STATISTICAL AND SIMULATION MO DELS FOR NATURAL MIXED FORESTS IN CHILE AND MEXICO By SEBASTIAN PALMAS PEREZ A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREM ENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2017
2017 Sebastian Palmas Perez
To Ceci, Oscar and Santiago To Cris tina
4 ACKNOWLEDGMENTS I am deeply grateful to my advisor Salvador Gezan fo r bei ng a great mentor, colleague and for all the time he dedicated to this project. I am very thankful to Wendell Cropper who accepted being my advisor and for all his insightful feedback I am indebted to Karen Kainer for giving me the opportunity to co me to UF and for her continuous encouragement. I also thank my committee members Denis Valle and Jeremy Lichstein for their input, suggestions and patience. This dissertation was made possible thanks to two incredible colleagues and friends: Antonio Sierr a Huelsz and Paulo Moreno. Antonio has shared with me his extensive experience, knowledge and passion for the Mexican forests since 2011. Antonio supported me during fieldwork, co urses, conferences and kayak trips. Paulo shared his brilliance and knowledge on the two Nothofagus chapters and, not only he opened his home to me, he supported me during difficult times in Gainesville. Their constant support and warm friendship have made this dissertation partly theirs Research in Quintana Roo was supported by a The Nature Conservancy grant (P116876 GLT). I am deeply grateful to Jack Putz, Bronson Griscom and Peter Ellis from TNC who have been an invaluable influence in my work in Quintana Roo. The Tropical Conservation and Development program at the University of Florida supported travel and research funding by a Field Res earch Grant. The TCD program also served as a second department (and home) these six years. It was because of TCD students, faculty and staff that I made sense of graduate school, UF and Gaines ville. I am also very grateful to the University of Florida and the School of Forest Resources and Conservation for the generous financial support through the Graduate School.
5 I am lucky to have found these research partners across the world: Francisco Esc obedo at the Universidad del Rosario, Colombia. Alicia Ortega who provided data and feedback for the project in Chile. The research was also supported by the NGOs Organizacin de Ejidos Productores Forestales de la Zona Maya in Felipe Ca rrillo Puerto, Quintana Roo. could not have happened without the friendship of many individuals in Gainesville: Sami Rifai, Todd Bertwell Antonio Sierra, Hermes Gerardo Natalie Cooper, Mandy Monroe, Constanza Ros, Paulo Moreno Milton Diaz, Claudia Navarro, Mauricio Nez, Cristina Nez Michael Bauman, Farah Carrasco, Johanna Espin et al. I am lucky enough to have such great friends that their good vibes have been felt from 2000 k m away. T hese are rez, Guillermo Monterrubio (a.k.a. El To), Israel Pliego (a.k.a. El Isris), Pablo Aceves (a.k.a. El Mitades), Talib Oliver (a.k.a. El Talibi), Kaheri Illescas (a.k.a. El K), and Silvestre Zepeda (a.k.a. El Gonzo) The love, patience and silliness from Cristina Ramos has b een my main support since 2015. She makes me enjoy the present and makes me excited about the future. She pushes me to achieve my goals and makes me a better person This is her dissertation too. And last but not least, I want to thank my family: Ceci, Oscar and Santiago for their always loving encouragement and support.
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 ABSTRACT ................................ ................................ ................................ ................... 10 C H A P T E R 1 INTRODUCTION AND JUSTIFICATION ................................ ................................ 12 2 STAND BASAL AREA AND MO RTALITY MODELS FOR MIXED NOTHOFAGUS FORESTS IN SOUTHERN CHILE ................................ ................ 15 Introduction ................................ ................................ ................................ ............. 15 Methods ................................ ................................ ................................ .................. 18 Data Description ................................ ................................ ............................... 18 Model Description ................................ ................................ ............................. 20 Basal area ................................ ................................ ................................ .. 20 Proportion of number of Nothofagus trees ................................ ................. 21 Mortality ................................ ................................ ................................ ..... 21 Model Evaluation ................................ ................................ .............................. 22 Results ................................ ................................ ................................ .................... 24 Basal Area ................................ ................................ ................................ ........ 24 Proportion of N othofagus Trees ................................ ................................ ....... 26 Mortality ................................ ................................ ................................ ............ 26 Discussion ................................ ................................ ................................ .............. 27 Conclusion ................................ ................................ ................................ .............. 30 3 VALIDATION AND COMP ATIBILITY OF INDIVIDUAL AND STAND LEVEL GROWTH AND YIELD MODELS FOR NOTHOFAGUS FORESTS ....................... 38 Introduction ................................ ................................ ................................ ............. 38 Methods ................................ ................................ ................................ .................. 40 Available Data ................................ ................................ ................................ .. 40 Growth and Yield Models ................................ ................................ ................. 41 Compatibility Methods and Evaluation ................................ ............................. 43 Results ................................ ................................ ................................ .................... 45 Number of Trees Goodness of Fit Statistics ................................ ..................... 46 Basal Area Goodness of Fit ................................ ................................ ............. 46 Diameter Distributions ................................ ................................ ...................... 47 Volume Goodness of Fit ................................ ................................ ................... 47 Discussion ................................ ................................ ................................ .............. 48 Conclusion ................................ ................................ ................................ .............. 50
7 4 TIMBER AND CARBON SCENARIOS FOR THE MAYA FOREST OF MEXICO: AN INDIVIDUAL BASED MODEL SIMULATION ................................ .................... 56 Introduction ................................ ................................ ................................ ............. 56 Data Sources ................................ ................................ ................................ .......... 58 Model Description ................................ ................................ ................................ ... 58 Age Increment and Growth ................................ ................................ ............... 59 Natural and Hurricane Mortality ................................ ................................ ........ 59 Natural Recruitment ................................ ................................ ......................... 60 Logging Scenarios and Minimum Cutting Diameters ................................ ........ 60 Felli ng Mortality and Cable Yarding ................................ ................................ .. 60 Gap Enrichment ................................ ................................ ............................... 61 Timber Volumes and Above Ground Biomass ................................ ................. 61 Definition of Scenarios ................................ ................................ ..................... 62 Results and Discussion ................................ ................................ ........................... 62 Number of Extracted Trees and Volume ................................ .......................... 62 Changes in Timber Basal Area and Aboveground Biomass ............................. 63 Hurricane Effects ................................ ................................ .............................. 63 Model Limitations ................................ ................................ ............................. 64 Conclusion ................................ ................................ ................................ .............. 64 5 CONCLUSIONS AND SUMMARY ................................ ................................ .......... 72 A P P E N D I X : ANALYSIS OF MEAN ANNUAL INCREMENTS AND RECRUITMENT DATA FOR SPECIES IN QUINTANA ROO, MEXICO ................................ ............ 76 LIST OF REFERENCES ................................ ................................ ............................... 79 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 91
8 LIST OF TABLES Table page 2 1 Mean (standard error) and range of stand parameters between plot networks .. 31 2 2 Distr ibution of dominant species for the Temporal Plots 1 Temporal Plots 2 and Management Plots networks ................................ ................................ ....... 32 2 3 Goodness of fit measures for models for basal area of No thofagu s basal area of c ompanion species total basal area proportion of number of Nothofagus trees ................................ ................................ ................................ 32 2 4 Parame ter estimates, standard errors and V ariance I nflation F actors for models of basal area of Nothofagus bas al area of companion species and proportion of number of Nothofagus trees ................................ .......................... 33 3 1 Mean (standard error) and range of stand parameters in the remeasured plots from the permanent network based on 33 plots ................................ ......... 51 3 2 Estimated parameters for b a s a l a r e a o f N o t h o f a g u s t o t a l n u m b e r o f t r e e s A I DBH equations ................................ ................................ ................................ 52 3 3 Definition of scenarios considered in this study ................................ .................. 53 3 4 Goodness of fit measures for each scenario for number of trees per hectare of Nothofagus basal area of Nothofagus P85/P15 and stand volume .............. 53 4 1 Selected literature for the forests of Quintana Roo and the Yucatan Peninsula ................................ ................................ ................................ ............ 66 4 2 Species and common names considered in the simulation ................................ 67 4 3 Hurricane categories annual occurrence probability and associated percentage of mortality by tree DBH ................................ ................................ ... 67 4 4 Characteristics of the scena rios simulated in this study. All scenarios ran for 40 years using a 25 year rotation cycle with directional felling and for 100 iterations ................................ ................................ ................................ ............. 67 4 5 Basal area and aboveground biomas s mean differences from the BAU scenario after 10, 25 and 40 years of simulation ................................ ................ 68 A 1 Summary of the mean diameter growth (standard error) and range of by species from the TNC d iametric bands ................................ ............................... 77 A 2 Average number of new recruits by hectare for species depending on percentage of stand canopy cover or timber bas al area ................................ ..... 78
9 LIST OF FIGURES Figure page 2 1 O bserved vs predicted values for basal area of Nothofagus basal area of compani on species to tal basal area and number of trees per hectare e s t i m a t e d from the Tempo ral Plots network s ................................ ..................... 34 2 2 Observed vs predicted values for basal area of Nothofagus basal area of companion species total basal area, and number of tr ees per hectare e s t i m a t e d f r o m t h e Management Plots network ................................ .................. 35 2 3 Relative residuals for different simulation years in projections using the M a n a g e m e n t P l o t d a t a as validation ................................ ................................ ... 36 2 4 Quadratic diamete r v s number of trees per hectare trajectories of measured stands of the M a n a g e m e n t P l o t network ................................ ............................ 37 2 5 Model projections of 60 years ................................ ................................ ............. 37 3 1 Relative residuals for predictions ................................ ................................ ........ 54 3 2 Relative residuals against simulation years for predictions ................................ 55 4 1 Map of the south and central municipalities of Quintana Roo ............................. 69 4 2 Dragging mortality and cable yarding ................................ ................................ 70 4 3 H arvested trees, h arveste d volume annual change in timber basal a rea and annual change abovegr ound timber biomass trajectories for the five considered scenarios ................................ ................................ .......................... 71
10 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy STATISTICAL AND SIMULATION MODELS FOR NATURAL MIXED FORESTS IN CHILE AND MEXICO By Sebastian Palmas Perez December 2017 Chair: Salvador A. Gezan Major: Forest Re sources and Conservation Forest professionals need reliable information on stand dynamics to improve management decisions in their forests. One of the most important tools for this purpose are forest growth and yield models (G&Y). G&Y models have a histor y of over 250 years but models for mixed forest stands were only first developed during the 20th century. This is because mixed forests have a large array of possible stand dynamics, species behaviors, interactions and productivity levels. This dissertati on builds different G&Y models for two interesting mixed forests in Latin America: the Nothofagus second growth forests of southern Chile and the tropical forests of Quintana Roo, Mexico Chapter 2 fitted : a stand basal area model specified by the cohorts of Nothofagus and companion species, a model for changes over time in the proportion of Nothofagus trees in a stand and a mortality model that considers the concept of self thinning. To our knowledge these are the first broadly applicable models for the N othofagus forest in southern Chile with dynamics of both companion species and Nothofagus cohorts. The models reported in this study constitute simple and valuable tools to support management decision for this resource in Chile.
11 Chapter 3 evaluated differ ent compatibility methods that integrate available individual and stand level models. A Proportional Growth compatibilization significantly improved prediction of stand attributes without compromising predictions of individual parameters such as volume. I t was also found that the length of the simulation considerably affects the fitness of the predictions C hapter 4 provides estimates on the potential effects of silvicultural activities by simulating different scenarios within a forested area in Quintana Ro o Mexico The simulation is an individual level model that compiles published models on forest growth, natural and hurricane induced mortality, recruitment and silviculture activities. The simulation shows that the recovery rates of basal area after the f irst 25 years are higher for those scenarios with improved management techniques such as gap enrichment and cable yarding. Simulations show that the currently applied 25 year cycle is not enough for a complete basal area recovery after two cycles.
