peru) and a locati on where harvesting is minimal to none (Ecuador). 3 To test the hypothesis that a plausible harvest history of the Peruvian palm population can be found through the use of genetic algorithms. Optimization parameters include harvest intensity, harv est frequency, length that harvest has occurred, and carrying capacity for the Peru population. 3.2 Methods 3.2.1 Study Site: Ecuador Data were collected in Ecuadorian Am azon from the Cuyabeno Faunal Reserve (Figure 3-1). The reserve is managed by i ndigenous groups (mostly Siona and Secoya) This 655,781-ha reserve is located between th e San Miguel and Aguarico river basins. Palm demographic data were collected over th e span of two years from five plots (each 20m x 100m) located in seasonall y flooded forests. In the first year of sampling all palms in the five plots (seedlings and non-seedlings ) were recorded for demographic data. In the second year of sampling the same pro cedure was used, except seedling data were recorded within ten subplots (5m x 5m) with in each of the larger plots. The data collection in Peru follows the same methods of data collection fr om the Ecuador study site, and will be discu ssed in further detail.

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46 3.2.2 Study Site: Peru Mauritia flexuosa demographic data were collect ed from sites in the lowland forests of the Peruvian Amazon, in the depart ment of Loreto, Peru during the summer of 2006. The field sites are approximately a 2-hou r boat ride south of Iquitos, Peru on the Amazon River and Tahuayo River (app. 90 mile s). Specifically, field locations are adjacent to the Tamshiyacu-Tahuayo Co mmunity Reserve (Figure 3-2). The Tamshiyacu-Tahuayo Reserve is a 322,500ha protect area created by the Peruvian government in 1991. Palm data were collected from five plot s in tropical forest swamps dominated by M. flexuosa palms. Mauritia flexuosa is the monodominant spec ies in these oligarchic forests called Aguajales. Three out of the five plots were in close proximity to rivers and seasonally flooded, while the remaining two pl ots were in low lying locations that remained partially flooded through out th e year and surrounded by terra firme. Demographic data were collected for each nonseedling palm in all five plots (20m x 100m). In plot 1 seedling counts were low, allowing for data to be recorded for each seedling. In plots 2-5 seedling counts were high and subplots were created to estimate seedling data. Seedling data were recorded within eight subplots (5m x 5m) within the larger 20m x 100m plots. In each of the pl ots the demographic data collected consisted of height measurements (actual for palms th at could be reached, and estimated with a clinometer for taller palms), leaf counts on seed lings and most juveniles, sex, leaf scars, diameter breast height (DBH), and raceme c ounts on females. Spatial distance was also measured between each palm to help construc t a layout of the plots and location of palms from each other.

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47 3.2.3 Study Species Role in Peru Mauritia flexuosa is an economically and ecologi cal important non-timber species in the Peruvian Amazon (Padoch 1988, Peters et al. 1989b). The fruit of M. flexuosa has been an important product in the Iquitos ma rket as far back as the mid-1980s, selling approximately 300 sacks per day and experiencing extreme rise in the cost per sack during times of fruit scarcity (Padoch 1988). The largest numbers of fruit are harvested from the large oligarchic palm swamps along the Maranon, Ucayali, and Chambira rivers (Peters et al. 1989a), making M. flexuosa one of the highest exploi ted fruit tree species in Peru. While income from harvesting thes e palms can average to high amounts, the female trees are cut down to retrieve the fru it from the tall palm, ending the production of fruit from harvested palms. Since, over half the total fruit sold in Iquitos is from wild harvested species (Vasquez and Gentry 1989) destructive harvesting methods are a matter of concern. The rise in Aguajale palm swamps do minated by males following harvest, leads to a need for better management and cons ervation, possibly thr ough increased knowledge of population dynamics in palm swamps. It ha s been suggested that a switch to growing M. flexuosa in agroforestry or homegardens plots is beneficial for wild stand management (Vasquez and Gentry 1989, Bodmer et al. 1997). It is hypo thesized, growing M. flexuosa in agricultural settings will reduce use of destructive harvesting techniques, maintain palm populations, and allow wild life to continue foraging on palm fruits. The following wildlife all consume M. flexuosa from most frequent consump tion to least, lowland tapir ( Tapirus terrestris ), white-lipped peccary ( Tayassu pecari ), collared peccary ( Tayassu tajacu ), gray brocket deer ( Mazama gouazoubira) and red brocket deer ( Mazama americana ) (Bodmer et al. 1989).

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48 3.2.4 Palm Distribution and Matrix Model Development: Stage-based matrix population models were used in the study. The development of the matrix models for the Ecuador palm popula tion was described in chapter two of this research. The matrix models from Ecuador will be used as a basis for further analysis in this chapter. The matrix model for palms populations in Ecuador consisted of 7 biological stages, based on size classes. Palms from Peru study sites were classified into the same seven size classes base d on height (Table 3-1) to be consistent with Ecuador methods. Stages consist of 1 seedling, 4 juve niles, and 2 adult stag es. The fecundity (fij) for the Peru population was estimated with th e same fecundity values used in Ecuador (i.e. seedling survival value) due to lack of data. The established number of seedlings in Peru at t+1 is also unknown; therefore the num ber of seedlings at t0 was used as an assumption to provide estimated values of fecundity. 3.2.5 GA Method Description A genetic algorithm is a method that finds optimal solutions by mimicking the process of evolution. A populat ion of individuals evolves over time in order to reach a desired goal or fitness func tion by the following procedure. 1) An initial population is created by randomly assigning genes from a defined range. 2) A reproductive generation cycle is run from the initial popula tion with selective re production (offspring being chosen), mutation, and crossover occurring in the generation cycle. 3) The population of individuals is evaluated for fitn ess. Individual solutions are represented in the next generation proportionally to their f itness. 4) Iteration of generation cycle until maximum fitness is met or until maximum iteration number is reached. During each generation the genetic algorithm contains components for a fixed population size, crossover and mutation rates, an acceptance or rejection criteria for optimal solution, and

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49 time of iteration cutoff. This study defined fitness as the abso lute deviation of the target size-class distribution from the simulated size class distribu tion. The perfect solution would have a fitness value of zero, indicati ng that each simulated size class was exactly equal to the target number. In this study problem-specific genetic al gorithms were generated to find optimal sets of M. flexuosa demographic parameters and pl ausible harvesting scenarios. Following Cropper and Anderson (2004), the first GA optimization was designed to calibrate seedling parameters and estimate carrying capacity. The in itial population was created by randomly selecting seedling survival (stasis) probability from range 0.1 0.8 and carrying capacity from range 100.0 2000.0 palms ha-1. The seedling growth parameter was set using equation 3-1: seedling growth = (1stasis probability) x (3-1) where x is a random value from 0.0-1.0. This equation was used because the sum of the seedling growth and stasis probabiliti es cannot be greater than one. These two seedling parameters along with a carr y capacity parameter are assigned to chromosomes in each individual in the popu lation. The size of the population in this GA was 500. The program was run for 25 gene rations with selection occurring in each generation. This programs fitness go al was to match the observed Ecuador M. flexuosa female distribution. The calibrated parameters were put into the new transition matrix and produced a new simulated population distri bution. Equation 3-2 evaluated the fitness score for all GA optimiza tions in this study: Fitness = (abs(Ntargeti Nsimulatedi)) (3-2)

