Ecological Modelling and Ecophysics (Second Edition): Agricultural and environmental applications(IOP ebooks)

Table of Contents:
Chapter 0. INTRODUCTION 0.1 The goal of ecology: understanding the distribution and abundance of organisms from their interactions. 0.2 Mathematical models 0.2.1 What is modelling? 0.2.2 Why mathematical modelling? 0.2.3 What kind of mathematical modelling? 0.2.4 Principles and some rules of mathematical modelling. 0.3 Community and population ecology modelling 0.3.1 Parallelism with physics and the debate of the 'biology-as-physics approach'. 0.3.2 Trade-offs and model strategies. PART I THE CLASSICAL POPULATION AND COMMUNITY ECOLOGY The focus of part I is on the classical theory of ecology, i.e. the Lotka-Volterra equations and Niche Theory. Chapter 1. From growth equations for a single species to Lotka-Volterra equations for two interacting species. 1.1 From the Malthus to the logistic equation of growth for a single species 1-2 1.1.1 Exponential growth 1-2 1.1.2 Resource limitation, density dependent per-capita growth rate and logistic growth 1-7 1.2 General models for single species populations and analysis of local equilibrium stability 1-9 1.2.1 General model and Taylor expansion 1-9 1.2.2 Algebraic and geometric analysis of local equilibrium stability 1-10 1.3 The Lotka–Volterra predator–prey equations 1-13 1.3.1 A general dynamical system for predator–prey 1-13 1.3.2 A first model for predator–prey: the original Lotka–Volterra predator–prey model 1-14 1.3.3 Realistic predator–prey models: logistic growth of prey and Holling predator functional responses 1-22 1.4 The Lotka–Volterra competition equations for a pair of species 1-24 1.4.1 A descriptive or phenomenological model 1-24 1.4.2 Stable equilibrium: competitive exclusion or species coexistence? 1-25 1.4.3 Transforming the competition model into a mechanistic model 1-29 1.5 The Lotka–Volterra equations for two mutualist species 1-31 Updated with a worked example for mutualistic species: On the correlation between traits & niche position in plant-pollinator networks. Key gaps to be filled in mutualistic systems, like plant–pollinator networks, are predicting the strength of species interactions and linking pattern with process to understand species coexistence and their relative abundances. This example discusses niche overlap and traits of nectar-producing plant species and nectar searching animal species. Chapter summary Exercises Application Chapter 1: Extensive livestock farming: a quantitative management model in terms of a predator-prey dynamical system. A1.1 Background information: the growing demand for quantitative livestock models A1-2 A1.2 A predator–prey model for grassland livestock or PPGL A1-3 A1.2.1 What is our goal? A1-3 A1.2.2 What do we know? and what do we assume? Identifying measurable relevant variables for grass and animals A1-4 A1.2.3 How? Adapting a predator–prey model A1-5 A1.2.4 What will our model predict? A1-9 A1.3 Model validation A1-9 A1.3.1 Are predictions valid? A1-9 A1.3.2 Sensitivity analysis A1-11 A1.3.3 Verdict: model validated A1-13 A1.4 Uses of PPGL by farmers: estimating gross margins in different productive scenarios A1-13 A1.5 How can we improve our model? A1-16 References A1-19 A1.5 will be updated with recent developments using agent-based modelling showing its usefulness as a tool for supporting stakeholders' decision making. Chapter 2. Lotka-Volterra models for multispecies communities and their usefulness as predicting tools. 2.1 Many interacting species: the Lotka–Volterra generalized linear model 2-2 2.2 The Lotka–Volterra linear model for single trophic communities 2-5 2.2.1 Purely competitive communities 2-5 2.2.2 Single trophic communities with interspecific interactions of different signs 2-5 2.2.3 Obtaining the parameters of the linear Lotka–Volterra generalized model from monoculture and biculture experiments 2-7 2.3 Food webs and trophic chains 2-8 2.4 Quantifying the accuracy of the linear model for predicting species yields in single trophic communities1 2-9 2.4.1 Obtaining the theoretical yields: linear algebra solutions and simulations 2-11 2.4.2 Accuracy metrics to quantitatively evaluate the performance of the LLVGE 2-13 2.4.3 The linear Lotka–Volterra generalized equations can accurately predict species yields in many cases 2-16 2.4.4 Often a correction of measured parameters, within their experimental error bars, can greatly improve accuracy 2-18 2.5 Working with imperfect information 2-20 2.5.1 The ‘Mean Field Matrix’ (MFM) approximation for predicting global or aggregate quantities 2-21 2.5.2 The ‘focal species’ approximation for predicting the performance of a given species when our knowledge on the set of parameters is incomplete 2-25 2.6 Beyond equilibrium: testing the generalized linear model for predicting species trajectories. 