Statistical Approaches for Hidden Variables in Ecology

The study of ecological systems is often impeded by components that escape perfect observation, such as the trajectories of moving animals or the status of plant seed banks. These hidden components can be efficiently handled with statistical modeling by using hidden variables, which are often called latent variables. Notably, the hidden variables framework enables us to model an underlying interaction structure between variables (including random effects in regression models) and perform data clustering, which are useful tools in the analysis of ecological data. This book provides an introduction to hidden variables in ecology, through recent works on statistical modeling as well as on estimation in models with latent variables. All models are illustrated with ecological examples involving different types of latent variables at different scales of organization, from individuals to ecosystems. Readers have access to the data and R codes to facilitate understanding of the model and to adapt inference tools to their own data.

Table of Contents:
Introduction xi Nathalie PEYRARD, Stéphane ROBIN and Olivier GIMENEZ Chapter 1. Trajectory Reconstruction and Behavior Identification Using Geolocation Data 1 Marie-Pierre ETIENNE and Pierre GLOAGUEN 1.1. Introduction 1 1.1.1. Reconstructing a real trajectory from imperfect observations 1 1.1.2. Identifying different behaviors in movement 3 1.2. Hierarchical models of movement 3 1.2.1. Trajectory reconstruction model 3 1.2.2. Activity reconstruction model 6 1.3. Case study: masked booby, Sula dactylatra (originals) 14 1.3.1. Data 14 1.3.2. Projection 15 1.3.3. Data smoothing 15 1.3.4. Identification of different activities through movement 16 1.3.5. Results 17 1.4. References 23 Chapter 2. Detection of Eco-Evolutionary Processes in the Wild: Evolutionary Trade-Offs Between Life History Traits 27 Valentin JOURNÉ, Sarah CUBAYNES, Julien PAPAÏX and Mathieu BUORO 2.1. Context 27 2.2. The correlative approach to detecting evolutionary trade-offs in natural settings: problems 28 2.2.1. Mechanistic and statistical modeling as a means of accessing hidden variables 29 2.3. Case study 31 2.3.1. Costs of maturing and migration for survival: a theoretical approach 31 2.3.2. Growth/reproduction trade-off in trees 37 2.4. References 44 Chapter 3. Studying Species Demography and Distribution in Natural Conditions: Hidden Markov Models 47 Olivier GIMENEZ, Julie LOUVRIER, Valentin LAURET and Nina SANTOSTASI 3.1. Introduction 47 3.2. Overview of HMMs 48 3.3. HMM and demography 50 3.3.1. General overview 50 3.3.2. Case study: estimating the prevalence of dog–wolf hybrids with uncertain individual identification 54 3.4. HMM and species distribution 55 3.4.1. General case 55 3.4.2. Case study: estimating the distribution of a wolf population with species identification errors and heterogeneous detection 57 3.5. Discussion 60 3.6. Acknowledgments 62 3.7. References 62 Chapter 4. Inferring Mechanistic Models in Spatial Ecology Using a Mechanistic-Statistical Approach 69 Julien PAPAÏX, Samuel SOUBEYRAND, Olivier BONNEFON, Emily WALKER, Julie LOUVRIER, Etienne KLEIN and Lionel ROQUES 4.1. Introduction 69 4.2. Dynamic systems in ecology 70 4.2.1. Temporal models 70 4.2.2. Spatio-temporal models without reproduction 74 4.2.3. Spatio-temporal models with reproduction 76 4.2.4. Numerical solution 77 4.3. Estimation 77 4.3.1. Estimation principle 77 4.3.2. Parameter estimation 78 4.3.3. Estimation of latent processes 80 4.3.4. Mechanistic-statistical models 82 4.4. Examples 83 4.4.1. The COVID-19 epidemic in France 83 4.4.2. Wolf (Canis lupus) colonization in southeastern France 86 4.4.3. Estimating dates and locations of the introduction of invasive strains of watermelon mosaic virus 90 4.5. References 94 Chapter 5. Using Coupled Hidden Markov Chains to Estimate Colonization and Seed Bank Survival in a Metapopulation of Annual Plants 97 Pierre-Olivier CHEPTOU, Stéphane CORDEAU, Sebastian LE COZ and Nathalie PEYRARD 5.1. Introduction 97 5.2. Metapopulation model for plants: introduction of a dormant state 99 5.2.1. Dependency structure in the model 99 5.2.2. Distributions defining the model 100 5.2.3. Parameterizing the model 101 5.2.4. Linking the parameters of the model with the ecological