12 CHAPTE R 1 INTRODUCTION A N D J U S T I F I C A T I O N Natural forests are currently being affected by pressures such as climate change, agricultural expansion, invasive species, and logging (Foley et al. 2005) In order to preserve value and promote sustainability of the natural forests, tool s such as growth and yield (G&Y) models are needed to provide information on forest dynamics A G&Y model is a representation of the natural dynamics of a forest, and includes growth, mortality, recruitment, and other changes in stand structure (Vanclay 19 94). These models can be used in combination with forest inventories to determine timber productivity and examine the potential impacts of management and harvesting regimes on the commercial value an d ensure sustainability of the se forest s For example, a researcher can estimate an optimal age of harvest to maximize profits without risking future productivity using predictions from G&Y mode l s (Lahvonen et al. 2010) G&Y models have a history of over 25 0 years (Skovsgaard and Vanclay 2008), particularly for commercial plantations but models for mixed stands were first developed during the 20th century (Porte and Barte link 2002). This is because mixed forests are highly complex presenting a large array of possible stand dynamics, species behaviors, interactio ns and productivity levels (Filotas et al. 2014) Another reason is that plantations historically have had a greater investment in research and record of publications (Nichols et al. 2006) Furthermore, Blanco et al. (2015) reported that G&Y models for mix ed forests are also limited geographically with most publications coming from North America and Europe. Nothofagus second growth forests of southern Chile and the tropical Maya forests of Quintana Roo in Mexico are two contrasting examples on this topic. W hile not as studied as pine plantations in Chile (Toro and Gessel 1999)
13 Nothofagus forests in central Chile have been monitored since 1980 with some of the first growth models published during that decade. In contrast, some of the first forest inventories and growth models published for the Maya f orest This dissertation serves as a guidebook for researchers trying to build G&Y models for a managed mixed forest. Each chapter deals with a critical step required when building such models and are ordered considering increasing complexity. Chapter 2 deals with one of the first steps for this objective: building statistical models to describe forest dynamics. C hapter 3 validates and adjusts previously developed models to improve predic tions of forest dynamics. In Chapter 4, the dissertation puts together many different models of forest dynamics to predict potential consequences of management activities. The dissertation deals with two different mixed forest in Latin America: the Nothofa gus forests in central Chile and the Maya forests in Quintana Roo, Mexico. This dissertation does not aim to compare the two research sites T hey are not comparable because of their very different characteristics such as different ecosystems, management s trategies and sources of pressure. In addition, c entral Chile and the Maya forest have different trends in forest cover : Chile has now a net forest cover growth while the Maya f orest cover continues to be negative (Hansen et al. 2013; Heilmayr et al. 2016 ). The selection of these two sites allows this dissertation to explore different approaches o n mixed forests with an array of levels of experience data availability and history in research about G&Y models. A forest professional working in a forest witho ut much background research can be gain more from the lessons in Chapter
14 2, while one in a forest with a stronger background of research can gain more from Chapter s 3 and 4. In summary t he main objective of this dissertation is to prop o se, fit, and valida te different G&Y model approaches for Nothofagus forests in Chile and tropical forests of Quintana Roo in Mexico. Chapter 2 builds statistical model s for : stand parameters such as stand basal area specified by the cohorts of Nothofagus and companion specie s, a model for changes over time in the proportion of Nothofagus trees and a mortality model that considers the concept of self thinning. C hapter 3 evaluates and adjusts existing models using independent data and two compatibility methods to link individu al and stand level G&Y models. Finally, Chapter 4 construct s a complete simulation model to estimate potential effects of different management scenarios within a forested area in Quintana Roo, Mexico.
15 CHAPTER 2 STAND BASAL AREA AND MORTALITY MODELS FO R MIXED NOTHOFAGUS FORESTS IN SOUTHERN CHILE Introduction Forest professionals need reliable information on stand dynamics and development to improve management decisions in their forests. One of the most important tools for this purpose are forest growth and yield models (G&Y). A G&Y model is a representation of the natural dynamics of a forest, and includes growth, mortality, and other changes in stand structure (Vanclay 1994). These models can be used in combination with forest inventories to determine timber productivity and examine the potential impacts of alternative management and harvesting regimes on the value an d sustainability of the forest. One on t he first step s to develop a G&Y model for mixed forests is to choose a modelling strateg y (Liu and Ashton 1995; Peng 2000 ; Porte and Bartelink 2002; Vanclay 1994). G&Y models can be classified into: stand (whole) or individual (tree) level models. Stand level models are those in which the modeling units are stand aggregated parameters such as basal ar ea, stocking, and site productivity. Individual level models obtain aggregate stand characteristics by keep ing track and describ ing, each tree as a unique enti ty in the stand (Liu and Ashton 1995) Proposed cohort models are in between stand and tree lev el models (Reed 1980). In cohort level models, trees of similar species are grouped into classes of a shared attribute (e.g. diameter size, growth rates or age). Individual level models have the disadvantage that they use data for parameterization beyond t hat required for stand level models, a resource that is not always available. In contrast, s tand level models have the advantage of being more robust for long term projections than individual models (Porte and Bartelink 2002). The
16 main advantage of a cohor t level model is that it gives further details than a stand level model without the amount of data that an individual level model requires. South American beeches Rauli ( Nothofagus alpina (Poepp. & Endl.) Oerst.), Roble ( N. obliqua (Mirb.) Oerst.) and Coig e ( N. dombeyi (Mirb.) Oerst.) are native emergent trees present in a forest type known locally as RORACO (for the first letters of the Nothofagus species) This forest type occurs in the region between Concepcion and Puerto Montt cities in both the Chilea n Andes and the coastal mountain range (Veblen et al. 1996) with some fragments in the Neuquen Province, Argentina (Sabatier et al. 2011). At the present, the RORACO forest type covers 1.96 million hectares, around 10% of the native forested area of Chile (CONAF 2011), and it represents a little over 45% of the sawtimber volume from native species for the country (INFOR 2016). The RORACO forest type is considered a second growth forest succession stage that colonizes areas after a disturbance such as tree f all gaps, volcanic activities and earthquakes (Donoso et al. 1993; Echeverria and Lara 2004; Pollmann 2003; Rebertus and Veblen 1993; Veblen et al. 1980; Veblen and Ashton 1978). The relative abundance of the three Nothofagus species varies considerably in the RORACO forests. Nothofagus obliqua prefers lower elevations and drier sites, while N. dombeyi prefers higher elevations and wetter sites, and N. alpina is more prevalent on intermediate sites (Veblen et al. 1996). The Nothofagus species, and primarily N. alpina are extensively studied in Chile with reports available on: height and diameter growth (Salas and Garcia 2006), taper and volume equations (Gezan et al. 2009), delimitation of growth zones (Donoso et al. 1993; Gezan and Moreno 1999), silvicultu re (Donoso et al. 2009), site index models
17 (Trincado et al. 2002), and regeneration (Weinberger and Ramirez 2001) ecology ( Donoso et al. 2013), among others. However, at present, there is no fully functional G&Y model system, except for some preliminary e fforts reported by Ortega and Gezan (1998). The main components of any G&Y model are tree growth recruitment and mortality. Stand level growth models are usually built by fitting an equation that predicts total basal area, usually depending on age, produ ctivity and stocking. For mixed forests, this component is often separated into cohorts defined by group of species. RORACO forests can be separated into two main cohorts: the first dominated by the emergent shade intolerant Nothofagus species and the seco nd comprised by companion species, which are primarily shade tolerant. Some of the most prevalent companion species found in these forests are Gevuina avellana Molina, Persea lingue (Ruiz & Pav.) Nees, Lomatia hirsuta (Lam.) Diels, Eucryphia cordifolia Cav ., Drymis winteri J.R. Forst. & G. Forst. and Laurelia phillippiana (Looser) Schodde. It is considered that these two cohorts present different, and probably additive, growth dynamics; implying that stand basal area growth of Nothofagus is likely to be ind ependent of the companion species (Donoso and Lusk 2007; Lusk and Ortega 2003). Stand mortality models usually depend on productivity, competition, and differences among species for their tolerance to crowdedness. Here, knowledge of the maximum stand densi ty for a given forest type is critical, as a stand that is close to its maximum density will experience higher levels of mortality, a process that is known as self thinning. Reineke (1933) proposed a theoretical self thinning rule that has been used extens ively for many pure stands. In Nothofagus several authors have used this
18 rule to define stand density diagrams (Chauchard et al. 2001; Gezan et al. 2007) for these mixed forests. Natural forests are currently being affected by global pressures, such as cl imate change, agricultural expansion, invasive species, and logging (Foley et al. 2005), as is the case with the RORACO forest type (Zamorano Elgueta et al. 2015). There has been a trend in reduction of native forests in south central Chile in the last thr ee decades mainly because of the its conversion to shrublands and exotic tree plantations (Heilmayr et al. 2016 Miranda et al. 2015 ); however, Chile is experiencing a forest transition trend towards a zero net deforestation. In addition, insect defoliator outbreaks present a threat to Nothofagus forests. It is estimated that damage has increased and will intensify with a warming climate (Paritsis and Veblen 2011). Because of these and other threats, it is essential to preserve value and promote sustainabil ity of this native ecosystem. This management goal will best be addressed with tools including G&Y models. The main objective of this study is to build models for a stand level G&Y model to improve predictions of stand dynamics for natural mixed secondary forests of the RORACO forest type in Chile. The specific objectives include to fit and validate stand level models for: 1) basal area specified by the cohorts of Nothofagus and companion species; 2) changes over time in the prop ortion of Nothofagus trees i n a stand; and 3) mortality that considers the concept of self thinning Methods Data Description The data for this study originated from three independent sets: two temporal plot (TP1, TP2), and a management plot (MP) networks All plots were established in and
19 Chile between 1999 and 2000 (Ortega and Gezan 1998). The TP1 data had a total of 5 0 plots with an area of 250 m 2 formed by a conglomerate of two subplots. For the TP2 data there were a total of 120 rectangular plots with areas ranging between 250 and 500 m 2 Both the TP1 and TP2 networks, were sampled according to a stratification of this for est type based on the national forest inventory (CONAF et al. 1999). The MP network consisted in three sites and measured between 1980 and 199 9 Each of these sites were remeasured up to four times. The original objective of the MP plots was to evaluate di fferent thinning regimes on RORACO stands (Puente et al. 1980). Because t he objective in this paper is to fit models for natural forests, the models are fitted with only 4 8 plots without treatment ( i.e. controls), low thinning (less than 5% of removed bas al area) and with girdling treatments. Because of the remeasurements in some of the 48 plots, the total of plot years is 183 Summary statistics of these three datasets are presented in Table 2 1. For all plots, trees above 5 cm of diameter at breast heigh t (DBH, cm) were inventoried for DBH and total height (H, m). The Nothofagus species were identified and the rest was recorded as companion species. For all plots, the following stand level variables were calculated: dominant age at breast height (AGE, yea rs), dominant height (HD, m), site index (SI, m), total basal area (BA, m 2 ha 1 ), and total density of trees (NHA, trees ha 1 ). Q uadratic diameter (DQ, cm) was measured and defined as the average tree diameter in the stand Dominant age at breast height (A GE) is defined as the average age of 100 trees per hectare with the largest DBH. Dominant height (HD) is the average total height of the thickest 100 trees per hectare. Site index (SI) is the stand
20 dominant height at 20 years. Also, for each of the cohorts basal area for Nothofagus and companion species (BAN and BAC, respectively, m 2 ha 1 ), and number of trees of Nothofagus and companion species (NHAN and NHAC, respectively, trees ha 1 ) were calculated. Finally, the proportion of basal area and number of t rees of Nothofagus (PBAN, PNHAN) and companion species (PBAC, PNHAC) were also obtained. All plots were assigned to a growth zone (ZONE) following to Gezan and Moreno (1999). For those plots without known SI, estimates were obtained using the model reporte d by Gezan and Ortega (2001). In order to only use stands that were dominated by Nothofagus, only those plots with PBAN > 0.6 were selected for this study. Additionally, the dominant species (DOM SP) of a given plot was defined as the Nothofagus species th at had more than 70% of BA. The TP1 and TP2 data are primarily of N. dombeyi but all dominant species are present; however, the MP data contains only plots dominated by N. alpina (Table 2 2). Model Description Basal a rea To predict basal area for the two c ohorts, BAN and BAC, this study fitted two independent models. Here, t he TP1 and TP2 plots were used as training data, while MP plots were used as validation data. For BAN and BAC, a linear model using a log transformation was fitted with different combina tions of predictors, including AGE, HD, SI, NHA, NHAN, NHAC, PBAN, and PBAC These predictors were considered in their original units and also transformed using the functions of natural logarithm, inverse, square of the inverse and square root of the inver se. ZONE for each stand was evaluated separately with no interactions with other predictors. To assist with model selection, a backward selection procedure was implemented based on a signi ficance