2.7 Conclusion 2-28 Chapter summary Exercises Application Chapter 2: Predicting optimal mixtures of perennial crops by combining modelling and experiments A2.1 Background information A2-2 A2.2 Overview A2-2 A2.3 Experimental design and data A2-3 A2.4 Modelling A2-4 A2.4.1 Model equations A2-4 A2.4.2 Data curation A2-4 A2.4.3 Initial parameter estimation from experimental data A2-5 A2.4.4 Adjustment of the initial estimated parameters to meet stability conditions A2-6 A2.4.5 On the types of interspecific interactions A2-7 A2.5 Metrics for overyielding and equitability A2-8 A2.6 Model validation: theoretical versus experimental quantities A2-9 A2.6.1 Qualitative check: species ranking A2-9 A2.6.2 Quantitative check I: individual species yields A2-10 A2.6.3 Quantitative check II: overyielding, total biomasses and equitability A2-13 A2.6.4 Verdict: model validated A2-15 A2.7 Predictions: results from simulation of not sown treatments A2-16 A2.7.1 Similarities and differences between theoretical results for sown and not sown polycultures A2-16 A2.7.2 Using the model for predicting optimal mixtures A2-16 A2.8 Using the model attempting to elucidate the relationship between yield and diversity A2-17 A2.8.1 Positive correlation between productivity and species richness. A2-17 A2.8.2 No significant correlation between productivity and SE A2-18 A2.9 Possible extensions and some caveats A2-18 A2.10Bottom line A2-19 PART II ECOPHYSICS: METHODS FROM PHYSICS APPLIED TO ECOLOGY Ecosystems are characterized by the recurrent emergence of patterns: power-law distributions, long-range correlations and structured self-organization. These features are also typical of thermo-dynamical systems. Therefore, Ecophysics can be defined as a novel interdisciplinary research field consisting in the application of theories and methods originally developed by physicists to solve problems in ecology, usually those including nonlinear dynamics. In this part I discuss how these non-linear, non-equilibrium complex systems, whose basic components obey simple rules based on local information, can produce emergent system-level properties. Chapter 3. The Maximum Entropy method and the statistical mechanics of populations. 3.1 Basics of statistical physics 3-2 3.1.1 The program of statistical physics 3-2 3.1.2 Boltzmann–Gibbs maximum entropy approach to statistical mechanics 3-3 3.2 MaxEnt in terms of Shannon’s information theory as a general inference approach 3-9 3.2.1 Shannon’s information entropy 3-9 Shannon’s information entropy theorem. 3.2.2 MaxEnt as a method of making predictions from limited data by assuming maximal ignorance 3-12 Worked example: the MaxEnt method to obtain the probability distribution associated to a fair and an unfair dice 3.2.3 Inference of model parameters from the statistical moments via MaxEnt 3-14 3.3 The statistical mechanics of populations 3-18 3.3.1 Rationale and first attempts 3-18 3.3.2 Harte’s MaxEnt theory of ecology (METE) 3-19 3.4 Neutral theories of ecology 3-26 3.5 Conclusion 3-29 Chapter summary Exercises Application Chapter 3 Combining the generalized Lotka–Volterra model and MaxEnt method to predict changes of tree species composition in tropical forests A3.1 Background information A3-2 A3.2 Overview A3-4 A3.3 Data for Barro Colorado Island (BCI) 50 ha tropical Forest Dynamics Plot A3-4 A3.3.1 Some facts about BCI A3-4 A3.3.2 Covariance matrices and species interactions A3-6 A3.4 Modelling A3-7 A3.4.1 Inference of the effective interaction matrix from the covariance matrix via MaxEnt A3-7 A3.4.2 Model equations A3-9 A3.5 Model validation using time series forecasting analysis A3-11 A3.5.1 Estimation of intrinsic growth rates and carrying capacities using a training set of data A3-11 A3.5.2 Generating predictions to be contrasted against a validation set