Verfügbarkeit: A practical guide to ecological modelling

A practical guide to ecological modelling: using R as a simulation platform

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Bibliographische Detailangaben
Hauptverfasser:	Soetaert, Karline (VerfasserIn), Herman, Peter M. J. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	[Dordrecht] Springer 2009
Schlagworte:	Mathematisches Modell Ökologie Ecology > Mathematical models R (Computer program language) R > Programm Biomathematik Modellierung
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XV, 372 S. Ill., graph. Darst.
ISBN:	9781402086236 9781402086243

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MARC


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Datensatz im Suchindex

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adam_text	Contents 1 Introduction ................................................... 1 1.1 WhatisaModel? ........................................... 1 1.1.1 A Simple Example: Zooplankton Energy Balance......... 3 1.2 Why Do We Need Models?.................................. 5 1.2.1 Models as Analysing Tools............................ 5 1.2.2 Models as Interpolation, Extrapolation, and Budgeting Tools 7 1.2.3 Models to Quantify Immeasurable Processes ............. 9 1.2.4 Model Prediction as a Management Tool ................. 10 1.3 Modelling Steps and Ingredients .............................. 10 1.4 The Modeller s Toolkit ...................................... 13 2 Model Formulation ............................................. 15 2.1 Conceptual Model .......................................... 15 2.1.1 The Balance Equation of a State Variable ................ 17 2.1.2 Example: Conceptual Model of a Lake Ecosystem ......... 19 2.1.3 Conservation of Mass and Energy as a Consistency Check .. 21 2.1.4 Dimensional Homogeneity and Consistency of Units ....... 23 2.2 Mathematical Formulations .................................. 24 2.3 Formulation of Chemical Reactions ........................... 25 2.3.1 The Law of Mass Action .............................. 25 2.3.2 Example: A Simple Chemical Reaction .................. 26 2.4 Enzymatic Reactions ........................................ 27 2.5 Basic Formulation of Ecological Interactions .................... 28 2.5.1 Example: Flows to and from Phytoplankton in the Lake Ecosystem ............................... 28 2.5.2 Maximal Interaction Strength, Rate Limitation and Inhibition ....................................... 31 2.5.3 One Rate-Limiting Resource, 3 Types of Functional Responses .............................. 35 2.5.4 More than One Limiting Resource ...................... 37 2.5.5 Inhibition Terms ..................................... 38 2.6 Coupled Model Equations ................................... 40 2.6.1 Flows Modelled as Fractions of Other Flows ............. 41 Contents 2.6.2 Coupled Dynamics of Source and Sink Compartments ..... 42 2.6.3 Stoichiometry and Coupling of Element Cycles ........... 43 2.7 Model Simplifications ....................................... 44 2.7.1 Carrying Capacity Formulation ......................... 45 2.7.2 Closure Terms at the Highest Trophic Level .............. 48 2.7.3 Simplification by Deletion of Intermediate Levels ......... 48 2.8 Impact of Physical Conditions ................................ 49 2.8.1 Temperature ........................................ 49 2.8.2 Light ............................................... 50 2.8.3 Other Physical Impacts ............................... 53 2.9 Examples ................................................. 54 2.9.1 NPZD, a Simple Ecosystem Model for Aquatic Environments 54 2.9.2 AQUAPHY, a Physiological Model of Unbalanced Algal Growth ()................................... 58 2.10 Case Studies in R ........................................... 63 2.10.1 Making Sense Out of Mathematical Formulations ......... 63 2.10.2 One Formula, Several Parameter Values ................. 64 2.11 Projects ................................................... 65 2.11.1 Conceptual Model: Lake Eutrophication ................. 65 2.11.2 Model Formulation: Nutrient-Limited Batch Culture ....... 66 2.11.3 Model Formulation: Detritus Degradation ................ 67 2.11.4 Model Formulation: An Autocatalytic Reaction ........... 69 Spatial Components and Transport .............................. 71 3.1 Microscopic and Macroscopic Models ......................... 72 3.2 Representing Space in Models ................................ 74 3.2.1 Spatial Dimensions ................................... 74 3.2.2 Discrete Spatial Models ............................... 74 3.2.3 Continuous Spatial Models ............................ 76 3.3 Transport in a Zero-Dimensional Model ........................ 