21 = 0.05, and models with variance inflation factors (VIF, Rawlins et al. 1998) larger than four in any of their predictors were discarded. The predictions of the final fitted models for each of these components were added to estimate total basal area; hence Later, projection equations were derived from the prediction models fitted above by differentiating with respect to age following the methodology described by Clutter (1963) and Moser and Hall (1969). These projections, allow to estimate the future values of the response over time given a starting condition. These models were evaluated using the MP permanent plot data, based on a total of 217 measurement pairs. Proportion of n umber of Nothofagus t rees To estimate the pro portion of trees corresponding to Nothofagus (PNHAN), a linear model was fitted with the logit transformation of PNHAN using the TP1 and TP2 plots as training data (150 plots), and the MP plots as validation data (183 plots). The same predictors used in th e BA model were tested and a final model was selected using a backward selection procedure as indicated above. Mortality For this component, the self thinning concept was used to formulate a simple mortality model that is defined by a single parameter. Th is study fitted a model for an annual projection of number of trees per hectare (NHA) using as training the mortality measurement pairs from the MP data. Note that TP1 and TP2 were not considered as their plots contain a single measurement. Based on the ex pression from Reineke (1933) (2 1)
22 where ln is the natural logarithm and and are the constant parameters, the proposed mortality model uses the current NHA 0 value to estimate the current maximum quadratic diameter (DQ 0max ) with (2 2) DQ 0max can be interpreted as the maximum DQ that is allowed at the tree density NHA 0 The parameters of above for are 11.6167, 11.3770, and 11.7639 for stands dominated by N. alpina N. obliqua and N. dombeyi = 1.4112, for all dominant species (Gezan et al. 2007). It is expected that as the current DQ 0 approaches DQ 0max there is an increase in mortality. Hence, a model can include the ratio between DQ 0 and DQ 0max interacting with the current number of trees (NHA 0 ). Hence, t he projection model suggested by this study is: (2 3) is the parameter to estimate, and can be interpreted as a maximum mortality rate when the stand is at DQ max and expressing NHA on a log arithmic scale. t is the years between measurements and ln is the na tural logarithm. Model Evaluation Predictions and projections for all four models described above were evaluated by calculating the following goodness of fit measures: R 2 emp RMSE%, Bias% and Akaike Information Criteria (AIC, Akaike 19 98 ) that are detailed below. These measures were obtained for the training and validation datasets providing two independent assessments of the models. (2 4)
23 (2 5) (2 6) (2 7) where y i i are the i th observed and predicted (or projected) value, L is the likelihood of the fitted model and p is the total number of parameters in the model. All goodness of fit measures were evaluated using the back transformed response variable s to its original units. Because the models for BAN and BAC use the natural logarithm transformation, their back transformed estimates were adjusted using the correction pr oposed by Baskerville (1972), i.e. i i 2 /2 2 is the mean square error. For graphical outputs, relative residuals were used, which were defined as the difference between observed and predicted values divided by the mean o bserved value. P rojections models were evaluated by using all 217 possibl e measurement pairs within the 4 8 remeasured plots in the MP data ( e.g. a plot with three measurements has three possible pairs for projection: measurement 1 to 2, 1 to 3, and 2 to 3). Time between measurement pairs ranged between 2 a nd 12 years. Normality and heterogeneity of residuals were also checked without noting important departures from these assumptions. All generalized linear and non linear models were done in R 3.3.2 (R Core Team 2016). Ordinary least squares procedure was u sed to estimate the parameters.
24 Results Basal Area For the plots considered in this study, the average total BA for Nothofagus and companion species corresponded to 38.48 and 3.41 m 2 ha 1 respectively. BAN ranged from 12.66 to 89.57 m 2 ha 1 and BAC from 0.00 to 26.40 m 2 ha 1 The final selected models for BA of Nothofagus and companion species are (2 8) (2 9) The logarithmic transformation of the predictors returned the best results and had t he additional advantage that use in the projection model is straightforward (see below). In addition, all selected predictors show ed low VIF values ( < 2), reflecting negligible levels of multicolinearity between them. In logarithmic terms, AGE and NHA had t he highest correlation with a value of 0.45, followed by AGE and SI with a value of 0.33. In addition, PBAN and NHA had a correlation of 0.32, and the other predictors had correlations below 0.15. The resulting fitted model for BAN had R 2 emp = 0.54, and th e fitted model for BAC had a higher R 2 emp with a value of 0.85 (Table 2 3). The pred iction of total basal area had an R 2 emp = 0.56. All models presented negligible bias values ( < 1%). Both BAN and BAC models had good goodness of fit measures with the MP val idation data. The goodness of fit measures for this validation dataset, for the BAN, BAC and BA predictions, returned slightly higher Bias% values when compared to the training data, but these were all lower than 4% (Table 2 3).
25 According to the estimated coefficients (Table 2 4), AGE was positively associated with both BAN and BAC (with slope coefficients of 1.23 and 0.09, respectively). Hence, as the stand gets older basal area increases, with larger effect for the Nothofagus cohort. For BAN, the positive coefficients for SI (0.68) and NHA (0.52) indicate that better site quality and higher levels of stocking result in higher Nothofagus basal area. In the BAC model, PNHAN and PBAN have negative coefficients ( 0.22 and 1.87, respectively) indicating that h igher proportions of Nothofagus abundance affect the quantity of basal area of companion species. Predicted BAN and BAC values corresponde d well with observed values in both training and validation data (Figure 2 1 and Figure 2 2). However, this correspond ence decreases with larger observed BAN and BAC values, and some under prediction is found for BAN values above 75 m 2 ha 1 Similar results were found for BA, as this mostly corresponds to Nothofagus basal area (Figure 2 1 C). Both basal area equations wer e used to derive their compatible projection equations. These models project future values (BAN 1 and BAC 1 ) based on the current stand conditions (BAN 0 and BAC 0 respectively). These are: (2 10) (2 11) For the evaluation of the projection equations using the validation dataset, a ll basal area models showed excellent goodness of fi t measures (all with R 2 emp > 0.94). The relative residuals obtained over time for BAN, BAC and BA projections (Figure 2 3
26 A, B and C) are centered around zero for shorter projections ( i.e. little bias) w hile they tend to depart for increasing projection times ( i.e. underestimate). Proportion of Nothofagus Trees For the plots considered in this study, the average proportion of Nothofagus trees corresponded to 82%, where the majority of the plots presente d values greater than 72%. The final selected model for PNHAN is: (2 12) For the training data, this model had reasonable goodness of fit measures with R 2 emp = 0.68 and Bias% = 1.5 0. Also, predicted PNHAN values tend to correspond with observed values, but large levels of uncertainty still exist (Figure 2 1 D). Also, for MP validation data these measures were R 2 emp = 0.56 and Bias% = 3.46. The estimated parameters of this model are shown in Table 2 1 The slope coefficient for PBAN (10.29) reflects the high association between this predictor and PNHAN (these predictors present a correlation of 0.89). For AGE, its coefficient ( 0.01) indicates a reduction of PNHAN with increasing sta nd age, reflecting the pioneer behavior of Nothofagus and the gradual establishment of companion species over time. These selected predictors all show low VIF values ( < 1.02). Mortality Mortality rates among the remeasured plots from the MP data had an annu al average of 3.0% with a maximum of 14.2%, and their patterns were consistent over time for most plots represented as parallel lines (Figure 2 4 A). This results in expected life times between 7 and 33 years.
27 The fitted model, using MP as training data, h ad a good fit with R 2 emp = 0.79, RMSE% = 18.46 and Bias% = = 0.003595746 (SE = 0.000213), indicating that, for future projections, the estimated number of trees always will be smaller than the current condition. For this simple model, predicted mortality values had good correspondence with observed ones over the entire range of values (Figure 2 4 B). Because errors can accumulate over time, the projections seem to differ increasingly from the observed N HA values with longer projection times. In this case, the model showed overestimated mortality at 6 years; however, the estimations were reasonable for projection times of 12 years (Figure 2 3 D). Discussion The fitted independent models for basal area of Nothofagus and companion species seem appropriate to represent the dynamics of these forests. Choosing independent models is reasonable, considering that some studies that support the hypothesis that companion species are not affected by competition with t he emergent Nothofagus cohort (Donoso and Lusk 2007). However, future studies should consider incorporating of additive effects of the species, allowing higher production of Nothofagus when other species are present (Danescu et al. 2016; Donoso and Soto 20 16; Vallet and Prot 2011) The fitted model for BAN presented here is robust and realistic as it accounts for stand age, productivity and stocking (using AGE, SI and NHA, respectively). AGE and SI are common predictors used to model Nothofagus growth (Esse et al. 2014; Lusk and Ortega 20 03; Salas and Garcia 2006). In contrast, the fitted model did not use the factor ZONE as a predictor as reported in other studies (Chauchard and Sbrancia 2003;
28 Echeverria and Lara 2004; Esse et al. 2013; Gezan et al. 2009; Lu sk and Ortega 2003). Differences among zones are possibly associated with the effect of the SI. Without a parameter for ZONE, the suggested models in this paper are appropriate to use in the geographical range of the RORACO forest type in southern Chile. M ore data should allow to explore the effects of other environmental factors that might affect Nothofagus growth, such as light conditions, soil compactness and nitrogen availability (Donoso et al. 2015; Soto et al. 2015, 2017; Walter et al. 2016). Evaluati ons of the BAN projections presented reasonable trajectories. For example, a simulated stand with an initial BAN of 15 m 2 ha 1 initial stand age of 15 years, SI of 10 m and PBAN of 1 is shown in Figure 2 5. Here, BAN patterns, for all densities, have an a symptotic behavior, with larger BAN growth rates for stands with fewer initial trees. In addition, for NHA projections, higher initial density resulted, as expected, in higher rates of mortality, following the patters considered in the proposed mortality m odel For projections under 6 years, the BAN model returned relative residuals lower than 10% and were centered a bout zero. After 6 years, the relative residuals reached higher values with a t endency to underpredict basal area. The BAC model had residuals centered around zero with no notable deviations even at 12 years of projections. However, there were some projections with residuals over 30%, which are not of relevant concern because of the low proportion of basal area from the companion cohort in the s ampled plots For the PNHAN model a reduction of this response as the stand gets older was observed; this can be explained by the pioneer behavior of the Nothofagus species that
29 are followed by gradual establishment of shade tolerant companion species afte r colonization (Veblen et al. 1996). The predictions for PNHAN tended to have less uncertainty with higher observed PNHAN as observed in Figure 1 2D. Most inventory plots had similar mortality trajectories, seen in almost parallel lines (Figure 2 4 A). Mor tality projections reached relative residuals ranging from 30% to 30% (Figure 2 3 D). While this may be considered as large model uncertainty, the fact that residuals are generally centered around zero, even after 12 years of projection, suggests a good o veral l accuracy of the model. While this might not be realistic, it is important to note that this model assumes that stands dominated by the same species respond to the self thinning rule evenly. Unfortunately, the management plot (MP) network used to fi t the mortality model is the only current source of remeasured plot data. For further evaluations, there is a need for additional permanent plot data to validate and further improve these models. Currently, there is not enough information to construct a sta nd mortality model that considers catastrophic environmental events, such as earthquakes or volcanic activity, that are key in the forest dynamics of RORACO stands (Veblen et al. 1996). Establishing and remeasuring inventory plots in natural forests over a wide geographical range is extremely time consuming and costly, resulting in too few high quality sample plots for the development and testing of forest models (Wulder et al. 2008). This problem is also exacerbated by the fact that forest inventory sampli ng is biased towards forests that are considered to have commercial value with little regard to natural forests (Rjou Mchain et al. 2011) with multiple ecosystem services
30 The models reported in this study adequately represent the dynamics of basal area and mortality of Nothofagus forests in Chile based on the available data. These, when combined with a stand volume model provide a complete system of equations to construct a growth and yield model for this resource to support management plans and decisio n making. Conclusion In this study, several stand level models were built to improve predictability of stand dynamics for natural mixed secondary forests of the RORACO forest type in Chile. Stand age, site index, number of trees and the proportion of basa l area of Nothofagus were important predictors to project basal area of Nothofagus and companion species. Dominant age, was a significant predictor for the proportion of Nothofagus trees model, that indicates that as the stand ages, there is a reduction on the presence of Nothofagus most likely due to the pioneer behavior of this dominant cohort. Finally, stand m ortality was successfully modelled by using the concept of self thinning with a single parameter model. To our knowledge these are the first broad ly applicable models for the RORACO forest type with dynamics of both companion species and Nothofagus cohorts. The models reported in this study constitute simple and valuable tools to support management decision for this resource in Chile.