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50 where Ntargeti are the size-specific palm number s that are the goal for calibration and Nsimulatedi are the size-specific palm numbers produced by the individuals parameter set. A smaller difference is desi red and indicates stronge r population fitness. The remaining GA optimizations used in th e study were similar to the seedling and carrying capacity optimization. The following GA was used to calibrate the observed non-seedling demographic parameters (growth and survival) that make up the transition matrix found in chapter one. There are thirteen non-seedling demographic parameters in the palm population transition matrix. This optimization program created an initial population by assigning random uniform paramete rs needed for calibration between zero and one, for all thirteen demographic parame ters. The demographic parameters for each size class were normalized, if necessary, to prevent transition pr obabilities summing to greater than one. Another set of calibrations used only eleven out of the thirteen values (all six stasis values and all five 1-size cla ss growth values) assuming that the rare 2-size class transitions (only 2 observed) dont occur. If the sum of these three values is greater than one then the parameters were normali zed by dividing each parameter by the sum of all parameters. Mortality is implicit and does not need to be normalized. For each size class (1-6) only the stasis and growth pa rameters (or genes) were assigned to chromosomes. The size of the GA populatio n is 1750 and ran for 75 generations. This programs fitness goal was also to reach the observed Ecuador M. flexuosa female distribution. The last GA optimization focused on the Peru M. flexuosa population. The goal of this GA was to find a plausible pa st harvest history on the Peru M. flexuosa palm population, a location of intens e female harvesting. I assumed that the unharvested

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51 Ecuador population is the starti ng point for a harvesting regime that leads to the size class distribution observed in Peru (the GA target distribution). The op timization initiated by using the values in the observed Ecuador tran sition matrix as initial parameters. The GA population was created with the following parameters to be optimized: harvest intensity percent, harvest frequency in years, length of harvesting (years), and carrying capacity. The value for the harvest intensity was ra ndomly picked from 0.0-100.0%. The harvest frequency was randomly selected from two se parate ranges 1-40 yrs and 1-80 yrs. The length of harvesting was randomly selected from two ranges 50-300 yrs, 100-500 yrs respectively correlating with the two harvest frequencies. The carrying capacity for the Peru population was randomly selected from multiple ranges 200-900, 300-1000, and 400-1000 non-seedling individuals per ha. The si ze of the GA population in this program was 500 and ran for 25 generations A second round of GA optimizations to find the past harvesting history of the Peru palm fo rests was ran using the optimal Ecuador demographic parameters found in this study, in place of the observed demographic parameters. 3.3 Results 3.3.1 Genetic Algorithms The genetic algorithm (GA) used to calib rate the seedling survival and growth parameters had an average fitness (differen ce between observed and simulated size class distributions) of 46.67 (Figur e 3-3). GAs cannot be gua ranteed to find the global optimum. The stochastic elements of initial parameter selection, mutation, and crossover are needed to reduce the computer time needed to exhaustively evaluate the parameter space. Multiple GA runs were used to evalua te the robustness of the solution; each run scored approximately 46. The probabilities for seedling survival (matrix position A00)

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52 and seedling growth (matrix position A10) varied over a wi de range (Table 3-2). The values for carrying capacity in a 1ha ar ea were found to range between 346 and 374 nonseedling palms (Table 3-2). I found that the observed demographic parameters do not closely match the observed size class distribution. The ma trix population model using the observed demographic data from the study sites in Ecuador simulated a size class distribution equivalent to a fitness score of 67.03 (Figur e 3-4). The transition probabilities (also called demographic parameters) of the Ec uador and seedling GA results were not consistent with the observed size class distributio n. I next explored calibration of all stasis and growth parameters (mortality is implicit) for each non-seedling size class. These GA optimizations are unconstrained, exce pt for the requirement that the sum of size class probabilities cannot exceed one. The result for the unconstrained GA that found a set of 13 optimal demographic parame ters has a fitness score of 14.14, producing a lambda of 1.007 (Figure 3-5). The unconstr ained GA with 11 demographic parameters (excluding the 2-size class growth parame ters) has a fitness score of 5.07, producing a lambda of 1.039 (Figure 3-6). Some of the optimal parameter values fell outside the range of plot variation (Figur e 3-7). The danger of optimiz ing a large set of unknowns is finding values that match the target, but do not have biologically plausibility. Optimization with values constrained to th e observed range (Table 3-3) was used to address this issue. Six separate GA runs used the constrai ned parameter ranges. Three GA runs optimized all 13 parameters, and three othe rs did not include 2-size class growth transition parameters. The three runs for op timizing all 13 demographic parameters have

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53 fitness scores of 6.29, 9.07, and 7.19 (Figure 3-8). The three runs for optimizing demographic parameters without the 2-size cl ass growth transitions have scores of 7.69, 12.03, and 13.96 (Figure 3-9). In figure 3-7, 3-8 and 3-9 the combined data is the values for the observed Ecuador stasis and gr owth parameters of the transition matrix created in chapter one of this thesis. These data were based on pooling all of the individual plot data. The best scoring r un (Figure 3-10) optimizing all 13 demographic parameters has a score of 6.29 and a lambda of 1.040. The best scor ing run (Figure 3-11) with no 2-size class growth parameters is 7.69, which has a lambda of 1.038. In figure 310 and 3-11, I found that size cl ass three and four have the largest differences between the observed and simulated size class distributions. Figure 38 and 3-9 shows that size class three and four also ha ve the largest difference obser ved and simulated demographic parameters. The new transition parameters from the two best constraine d GA optimizations were compared to the empirical transiti on parameters (Table 3-4). The CAV6.29 (constrained, all values) GA parameter set produ ced stasis parameters (except size class 1) that are lower then the empirical stasis parameters. The same GA optimization also shows that the growth parameters are gene rally greater than th e empirical growth parameters (except size class 1 and both size class 2 growth transiti ons). Similar results are seen for the optimal parameters in th e matrix with CNT 7.69 (constrained, no twosize class transitions). In the CNT 7.69, the optimal demographic parameters have a larger difference from the empirical demographic parameters, then the optimal parameters in the CAV6.29 run.