77 3.4 Transport in a One-Dimensional Model ........................ 79 3.4.1 Flux Divergence ..................................... 80 3.4.2 Macroscopic Formulation of Fluxes: Advection and Dispersion ............................ 82 3.4.3 The General 1-D Advection-Dispersion-Reaction Equation . 84 3.4.4 The 1-D Advection-Dispersion-Reaction Equation in Estuaries, Rivers and Lakes ......................... 85 3.4.5 The 1-D Advection-Dispersion-Reaction Equation in Shapes with Different Symmetries ................... 86 3.4.6 One-dimensional Diffusion in Porous Media (Sediments) () 89 3.4.7 The 3-D Advection-Dispersion-Reaction Equation ()...... 92 3.5 Boundary Conditions in Spatially Explicit Models ............... 92 3.5.1 Boundary Conditions in Discrete Models ................ 94 3.5.2 Boundary Conditions in Continuous Models .............. 95 3.5.3 Boundary Conditions in Multi-layered Models ()........ 98 Contents 3.6 Case Studies in R ...........................................102 3.6.1 An Autocatalytic Reaction in a Row-Through Stirred Tank . 102 3.6.2 A 1-D Microscopic and Macroscopic Model of Diffusion ... 103 3.6.3 Cellular Automaton Model of Diffusion ()..............107 3.6.4 Competition in a Lattice Grid ..........................110 3.6.5 Transport and Reaction in Porous Media: Silicate Diagenesis.................................. 114 Parameterization ...............................................117 4.1 In Situ Measurement ........................................117 4.2 Literature-Derived Parameters ................................118 4.3 Calibration ................................................119 4.3.1 Linear Regression ....................................120 4.3.2 Nonlinear Fitting ....................................122 4.4 Case Studies in R ...........................................123 4.4.1 Nonlinear Parameter Estimation: P-I Curve ...............123 4.4.2 Linear Versus Non-Linear Parameter Estimation: Sediment Bioturbation ............................... 125 4.4.3 Pseudo-Random Search, a Random-Based Minimization Routine ................................ 128 4.4.4 Calibration of a Simple Model .........................132 Model Solution - Analytical Methods .............................139 5.1 An Everyday Life Example ..................................139 5.2 Finding an Analytical Solution ................................140 5.3 Examples .................................................141 5.3.1 A Very Simple First-Order Differential Equation ..........141 5.3.2 The Logistic Equation ................................143 5.3.3 A Second-Order Differential Equation: Carbon Dynamics in Sediments ()............................ 144 5.3.4 Coupled BOD and Oxygen Equations ()................146 5.3.5 Multilayer Differential Equations ()...................147 5.4 Case Studies in R ...........................................150 5.4.1 Transient Dispersion-Reaction in One Dimension .........150 5.4.2 Transient Diffusion-Reaction on a 2-Dimensional Surface .. 151 5.4.3 Steady-State Oxygen Budget in Small Organisms Living in Suboxic Conditions ......................... 152 5.4.4 Analytical Solution of the Non-Local Exchange Sediment Model ()................................ 158 5.5 Projects ...................................................161 5.5.1 Organic Matter Sinking Through a Water Column .........161 5.5.2 Oxygen Dynamics in the Sediment ......................162 5.5.3 Carbon Dynamics in the Sediment ......................164 Contents Model Solution -Numerical Methods .............................165 6.1 Taylor Expansion ...........................................165 6.2 Numerical Approximation and Numerical Errors ................167 6.3 Numerical Integration in Time - Basics ........................169 6.3.1 Euler Integration .....................................170 6.3.2 Criteria for Numerical Integration ......................171 6.3.3 Interpolation Methods - 4th Order Runge-Kutta () ......173 6.3.4 Flexible Time Step Methods -5th Order Runge-Kutta ().. 174 6.3.5 Implicit and Semi-Implicit Integration Routines ().......174 6.3.6 Which Integrator to Choose? ...........................175 6.4 Approximating Spatial Derivatives ().........................176 6.4.1 Approximating the Flux Divergence Equation ............176 6.4.2 Approximating Dispersion .............................177 6.4.3 Approximating Advection .............................178 6.4.4 The Boundaries with the External World .................179 6.5 Numerical Dispersion (* ).................................180 6.5.1 Example: Sediment Model ............................182 6.6 Case Studies in R ...........................................183 6.6.1 Implementing the Enzymatic Reaction Model ............184 6.6.2 Growth of a Daphnia Individual ........................188 6.6.3 Zero-Dimensional Estilarme Zooplankton Model ..........195 6.6.4 Aphids on a Row of Plants: Numerical Solution of a Dispersion-Reaction Model ....................... 