31 Table 2 1. Mean (standard error) and range of stand parameters between plot networks TP1 (n = 5 0 ) TP2 (n = 120) MP (n = 48, m = 183 ) Mean (SE) Range Mean (SE) Range Mean (SE) Range AGE 39.76 (1.89) 14.21 67.9 39.58 ( 1.54) 12.71 86.81 41.08 ( 0.6 0 ) 25 5 1 HD 21.29 ( 0.84) 9.99 34.65 21.84 ( 0.66) 7.83 42.4 0 23.49 ( 0.46) 15.25 37 SI 10.40 ( 0.42) 3.61 17.13 11.09 ( 0.39) 1.81 23.01 10.62 ( 0.32) 6.15 17.24 BA 47.41 ( 2.53) 14.48 98.42 41.75 ( 1.46) 9.54 86.28 40.91 ( 0.59) 13.35 69.82 N HA 2 ,442.11 ( 149.67) 880 5 560 2 ,513.83 ( 122.79) 200 5 600 1 ,276.58 ( 37.66) 340 3 560 DQ 16.81 (0.77) 7.74 30.41 16.74 (0.75) 6.78 70.42 22.17 (0.4 0 ) 10.38 40.87 BAN 42.17 ( 2.34) 13.9 89.57 36.30 ( 1.31) 8.76 85.99 38.67 ( 0.57) 12.66 63.83 BAC 5.24 ( 0.85) 0 .00 23.1 0 5.45 ( 0.56) 0 .00 26.4 0 2.24 ( 0.17) 0 .00 15.44 NHAN 1 ,825.96 ( 135.04) 280 5 560 1 ,784.17 ( 105.79) 200 5 040 1 ,126.72 ( 32.47) 160 2 880 NHAC 616.14 (88.12) 0 3 040 729.67 (69.21) 0 3 480 149.86 ( 11 .81) 0 1180 PNHAN 0.75 ( 0.03) 0.23 1 .00 0.72 ( 0.02) 0.18 1 .00 0.89 ( 0.01) 0.47 1 .00 PNHAC 0.25 (0.03) 0 .00 0.77 0.28 ( 0.02) 0.00 0.82 0.11 ( 0.01) 0 .00 0.53 PBAN 0.89 ( 0.02) 0.61 1 .00 0.88 ( 0.01) 0.6 0 1 .00 0.95 (0 .01 ) 0.63 1 .00 PBAC 0.11 ( 0.02) 0 .00 0.39 0.12 ( 0.01) 0 .00 0.4 0 0.05 (0 .01 ) 0 .00 0.37 Note. TP1: Temporal Plots 1, TP2: Temporal Plots 2 and MP: Management Plots. n is the number of plots and m is the number of measurements. m = n in TP1 and TP2. AGE: dominant a ge (years), HD: dominant height (m), SI: site index (m), BA: total basal area (m 2 ha 1 ), NHA: total number of trees (trees ha 1 ), DQ: mean quadratic diameter (cm), BAN: basal area of Nothofagus (m 2 ha 1 ), BAC: basal area of companion species (m 2 ha 1 ), NHA N: number of Nothofagus trees (trees ha 1 ), NHAC: number of trees of companion species (trees ha 1 ), PNHAN: proportion number of trees of Nothofagus (0 1), PNHAC: proportion number of trees of companion species (0 1), PBAN proportion of BA of Nothofagus ( 0 1), PBAC: proportion of BA of companion species (0 1)
32 Table 2 2. Distribution of dominant species (DOM SP) for the Temporal Plots 1 (TP1), Temporal Plots 2 (TP2) and Management Plots (MP) networks Network N.alpina N. dombeyi N. obliqua Mixed Total TP 1 6 2 1 14 9 5 0 TP2 8 49 2 0 23 120 MP 41 0 0 7 4 8 Table 2 3. Goodness of fit measures for models for basal area of Nothofagus ( BAN, E q 2 8 and 2 10), basal area of companion species ( BAC, Eq 2 9 and 2 11), total basal area (BA) p roportion of n umber of Nothofagus t rees ( PNHAN, Eq. 2 1 2 ) Model Prediction Projection Training Validation BAN N 150 51 217 R 2 emp 0.54 0.51 0.8 0 RMSE% 27.31 13.63 9.04 Bias% 0.29 2.25 5.24 BAC n 150 183 217 R 2 emp 0.85 0.89 0.94 RMSE% 44.6 41. 68 33.52 Bias% 0.86 3.72 12.48 BA n 150 51 217 R 2 emp 0.56 0.5 0.84 RMSE% 26.29 13.36 7.83 Bias% 0.16 1.69 4.51 PNHAN n 150 183 R 2 emp 0.68 0.56 RMSE% 16.92 8.07 Bias% 1.5 3.46 Note: The TP1 and TP2 networks we re used as training data and the MP network as validation data. Validation data for the BAN and PNHAN models only includes stands with known AGE
33 T able 2 4. Parameter estim ates, standard errors (SE) and V ariance I nflation F actors (VIF) for models of basa l area of Nothofagus ( BAN, Eq 2 8 and 2 10 ), basal area of companion species ( BAC, Eq 2 9 and 2 1 1 ) and p roportion of number of Nothofagus trees ( PNHAN, Eq. 2 1 2 ). All model parameters were found to be significant (p<0.001) Model 0 1 2 3 4 BAN Estimate 6.16977 1.21163 0.65197 0.51841 1.24957 SE 0.71314 0.07496 0.06801 0.0529 0 0.17498 VIF 2.06 1.53 2.1 0 1.25 BAC Estimate 1.99503 0.09436 0.21578 1.87264 SE 0.08904 0.02513 0.04885 0.12278 VIF 1.23 3.62 3.27 PN HAN Estimate 7.13684 10.29084 0.01404 SE 0.55383 0.56703 0.00429 VIF 1.02 1.02 Note: The TP1 and TP2 networks we re used for training
34 Figure 2 1. O bserved vs predicted values for (A) basal area of Nothofagus ( BAN, Eq. 2 8 ), (B) basal area of companion species ( BAC Eq. 2 9), (C) total basal area, BA = BAN + BAC and (D) number of trees per hectare ( NHA Eq. 2 3). All panels are estimates from the Temporal Plots networks (TP 1 and TP2)
35 Figure 2 2. O bserved vs predicted values for (A) basal area of Nothofagus ( BAN, Eq. 2 8), (B) basal area of companion species ( BAC Eq. 9), (C) total basal area, BA = BAN + BAC and (D) number of trees per hectare ( NHA Eq. 2 3). All plots are estimates using the Management Plots (MP) netwo rk
36 Figure 2 3. Relative residuals for different simulation years in projections of (A) basal area of Nothofagus ( BAN, Eq. 2 10), (B) basal area of companion species ( BAC Eq. 2 11), (C) total basal area, BA = BAN + BAC and (D) number of trees per hec tare ( NHA Eq. 2 3) using the MP data as validation
37 Figure 2 4. (A) Q uadratic diameter (DQ) vs number of trees per hectare (NHA) trajectories of measured stands of the MP network Dashed line is the DQ max for N. alpina (B) are the observed v s. projec ted values of number trees Figure 2 5. Model projections of 60 years of b asal a rea of Nothofagus (BAN, Eq. 2 3 and Eq. 2 10 ) with different initial number of trees per hectare (NHA). Projections are based on an initial BAN of 15 m 2 ha 1 dominant age of 15 years, SI of 10 m and PBAN of 1. (A) Dominant age vs BAN trajectories. ( B) DQ vs NHA trajectories. Dashed line is the DQ max line for N. alpina
38 CHAPTER 3 VALIDATION AND COMPATIBILITY OF INDIVIDUAL AND STAND LEVEL GROWTH AND YIELD MODELS FOR NOTHOFAG US FORESTS Introduction A growth and yield (G&Y) model is a representation of t he natural dynamics of a forest and includes growth, mortality, and other changes in stand structure (Vanclay 1994). Forest G&Y models can be classified into stand level (low r esolution) or individual level (high resolution) models (Porte and Bartelink 2002) Stand level models are those in which the modeling units are aggregated parameters such as basal area, stocking, and site productivity (Vanclay 1995) In contrast, individu al level models can keep track and describe each tree in the stand. Both levels have advantages and disadvantages: stand level models pres ent well behaved predictions on the long term for stand parameters ; however, they are inadequate to predict tree varia bles (such as diameter distributions or individual competition ). In contrast, i ndividual level models are better at predicting tree s structure but lack p recision when aggregating to stand level parameters (Qin and Cao 2006) Mathematical methods have been developed to link stand and individual level models into a compatible system to exploit the advantages of both and to improve predictions ( Cao 2014; Hevia et al. 2015; Zhang et al. 2010). One popular method is to a d just the predicted tree yield to match the predicted stand basal area from a stand level simulation ( Qin and Cao 2006) Similarly, this method can also adjust the predicted individual mortality probabilities from a n individual level simulation to match the predicted total num ber of trees from a stand level simulation (Cao 2017) A second commonly used method is the calibration of individual growth rates to match the BA growth from stand level simulation (Cao 2006 ) The adjusted predictions from both
39 methods keep individual tree information such as diameters and mor tality probabilities, therefore, they are expected to provide better individual volume and diameter distribution predictions. T he above calibration methods have been mostly applied outside natural mixed forests because, i n contrast to f orest plantations, establishing and remeasuring inventory plots in mixed forests over a wide geographical and temporal range is more time consuming and costly and this causes a lack of sufficient and high quality sample plots for the development and valida tion of sound forest models. Therefore, mixed forests G&Y simulations could benefit from compatibility methods to improve existing individual and stand level models particularly as they could calibrate each cohort individually A natural forest that can b e benefited by model calibration is the Nothofagus forest type in souther n Chile, known as RORACO for the dominance of the emergent trees of Rauli ( Nothofagus alpina (Poepp. & Endl.) Oerst.), Roble ( N. obliqua (Mirb.) Oerst.) and Coige ( N. dombeyi (Mirb.) Oerst.). The se Nothofagus species have been previously studied in Chile with several reports available for example on basal area and diameter growth ( Palmas et al. 2017 ; Moreno 2017) ; w hile these studies can have good accuracy, they could be improved by combining them into a calibrated G&Y system The main objective of this study is to evaluate different compatibility methods t hat integrate two available individual and stand level models for mixed Nothofagus forests in southern Chile. The specific object ives are : (1) to validate predictions of individual and stand level models against independent data not used for model fitting ; and (2) to
40 evaluate different methods and approaches for compatibilization that link individual and stand level models Method s Available Data The data for this study originated from a permanent plot network established in second growth RORACO forests in southern Chile, located between the 36 and 42 S latitude. The plot network was established by the Universidad Austral de Chile between 1999 and 2000 and had a total of 1 28 plots, each with an area of 500 m 2 Only 17 of those plots were r emeasured in 2006 and a subset of seven plots was remeasured a third time in 2012 These remeasured plots can be matched in to 33 pairs of plot ch anges with 6 or 12 years between measurements For all plots, trees above 5 cm of diameter at breast height (DBH, cm) were inventoried for DBH and total height (H, m). Nothofagus species were identified and the rest was recorded as companion species. For all plots, the following stand level variables were calculated: dominant age at breast height (AGE, years) as the average age of the thickest 100 trees per hectare dominant height (HD, m) as the average total height of the thickest 100 trees per hectare site index (SI, m), total basal area (BA, m 2 ha 1 ), total number of trees (NHA, trees ha 1 ), and quadratic diameter (DQ, cm). Also, for each of the cohorts, basa l area for Nothofagus (BAN, m 2 ha 1 ) and number of tre es of Nothofagus (NHAN, trees ha 1 ) were calculated. T he proportion of basal area and number of trees of Nothofagus (PBAN, PNHAN) w as also obtained. Only those plots dominated by Nothofagus (i.e., PBAN > 0.6) were selected for this study. For those plots without known SI, estimates were obtained using the site curve model reported by
