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Introduction and objectives: The correct assessment of resources is a key condition for ensuring the sustainable supply of forest resources. In Syria, sustainable forest management is limited, because there is practically not enough knowledge on how to determine an annual growth, how future developments can be predicted, how the site productivity and the optimal rotation age can be accurately estimated, or which thinning regime is best suitable. To cover these gaps and to answer the questions, objective of the work is to develop an individual-tree growth model based on real-time series. Methodology and results: The study analyzed existing inventory data that came from 61 plots (51 for modeling and 10 for validation). The data used to develop the individual tree growth model could be categorized into four groups: Measured and calculated individual trees, variables describing the growth, measured plot variables, calculated stand variables.e.g. Stand basal area, stand volume, mean stand height…. Plot-wise equations for tree height, crown diameter and crown length were used to model the missing data values. The also analyzed the factors affecting the individual tree growth: competition and the site index. The study analyzed the competition using a set of distance-dependent and independent competition indices. The results found it that distance-independent and dependent competition indices have a consistent negative impact on tree basal area increment. On another hand, competition stimulates a little the height increment before start decreasing as competition increases. The best distance-independent indices were candidate for further modeling. Site index which is a measure of potential site productivity and it is defined in this work as stand dominant height at given age. The study tested 10 equations. Sloboda equation was confirmed as most appropriate for site index characterization of Pinus brutia stands in Syria. Then, the study tested the statistical models for describing the important life processes of single trees which consists of growth and mortality equations. Growth equations included diameter increment, height increment, crown ratio and generalized height-diameter equation. The study developed diameter increment equation as function of tree size, site characteristics (site index and geo-climatic variation OGV), and competition variables. The equation showed good performance for explaining the variations in diameter increment, where the coefficient of determination (R2) was 0.58. One supplementary equation for diameter increment equation was fitted without geo-climatic variation (OGV) and showed similar performance. XVIII The study developed two individual tree height increment equations: linearized height increment in similar way to that developed to diameter increment, and the second equation is Modifier-Potential height increment by achieving Nagel‟s equation (1999). Modifier-Potential height increment is more desirable to be applied in pure even stands of Pinus brutia forests because it gave better results than linearized height increment, and requires less information. The study also developed the crown ratio equation using tree size, competition, and site variables. The exponential equation performed best. Concerning the height-diameter relationship, the study tested 4 equations. The equation proposed by Mirkovich (1958) provides more satisfactory results as compared to the other tested equations. Finally, the study developed the mortality equation as function of stand variables, competition and site variables and could be applied deterministically or stochastically. The study implemented the forest simulation PINUS-SYRIA in NETLOGO. The simulation model allowed us to simulate the behavior of the individual-tree growth mortality dynamics under different conditions (site characteristics and competition) which allowed deep understanding of dynamic of Pinus brutia stands in Syria, and it showed that stochastic and deterministic simulations of mortality equation yield different results for the same single-tree model and the same initial conditions. The model applied forest management scenarios to suggest the optimal rotation age and most appropriate thinning regime. Thinning improved the growth rates for diameter at breast height, tree height and tree volume, the improvement on diameter increment is clearer than on height increment, and optimal rotation age was determined upon site index and density. Finally, the study tested the individual-tree growth model by using independent data and applying the global sensitivity analysis. Conclusions: The PINUS-Syria