197 6.6.5 Fate of Marine Zooplankton in an Estuary ( * ).........200 6.7 Projects ...................................................206 6.7.1 Numerical Solution of the Autocatalytic Reaction in a Flow-Through Stirred Tank ........................ 206 6.7.2 Numerical Solution of a Nutrient-Algae Chemostat Model - Euler Integration ............................ 207 6.7.3 Rain of Organic Matter in the Ocean: Numerical Solution of the Advection-Reaction Model ...................... 209 6.7.4 AQUAPHY Model Implementation .....................209 Stability and Steady-State .......................................211 7.1 Basics ....................................................211 7.2 Stability of One First-Order Differential Equation ................213 7.2.1 Equilibrium Points, Stability, Domain of Attraction ........213 7.2.2 Multiple Steady States ................................215 7.2.3 Bifurcation ..........................................216 7.3 Stability of Two Differential Equations - Phase-Plane Analysis ___218 7.3.1 Example. The Lotka- Volterra Predator-Prey Equation ......220 7.4 Multiple Equations .........................................224 7.5 Steady-State Solution of Differential Equations ()...............224 7.5.1 Direct Root Finding: Analytical Solution ................225 7.5.2 Iterative Root Finding ................................225 Contents 7.5.3 From Partial to Ordinary Differential Equations ...........225 7.6 Formal Analysis of Stability ()..............................226 7.7 Limit Cycles ()..........................................231 7.8 Case Studies in R ...........................................232 7.8.1 Multiple Stable States: the Spruce Budworm Model .......232 7.8.2 Phase-Plane Analysis: The Lotka- Volterra Competition Equations ..........................................237 7.8.3 The Lorenz Equations - Chaos .........................242 7.8.4 Steady-State Solution of the Silicate Diagenetic Model () . 243 7.8.5 Fate of Marine Zooplankton in an Estuary - Equilibrium Condition () ......................................248 7.9 Projects ...................................................250 7.9.1 The Schaefer Model of Fisheries .......................250 7.9.2 A Fisheries Model with Allee Effect ....................252 7.9.3 Ecological-Economical Fisheries Model .................253 7.9.4 Predator-Prey System with Type -П Functional Response ... 254 7.9.5 Succession of Nutrients, Phytoplankton and Zooplankton in a River ..........................................254 Multiple Time Scales and Equilibrium Processes ...................257 8.1 Simple Chemical Equilibrium Calculation: Ammonia and Ammonium ............................................258 8.2 Chemical Equilibrium Combined with a Slow Reaction Process ___259 8.3 General Approach to Equilibrium Reformulation ................261 8.3.1 Enzymatic Equilibrium in a Slow Reaction Process: The Michaelis-Menten Equation () ...................261 8.3.2 Equilibrium Adsorption in Porous Media ().............264 8.4 Examples in R .............................................267 8.4.1 Solving pH in Aquatic Systems ........................267 8.4.2 A Model of pH Changes Due to Algal Growth (*)........269 Discrete Time Models ...........................................273 9.1 Difference Equations ........................................274 9.2 Discrete Logistic Models ....................................275 9.3 Host-Parasitoid Interactions ...................................276 9.4 Dynamic Matrix Models .....................................278 9.4.1 Example: Age Structured Population Model ..............278 9.4.2 Matrix Notation .....................................280 9.4.3 Stable Age Distribution and Rate of Increase .............281 9.4.4 The Reproductive Value ...............................282 9.5 Case Studies in R ...........................................283 9.5.1 Bifurcations in the Discrete Logistic Model ..............283 9.5.2 Bifurcations in the Host-Parasitoid Model ................283 9.5.3 Attractors in the Host-Parasitoid Model ..................285 9.5.4 Population Dynamics of Teasel .........................287 xiv Contents 9.6 Projects ...................................................292 9.6.1 Bifurcation of the Logistic Map ........................292 9.6.2 Equilibrium Dynamics of a Simple Age-Class Matrix Model 292 9.6.3 Equilibrium Dynamics of a US Population ...............292 10 Dynamic Programming .........................................295 10.1 Sequential Decisions ........................................296 10.2 