41 Gezan and Ortega (2001) and Moreno (2017) All plots were assigned to a growth zone (ZONE) according to Gezan and Moreno (1999) Stand Density Index (SDI, trees ha 1 ) was calculated using: SDI = N HA (25.4/ D Q ) (Aver y and Burkhart 2002) 1.4112, as reported by Gezan et al. (2007) Additionally e ach tre e had an average annual increment in DBH (AIDBH, mm year 1 ) an estimated basal area of Nothofagus trees with larger DBH (BALn m 2 ha 1 ) and a sociological st atus (S S defined according to vertical stratification with 1: dominant ; 2: codominant, 3: intermediate ; or 4: suppressed ) Summary statistics for the plot network are presented in Table 3 1. Growth and Yield Models In this study, s tand level models (Palma s et al. 2017) of basal area and mortality, together with individual level models of diameter growth (Moreno 2017) will be validated against independent data The stand level basal area growth model uses the predictors of AGE SI NHA and PBAN (Equation 3 1 ; Palmas et al. 2017 ) This model is (3 1) w here is the natural logarithm The stand mortality model is a simple annual projection of NHA de fi ned by th e single parameter and it is b ased on the expression from Reineke (1933) T h e stand mortality model uses the current NHA 0 to estimate the current maximum quadratic diameter (DQ 0max ) with (3 2) w it h different values for stands dominated by N. alpina N. obliqua and N. dombeyi and a common for all stands (Gezan et al. 2007). The stand level model to project future values of the number of trees of Nothofagus ( ) i s
42 (3 3 ) where is the parame ter to estimate and i s the number of years between measurements The parameters for all stand level equa tions can be found in Table 3 2 Two individual level models for annual diame ter growth ( AI DBH m m y ea r 1 ) will be considered (Moreno 2017) Both models include coefficients for BAL, SDI, DBH and AGE but only the first model includes a combined factor SpZone, of growth zone and species (Equation 3 4 and 3 5, respectively ; Moreno 2 017 ) The models are (3 4) (3 5 ) where the represent the different coefficients for each interaction between species and ZONE. T otal stand volume (VOL, m 3 ha 1 ) from stand level simulations can be obtained using two different equations reported by Gezan and Ortega (20 01 ) ( Equation s 3 6 and 3 7 ). VOL models 1 and 2 require BA, HD and only the latter also requires PNHAN The models are : (3 6 ) (3 7) A third VOL calculation originates from a diametric distribution equation with stand parameters as predictors using a Weib ull distribution and using r eported DBH
43 class volumes model s ( Gezan et al. 2001 ) Th is diametric distribution equation is based on a Weibull distribution with three parameters (Clutter et al. 1983; Gadow and Hui 1999) and provides frequencies for each DBH class Later, volumes for these classes were calculated using available height and taper equations by Gezan et al. ( 2009) which are then aggregated to the stand level. Finally, for the simulations at the individual tree level, their p redicted tree volumes were estimated from reported taper and volume models (Gezan et al. 2009) and then aggregated to the stand level Compatibility Methods and Evaluation Two compatibility methods were used to calibrate the projections of the individual level models We refer red to them as the Proportional Yield (PY) and the Proportional Growth (PG ; also known as d isaggregation method ) ( Cao 2006 and Qin and Cao 2006 ) Both methods of calibration use two equations, one to calibrate the individual mortality probabilities based o n the stand level NHA projection (NHA 1 Equation 3 3), and another to calibrate the individual diameter growth to the stand level BA projection (Equation 3 1) The equations for the PY method are : (3 9) (3 10) where and are the calibrated and predicted expansion factors (the number of trees that each sample tree represents) for th tree at time 1 respectively ; is the trees per hectare at time 1 from Eq uation 3 3 ; and are the calibrated and predicted squared diameter s for the th tree at time 1 respectively is estimated
44 by adding the estimated AIDBH from Eq uation 3 4 or 3 5 to the to the is the basal area at time 1 from Eq uation 3 1 ; and is a constant The equations for the PG method are: subject to (3 11 ) (3 12 ) W here is the square d diameter of the th tree at time 0 and all other terms were previously defined Equation 3 11 requires to find a power value m that makes the sum of the predicted expansion factors equal to The predictions of the tw o com patibility methods (PY and PG) were comp ared with unadjusted stand level simulations using the three VOL models and unadjusted tree level simulations using the two AIDBH models T he total number of scenarios compared in this study is nine ( Table 3 3 ) Model evaluation with independent data and compatibility methods were compared using the observed and projected basal area growth and mortality based on the information from the available 17 remeasured plots, with the following goodness of fi t measures: R 2 emp RMSE% and Bias%, t hat are detailed below. (3 13 ) (3 14 ) (3 15 ) where and are the th observed and projected value, respectively; i s the mean response of the observed value, and is the numb er of observations.
45 In order t o compare the final diameter distribution s, t he r atio between the 85 th and 15 th percentile of DBH ( P 85/ P 15) was calculated. A large P85/P15 ratio would be evidence of skewness of the s tand DBH distribution to the right towards larger trees. As stand scenarios S1 and S2 do not use diameter distribu tion m odel, they do not have a calculation of P 85/ P15 For graphical outputs comparing scenarios, relative residuals were used, which were defined as the difference between observed and predicted values divided by the mean o bserved value and represented as a pe rcentage. All calculations were done in R 3.3.2 (R Core Team 2016). Results Scenarios had different g oodness of fit measures for their predictions of NHAN, B AN DQ and VOL ( Table 3 4 ) As expected, t he three previously reported stand scenarios, S1, S2 and SD, are better behaved for stand attributes as N HAN and BAN with ranges of R 2 emp between 0.9 1 and 0. 9 4 respectively. S1 and S2 scenarios have the lowest fitness values for VOL predictions with R 2 emp of 0.1 1 and 0.1 0 The SD scenario demonstrates that the reported diameter distribution equation can impr ove the prediction of VOL from the stand level VOL models 1 and 2 The two AIDBH models result in small or no differences in predictions as shown by the almost equal goodness of fit measures in T1 and T2, PY1 and PY2 and PG1 and PG2 AIDBH model 2 resulted in marginally better RMSE% and Bias% for compatibility scenarios than AIDBH model 1 PY2 better than PY1, and PG2 is better than PG1 Results below disregard the small differences between the two BAN models and the two AIDBH models.
46 N umber of Trees Goodness of F i t Statistics All scenarios presented NHAN predictions with R 2 emp above 0. 91 with compatibility scenarios PG1 PG 2 and PY 1 P Y 2 showing the highest values followed by the S1 S2 SD and T1 T2 PG1 PG2 had the lowest RMSE% and Bias% across all simulations followed by PY 1 PY2 scenarios For NHAN, the s cenarios predictions showed variable trends of underpredictions and overprediction in all scenarios (Figure 3 1 A ) The length of the simulation considerably a ffect ed the fitness of the predictions. Relative residuals had larger departures from zero in 12 year than 6 year simulations 12 year simulations had in average over 12% more of error than 6 year simulations For NHAN, S1 S2 and T1 T2 scenarios had lower relative residuals using simulations of 6 years; while compatibility scenarios PY1 PY2 and PG1 PG2 had better residuals for simulations of 12 years (Figure 3 2 A). M ean relative residual s increase d for all scenario s when the simulation years increase from 6 years to 12 simulations B asal Area Goodness of F i t In terms of BAN the S1 S2 SD and PY1 PY 2 scenario s had the highest goodness of fit values with average R 2 emp of 0. 90 and 0.8 8 respectively These scenarios also had the lowest RMSE% and Bias% v alues. The PG1 PG 2 compatibility method had the poorest fit with R 2 emp R MSE% and Bias% of 0.7 6 12. 54 and 9. 57 respectively. T he S1 S2 SD and PY 1 PY2 models had consistent overpredictions across all ranges of BA N ( Figure 3 1 B), and they departed to a m inimum o f 20 % In contrast, T1 T2 and PG1 PG2 scenario s consistently underpredicted across the entire range of observed values reaching relative residuals close to 35 %. At 6 year s imulations the
47 relative residuals for S1 S2 SD and PY1 PY2 scenario s were closer t o zero than T1 T2 and PG 1 PG2 scenario s (Figure 3 2 B) The relative residual trend of all scenarios was maintained in 12 year simulations, with S1 S2 and PY1 PY2 increasing overprediction and T1 T2 and PG1 PG2 increasing underprediction Diameter Distribu tions The ratio of P85/P15 using the diametric distribution was almost equal between T1 T2, PY1 PY2 and PG1 PG2 scenarios (Figure 3 1 C) These simulations had a R 2 emp of 0.48 and range of residual errors between 30% and 10%. S imulations tended to under a nd overestimate across the range of P15/P85. SD greatly differed from the other scenarios with constant underprediction that reached almost 40% for 6 year and 25% for 12 year s imulations Estimating diametric distribution from the Weibull distribution favo red large trees T1 T2, PY1 PY2 and PG1 PG2 scenarios are closer to the measured distribution. V olume Goodness of Fit The S1 S2 and SD scenario s had the lowest goodness of fit measures for VOL with R 2 emp values of 0.1 1 0.1 0 and 0. 58 ; respectively and th e highest RMSE%. VOL from S1 S2 scenario s w as highly variable in terms of relative residuals ranging from 30 % to 40% (Figure s 3 1 D and 3 2 D ). Calculating volume using diameter distribution equations (scenario SD) performed better than the stand volume e quations with relative residuals closer to zero T1 T2 scenario s had the high est goodness of fit for VOL predictions with an R 2 emp RMSE% and Bias% of 0. 8 9 8. 23 and 4. 12 respectively Relative residuals for T1 T2 scenario s were consistently closer to zer o denoting poor goodness of fit of the two stand level VOL equations.