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54 Optimization of seedling parameters a nd carrying capacity was conducted a second time using the new optimal demographic parameters from both unconstrained and constrained GA versions. Four separate replicates were run in each of the four GA versions to assist in accessi ng variation. Table 3-5 shows th e new results of the optimal seedling survival, seedling growth, and carry ing capacity for the Ecuador population. All of the replicates in the tw o unconstrained GA versions (s core 14.14 and 5.07) as well as in the two constrained GA versions (score 6.29 and 7.69) show seedling parameter values which vary over a wide range. In each of the four GA versions, the four separate replicates all produce a very similar fitness sc ore to each other, showing that the seedling parameters are insensitive to contributing to the number of individuals in the nonseedling size classes. While all the ne w fitness scores are preferable, seedling demographic values vary and show inconsistency in each of the four re plicates in all four GA versions, and seedling parameters are insensitive during GA optimization. There should be little confidence that the GA is a useful tool for seedling parameter optimization based when each run finds a greatly different local optimum. 3.3.2 Peru Size Class Distribution and Demographic Characteristics At the Peruvian study site 198 non-seedling individuals were present in the 1ha area (seedling size class = 2342). The distribution of indi viduals shows the largest amount of palms in size class 1, followed by size class 5, with the lowest amount of palms in size class 2, 3, 4, and 6 (Table 3-1 and Figure 3-12). The total number of nonseedling individuals in the Ecuador study site is 336 (seed ling number were 260 and 1460 respectively during two years of sampling). The number of adult male and adult female palms per ha area sampled in Peru is 54 a nd 23 respectively (Figure 3-13). The number of adult male and adult female palms in Ec uador, where harvesting palms in minimal, is

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55 54 and 35 respectively. The estimated averag e fecundity for females in the Peruvian palm population is 18.2, with 5.2 for size class five and 31.2 for size cl ass six. Size class six has fewer reproductive females compared to size class five (3 to 18 respectively, Table 3-1). The taller female palms in si ze class six are more likely to be felled for retrieval of the M. flexuosa fruit. Further results of the Ecuador palm population dynamics can be found in chapter 2. Peru palm demographic data on number of leaf scars, DBH, and trunk height for palm individuals in size class 3, 4, 5, and 6 can be found in table 6. Demographic data were recorded for palms in all size classes, and in the juvenile and adult size classes (three through six); data related to palm tr unks is available. At size class three some palms transitioned from multiple petioles to beginning to form a trunk. Palms in the increasing size classes (4-6) ha ve trunks formed. The numbe r of leaf scars was highest for palms in size class 5 (20-28m), with an average of 61.5 scars present on the trunk. The tree diameter at breast height was larges t for palms in size cla ss 6 (>28m), with an average of 99.2 cm. Palms are originally a ssigned into size classe s based on their total height (trunk height and leaf height). The average height of only trunks (not total height) for pre-reproductive palms in size class three was 2.6m and in size class four was 9.0m (Table 3-6). Between each size class ther e was approximately 6.5 7.5m difference in average trunk height. 3.3.3 Genetic Algorithm: Harvest History for Peru M. flexuosa Palm Population GA optimizations have been run to find pl ausible harvesting histories that could lead from a population distribut ion observed in Ecuador to the distribu tion that is currently seen in Peru. Although this t echnique cannot reconstr uct actual harvest histories, it may illustrate harvest regimes of realistic magnitude. The transition matrix

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56 from the study site in Ecuador produced a lambda of 1.046 (a growing population projection) and 336 non-seedling individuals pe r ha. It is assumed that Ecuadors population demographic parameters and distri bution of individuals are at a somewhat stable, healthy state. The lambda for the population in Peru in unknown at this point, but as reported there are 198 non-seedling indi viduals per ha. Six GA runs using the observed Ecuador demographic parameters had fitness scores ranging from 62.8 to 135.4 (Table 3-7) and varying parameter results (harvesting percent, harvesting frequency, harvest length, and fitness scor es). In all six runs the carrying capacity value showed a trend of reaching the lowest value allowed in the range. Harvest lengths were highly variable and tended to be extreme values within the range. Th ese optima represented poor fits to the target and do not represen t plausible harvesting regimes for transition from the Ecuador to Peru size class distribution. The GA-based optimal demographic parameters were used in a second round of GA optimizations to find plau sible harvest histories in Peru, using the same parameter inputs. Each of the four optimal demogr aphic parameter results (two unconstrained trails: score 14.14 and 5.07, and two constrai ned trails: score 6.29 and 7.69) had six separate GA runs for a total of 24 harves ting optimizations, which produced fitness scores varying from 41.4 to 74.7 (Table 3-8) Harvest percent and harvest frequency were the most variable; changing in each of the 24 runs. Typically the optimal carrying capacity was found at the lowest end of the range possible, except for the six versions in the GA with all 13 unconstrained demographic parameters. Another trend was that the length of harvest is typically found at the highest end of the ra nge, except for the six versions in the GA with all 13 uncon strained demographic parameters.

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57 3.4 Discussion 3.4.1 Genetic Algorithms The first GA approach was to calibrate seedling survival and growth in the transition matrix and carrying capacity for a palm population from Ecuador. As noted earlier in this study, Cropper and Anders on (2004) successfully found the seedling survival and growth parameters for the palm Iriartea deltoidea. Our study did not find seedling survival and growth parameters that closely matched the observed Ecuador population distribution. The s eedling parameters found by the GA created a simulated size class distribution that had a difference of 46.62 individuals from the observed population. Furthermore, an assortment of s eedling survival and growth transition values repeatedly produced a similar population di stribution for each size class. Seedling parameters found by the GA were insensitive to matching non-seedling size classes with the observed size classes. This led us to be lieve that other demographic parameters might be poorly estimated. The carrying capacity found by the GA is similar to the observed Ecuador carrying capacity. Assuming that the Ecuador size class distri bution was measured with less error than the transition rates, GA optimization should lead to improved parameter estimates. Separate runs of GAs were able to generate optimal non-seedling demographic parameters that did match the observed populatio n distribution. It was first found that the empirical demographic parameters from the pool ed data in the Ecuador study plots did a relatively poor job of matching the obse rved Ecuador population distribution (a difference of 67.03 individuals). Poorly es timated demographic parameters are most likely a result of sampling erro r in this study. All four GAs that estimated optimal demographic parameters produced a good fit to the fitness goal, the observed population

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58 distribution. Interestingly, th e unconstrained GA (with a diffe rence of 14.14 individuals) had an optimum matrix, which was not similar to the observed transition matrix, even though the simulated and observed size class dist ributions were similar. The consistent deviations of GA estimates of size classes th ree and four parameters from the observed data may implicate these data as poorly sample d. In the observed data there were rare 2size class growth transition proba bilities in size class 1 and 2. Only one palm in each size class makes this rare 2-size class growth tran sition. The next GA a ssumes that there are never these rare 2-size class growths. This GA produced demographic parameters that had the best fitness (a summed difference of 5.07 individuals). Optimal demographic parameters from the two previous GAs were a good fit to the observed size class distribution, but optimal st asis and growth parameters fell outside the observed range of demographic parameters. By constraining the optimal parameters to within the range of observed parameters, mo re realistic parameters can be found which still have a strong fitness score. Usually it is not be neficial to constrain initial parameters in a GA, but results from the unconstrained GAs produced stasis and growth parameters in size class 1, 3, and 4 that were unlikely. Both constrained GAs create good fits to the observed distribution, with similar fitness scores (6.29 and 7.69). Abandoning the 2-size class growth transition does not notably affect the GA optimizations. Multiple runs of the same GA are recommended because GA optimizations can get stuck in a local parameters space minimum. Since the GA technique was able to calibrate the non-seedling demographic parameters, it was beneficial to use these new parameters to re-estimate the seedling survival and growth parameters. Using th e optimal demographic parameters did find