Finding the Optimal Solution .................................296 10.3 A Simple Example ..........................................297 10.4 Case Study in R: The Patch-Selection Model ....................301 11 Testing and Validating the Model ................................309 11.1 Coupled BOD-O2 Model Revisited ............................309 11.2 Testing the Correctness of the Model Solution ...................310 11.3 Testing the Internal Logic of the Model ........................312 11.4 Model Verification and Validity ...............................313 11.5 Model Sensitivity ...........................................314 11.6 Case Studies in R ...........................................315 11.6.1 Time-Varying Oxygen Consumption in a Small Cylindrical Organism .......................................... 315 11.6.2 R for Validation and Verification ........................319 11.6.3 Univariate Local Sensitivity Analysis ...................319 11.6.4 Bivariate Local Sensitivity Analysis .....................325 12 Further Reading and References .................................329 12.1 Model Formulations ........................................329 12.2 Spatial Pattern .............................................330 12.3 Parameterization ...........................................331 12.4 Model Solution ............................................331 12.5 Stability and Equilibrium Analysis ............................332 12.6 Discrete Time and Dynamic Programming Models ...............332 Appendix A About R ...............................................335 A.I bstalling R ................................................335 A.2 A Very Short Introduction ....................................336 A.2.1 Console Versus Scripts ................................336 A.2.2 Getting Help ........................................337 A.2.3 Vectors and Matrices .................................337 A.2.4 More Complex Data Structures .........................339 A.2.5 User-defined Functions and Programming ................340 A.2.6 R Packages .........................................341 A.2.7 Graphics ............................................341 A.2.8 Minor Things to Remember ...........................342 A.3 Interfacing R with Low-Level Languages: The Competition in a Lattice Grid Model Revisited .............................343 Contents xv Appendix В Derivatives and Differential Equations ....................347 B.I Derivatives ................................................347 B.2 Taxonomy of Differential Equations ...........................348 B.3 General Solutions of Often Used Differential Equations ...........349 B.3.1 Simple Time-Dependent Equations .....................349 B.3.2 Steady-State Transport - Reaction in 1-D, Constant Surface . 350 B.3.3 Steady-State Transport - Reaction in 1-D, Cylindrical Coordinates ........................................350 B.3.4 Steady-State Transport - Reaction in 1-D, Spherical Coordinates ........................................ 351 B.4 Particular Solutions of Dynamic Diffusion-Reaction Equation .....351 B.5 Derivatives and Integrals .....................................352 Appendix С Matrix Algebra .........................................353 C.I Matrices ..................................................353 C.2 Linear Equations ...........................................354 C.3 Eigenvalues and Eigenvectors, Determinants ....................355 C.4 R-Examples ...............................................355 C.5 The Jacobian Matrix ........................................357 Appendix D Statistical Distributions ..................................359 D.I Probability Distribution ......................................359 D.2 Normal Distribution .........................................359 D.3 The Poisson Distribution .....................................360 References .........................................................361 Index .............................................................367
adam_txt	Contents 1 Introduction . 1 1.1 WhatisaModel? . 1 1.1.1 A Simple Example: Zooplankton Energy Balance. 3 1.2 Why Do We Need Models?. 5 1.2.1 Models as Analysing Tools. 5 1.2.2 Models as Interpolation, Extrapolation, and Budgeting Tools 7 1.2.3 Models to Quantify Immeasurable Processes . 9 1.2.4 Model Prediction as a Management Tool . 10 1.3 Modelling Steps and Ingredients . 10 1.4 The Modeller's Toolkit . 13 2 Model Formulation . 15 2.1 Conceptual Model . 15 2.1.1 The Balance Equation of a State Variable . 17 2.1.2 Example: Conceptual Model of a Lake Ecosystem . 19 2.1.3 Conservation of Mass and Energy as a Consistency Check . 21 2.1.4 Dimensional Homogeneity and Consistency of Units . 23 2.2 Mathematical Formulations . 24 2.3 Formulation of Chemical Reactions . 