48 For the 6 year and 1 2 year s imulations the relative residuals for T1 T2 scenario s had the best performance among the systems. VOL predictions also show ed the accumulation of errors tre nd when increasing the simulation length from 6 to 12 years ; where r elative residuals increased their trend betwee 5 to 10% PY1 PY2 scenario s had R 2 emp at 0. 80 smaller than T1 T2, with values of RMSE% and Bias% of 11.06 and 8.04 Relative residuals cons istently showed overpredictions with values that reached 25 % VOL predictions using PY1 PY2 scenario returned residual error means of 8% and 12% at 6 and 12 years, respectively. The compatibilization using the PG1 PG2 method returned slightly higher goo dness of fit values than PY1 PY2 scenarios with R 2 emp of 0.8 5 and RMSE% of 9. 48 Discussion T here were small differences found from the two AIDBH models meaning that the addition of the factor SpZone, that combines growth zone and species to the model d id not markedly improve d predictions. This definition of zones was reported as significant in other studies in contrast to our results (Chauchard and Sbrancia 2003; Echeverria and Lara 2004; Esse et al. 2013; Gezan et al. 2009; Lusk and Ortega 2003). This also suggests that DBH growth for RORACO stands is highly correlated with current size, competition and site factors Similar conclusion s were found in ot her mixed species forests ( Wykoff 1990 ; Monsreud and Sterba 1996) Model evaluation suggested that st and and tree level models presented limitations according to their resolution while compatibility methods improved predictions. Stand level models performed better than the individual level models t o predict NHAN and BAN, but had inadequate VOL estimations as seen in the poor goodness of fit measures using both VOL models On the contrary, individual level
49 models do poorly when aggregating the DBH predictions to the stand parameters of NHAN and BAN. Individual level models return the best fitness properties for VOL agreeing with the reported advantages of both stand and individual level models (Qin and Cao 2006). Therefore, the performance of the previously reported stand scenarios (S1, S2 and SD) is higher when predicting BAN while the tree scenarios (T1 and T2) have higher performance when predicting VOL. PY1 PY2 and PG1 PG2 both had higher accuracy of NHAN predictions than S1 S2 SD and T1 T1 scenarios However, Proportional Y ield and P roportional G rowth methods sho wed different performance in predictions for BAN Here s cenarios with PY1 PY2 improved and PG1 PG2 worsened prediction fitness compared to T1 T2 scenarios. D ifferent results were found in b irch ( Betula alba Hevia et al. 2015) and l oblolly p ine plantations ( Pinus taeda Cao 2006) where predict ion fitness of BA was higher using the Proportional Growth than using the Proportional Yield method In terms of VOL, PY1 PG2 and PG1 PG2 scenarios had lower goodness of fit than the unadjusted T1 and T2 scenarios. This result contrast with im provement s o f individual volume predictions when using P roportional G rowth method in Douglas Fir stands (Zhang et al. 1993) The compatibility adjustments, as well as the unadjusted predictions, suffer from accumulation of errors and reduction of goodness of fit of pr edictions when increasing simulation years. The compatibility methods are not only limited in their accuracy by the length of the simulation, but also by the accuracy of the stand level of predictions. T he permanent plot network used to validate these scen arios systems is the only current re source of independent remeasured plot data for RORACO forests which in
50 this case is mainly dominated by N. dombeyi Thus, th ere is the need for additional permanent plot data to further validate and improve these models Conclusion This study validates previously published models, is a crucial step for effective evaluation of forest growth models. It was shown that validations with the stand level scenarios have high goodness of fit when predicting stand level parameters such as BAN and NHAN. On the other hand, tree level scenarios had higher performance when predicting VOL. This study evaluated two compatibility scenarios that uses published stand and individual level models to improve predictions for the RORACO forests in southern Chile. The c ompatibility scenarios evaluated resulted in better pre dictions for NHAN and BA than unadjusted stand and individual level simulations. Adjusting individual level predictions to match stand level predictions with a Proportional Yi eld method returned the best results for number of trees and basal area of Nothofagus T his compatibilization study provides with the first evaluation and implementation of compatibility methods to link stand and individual level models in mixed and uneve n aged forests.
51 Table 3 1 Mean (standard error) and range of stand parameters in the remeasured plots from the permanent network based on 33 plots Variable Mean (SE) Range AGE 45.68 (1.47) 20.73 63.58 HD 29.29 (0.89) 19 .00 42.65 SI 14.71 (0.55) 8.31 22.61 BA 43.47 (1.49) 23.49 64.84 NHA 1 826.51 (163.43) 460 4 360 DQ 19.86 (1.03) 8.48 34.53 BAN 38.89 (1.50) 20.72 61.55 NHAN 1 283.26 (123.14) 460 3 440 PNHAN 0.72 (0.03) 0.44 1 .00 PBAN 0.89 (0.01) 0.69 1 .00 SDI 289.11 (5.95 ) 225.32 376.16 AIDBH 3.08 (2.10) 0.1 0 12.1 0 SS 3.24 (0.03) 2.82 3.68 BALn 32.44 (1.20) 16.08 49.68 Note. AGE: dominant age (years), HD: dominant height (m), SI: site index (m), BA: total basal area (m 2 ha 1 ), NHA: total number of trees (trees ha 1 ), DQ: mean quadratic diameter (cm), BAN: basal area of Nothofagus (m 2 ha 1 ), NHAN: number of Nothofagus trees (trees ha 1 ), PNHAN: proportion number of trees of Nothofagus (0 1), PBAN: proportion of BA of Nothofagus (0 1), SDI: stand density index, AI DBH: average annual increment in DBH (m m year 1 ) SS: sociological status, BALn: basal area of larger trees of Nothofagus (m 2 )
52 Table 3 2 Estimated p arameters for BAN, NHA, AIDBH equations Parameter Eq. 3 1 Eq. 3 2 Eq. 3 3 Eq. 3 4 Eq. 3 5 Eq. 3 6 Eq. 3 7 a 3 59 6 10 3 2.702 2.908 3.065 2.538 2.587 2.84 1 2.678 2.946 2.948 2.941 2.902 6.1 70 2.410 4 33 2 10 1 3 46 9 10 1 1.21 2 1.411 10 3 10 3 9 79 4 10 1 9 93 8 10 1 0.65 2 10 1 10 4 9 39 6 10 1 9 30 5 10 1 0.51 8 1.175 10 1 4 63 7 10 2 1.2 50 10 1 1.138 10 1 a 11.61 7 11. 377 and 11.76 4 for plots dominated by N alpin a N. dombeyi and N. obliqua respectively
53 Table 3 3 Definition of scenarios considered in this study Scenario Level Model Compatibility S1 Stand VOL Model 1 S2 Stand VOL Model 2 S D Stand Diametric distribution T1 Tree AIDBH Model 1 T2 T ree AIDBH Model 2 PY1 Tree AIDBH Model 1 Proportional Yield PY2 Tree AIDBH Model 2 Proportional Yield PG1 Tree AIDBH Model 1 Proportional Growth PG2 Tree AIDBH Model 2 Proportional Growth Table 3 4 Goodness of fit measures for each scenario for number of trees per hectare of Nothofagus (NHAN), basal area of Nothofagus (BA N ), P85/P15 and stand volume (VOL ) Scenario NHAN BAN P85/P15 VOL R 2 emp RMSE% Bias% R 2 emp RMSE% Bias% R 2 emp RMSE% Bias% R 2 emp RMSE% Bias% S1 0.94 15.60 4.36 0.9 0 8.15 4.19 0.11 24.14 4.57 S2 0.94 15.60 4.36 0.90 8.15 4.19 0.10 24.29 4.92 SD 0.94 15.60 4.36 0.90 8.15 4.19 0.10 28.85 14.62 0.58 14.42 7.52 T1 0.91 19.52 6.40 0.80 11.41 7.76 0.48 22.67 0.85 0.89 8.23 4.12 T2 0.91 19.59 6.42 0.79 11.65 8.17 0.50 22.42 0.34 0.88 8.48 4.50 PY1 0.95 15.21 2.32 0.88 8.67 4.35 0.48 22.82 0.85 0.80 11.06 8.04 PY2 0.95 15.21 2.32 0.89 8.63 4.32 0.50 22.40 0.17 0.80 10.97 7.97 PG1 0.95 14.43 1.45 0.76 12.54 9.57 0.48 22.66 0 .24 0.85 9.48 6.10 PG2 0.95 14.40 1.44 0.76 12.45 9.22 0.50 22.41 0.18 0.85 9.45 5.82
54 Figure 3 1. Relative residuals for predictions of (A) Number of trees per hectare of Nothofagus (NHA N ), (B) Basal Area of Nothofagus (BA N ), (C) P85/P15 and (D) S tand Volume (VOL) against observed values Lines are smoothed average of the points for each scenario
55 Figure 3 2. Relative residuals against simulation years for predictions of (A) Number of trees per hectare of Nothofagus (NHA N ), (B) Basal Area of Not hofagus (BA N ), (C) P85/P15 and (D) Volume (VOL)
56 CHAPTER 4 TIMBER AND CARBON SCENARIOS FOR THE MAYA FOREST OF MEXICO: AN INDIVIDUAL BASED MODEL SIMULATION Introduction More than 400 million hectares of tropical forest are designated for timber producti on (Blaser et al. 2011) and at least 20% of the ir total area was logged between 2000 and 2005 (Asner et al. 2009). Even small l ogging operations can cause damage to the residual stand resulting in poor forest recovery, degradati on, reduction of timber stoc ks and eventual net carbon emissions ( Putz et al. 2012; Bryan et al. 2013 ). A set of silvicultural techniques that has been proposed for several years are the called Reduced I mpact Logging (RIL) techniques aimed to reduce forest damage and carbon emissi o ns, stabilize timber production and increase biomass sequestration rates (Pe a Claros et al. 2008 a ; Putz et al. 2008 ; Sasaki et al. 2016; Bicknell et al. 2015 ; Lussetti et al. 2016; Vidal et al. 2016). These techniques vary in their effects in timber sto cks sustainability conservation effectiveness and costs of application (Medjibe and Putz 2012). Even though experimental plots have demonstrated the benefits of some RIL techniques (e.g. Pea Claros et al. 2008b; Villegas et al. 2009; Gourlet Fleury et al 2013 ), there is not enough empirical data on all of them requiring that researchers provide answers with the use of simulation models Accurately accounting the carbon dynamics that arise from the use of various silvicultural techniques and harvested sp ecies, characteristic of tropical forest operations, can reduce the reported large uncertainties of the carbon balances for the tropical forests (Pan et al. 2011; Baccini et al. 2017). A simulation model for a tropical forest can become highly complex depe nding on the inclusion of submodels that recreate the multiple species, ages or growth strategies
57 that are part of the forest (Filotas et al. 2014) Therefore, in the final predictions can be highly biased due to the accumulation of errors from each submod el. This accumulation of error occurs even if each submodel has a proven high precision This problem can be avoided with the implicit inclusion of random effects through stochastic model s. Iterations of a stochastic model generate a range of plausible val ues that can be more realistic and insightful th an a single and potentially biased value f rom a deterministic model ( Vanclay 1991; Black and McKane 2012 ). A stochastic approach also allows accurate representation of random but nevertheless important ecosys tem processes such as hurricane caused mortalit y. Quintana Roo is the Mexican state that harvests the largest volume of tropical timber in Mexico (Ellis et al. 2014). Historically, the state forest industry has focused on the extraction of timber species s uch as mahogany ( Swietenia macrophylla ), Spanish cedar Cedrela odorata hardwoods for railroad ties (Shoch 1999) and on latex (chicle) tapping o f Manilkara zapota Recently, the forest industry in Quintana Roo diversified to include a cohort of polewood sp ecies and palm leave s useful for the local tourism industry (Sierra Huelsz et al. 2017). Given that many forests in Quintana Roo are now being logged in a second rotation, and in response to the frequent calls for improved carbon retention, th ese forests c ould benefit from a simulation model to estimate the effects of silvicultural interventions on the forest basal area and biomass. As with many tropical forests of the world currently there is no forest simulation available for the natural forests in Quint ana Roo, Mexico. This study suggests that a complete simulation model for these forests can now be completed using t he wide array of ecologic al and silvicultural studies that have taken place in the region.