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59 seedling parameters that produced a size cl ass distribution that matched the observed population distribution, but as seen before th e seedling parameters varied over a wide range in each separate trial. It would be premature to conclu de that seedling survival is of little demographic importanc e in these populations, but variation in seedling survival and growth may not contribute significantly to the size class di stribution of larger palms. 3.4.2 Peru Size Class Distribution and Demographic Characteristics The ratio of adult males to female palms in Peru implies that removal of female palms has been occurring. The main target of female palm removal is size class six, which contains the tallest palms and is assume d to be the most difficult to climb. This removal of adult female palms can alter th e seedling regeneration, density dependence, and interactions with other specie s. Comparing the distribution of M. flexuosa palms in Ecuador and Peru displays the impact of harvesting in Peru and consequently the eradicate number of individua ls in each size class. Th is study has shown there is difficulty in estimating demographic transition values in Ecuador, lead ing to the use of a GA to calibrate parameters, it is also predicted that the difficulty will be just as challenging if not more fo r the Peru population. Leaf scars on palms are one method to estimate the rate at which palms are growing, as well as the length in time palms have been growing. It is predicted that the palms in the larger size class six are growi ng at a fast rate, presumably to reach the canopy and become emergent. Size class six M. flexuosa have on average fewer leaf scars than size class five M. flexuosa palms, and may indicate growing at a faster rate than shorter M. flexuosa palms. It is also interesting to look into the difference in trunk height between size classes. The large incr ease in trunk height from size class three to size class four, (as well as into size class five), might suggest that palm growth is rapid in

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60 late juvenile and possibly early reproductive stages. This co incides with data collected on palms in Ecuador (see second chapter). The Ecuador transition matrix shows a high growth probability in size class three (a lthough GA parameter estimates indicate that the observed rate could be an overestimate). Th e relatively low numbers in size classes three and four may also indicate a ra pid growth to the adult sizes. 3.4.3 Genetic Algorithm: Peru M. flexuosa Palm Population Estimating the harvesting hi story and carrying capacity of the Peruvian palm population was challenging. Our study did not find harvesting valu es that closely matched the observed Peru size class distri bution. There are many combinations of harvesting parameters that could have occu rred in the past to produce the observed population distribution. Cons equently, the GA technique was not able to provide plausible levels of prior palm removal in Peru. Reasons might include: 1) the Peru population has different demogr aphy (survival, growth, fecundity) than Ecuadors population and 2) the actual history of harv est was not regular and uniform. Estimating the optimal carrying capacity was also a challe nge, but it is possible that the carrying capacity in Peru is lower than observed in other M. flexuosa popul ations, because the GA generally converges on lowest carrying capaci ty possible. Through communication with local Peruvians and knowledge of past area hi story, we know that female palm harvesting has occurred in our area of data collection. 3.5 Conclusions Genetic algorithms may be useful for calibrating demographic parameters in a matrix model. Constraining the demographic pa rameters to be chosen within a realistic range resulted in the best procedure. Usua lly GA initial search parameters are limited when they are constrained, providing lower fitness results than unconstrained GAs, but

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61 that was not the case in this study. The dem ographic data showed that this particular palm population has rare transi tions (two individuals grew two size classes in one time step). I found that excluding the rare, two size class growth transitions did not strongly affect the GA optimizations. These large, rare transitions and other vital rates might have been incorrectly recorded due to sampling e rror. Sampling error is a common problem in population data collection. Th is study found that sampling error (specifically in estimating stasis parameters) could affect the accuracy of transition matrix models, while rare growth transitions do not have an effect. While a previous GA has estimated seedli ng survival and growth parameters for a tropical palm, this study was unable to estimate consistent seedling parameters that matched the non-seedling population distribution. In this study, th e value of seedling survival and growth parameters for the Ecuador palm population is insensitive to optimization. The recorded palm data fr om Peru does show that the population is experiencing loss of females due to harvesti ng. This study was also unable to accurately estimate the harvesting trends that have occurr ed in the past to produce the observed Peru study site distribution. Palm remo vals in wild locations in Peru are likely to continue in the future, until there is a full sw itch to agricultural gardens of M. flexuosa Accurately understanding demographic parameters through th e use of parameter calibration is greatly needed for management of harvesting or sp ecies recovery and restoration efforts.

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62 Table 3-1. M. flexuosa population distribution, for palms in a 1ha area, from Peru and Ecuador, as well as the number of male and female palms in each size class from both locations. (Palms generally b ecome reproductive at size class 5, but in Peru some palms were seen to become reproductive in size class 4). Peru Peru Peru Ecuador Ecuador Ecuador Size Classes N(t) 2006 Males FemalesN Males Females 0 <1.0 2342.01171.01171.0260.0130.0 130.0 1 1.01-3.0 72.036.036.087.043.5 43.5 2 3.01-6.0 22.011.011.0101.050.5 50.5 3 6.01-10.0 10.05.05.027.013.5 13.5 4 10.01-20.0 20.010.0 10.032.016.0 16.0 5 20.01-28.0 60.041.0 18.047.029.0 18.0 6 >28.01 14.011.03.042.025.0 17.0 Total 198.054.0a23.0a336.054.0a 35.0a a Total number of only re productive individuals.

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63 Table 3-2. Optimal values for two seedli ng parameters (seedling stasis probability (matrix position A00), seedling growth probability (matrix position A10)), and for Ecuadors carrying capacity (K ) in a 1ha area, using observed demographic data. Seedling and K runs with observed data K A00 A10 Opt Score 348 0.5899 0.005046.766 346 0.1734 0.717846.624 374 0.0257 0.005646.617

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64 Table 3-3. Observed range of the 13 non-seed ling demographic transition probabilities, found from data collected at 5 se parate study plots in Ecuador. Ecuador Plot Observations Matrix position Low range High range 1 A11 0.500.9290 2 A21 0.070.5000 3 A22 0.620.9600 4 A31 0.000.0115 5 A32 0.040.3800 6 A33 0.660.8500 7 A42 0.000.0099 8 A43 0.140.3300 9 A44 0.500.8800 10 A54 0.000.5000 11 A55 0.671.0000 12 A65 0.000.3300 13 A66 0.670.9230

