Ecological Modelling and Ecophysics: Agricultural and environmental applications

299 Pages·2020·23.478 MB·English

by  Hugo Fort

Ecological Modelling and
Ecophysics
Agricultural and environmental applications

Ecological Modelling and
Ecophysics
Agricultural and environmental applications
Hugo Fort
Department of Physics, Republic University, Montevideo, Uruguay
IOP Publishing, Bristol, UK
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ISBN 978-0-7503-2432-8(ebook)
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DOI 10.1088/978-0-7503-2432-8
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To Silvia, José and Rodrigo

Contents
Preface xiii
Acknowledgements xv
Author biography xvi
0 Introduction 0-1
0.1 The goal of ecology: understanding the distribution and abundance 0-1
of organisms from their interactions
0.2 Mathematical models 0-3
0.2.1 What is modelling? 0-3
0.2.2 Why mathematical modelling? 0-3
0.2.3 What kind of mathematical modelling? 0-5
0.2.4 Principles and some rules of mathematical modelling 0-6
0.3 Community and population ecology modelling 0-15
0.3.1 Parallelism with physics and the debate of the 0-15
‘biology-as-physics approach’
0.3.2 Trade-offs and modelling strategies 0-17
References 0-21
Part I Classical population and community ecology
1 From growth equations for a single species to Lotka–Volterra 1-1
equations for two interacting species
1.1 From the Malthus to the logistic equation of growth 1-2
for a single species
1.1.1 Exponential growth 1-2
1.1.2 Resource limitation, density dependent per-capita 1-7
growth rate and logistic growth
1.2 General models for single species populations and analysis 1-9
of local equilibrium stability
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 1-14
Lotka–Volterra predator–prey model
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EcologicalModellingandEcophysics
1.3.3 Realistic predator–prey models: logistic growth 1-22
of prey and Holling predator functional responses
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 1-25
or species coexistence?
1.4.3 Transforming the competition model into 1-29
a mechanistic model
1.5 The Lotka–Volterra equations for two mutualist species 1-31
References 1-41
A1 Extensive livestock farming: a quantitative management A1-1
model in terms of a predator–prey dynamical system
A1.1 Background information: the growing demand for quantitative A1-2
livestock models
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 A1-4
measurable relevant variables for grass and animals
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 A1-13
productive scenarios
A1.5 How can we improve our model? A1-16
References A1-19
2 Lotka–Volterra models for multispecies communities and 2-1
their usefulness as quantitative 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 2-5
of different signs
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EcologicalModellingandEcophysics
2.2.3 Obtaining the parameters of the linear Lotka–Volterra 2-7
generalized model from monoculture and
biculture experiments
2.3 Food webs and trophic chains 2-8
2.4 Quantifying the accuracy of the linear model for predicting 2-9
species yields in single trophic communities1
2.4.1 Obtaining the theoretical yields: linear algebra solutions 2-11
and simulations
2.4.2 Accuracy metrics to quantitatively evaluate the 2-13
performance of the LLVGE
2.4.3 The linear Lotka–Volterra generalized equations 2-16
can accurately predict species yields in many cases
2.4.4 Often a correction of measured parameters, within their 2-18
experimental error bars, can greatly improve accuracy
2.5 Working with imperfect information 2-20
2.5.1 The ‘Mean Field Matrix’ (MFM) approximation for 2-21
predicting global or aggregate quantities
2.5.2 The ‘focal species’ approximation for predicting 2-25
the performance of a given species when our knowledge
on the set of parameters is incomplete
2.6 Conclusion 2-28
References 2-33
A2 Predicting optimal mixtures of perennial crops A2-1
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 A2-6
stability conditions
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
ix