parameters of the dynamics of an annual plant 103 5.2.5. Estimation 104 5.2.6. Model selection 105 5.3. Dynamics of weed species in cultivated parcels 105 5.3.1. Dormancy and weed management in agroecosystems 105 5.3.2. Description of the data set 106 5.3.3. Comparison with an HMM with independent patches 108 5.3.4. Influence of crops on weed dynamics 109 5.4. Discussion and conclusion 110 5.5. Acknowledgments 113 5.6. References 113 Chapter 6. Using Latent Block Models to Detect Structure in Ecological Networks 117 Julie AUBERT, Pierre BARBILLON, Sophie DONNET and Vincent MIELE 6.1. Introduction 117 6.2. Formalism 119 6.3. Probabilistic mixture models for networks 120 6.3.1. SBMs for unipartite networks 121 6.3.2. Stochastic block model for bipartite networks 122 6.4. Statistical inference 124 6.4.1. Estimation of parameters and clustering 125 6.4.2. Model selection 126 6.5. Application 127 6.5.1. Food web 127 6.5.2. A bipartite plant–pollinator network 129 6.6. Conclusion 130 6.7. References 132 Chapter 7. Latent Factor Models: A Tool for Dimension Reduction in Joint Species Distribution Models 135 Daria BYSTROVA, Giovanni POGGIATO, Julyan ARBEL and Wilfried THUILLER 7.1. Introduction 135 7.2. Joint species distribution models 138 7.3. Dimension reduction with latent factors 139 7.4. Inference 140 7.5. Ecological interpretation of latent factors 141 7.6. On the interpretation of JSDMs 142 7.7. Case study 142 7.7.1. Introduction of the dataset 142 7.7.2. R package used 144 7.7.3. Implementation and convergence diagnosis 144 7.7.4. Results and discussion 144 7.8. Conclusion 152 7.9. References 153 Chapter 8. The Poisson Log-Normal Model: A Generic Framework for Analyzing Joint Abundance Distributions 157 Julien CHIQUET, Marie-Josée CROS, Mahendra MARIADASSOU, Nathalie PEYRARD and Stéphane ROBIN 8.1. Introduction 157 8.2. The Poisson log-normal model 159 8.2.1. The model 159 8.2.2. Inference method 162 8.2.3. Dimension reduction 164 8.2.4. Inferring networks of interaction 165 8.3. Data analysis: marine species 167 8.3.1. Description of the data 167 8.3.2. Effects due to site and date 168 8.3.3. Dimension reduction 170 8.3.4. Inferring ecological interactions 171 8.4. Discussion 176 8.5. Acknowledgments 177 8.6. References 177 Chapter 9. Supervised Component-Based Generalized Linear Regression: Method and Extensions 181 Frédéric MORTIER, Jocelyn CHAUVET, Catherine TROTTIER, Guillaume CORNU and Xavier BRY 9.1. Introduction 181 9.2. Models and methods 184 9.2.1. Supervised component-based generalized linear regression 184 9.2.2. Thematic supervised component-based generalized linear regression (THEME-SCGLR) 187 9.2.3. Mixed SCGLR 189 9.3. Case study: predicting the abundance of 15 common tree species in the forests of Central Africa 191 9.3.1. The SCGLR method: a direct approach 191 9.3.2. THEME-SCGLR: improved characterization of predictive components 194 9.3.3. Mixed-SCGLR: taking account of the concession effect 196 9.4. Discussion 200 9.5. References 201 Chapter 10. Structural Equation Models for the Study of Ecosystems and Socio-Ecosystems 203 Fabien LAROCHE, Jérémy FROIDEVAUX, Laurent LARRIEU and Michel GOULARD 10.1. Introduction 203 10.1.1. Ecological background 203 10.1.2. Methodological problem 204 10.1.3. Case study: biodiversity in a managed forest 205 10.2. Structural equation model 206 10.2.1. Hypotheses and general structure of an SEM 206 10.2.2. Likelihood and estimation in an SEM 209 10.2.3. Fit quality and nested SEM tests 211 10.3. Case study: biodiversity in managed forests 213 10.3.1. Preliminary steps 213 10.3.2. Evaluating the measurement model alone 213 10.3.3. Evaluating the relational model 214 10.3.4. Significance of parameters in the relational model 219 10.3.5. Findings 221 10.4. Discussion 223 10.4.1. A confirmatory approach 223 10.4.2. Gaussian framework 224 10.4.3. Centered-reduced observed variables 224 10.4.4. Structural constraints 224 10.4.5. Use of resampling 225 10.5. Acknowledgments 225 10.6. References 226 List of Authors 229 Index 233

About the Author :
Nathalie Peyrard is a Senior Scientist at INRAE. Most of her current research focuses on computational statistics, with applications in ecology. Olivier Gimenez is a Senior Scientist at CNRS. His research focuses on animal ecology, statistical modeling and social sciences.