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65 Table 3-4. Transition matrices for 1) th e observed pooled data in Ecuador, 2) GA optimization for all 13 demographic parameters, with constraints on parameters, and 3) GA optimization for all demographic parameters expect 2 size class growth transitions, w ith constraints on parameters. Observed transition values Seedlings Young Juveniles Old Juveniles Adult <1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m 0.4923 0.0 0.00.00.016.8 16.8 0.0115 0.7471 0.00.00.00.0 0.0 0.0 0.2184 0.89110.00.00.0 0.0 0.0 0.0115 0.09900.77780.00.0 0.0 0.0 0.0 0.00990.22220.78130.0 0.0 0.0 0.0 0.00.00.18750.8723 0.0 0.0 0.0 0.00.00.00.0851 0.8810 Score 6.29 Optimal GA values all demographic parameters Seedlings Young Juveniles Old Juveniles Adult <1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m 0.4923 0.0 0.00.00.016.8 16.8 0.0115 0.8204 0.00.00.00.0 0.0 0.0 0.1700 0.85360.00.00.0 0.0 0.0 0.0077 0.12760.64400.00.0 0.0 0.0 0.0 0.00590.31710.60400.000 0.0 0.0 0.0 0.00.00.34500.8150 0.0 0.0 0.0 0.00.00.00.1310 0.8460 Score 7.69 Optimal GA values no 2 size class transition parameters Seedlings Young Juveniles Old Juveniles Adult <1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m 0.4923 0.0 0.00.00.016.8 16.8 0.0115 0.8210 0.00.00.00.0 0.0 0.0 0.1590 0.86020.00.00.0 0.0 0.0 0.0 0.13890.62340.00.0 0.0 0.0 0.0 0.00.30980.64570.000 0.0 0.0 0.0 0.00.00.32950.8250 0.0 0.0 0.0 0.00.00.00.1698 0.7800

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66 Table 3-5. Optimal values for two seedling para meters, seedling stasis probability (matrix position A00), seedling growth probabil ity (matrix position A10), and for Ecuadors carrying capacity (K) in a 1ha area. Results from using unconstrained parameters All Transitions (14.14) No 2-size Class Transitions (5.07) K A00 A10 Opt Score K A00 A10 Opt Score 380 0.03061 0.77135 14.1933500.43410.00507 5.008 380 0.13129 0.82250 14.1933500.49310.00463 5.008 1660 0.53000 0.00971 13.8703480.17860.00814 5.214 379 0.11627 0.51079 14.2524300.77000.00173 4.958 Results from using constrained parameters All Transitions (6.29) No 2-size Class Transitions (7.69) K A00 A10 Opt Score K A00 A10 Opt Score 368 0.16995 0.19438 6.225 3610.647870.13415 7.674 475 0.76935 0.00201 6.362 3620.632580.00407 7.683 369 0.23126 0.00898 6.212 3610.105010.89291 7.674 370 0.31195 0.00676 6.210 3610.173420.80883 7.674

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67 Table 3-6. Demographic traits for the Peru popul ation in size classes 3-6 (palms that have developed trunks). Pre-reproductive Juveniles Reproductive Adults Size Class 3 Size Class 4 Size Class 5 Size Class 6 Avg. # of Leaf Scars na29.461.560.4 Avg. DBH (cm) na84.286.699.2 Avg. Trk. Height (m) 2.69.016.524.2

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68Table 3-7. GA estimates of harvest regimes consis tent with the observed size class distribution. RESULTS USING OBSERVED DEMOGRAPHIC PARAMETERS Parameter Inputs Parameter Outputs harvest percent harvest frequency (yr) harvest length (yr) carrying capacity harvest percent harvest frequency (yr) harvest length (yr) carrying capacity opt score 0.0-100.0 1.0-41.0 50-30140010000.7431.0 50.0400.0130.8 0.0-100.0 1.0-81.0 100-50140010000.4221.0 101.0400.0135.4 0.0-100.0 1.0-41.0 50-30130010000.496.0 300.0300.099.7 0.0-100.0 1.0-81.0 100-50130010000.0113.0 500.0300.099.7 0.0-100.0 1.0-41.0 50-301 200-9000.706.0 300.0200.062.8 0.0-100.0 1.0-81.0 100-501200900 0.2779.0 482.0200.062.8

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69Table 3-8. Perus harvesting hist ory found using separate GAs which uses the four sets of Ecuador optimal demographic paramete rs to reach Perus observed populat ion distribution. Optimization found harvest percent, harvest frequency, length harvesting has occurred, and carrying capacity. RESULTS USING CAV 6.29 (CONSTRAINED, ALL VALUES) OPTIMAL DEMOGRAPHIC PARAMETERS Parameter Inputs Parameter Outputs harvest percent harvest frequency (yr) harvest length (yr) carrying capacity harvest percent harvest frequency (yr) harvest length (yr) carrying capacity opt score 0.0-100.0 1.0-41.0 50-30140010000.7127.0 300.0400.059.9 0.0-100.0 1.0-81.0 100-50140010000.611.0 414.0400.059.9 0.0-100.0 1.0-41.0 50-30130010000.5623.0 300.0300.048.1 0.0-100.0 1.0-81.0 100-50130010000.1454.0 429.0300.048.1 0.0-100.0 1.0-41.0 50-301 200-9000.4237.0 300.0200.047.0 0.0-100.0 1.0-81.0 100-501200900 0.4645.0 451.0200.047.0 RESULTS USING CNT 7.69 (CONSTRAINED, NO TWO SIZE-CLASS TRANSITIONS) OPTIMAL DEMOGRAPHIC PARAMETERS Parameter Inputs Parameter Outputs harvest percent harvest frequency (yr) harvest length (yr) carrying capacity harvest percent harvest frequency (yr) harvest length (yr) carrying capacity opt score 0.0-100.0 1.0-41.0 50-30140010000.3918.0 300.0400.055.8 0.0-100.0 1.0-81.0 100-50140010000.2936.0 462.0400.055.8 0.0-100.0 1.0-41.0 50-30130010000.7719.0 300.0300.045.8 0.0-100.0 1.0-81.0 100-50130010000.6156.0 444.0300.045.8 0.0-100.0 1.0-41.0 50-301 200-9000.6536.0 297.0200.045.5 0.0-100.0 1.0-81.0 100-501200900 0.1472.0 459.0200.045.5

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70 Table 3-8. Continued RESULTS USING UCNT 5.07 (UNCONSTRAINED, NO TWO SIZE-CLASS TRANSITIONS) OPTIMAL DEMOGRAPHIC PARAMETERS Parameter Inputs Parameter Outputs harvest percent harvest frequency (yr) harvest length (yr) carrying capacity harvest percent harvest frequency (yr) harvest length (yr) carrying capacity opt score 0.0-100.0 1.0-41.0 50-30140010000.8634.0 300.0400.074.7 0.0-100.0 1.0-81.0 100-50140010000.631.0 469.0400.074.7 0.0-100.0 1.0-41.0 50-30130010000.5917.0 300.0300.048.5 0.0-100.0 1.0-81.0 100-50130010000.4480.0 491.0300.048.5 0.0-100.0 1.0-41.0 50-301 200-9000.5111.0 300.0200.046.4 0.0-100.0 1.0-81.0 100-501200900 0.5110.0 499.0200.046.4 RESULTS USING UCAV 14.14 (UNCONSTRAINED, ALL VALUES) OPTIMAL DEMOGRAPHIC PARAMETERS Parameter Inputs Parameter Outputs harvest percent harvest frequency (yr) harvest length (yr) carrying capacity harvest percent harvest frequency (yr) harvest length (yr) carrying capacity opt score 0.0-100.0 1.0-41.0 50-30140010000.3623.0 50.0999.041.4 0.0-100.0 1.0-81.0 100-50140010000.856.0 100.0999.045.0 0.0-100.0 1.0-41.0 50-30130010000.3835.0 50.0999.041.4 0.0-100.0 1.0-81.0 100-50130010000.2969.0 101.0998.045.1 0.0-100.0 1.0-41.0 50-301 200-9000.7234.0 50.0896.042.3 0.0-100.0 1.0-81.0 100-501200900 0.2557.0 102.0897.045.9