Model can be applied effectively in several aspects of forest management. Firstly, it can be used for sustainable forest management as determining the rotation length in the absence of thinning and simulating the effect of different scenarios of thinning regimes on the stand development. Based on the simulation results, this study suggests one thinning scenarios with heavy intensity in good and very good sites, and one or two thinning with moderate, heavy or very heavy thinning in medium and poor sites depending on the density.:ACKNOWLEDGEMENTS V TABLE OF CONTENTS VII LIST OF FIGURES X LIST OF TABLES XII APPENDICES XIV ABBREVIATIONS XV SUMMARY XVII ZUSAMMENFASSUNG XIX 1 INTRODUCTION 1 1.1 Background 1 1.2 Forest growth and yield models 2 1.2.1 Site productivity 5 1.2.2 Competition 6 1.2.3 Individual-tree diameter increment 9 1.2.4 Individual-tree height increment 11 1.2.5 Individual-tree mortality 12 1.2.6 Individual-tree crown ratio 15 1.2.7 Height-diameter relations 15 1.2.8 Model evaluation 16 1.2.9 Thinning treatment 17 1.3 Individual-based simulation tools 18 1.4 Objective and research questions of this thesis 19 2 MATERIAL AND METHODS 21 2.1 Study area and sites 21 2.2 General research framework 26 2.3 Data collection 28 2.3.1 Tree level variables 28 2.3.2 Stand level variables 29 2.4 Data preparation 30 2.4.1 Height, crown diameter and crown length curves 30 2.4.2 Calculation of tree variables 31 2.4.3 Calculation of stand level variables 34 2.5 Studying the factors that affect individual-tree growth 36 2.5.1 Competition Analysis 36 2.5.2 Developing the site index 40 2.5.2.1 Fitting the site index equation 40 2.5.2.2 Selection of reference age for site index 41 2.6 Individual-tree growth model 43 2.6.1 Development of diameter increment equation 43 2.6.2 Development of height increment equation 44 2.6.2.1 Development of linearized height increment equation 44 2.6.2.2 Development potential modifier height increment 45 2.6.3 Development of individual-tree crown ratio 46 2.6.4 Generalized height- diameter equation 48 2.6.5 Development of individual-tree mortality equation 48 2.7 Simulation of individual-tree growth model 51 2.7.1 The purpose 51 2.7.2 Entities stand variables and scales 51 2.7.3 Process overview and scheduling 52 2.7.4 Design concepts 53 1. Basic principles 53 2. Emergence 53 3. Interaction 55 4. Observation 55 5. Sensing 55 6. Stochasticity 55 7.Initialization 55 2.7.5 Sub-models 56 2.8 Methods used for model evaluation 57 2.8.1 Sensitivity analysis 57 2.8.2 Validation procedure 57 3 RESULTS 59 3.1 Results of initial data processing 59 3.1.1 The results of height curve fitting 59 3.1.2 Calculation of stand variables 60 3.1.3 Crown diameter curves 61 3.1.4 Crown length curves 62 3.2 Competition indices 62 3.2.1 Spearman correlation test 63 3.2.2 Determination of appropriate competition indices 63 3.3 Site index 67 3.4 Individual-tree growth model 70 3.4.1 Diameter increment equation 70 3.4.2 Development of height increment equations 73 3.4.2.1 Development of realized height increment equation 73 3.4.2.2 Development of potential-modifier height increment 75 3.4.3 Crown ratio equation 76 3.4.4 Generalized height-diameter relationship 78 3.4.5 Mortality equation 79 3.5 Simulation of individual-tree growth model 82 3.5.1 Short-term prediction of a eight-year period 82 3.5.2 Model plausibility 84 3.5.3 Sensitivity analysis 89 3.5.4 Application of the PINUS-Syria Model 92 3.5.4.1 Optimal rotation age 92 3.5.4.2 Thinning treatment 93 4 DISCUSSION 96 4.1 Data collection, size and representation 96 4.2 Individual tree’s response to competition 98 4.3 Site curves of Pinus brutia and forest yield 100 4.4 Individual-tree growth model 102 4.4.1 Diameter increment equation 102 4.4.2 Height increment equations 103 4.4.3 Crown ratio 105 4.4.4 Height-diameter equations 106 4.4.5 Mortality equation 107 4.5 Model Applications 110 4.6 Outlook on the future 112 REFERENCES 114 APPENDICES 125

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In this thesis we develop a mathematical model to describe HIV-1 evolution during the first stages of infection (approximately within 40-60 days since onset), when one can assume exponential growth and random accumulation of mutations under a neutral drift. We analyze the Hamming distance (HD) distribution under different models (synchronous and asynchronous) in the absence of selection and recombination. In the second part of the thesis, we introduce recombination and develop a combinatorial approach to estimate the new HD distribution. We conclude describing a T statistic to test significance differences between the HD of two genetic samples, which we derive using U-statistics.