58 T his study aims to provide estimates on the poten tial effects o f RIL techniques by simulating a forested area in Quintana Roo dedicated to the management and harvest of timber species. T he specific objectiv es are : 1) to generate and code an individual tree based growth model capable of simulating forest management activities; 2) to validate the simulation model with known harvesting rates and timber biomass from Quintana Roo ; and, 3) to estimate and evaluate the extent to which R IL activities can reduce timber and above ground timber biomass stocks in the region Data Sources Diameter growth, recruitment, mortality and harvesting rates used to build the simulation model came from multiple studies based in Quintana Roo forests, which are identified in Table 4 1. I nitial forest conditions (i.e. number, spec ies and diameter of trees present in each stan d ) of the were based on the permanent National Forest Inventory plots measured in the central municipalities of Quintana Roo by the National Forestry Commission (CONAFOR 2008). Model Description The simulation coding was done in R 3.3.2 (R Core Team 2016), and the complete code can be found in www.github.com/spalmas/RIL Simulator and the simulation web application in https://spalmas.shinyapps.io/RIL Simulator The model simulate s a managed forest in the south and central municipalities of Quintana Roo : Felipe Carrillo Puerto, Jose Maria Morelos, Bacalar and Othon P. Blanco (Figure 4 1). Th is mode l is based on an individual tree, distance independent approach as it follows individual trees without consideration of spatial effects and the simulation cycles through a sequence of submodels of diameter growth, natural mortality, hurricane mortality, n atural recruitment and logging scenarios logging mortality and gap
59 enrichment. To incorporate uncertainty to the simulation, several submodels are modeled in a stochastic approach following the reported distributions of the model parameters. Finally, it r eports the resulting volumes of extracted timber volume and densities of above ground biomass The simulation occurs on 1 ha plots of forested area. To simulate the rotation of annual cutting areas (ACA), the number of 1 ha plots is equal to the rotation c ycle years. Each ACA is harvested only one year every rotation cycle. There are eleven simulated species in the mode l ( Table 4 2 ) and hereafter r eferred to by the generic names These species were chosen because they account for most of harvested volume fo r community forest enterprises in the Yucatan P en insula ( Wilshusen 2005; Racelis and Barsimantov 2008 ) Further details of the different submodels are presented below. Age I ncrement and G rowth Diameter at breast height (DBH, cm) growth is randomized annual ly from normal distributions with means and standard devi ations for each species ( Appendix A ). Growth increments are limited to change by up to only 15% between years t o simulate autocorrelation in growth rates over time These diameter growth distribution s were considered to not be affected by stand competition or weather patterns this is d ue to lack of data and literature reported in the region Natural and Hurricane Mortality The simulation varies the probability of tree mortality depending on hurricane strength category and tree size (Table 4 4) The annual probability of mortality during a non hurricane year is assumed to be 3% for trees with less than 10 cm DBH and 1% for larger individuals (Negreros Castillo and Mize 2014). Mortality during hurricane years
60 vary depending on the strength category of hurricane that hits the forest ( Snchez Snchez and Islebe 1999 ; Navarro Martnez et al. 2012 ; McGroddy et al. 2013 ; Sierra Huelsz et al. 2017) The annual probability that the forest is hit by a category 3 4, or 5 hurricanes was set to be 30%, 20% and 10%, respectively (Bitr n Bitr n 2001). Natural Recruitment The simulation adds each year trees of 10 cm DBH to the forest depending on the specific mean recruitment rates that vary in terms of stand basal a rea (Table A 2) Because the simulation does not have a model for canopy co ver to assign recruitment rates based on Toledo Aceves et al. (2009) stand basal area is used as a predictor of canopy cover using a simple l inear relation. A mean recruitment rate per hectare was assigned to those species with no specific recruitment rate reported by Toledo Aceves et al. (2009). Logging Scenarios and M inimum Cutting Diameters The logging intensities vary the percentage of trees harvested in the ACA Five categories are considered. A B usiness a s U sual ( BAU ) intensity harvests 50% of the biggest eligible trees in the stand was considered (Ellis et al. 2015). No logging Low High and All intensities harvest 0%, 25%, 75% and 100% of eligible trees, respectively. T rees must be larger than the allowed minimum cutting diameters (MCD) for its species to be eligible to harvest Swietenia timber species and the polewood cohort have a MCD of 55 cm, 35 cm and 10 cm, respectively (Sierra Huelsz et al. 2017). Felling Mortality a nd Cable Yarding Felling mortality is caused by the downing of timber trees. The technique of directional felling can avoid a ll felling mortality in the nearby trees from a harvested tree (Sist et al. 2003) If directional felling is selected in the simula tion, there are not killed
61 trees in the nearby area of the harvested tree. If directional felling is not employed trees within a distance equivalent to the height of the felled tree have a 50% chance of mortality. The probability of skid trail mortality i s based on the locations of each tree within the 1 ha plot. A skid trail 6 m wide runs from the location of each harvested tree to the closest edge of the 1 ha plot. To simulate the avoidance of large trees (whic h are potentially future crops) a ll trees wi th DBH > 20 cm are spared in the skid trails (Figure 4 2 ). It was assumed, that n o trees are killed along the skid trail in scenarios in which cable yarding is employed Gap Enrichment It was considered that for e very three harvested trees a simulated enr ichment gap area is randomized from a log normal distribution with = 0.1 and = 0.039 (Navarro Martinez et al. 2017) The simulator then adds seedlings of Swietenia to the open area at a density of 2 000 plants per hectare. To simulate the preference of Swietenia to sunlight, seedlings inside enrichment gaps grow at a higher rate than outside gaps with a diameter growth distribution of = 0.039 and = 0.31. Timber Volumes and Above Ground Biomass Harvested tree volumes ( VT, m 3 ) from harvested trees are estimated using a model for Swietenia (Equation 4 1) and a general model for the rest of the species ( Equation 4 2 ). The following models, first reported by Alder ( 1997 ), are used in the region for the estimates of the tree volume. (4 1) (4 2 ) where H i s the total height of the tree in m
62 Tree a bove ground biomass is estimated using Chave et al ( 2014) with spec wood densities from the Global Wood Density Database ( Chave et al. 2009; Zanne et al. 2009). Tree volumes and above ground biomass are added to find the stand harvested volumes (VOL, m 3 ha 1 ) and above ground biomass (AGB, Mg C ha 1 ) Definition of Scenarios In order to evaluate the proposed model, five sc enarios were simulated to represent business as usual, hurricane mortality and ideal RIL conditions. The scenarios are detailed in Table 4 4. All scenarios ran for 40 years with a 25 year rotation cycle with directional felling. The scenarios ran for 100 i terations to obtain prediction distributions given the presence of the stochastic submodels. Also, each iteration randomizes the initial trees in the forest. Results and Discussi on Number of Extracted T rees and Volume BAU scenarios can extract between 5 1 5 trees ha 1 and 7 20 m 3 ha 1 of VOL during the first rotation cycle For the same period, RIL B and R IL WB scenarios had annual harvests of betw een 3 6 trees ha 1 corresponding to 2 7 m 3 ha 1 of timber volume These extraction rates for RIL scenarios are common for RIL managed forests For instance, harvest rates in Amazonian and Guyana studies average d 3.6 and 2.5 trees ha 1 respectively ( Miller et al. 2011; Arevalo et al. 2016) All simulations had very low or no harvested trees after the first rotation cycle, suggesting that the growth and recruitment rates assumed in this study are too low to allow for mai ntenance of species populations in BAU or RIL scenarios It is important to note that the simulated growth rates for the species are in use by the fo rest communities in Quintana Roo Management plans in the region for mahogany assume a mean DBH growth of MAI of
63 0.73 cm y ea r 1 (Negreros Castillo and Mize 2014), which would result in a tree reaching the MCD of 55 cm in 75 years. Changes in Timber Basal A rea and Aboveground B iomass BAU scenarios showed lower values of annual changes of BA ( ) during the first rotation than RIL scenarios (Figure 4 3 C ) For the first 25 years of management, BAU scenarios had a e range of 0.05 to 0.15 m 2 ha 1 year 1 Simil ar annual (Mize and Negreros Castillo 2007). After the first cycle, BAU B had almost the same BA than the BAU scenario. This difference was maintained until the 40th simulation year ; however RIL B and RIL WB scenarios h ad between 0. 03 to 0.1 m 2 ha 1 year 1 RIL B and RIL WB scenarios end ed the first cycle with 1 05 and 1.1 4 m 2 ha 1 of BA more than the BAU scenario (Table 4 5) In terms of AGB, BAU scenarios had annual changes of AGB ( AGB ) between 1.5 to 0.06 Mg C ha 1 year 1 RIL scenarios had lower losses of AGB with AGB between 0 .1 0 Mg C ha 1 year 1 At the end of the first cycle, AGB for RIL B and WIL WB scenarios was more than 6 Mg C ha 1 higher than the BAU scenario If we consider that forests of central Quintana Roo have 110 225 Mg C ha 1 (Cairns et al. 2000; 2003), going from BAU to RIL scenarios could avoid between 2 5% of emissions in 25 years Hurricane Effects After the first cycle, the hurricane had 1.0 5 m 2 ha 1 less BA than the BAU scenario. This e stimate is in line with experimental plots in the region where BA measured basal area was reduced between 0.1 1.4 m 2 ha 1 after H urricane Dean ( Navarro Martinez et al. 2012) For the simulations, t his difference between BAU and
64 BAU H was reduced from 1.0 5 to 0.8 2 m 2 ha 1 15 years after the hurricane due to the higher number of seedlings recruited in the stands For AGB, BAU H had 6. 33 and 5. 05 Mg C ha 1 less AGB than the BAU scenario 5 and 20 years after the hurricane. BAU H had maximum reduction of 2 .5 Mg C ha 1 which could mean a reduction of 2% of the AGB for stands in Quintana Roo. T hese losses of AGB can increase if coarse woody debris is considered ( Whigh am et al. 1991) Model Limitations An important limitation of this mode l is that it does not consider component s such as competition, canopy openness or climatic conditions for m any processes For instance, sun tolerant large tree species such as Manilkara can have higher growth The simulation is also limited since only considers eleven species of the more 50 commercially species used in Quintana Roo (Sierra Huelsz et al. 2017). Futur e improvements of the model should attempt to solve some of these limitations. The correlation that the simulation uses between canopy cover and basal area is not validated and should be studied further, perhaps with a model for canopy openness. The use o f this method is defended because the study by Toledo Aceves et al. (2009) considers more species than any other study in Quintana Roo. Further advancement of simulations depends on updated studies on recruitment rates. Conclusi on The publicly available si mulat or together with its computer code gives the opportunity to further explore more scenarios than those considered in this study. In this study, the evaluated simulations showed that the current 25 year cycle is not enough for
65 a complete basal area reco very even after 40 years after tree harvest even when RIL parameters are considered. The simulation results suggest there is a need to change the management from business as usual if there is the objective to have constant harvesting of trees. The scenario s simulated for this study are just a few of the many possible scenarios that can be projected with this system. The simulator can be used to further evaluate the effects of extending cutting cycles, enhancement of tree growth or enrichment with multiple s pecies.
66 Table 4 1 Selected literature for the forests of Quintana Roo and the Yucatan Peninsula Study Description Growth Alder (1997 1998 ) Growth rates and volume equations and for several timber species. Negreros Castillo and Martnez Salazar (20 11) Ann ual increment rates from Lysiloma latisiquum trees Recruitment Alder (1997) Number of seedlings per hectare recruited every 4 years. Toledo Aceves et al. (2009) Regeneration rates for 22 commercial tree species in plots with differen t canopy op enings, disturbances conditions such as log landings, skid trails and roads. Mortality Mize and Negreros Castillo (2007) Species presented annu a l mortality probabilities from 0.2 3.7%. Negreros Castillo and Mize (2014) 1 % annual mortality probability u sing seven years of measurements. Hurricane mortality Bitr n Bitrn (2001) Official figures of damaged forest hectares from Hurricanes Gilbert, Roxanne and Opal. Navarro Martinez et al. (2012) Estimates of types of hurricane stand and tree damage. Hurr icane Dean red uced stand BA from 0.1 to 1.4 m 2 ha 1 Smaller DBH trees have a greater probability of mortality. McGroddy et al. (2013) After H urricane Dean, an average of 49 % of the trees had no or little damage. 57% of the trees had damages. Whigman et al. (1991) Estimates of mortality after Hurricane Gilbert. Measured that l arger trees had lower mortality probabilities Silviculture and RIL Cairns et al. (2003) Estimates of AGB in permanent forest areas. Mize and Negreros Castillo (2007) Experimented with basal area reduction plots and measured growth for 25 canopy and subcanopy species in X Hazil Navarro Martinez et al. (2017) Areas of enrichment gaps and survival pro growth rates of Swietenia macrophylla inside these. Sierra Huelsz et al. (2017) E volution of management and use of polewood, thatching materials and chicozapote tree ( Manilkara zapota ) posts Snook and Negreros Castillo (2004) Analysis of diameter and height growth has also been analyzed for seedling inside felling gaps.