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71 Figure 3-1. Map of study site in Ecuador. Cuyabeno Faunal Re serve is located in the north-eastern section of Ecuador in the highlighted area. (Source: http://www.ecuaworld.com/map_of_ecuador.htm last accessed July 25, 2007). N

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72 Figure 3-2. Map of study s ite in Peru. (Source: http://www.micktravels.com/peru/images/peru_map.jpg last accessed July 22, 2007). Study site along Tahuayo River, adjacent to TamshiyacuTahuayo Communal Reserve. N

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73 Figure 3-3. Genetic algorithm simulated (red ba rs) and observed distribution (blue bars) for the Ecuador palm population after running a GA to find optimal seedling survival and growth parameters using the observed transi tion parameters. Fitness score for this GA is 46.67, found by (( (abs(observed distribution simulated distribution)).

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74 Figure 3-4. Genetic algorithm simulated and observed distribution for the Ecuador palm population after running a GA using the observed transition parameters and evaluating how well it matches the observed population distribution. Fitness score for this GA is 67.03, found by (( (abs(observed distribution simulated distribution)).

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75 Figure 3-5. Genetic algorithm simulated and observed distribution for the Ecuador palm population after running an unconstraine d GA to optimize all non-seedling demographic parameters in the transition matrix. Fitness score for this GA is 14.14, found by (( (abs(observed distribution simulated distribution)).

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76 Figure 3-6. Genetic algorithm simulated and observed distribution for the Ecuador palm population after running an unconstrained GA to optimize non-seedling stasis and growth parameters in the transition matrix (two size class growth transitions not included). Fitness score for this GA is 5.07, found by (( (abs(observed distribution simulated distribution)).

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77 0 0.2 0.4 0.6 0.8 1 1.2 123456 Size ClassesTransition Probability Low range High Range Combined data GA optimum 14.14 GA optimum 5.07 A 0 0.1 0.2 0.3 0.4 0.5 0.6 12345 Size ClassesTransition Probability Low range High range Combined data GA optimum 14.14 GA optimum 5.07 B Figure 3-7. Stasis and growth demographic points generated from an unconstrained GA. The red lines in both figures A and B, are the lo w and high ranges of possible demographic points measured from the five plots in Ecuador. (A) Demographic data of stasis transition parameters for three separate trials, 1) the combined data from the observed study plots, 2) the unconstr ained GA run with all 13 demographic parameters, and 3) the unconstrained GA run without the 2 size class growth parameters. (B) Demographic data of grow th transition parameters for the same three separate trials.

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78 0 0.2 0.4 0.6 0.8 1 1.2 123456 Size ClassTransition Probabilit y Low range High range Combined data GA optimum 6.29 GA optimum 9.07 GA optimum 7.19 A 0 0.1 0.2 0.3 0.4 0.5 0.6 0123456 Size ClassTransition Probabilit y Low range High range Combined Data GA optimum 6.29 GA optimum 9.07 GA optimum 7.19 B Figure 3-8. Stasis and growth demographic poin ts generated from a constrained GA. The red lines in both figures A and B, are the lo w and high ranges of possible demographic points measured from the five plots in Ecuador. (A) Demographic data of stasis transition parameters for the combined data from the observed study plots, and three separate constrained GA trials that calib rate estimates of all 13 demographic parameters. (B) Demographic data of growth transition parameters for the combined data from the observed study plots, and the same three separate trials

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79 0 0.2 0.4 0.6 0.8 1 1.2 123456 Size ClassTransition Probability Low range High range Combined Data GA optimum 7.69 GA optimum 12.03 GA optimum 13.96 A 0 0.1 0.2 0.3 0.4 0.5 0.6 0123456 Size ClassTransition Probability Low range High range Combined Data GA optimum 7.69 GA optimum 12.03 GA optimum 13.96 B Figure 3-9. Stasis and growth demographic poin ts generated from a constrained GA. The red lines in both figures A and B, are the lo w and high ranges of possible demographic points measured from the five plots in Ecuador. (A) Demographic data of stasis transition parameters for the combined data from the observed study plots, and three separate constrained GA trials that calibra te estimates of demographic parameters without the 2 size class growths. (B) De mographic data of growth transition parameters for the combined data from th e observed study plots, and the same three separate trials.

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80 Figure 3-10. Simulated output of the best constrained GA run with all 13 demographic parameters. Simulated and observed dist ribution for the Ecuador palm population after running a GA to optimize all non-s eedling demographic parameters in the transition matrix. Fitness score for this GA is 6.29 found by (( (abs(observed distribution simula ted distribution)).

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81 Figure 3-11. Simulated output of the best constraine d GA run with demographic parameters that do not include 2 size class growths. Simu lated and observed distribution for the Ecuador palm population after running a GA to optimize all stasis and 1 size class growth non-seedling demographic parameters in the transition ma trix. Fitness score for this GA is 7.69 found by (( (abs(observed distribution simulated distribution)).

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82 0 20 40 60 80 100 120 123456 Size ClassN Peru Ecuador Figure 3-12. M. flexuosa population distribution for palm populations in a 1ha area in Peru and Ecuador (seedling, size cla ss zero, not included).

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83 0 10 20 30 40 50 60 Male Female Avg. FecundityN Peru Ecuador Figure 3-13. Distribution of male vs. female pa lms and estimated, averaged fecundity values from Peru and Ecuador.

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84 CHAPTER 4 SUMMARY 4.1 Applicability This research has potential use for creation of Mauritia flexuosa management plans that can be applied to the studied Ecuadorian palm population. Forest-dwe lling people who utilize M. flexuosa can use the results from the harvesting simulations for specifically the examined Ecuador population. Multiple communities who harvest wild M. flexuosa from the same populations will need to create co llaborative harvesting plans that meet all stakeholders needs as well as abide by sustainable harvesti ng limits proposed in this resear ch. It is the hopes of this author that these methods can also be applied to M. flexuosa palm populations in all parts of the Amazon. To do so, specific population dynamics such as transition probabilities and growth rate will have to be estimated for populations in se parate locations. Then similar methods of development for modeling sustainable harvesting s cenarios can be applied. This study is also applicable to other ha rvested palm species through the tropics. The results found from the genetic algorithm (GA) optimization conclude that matrix model parameters can be calibrated to fi nd optimal demographic parameters. The GA optimizations in this study have applicability to aid in parameterization of current and future matrix population models that ar e developed with sampling error. Accurate matrix population models can be applied to improvement of population management plans. 4.2 Future for M. flexuosa It is difficult to predict the exact future for a species, but it is estimated that fruit from M. flexuosa will continue to be a marketable resource. In Peru there is a switch from harvesting palms in the wild, to growing M. flexuosa in gardens and small agricultu ral plots. It is predicted that this palm could become a do mesticated crop in other Amazon locations and countries. Data