of data A3-13 A3.5.3 Verdict: model validated A3-14 A3.6 Predictions A3-15 A3.7 Extensions, improvements and caveats A3-15 A3.8 Conclusion A3-18 Chapter 4 Catastrophic shifts in ecology, early warnings and the phenomenology of phase transitions 4.1 Catastrophes 4-2 4.1.1 Catastrophic shifts and bifurcations 4-2 4.1.2 A simple population (mean field) model with a catastrophe 4-4 4.2 When does a catastrophic shift take place? Maxwell versus delay conventions 4-7 4.3 Early warnings of catastrophic shifts 4-10 4.4 Beyond the mean field approximation 4-12 4.4.1 Spatial model: cellular automaton 4-14 4.4.2 Examples of statistical mechanics lattice models applied to ecology and environmental science. 4.4.3 Early warning signals 4-15 4.5 A comparison with the phenomenology of the liquid–vapor phase transition 4-20 4.5.1 Beyond the ideal gas: the van der Waals equation of state for a fluid and its formal correspondence with the grazing model 4-20 4.5.2 Similarities and differences between desertification and the liquid–vapor transition 4-25 4.6 Final comments 4-28 Chapter summary Exercises Gradual changes in exploitation, nutrient loading, etc produce shifts between alternative stable states (ASS) in ecosystems which, quite often, are not smooth but abrupt or catastrophic. Early warnings of such catastrophic regime shifts are fundamental for designing management protocols for ecosystems. In this chapter I illustrate such a catastrophic transition by using a popular ecological model, involving a logistically growing single species subject to exploitation, which is known to exhibit ASS. The chapter will include the following sections: Application Chapter 4 Modelling eutrophication, early warnings and remedial actions in a lake A4.1 Background information A4-2 A4.2 Overview A4-4 A4.3 Data for Lake Mendota A4-5 A4.4 Modelling A4-6 A4.4.1 The Mendota Lake cellular automaton A4-6 A4.4.2 Catastrophic shifts in lakes and their spatial early warnings A4-8 A4.5 Model validation A4-9 A4.5.1 Simulations and results A4-9 A4.5.2 Verdict: model validated, but… A4-12 A4.6 Usefulness of the early warnings A4-15 A4.7 Extensions, improvements and caveats A4-16 Chapter 5 Nonequilibrium statistical mechanics and stochastic processes in ecology 5.1 The random walk. 5.2 Markov chains. 5.2.1 Regular Markov chains. 5.2.2 The random walker as a Markov chain. 5.2.3 Absorbing Markov chains. 5.2.4 Ergodic Markov chains. 5.3 The master equation. 5.3.1 The random walker master equation. 5.3.2 Detailed balance. Solutions of the Master Equation. Chapter summary Exercises ►Random walkers with asymmetric transition matrix. ►The Stepping Stones model. ►Solution of a maze. Application Chapter 5 Forecasting land-use and land-cover (LULC) changes. A5.1 Background information A5.2 Overview A5.3 Data for Pampa biome A5.4 Modelling A5.4.1 Analysing quadrats A5.4.2 1 Estimating transition matrices A5.5 Model validation A5.5.1 Simulations and results A5.5.2 Verdict: model validated, but… A5.6 Predictions of LULC changes A5.7 Extensions, improvements and caveats

About the Author :
Hugo Fort is a Professor at the Physics Department of the Faculty of Sciences of the Republic University (Montevideo, Uruguay) and Head of the Complex System Group. After earning his PhD in physics from the Autonomous University of Barcelona in 1994, he conducted research on quantum field theory. Since 2001, his scientific interests evolved from theoretical physics to complex systems and mathematical modelling applied to problems in biology, with a focus in ecology & evolution. A main goal of his research is to develop quantitative methods and tools for a wide variety of practical problems in fields ranging from agro-economy to environmental and real-time evolution. Fort is currently involved in several international research collaborations pursuing used-inspired basic science. A central aim is to connect ecological and evolutionary problems with well-studied phenomena in physics to gain deeper insight into these problems, to identify novel questions and problems, and to get access to alternative powerful computational tools. Professor Fort has previously published two books with IOP, the first edition of Ecological Modelling and Ecophysics and Forecasting with Maximum Entropy: The Interface Between Physics, Biology, Economics and Information Theory.