67 Table 4 2 Species and common names considered in the simulation Species Common local name Brosimum alicastrum Sw. Ramon Bursera simaruba (L.) Sarg. Chaka rojo Dendropanax arboreus (L.) Decne. & Planch. Chaka blanco Lysiloma latisiliquum (L.) Benth. Tzalam Mani lkara zapota (L.) P. Roye n Chicozapote Metopium brown ei (Jacq.) Urb. Chechem Piscidia piscipula (L.) Sarg. Jabin Pouteria unilocularis (Donn. Sm.) Baehni Zapotillo Simarouba glauca DC. Paasak Swartzia cubensis (Britton & P. Wilson) Standl. Katalox Sw ietenia macrophylla King Caoba Table 4 3 Hurricane categories annual occurrence probability and ass ociated percentage of mortality by tree DBH Hurricane category Annual occurrence probability Mortality DBH < 20 cm DBH > 20 cm 3 30% 10% 20% 4 20% 20% 30% 5 10% 30% 40% Table 4 4 Characteristics of the s cenarios simulated in this study. All scenarios ran for 40 years using a 25 year rotation cycle with directional felling and for 100 iterations Scenario Harvesting intensity Gap enrichment Cable yarding Hurricane BAU 50% No No BAU B 50% Yes No BAU H 50% No No Cat 5, at year 20 RIL B 25% Yes No RIL WB 25% Yes Yes Note. BAU : business as usual RIL: r educed impact logging B: gap enrichment ( bosquetes ), H : hurricanes and W : cabl e yarding (winching)
68 Table 4 5 Basal area (BA) and aboveground biomass (AGB) mean d ifferences from the BAU scenario after 10, 25 and 40 years of simulation BA (m 2 ha 1 ) AGB (Mg C ha 1 ) Scenario Years 10 25 40 10 25 40 BAU B 0.02 0.03 0.03 0 .06 0.05 0.05 BAU H 0.01 1.05 0.82 0.04 6.33 5.05 RIL B 0.45 1.05 1.07 2.64 6.17 6.37 RIL WB 0.51 1.14 1.15 2.92 6.51 6.67 Note. BAU : business as usual RIL: r educed impact logging, B: gap enrichment ( bosquetes ), H : hurricanes and W : cab le yarding (winching)
69 Figure 4 1 Map of the s outh and central m unicipalities of Quintana Roo
70 Figure 4 2. Dragging mortality and cable yarding. Small trees (DBH < 20 cm) between the harvested tree and the road are killed due to dragging. If a yardin g cable is used, there is avoided mortality
71 Figure 4 3 (A) h arvested trees, (B ) harvested volume ( VOL m 3 ) (C) annual change in timber b asal area ( m 2 ) and (D annual change aboveground timber biomass ( AGB Mg ha 1 ) trajectories for the five considered scenarios
72 CHAPTER 5 CONCLUSIONS A ND SUMMARY The models reported in this study constitute simple and valuable tools to support management decision for for est resources in southern Chile and Quintana Roo Mexico In both sites, the models can be used as part of cost benefit analys e s to promote sustainable yields and decrease deforestation and degradation pressures Models in Chapter 2 can predict when the ba sal area has such a reduced growth that the cost of maintaining the forest is higher than the incomes from a timber sale. The mortality model can be used to project how a thinning or selective harvest can reduce the tree mortality and promote basal area gr owth. Thinning is a silvicultural strategy that, if accurately planned, can significantly increase the value of the se forests. The model for the proportion of number of Nothofagus trees is important to predict the cohort dominance, an important characteris tic in any mixed forests. The m odels presented in Chapter 3 answer frequent ly asked question s in forest management such as : how accurate are the existing G&Y models? And, how can we improve future predictions? Th e validation of the models presented in Cha pter 3 is certainly not exhaustive because the validation dataset does not represent the entire range of the RORACO forest type and does not include a long span of measurements and all species However, it does show that the models accurately predict futur e stand basal area conditions within the range of parameters of the fitting dataset and, crucially, that the models are sound and appropriate to use in Nothofagus forests. Answering the second question, the Proportional Yield and Proportional Growth method s resulted in better predictions for basal area than unadjusted stand and individual level models This encourages forest professionals to make use of these compatibility methods to
73 improve the predictions of existing models for Nothofagus forest or any o ther G&Y with mixed forest Since, validation is a crucial step for effective evaluation of forest growth models (Vanclay and Skovsgaard 1997), the models in Chapter 2 and 3 are validated against independent data resulting in high goodness of fit (higher t han with the training data). This high goodness of correct in other words, completely valid; however, they are reasonable and are a faithful representation of the dynamics of the system s they m odel Developers of forest management plans may have the problem of selecting and implement silvicultural practice s depending on its cost and potential analysis of benefits. Chapter 4 deals with the problem of estimating carbon emissions as a consequence o f the implementation of different silvicultural practices in the context of mixed forests. This estimate is necessary when to calculate payments from the reduction in carbon emissions (e.g. REDD+ programs). The simulation s presented in Chapter 4 also give the opportunity to include models that require information on each tree For instance, a module can be added that predicts the response of a tree to plot conditions such soil nutrients. Because the model records the position each tree in the plot; a module can be added that estimates tree responses to a local condition such as canopy openness. It is important to note the models reported in this study require stand or individual parameters that come directly (or easily estimated) from forest inventories. The refore, their use is not restricted to forests with a high investment in research and are not highly complex in their mathematical methods. The online interactive simulations available
74 from this study for the Nothofagus and Maya forests also represent an e ffort to broaden the access to the final research products Many improvements can be made to these models reported in this study. Further model validations can be done because of the advances in technology that are now increasing the amount of forest data available (e.g. remote sensing products). Validating and fitting models with the inclusion of information with higher spa tial and temporally significance can increase the accuracy of the models. Also, Bayesian statistics is a technique that is appropriate for this improvement. The construction of the simulation models using submodels gives the possibility of adding more submodules to increase the reali sm of the system For instance, realism can be improved with submodels of competition models that take into acc light preferences or one for the re s ponse to c limate change scenarios. Sensitivity analysis is another important improvement that can be done with the simulation systems presented in this study. Sensitivity analyses estimates how the vari ation in the output of a numerical model can be attributed to variations of its input factor s (Pianosi et al. 2016). For instance, an analysis could be done to estimate how much the site index affects the final basal area projections This sensitivity analy sis can provide information on model uncertainty and validity of the evaluated model s One of the characteristics that makes the models reported in this study easy to improve is the availability of the code and interactive simulations. Open source code can make science reproducible, facilitate and accelerate research and improvements by other scientists (Hampton et al. 2015; Mislan et al. 2016). The code in this study is written in R, a language that has had increased its importance in research on
75 agricultu ral and biological sciences (Tippmann 2015). The author of this study encourages other scientists to use and improve the published code and simulators in their own research.
76 APPENDIX ANALYSIS OF MEAN ANNUAL INCREMENTS AND RECRUITMENT DATA FOR SPECIES IN QU I NTANA ROO MEXICO The Nature Conservancy (TNC) installed dendrometer bands in several ejidos in the Yucatan Peninsula. This appendix uses the data collected by these permanent dendrometer bands to estimate mean annual increments of important and lesser kn own species in the Yucatan Peninsula. The growth rates estimated in this study will then be used to calibrate an individual tree model for forest management in the Yucatan Peninsula. A total of 5 073 diameter were installed in 2007 and 2014 in 7 ejidos of the Yucatan Peninsula. Two bands projects were established: Purata and Snook. The Purata project installed bands on Bursera simarouba Dendropanax arboreous Lonchocarpus castilloi Lysiloma latisiliquum Manilkara zapota Metopium brownei Piscidia piscip ula Pl atymiscium yucatanum and Swietenia macrophylla The Snook project installed bands on 84 lesser studied species. For this short study, only those species with more than 30 individuals measured were analyzed for mean annual increment The Snook projec t included measurements of trees in areas with several treatments: partial clear ing such as mechanic, and slash and burn. Table A 1 summarizes the means, standard error of the mean and ranges of diameter growth using th e bands Th e growth rates reported in this Appendix are simple mean annual inc rements found from different bands installed in the region It is evident that the se growth rates cannot be generalized to the whole region Further analysis with more sophisticated statistical methods will need mor e diameter measurements and environmental data from the study sites
77 Table A 1 Summary of the mean diameter growth ( s tandard error ) and range of by species from the TNC diametric bands Species n Mean (SE) Range Bursera simarouba 374 0.17 ( 0.01) 0.19 1.3 0 Croton reflexifolius 119 0.16 ( 0.01) 0.1 0.58 Dendropanax arboreus 109 0.34 ( 0.03) 0 00 1.46 Guettarda combsii 208 0.11 ( 0.01) 0.13 0.73 Gymnantes lucida 105 0.09 ( 0.01) 0.19 0.43 Lonchocarpus castilloi 119 0. 37 ( 0.03) 0 .00 1.11 Lysiloma latisiliquum 588 0.32 ( 0.01) 0.44 1.49 Manilkara zapota 221 0.12 ( 0.01) 0.03 0.76 Metopium brownei 107 0.35 ( 0.02) 0 00 0.93 Nectandra coriacea 287 0.16 ( 0.01) 0.19 0.91 Piscidia piscipula 297 0.13 ( 0.01) 0.12 0.81 Pouter ia unilocularis 71 0 .17 ( 0.02) 0.07 0.59 Sebastiana adenophora 115 0.2 0 ( 0.02) 0.29 1.11 Swietenia macrophylla 68 0.39 ( 0.04) 0 .00 1.27 Vitex gaumerii 159 0.19 ( 0.02) 0.26 1.36 All 4 497 0.18 (0 .00 ) 0.49 1.49
78 Table A 2 Average numb er of new recruits by hectare for species depending on percentage of stand canopy cover or timber basal area (BA) Data from Toledo Aceves et al. (2009) Canopy cover (%) 50 60 65 70 75 80 85 Species BA (m 2 ha 1 ) 1 2 3 4 5 6 7 Mean Brosimum alicastrum 0 .0 0 .0 12.3 10.8 14.1 19.9 14.5 9.0 Bursera simarouba 25 .0 0 .0 84.3 218.6 13.8 10.8 2.8 44.4 Dendropanax arboreus 0 .0 66.7 82.1 31.5 59.6 30.5 23.5 36.7 Manilkara zapota 0 .0 13.8 81.1 165.8 200.9 212.2 219.9 111.7 Metopium brownei 0 .0 242.9 53.4 3 7.9 12.6 3.8 6.4 44.6 Simarouba glauca 0 .0 49 .0 44 .0 9.3 10.4 13.1 5.7 16.5 Swartzia cubensis 8.3 0 .0 0 .0 3.2 9.4 8.5 21.3 6.3 Swietenia macrophylla 0 .0 19.8 2.6 10.3 5.7 1.4 0 .0 5.0 Mean from all species 49.0
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91 BIOGRAPHICAL SKETCH Born in Mexico City, Sebastian has been a Chilango most of his life He developed an interest i n numbers, formulas and scienc e from his parents and brother all mathematician s He always intended in pursuing a degr ee in mathematics or engineering, however that changed after only one semester at the School of Engineering at UNAM, when he left to pursue a BSc in biology at UAM Xoc himilco. Studying biology, Sebastian greatly enjoyed field trips to many ecosystems of Mexico with particular interest in tropical regions. In 2011, while he was working with researchers at the Center for Tropical Research of the University of Veracruz M exico he met Dr. Karen Kainer, who was a visiting scholar from UF. She offered him a graduate assistantship to study a MS at the UF School of Fore st Resources and Conservation, where he got his degree with a concentration in Tropical Conservation and Devel opment in 2013. During the program he worked along Dr. Salvador Gezan and Sebastian kept going into his PhD under his guidance. This dissertation is the end of 6 years in Gainesville for Sebastian He does not know where he is going next.