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85 collected on palms grown in homegardens in Peru s how that palms mature at a shorter height and in a faster time span (Figure A1). Data collected on juvenile M. flexuosa in homegardens also show that the number of petioles is on average higher than palms located in wild populations (Figure A-2). Palms that are maintained in gardens with initial w eeding, spacing, and some maintenance can develop into each size class at a faster rate then seen in the wild (Figure A-3). This data shows that M. flexuosa has the potential to succe ssfully be domesticated. 4.3 Future Research To fully understand the switch to growing M. flexuosa as a cultivated palm, crop evolution and genetics should be studied for the species. There is a potential that a genetic selection is already occurring for choosing dwarf palms. Ag ricultural research, su ch as planting season, intercropping management, pl ant nutrition, and disease and pest management, should be considered for this species before it goes in to large-scale tropical crop production. Future research on understanding the population dynamics of this species is still needed. For example, each size classs role in density dependence s hould be further understood. Fecundity rates for female palms during different stages of popula tion equilibrium and non-equilibrium should be understood in more detail. A prompt future st udy should use the optimal transition matrices containing optimal demographic parameters to immediately re-estimate sustainable harvesting scenarios for Ecuador populations. It is pr oposed that the demographic parameters found by GAs in this study should estimate more accurate harvesting regimes.

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86 APPENDIX A PERU GARDEN DATA FOR MAURITIA FLEXUOSA Data collected from three separate home gardens in the Peruvian Amazon show the difference between palms grown in gardens and palm s in wild locations. This difference is seen in palm height, number of petioles, and the size of petiole sheaths. A main difference is that cultivated palms become mature and reproductive at a shorter height. This is an important process for harvesting fruit in a non-destructive manner. I believe more data on cultivated M. flexuosa is needed to understand the difference be tween palms growing in the wild and palms in gardens. In Figure A-1 the following is the number measured (N) for each category of palms. Wild population: 76, 12, and 36 for young juveniles, old juveniles, and ad ults respectively. Garden population: 104, 26, and 11 for young juveniles, old juveniles, and adults respectively. Seedlings were not measured in garden locations In Figure A-2 the following is the number measured (N) for each category of palms. Smalle r juveniles: 34 and 32, respectively for garden palms and wild palms. Larger juveniles: 70 and 50, respectively for garden palms and wild palms.

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87 0 5 10 15 20 25 30 Seedling Young Juv. Old Juv. Adult Palm StagesHeight (m) Wild population Garden population Figure A-1. Average height (m) for M. flexuosa palms in the seedling stage, young juvenile stage, old juvenile stage, a nd adult (reproductive) stage; from palms sampled in wild population and gardens in Peru. pjg 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Garden height (m) Wild pop. height (m) Garden petiole count Wild pop. petiole countHeight and petiole counts Smaller Juveniles Larger Juveniles Figure A-2. Comparison of average palm height and average number of petioles, for juvenile M. flexuosa located in gardens and w ild populations (in Peru).

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88 A B Figure A-3. M. flexuosa palms in Peru homegardens. (A) Pi cture of juvenile (pre-reproductive) M. flexuosa palms in a homegarden. (B) Picture of dwarf, reproductive female palm. Both pictures were ta ken by Dr. Jim Penn in 2006.

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89 LIST OF REFERENCES ALVAREZ-BUYLLA, E. R., R. GARCIA-BARRIOS, C. LARA-MORENO, AND M. MARTINEZ-RAMOS. 1996. Demographic and genetic models in c onservation biology: applications and perspectives for tropical rain forest tr ee species. Annu. Rev. Ecol. Syst. 27: 387-421. ANDERSON, A. B., M. J. BALICK, AND P. MAY. 1991. The subsidy from nature: palm forests, peasantry, and development on an Amazon fron tier. Columbia University Press, New York City, New York. ANDERSON, P. J., AND F. E. PUTZ. 2002. Harvesting and conservation: are both possible for the palm, Iriartea deltoidea ? For. Ecol. Manage. 170: 271-283. ASANZA, E. 1985. Distribucin, biologa, y alimentacin de cuatro especies de Alligatoridae, especialment Caiman crocodilus en la Amazonia de Ecuador Thesis. Departmento Ciencias Biolgicos. P. Univer sidad Catlica del Ecuador, Quito. AUGSPURGER, C. K., AND C. K. KELLY. 1984. Pathogen mortality of tropical tree seedlings: experimental studies of the effects of di spersal distance, seedling density, and light conditions. Oecologia. 61: 211-217. BALICK, M. J. 1988. The use of palms by the Apinay a nd Guajajara Indians of Northeastern Brazil. Adv. in Econ. Bot. 6: 65. BALICK, M. J., AND H. S. BECK. 1990. Useful palms of the wo rld: a synoptic bibliography. Columbia University Press, New York City, New York. BATES, D. M. 1988. Utilization pools: A framework for comparing and evaluating the economic importance of palms. In Balick, M. (Ed.). The palm tree of life: biology, utilization and conservation, pp.56-64. Proceedings of a Symp osium at the 1986 Annual Meeting of the Society for Economic Botany. New York City, New York. BERRY, E. J., AND D. L. GORCHOV. 2007. Female fecundity is depende nt on substrate, rather than male abundance, in the wind-pollin ated, dioecious understory palm Chamaedorea radicalis Biotropica. 39: 186-194. BODMER, R. E. 1989. Frugivory in Amazonian artiodactyl a: evidence for the evolution of the ruminant stomach. J. of Zoo. 219: 457-467. BODMER, R. E. 1990. Fruit patch size and fr ugivory in the lowland tapir ( Tapirus terrestris ) J. Zoo. 222: 121-128. BODMER, R. E. 1991. Strategies of seed dispersal a nd seed predation in Amazonian ungulates. Biotropica 23: 255-261.