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Crop simulation models (CSMs) are used to evaluate management and environmental scenarios on crop growth and yields. Two corn (Zea Mays L.) crop growth simulation models, Hybrid-Maize, and CERES-Maize were calibrated and validated under Virginia conditions with the goal of better understanding corn response to variable environmental conditions and decreasing temporal yield variation. Calibration data were generated from small plot studies conducted at five site-years. Main plots were plant density (4.9, 6.2, 7.4, and 8.6 plants m-2); subplots were hybrids of differing relative maturity (RM) [early = Pioneer® Brand "34B97" (108 day RM); medium = Pioneer® Brand "33M54" (114 day RM); and late = Pioneer® Brand "31G66" (118 day RM)]. Model validation was generated from large scale, replicated strip plot trials conducted at various locations across Virginia in 2005 and 2006. Prior to model adjustments based on calibration data, both CSMs under predicted corn grain yield in calibration and validation studies. CERES-Maize grain yield prediction error was consistent across the range of tested plant density while accuracy of Hybrid-Maize varied with plant density. Hybrid-Maize-estimated biomass production was highly accurate. Greater leaf area index (LAI) and biomass production were measured than was predicted by the CERES-Maize CSM. Both CSMs were modified based on calibration data sets and validated. Validation results of the calibrated CSMs showed improved accuracy in simulating planting date and environmental effects on a range of corn hybrids grown throughout Virginia over two years. We expect that both modified models can be used for strategic research and management decisions in mid-Atlantic corn production. / Master of Science

Neste trabalho de tese, estudamos o modelo de crescimento logístico de populações biológicas utilizando a abordagem de espaço de estados. Os estados não observados são as biomassas anuais, a equação de observação é linear e a equação de estado é não linear. As distribuições de probabilidade utilizadas para os termos de erro de observação aditivos são: Normal, t-student, Skew-normal e Skew-t. As distribuições Log-normal, Log-t, Log-skew-normal e Log-skew-t são consideradas para os erros de observação multiplicativos. A inferência nos modelos é realizada considerando-se métodos Bayesianos e as distribuições a posterior de interesse são aproximadas utilizando-se algoritmos MCMC e a aproximação de Laplace. Apresentamos duas aplicações, a primeira referente a pesca de camarão marinho na costa do Chile, na qual a variável observável é o rendimento médio anual de pesca (captura por unidade de esforço média). Na segunda é considerada a pesca de lagostim vermelho na costa de Chile, na qual além do rendimento médio anual da pesca, observa-se as estimativas anuais de biomassa vulnerável, obtidas através de estudos de área varrida. Para o primeiro conjunto de dados, os modelos com erros de observação multiplicativos têm melhor performance, particularmente os modelos Log-skew-normal e Log-skew-t. Considerando estes resultados, no segundo caso utilizamos somente erros multiplicativos e a distribuição a posteriori preditiva mostra que cada variável observável parece ter sua própria família de distribuição de probabilidades. Além disso, os resultados também revelam uma crescente complexidade do modelo ao incorporar a classe mais geral de distribuições assimétricas. / We study the logistic population growth model using a state-space approach. The non observable states are the annual biomass of the population with a linear observation equation and a non-linear state equation. The probability distribution used for the additives observation error terms are Normal, Student-t, Skew-normal and Skew-t, and Log-normal, Log-t, Log-skew-normal and Log-skew-t for multiplicative observation errors terms. The inference about the parameters of the models is performed using Bayesian methods, with MCMC algorithms and Laplace approximations. We present two applications to real data sets. The first in marine shrimp population off the coast of Chile, where observable variable is the average annual fishing yield. The second application is for the population of the red squat lobster off Chile, where in addition to the average annual fishing yield, a second observable variable was included. In the first case, the multiplicative observational errors models presented the best results. Particularly the Log-skew-normal and Log-skew-t models has the better performances. Considering these results, in the second application we use only multiplicative observation errors models.