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90 BODMER, R. E., J. W. PENN, P. PUERTAS, L. MOYA, AND T. G. FANG. 1997. Linking conservation and local people through sust ainable use of natural resources: community based management in the Peruvian Amazon. In C. H. Freese (Ed.). Harvesting wild species: Implications for biodiversity conservati on, pp. 315-358. The Johns Hopkins University Press, Baltimore, Maryland. BOOM, B. M. 1988. The Chcobo Indians and their pa lms. Adv. in Econ. Bot. 6: 91 BRUNA, E. M. 2003. Are plant populations in fragmented hab itats recruitment limited? Tests with an Amazonian herb. Ecology. 84: 932-947. CAMPOS, M. T., AND C. EHRINGHAUS. 2003. Plant virtues are in th e eye of the beholder: a comparison of known palm uses among indigenous and folk communities of southwestern Amazonian. Econ. Bot. 57: 324-344. CARDOSO, G. DE L., G. M. DE ARAUJO, AND S. A. DA SILVA. 2002. Structure and dynamics of a Mauritia flexuosa (Arecacceae) population in a palm swamp of Estacao Ecologia do Panga, Uberlandia, Minas Gerais, Brazil. Bol. Herb. Ezechias Paulo Heringer. 9: 34-48. CARRERA, L. 2000. Aguaje ( Mauritia flexuosa ) a promising crop of the Peruvian Amazon. Acta Horti. 531: 229-235. CASWELL, H. 2001. Matrix population models : construction, analysis, and interpretation. (2nd ed.) Sinauer Associates, Sunderland, Massachusetts. CLAY, J. 1997. The impact of palm heart in the Amazon estuary. In C. H. Freese (Ed.) Harvesting wild species: implications for biodive rsity conservation. pp. 283-314. John Hopkins University Press, Baltimore, Maryland. COOMES, O.T., B. L. BARHAM, AND Y. TAKASAKI. 2004. Targeting conservation-development initiatives in tropical forests: insights from analyses of rain forest use and economic reliance among Amazonian peasants. Ecol. Econ. 51: 47-64. CROPPER, W.P., JR., AND D. DIRESTA. 1999. Simulation of a Biscayne Bay, Florida commercial sponge population: effects of harvesting afte r Hurricane Andrew. Ecol. Model. 118: 1-15. CROPPER, W.P., JR., AND P.J. ANDERSON. 2004. Population dynamics of a tropical palm: Use of a genetic algorithm for inverse paramete r estimation. Ecol. Model. 177: 119-127. CROPPER, W.P., JR., AND N.B. COMERFORD. 2005. Optimizing simulated fertilizer additions using a genetic algorithm with a nutrient uptake model. Ecol. Model. 185: 271-281. CROUSE, D.T., L. B. CROWDER, AND H. CASWELL. 1987. A stage-based population model for loggerhead sea-turtles and implications for conservation. Ecology. 68: 1412-1423.

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91 DE FRANCA, L. F., G. REBER, A. A. MEIRELES, N. T. MACHADO, AND G. BRUNNER. 1999. Supercritical extraction of carotenoids and lipids from buriti ( Mauritia flexuosa ), a fruit from the Amazon region. J. Supercrit. Fluid. 14: 247-256. DENEVAN, W. M., AND J. M. TREACY. 1987. Swidden fallow agroforestry in the Peruvian Amazon: Young managed fallows at Brillo Nuevo. New York Bot. Gard. Bronx, New York. DREYFUS-LEON, M., AND D. G. CHEN. 2007. Recruitment prediction with genetic algorithms with application to the Pacific Herring fishery. Ecol. Model. 203: 141-146. DURANT, S. M., AND J. HARDWOOD. 1992. Assessment of monitoring and management strategies for local populations of the Mediterranean monk seal Monachus monachus Bio. Conserv. 61: 81-92. ENDRESS, B. A., D. L. GORCHOV, M. B. PETERSON, AND E. P. SERRANO. 2004a. Harvest of the palm Chamaedorea radicalis its effects on leaf produc tion, and implications for sustainable management. C onserv. Biol. 18: 822-830. ENDRESS, B. A., D. L. GORCHOV, AND R. B. NOBLE. 2004b. Non-timber forest product extraction: effects of harvest and browsing on an understory palm. Ecol. Appl. 14: 1139-1153. FONSECA, S. O. 1999. Diversity and ecology of Mexican palms and their exploitation. In Ruano, M. C. (Ed.) Proc. of the 2nd Int. Symp. on ornamental palms and other monocots from the tropics. Acta. Hort. 486: 59-63. FRAGOSO, J. M. V. 1999. Perception of scale and resource partitioning by peccaries: behavioral causes and ecological implicati ons. J. Mammology 80: 993-1003. FRECKLETON, R. P., D. M. SILVA MATOS, M. L. A. BOVI, AND A. R. WATKINSON. 2003. Predicting the impacts of harvesting using structured population models: the importance of density-dependence and timing of harvest fo r a tropical palm tree. J. Appl. Ecol. 40: 846-858. GOULDING, M. 1989. Amazon: The flooded forest. BBC Books, London, UK. HAMBY, D. M. 1994. A review of techniques for parameter sensitivity analysis of environmental models. Environ. Monitor. Assess. 32: 135-154. HENDERSON, A. 1994. Palms of the Amazon. Oxford University Press, New York City, New York. HENDERSON, A., G. GALEANO, AND R. BERNAL. 1995. Field guide to the palms of the Americas. Princeton University Press, Princeton, New Jersey.

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96 BIOGRAPHICAL SKETCH Jennifer grew up in the wooded ar ea of Douglasville, Georgia, a suburb of Atlanta. Her parents always encouraged her to play and explore outside, and it was through this encouragement that she developed a love for the interactions in the forested environment around her. In her early education she was always ex cited to read many books and learn about anything related to science. From a young age she knew that she wanted to get a higher education in the biological sciences and hopefully become a scientist at some point Jennifers father, being a physicist had a large influence on her. Jennife r graduated high school with a 4.0 GPA and was valedictorian. Her next stop on her educational path was Emory University in Atlanta, GA in 2000. At Emory University Jennifer majored in environmental studies and minored in anthropology. Her classes ranged between many sub-disciplines in environmental education, including classes in geology, earth systems dynami cs, behavioral ecology, and tropical ecology. The summer before her junior year made the larg est impact on her decision for future path of studies. Jennifer was accepted into the School for Field Studies and traveled to Queensland, Australia where she took a field course in tropical restoration. During this trip she partially worked on a 5-year project that focused on tropic al corridor construction in the rainforests of northern Australia. Upon her return to Emory Univ ersity and Atlanta, she began an internship at the Atlanta Botanical Gardens working with neo-tropical plants, Nepenthes She wanted to learn anything she could about tropical plants and tropical ecology. Du ring Jennifers time at Emory University she also took a field course that offered a trip to Costa Rica to learn about its environment. After her four years at Emory Un iversity, she next enrolled at University of Florida in the Interdisciplin ary Ecology program in the Sc hool of Natural Resources and Environment.

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97 At University of Florida Jennifer worked unde r the guidance and leadership of Dr. Wendell P. Cropper Jr. in the School of Forest Resources and Conservation. She considered her graduate studies to have two different co ncentrations, 1) forest ecology and 2) tropical conservation and development. During her 2 years as a masters student at University of Florida, one of her biggest moments was conducting field research in the Peruvian Amazon. This was a big step for Jennifer as a researcher and help ed her develop field data collec tion experience. Another large moment for her was presenting at the 2006 Ecological Society of American annual meeting, and at various other conferences and meetings. Jennif ers classes and work at University of Florida have been worthwhile and a good learning expe rience. After finishing her research and graduating with a masters degree, she considers herself a tropical forest ecologist who focuses on population and simulation modeling. It is wi th the help and guidance of her advisor, committee, fellow graduate students, and especially her family that she has gotten to where she is today.