25 2.3.1 The Law of Mass Action . 25 2.3.2 Example: A Simple Chemical Reaction . 26 2.4 Enzymatic Reactions . 27 2.5 Basic Formulation of Ecological Interactions . 28 2.5.1 Example: Flows to and from Phytoplankton in the Lake Ecosystem . 28 2.5.2 Maximal Interaction Strength, Rate Limitation and Inhibition . 31 2.5.3 One Rate-Limiting Resource, 3 Types of Functional Responses . 35 2.5.4 More than One Limiting Resource . 37 2.5.5 Inhibition Terms . 38 2.6 Coupled Model Equations . 40 2.6.1 Flows Modelled as Fractions of Other Flows . 41 Contents 2.6.2 Coupled Dynamics of Source and Sink Compartments . 42 2.6.3 Stoichiometry and Coupling of Element Cycles . 43 2.7 Model Simplifications . 44 2.7.1 Carrying Capacity Formulation . 45 2.7.2 Closure Terms at the Highest Trophic Level . 48 2.7.3 Simplification by Deletion of Intermediate Levels . 48 2.8 Impact of Physical Conditions . 49 2.8.1 Temperature . 49 2.8.2 Light . 50 2.8.3 Other Physical Impacts . 53 2.9 Examples . 54 2.9.1 NPZD, a Simple Ecosystem Model for Aquatic Environments 54 2.9.2 AQUAPHY, a Physiological Model of Unbalanced Algal Growth (). 58 2.10 Case Studies in R . 63 2.10.1 Making Sense Out of Mathematical Formulations . 63 2.10.2 One Formula, Several Parameter Values . 64 2.11 Projects . 65 2.11.1 Conceptual Model: Lake Eutrophication . 65 2.11.2 Model Formulation: Nutrient-Limited Batch Culture . 66 2.11.3 Model Formulation: Detritus Degradation . 67 2.11.4 Model Formulation: An Autocatalytic Reaction . 69 Spatial Components and Transport . 71 3.1 Microscopic and Macroscopic Models . 72 3.2 Representing Space in Models . 74 3.2.1 Spatial Dimensions . 74 3.2.2 Discrete Spatial Models . 74 3.2.3 Continuous Spatial Models . 76 3.3 Transport in a Zero-Dimensional Model . 77 3.4 Transport in a One-Dimensional Model . 79 3.4.1 Flux Divergence . 80 3.4.2 Macroscopic Formulation of Fluxes: Advection and Dispersion . 82 3.4.3 The General 1-D Advection-Dispersion-Reaction Equation . 84 3.4.4 The 1-D Advection-Dispersion-Reaction Equation in Estuaries, Rivers and Lakes . 85 3.4.5 The 1-D Advection-Dispersion-Reaction Equation in Shapes with Different Symmetries . 86 3.4.6 One-dimensional Diffusion in Porous Media (Sediments) () 89 3.4.7 The 3-D Advection-Dispersion-Reaction Equation (). 92 3.5 Boundary Conditions in Spatially Explicit Models . 92 3.5.1 Boundary Conditions in Discrete Models . 94 3.5.2 Boundary Conditions in Continuous Models . 95 3.5.3 Boundary Conditions in Multi-layered Models (). 98 Contents 3.6 Case Studies in R .102 3.6.1 An Autocatalytic Reaction in a Row-Through Stirred Tank . 102 3.6.2 A 1-D Microscopic and Macroscopic Model of Diffusion . 103 3.6.3 Cellular Automaton Model of Diffusion ().107 3.6.4 Competition in a Lattice Grid .110 3.6.5 Transport and Reaction in Porous Media: Silicate Diagenesis. 114 Parameterization .117 4.1 In Situ Measurement .117 4.2 Literature-Derived Parameters .118 4.3 Calibration .119 4.3.1 Linear Regression .120 4.3.2 Nonlinear Fitting .122 4.4 Case Studies in R .123 4.4.1 Nonlinear Parameter Estimation: P-I Curve .123 4.4.2 Linear Versus Non-Linear Parameter Estimation: Sediment Bioturbation . 125 4.4.3 Pseudo-Random Search, a Random-Based Minimization Routine . 128 4.4.4 Calibration of a Simple Model .132 Model Solution - Analytical Methods .139 5.1 An Everyday Life Example .139 5.2 Finding an Analytical Solution .140 5.3 Examples .141 5.3.1 A Very Simple First-Order Differential Equation .141 5.3.2 The Logistic Equation .143 5.3.3 A Second-Order Differential Equation: Carbon Dynamics in Sediments (). 144 5.3.4 Coupled BOD and Oxygen Equations ().146 5.3.5 Multilayer Differential Equations ().147 5.4 Case Studies in R .150 5.4.1 Transient Dispersion-Reaction in One Dimension .150 5.4.2 Transient Diffusion-Reaction on a 2-Dimensional Surface . 151 5.4.3 Steady-State Oxygen Budget in Small Organisms Living in Suboxic Conditions . 152 5.4.4 Analytical Solution of the Non-Local Exchange Sediment Model (). 158 5.5 Projects .161 5.5.1 Organic Matter Sinking Through a Water Column .161 5.5.2 Oxygen Dynamics in the Sediment .162 5.5.3 Carbon Dynamics in the Sediment .164 Contents Model Solution -Numerical Methods .165 6.1 Taylor Expansion .165 6.2 Numerical Approximation and Numerical Errors .167 6.3 Numerical Integration in Time - Basics .169 6.3.1 Euler Integration .170 6.3.2 Criteria for Numerical Integration .171 6.3.3 Interpolation Methods - 4th Order Runge-Kutta () .173 6.3.4 Flexible Time Step Methods -5th Order Runge-Kutta (). 174 6.3.5 Implicit and Semi-Implicit Integration Routines ().174 6.3.6 Which Integrator to Choose? .175 6.4 Approximating Spatial Derivatives ().176 6.4.1 Approximating the Flux Divergence Equation .176 6.4.2 Approximating Dispersion .177 6.4.3 Approximating Advection .178 6.4.4 The Boundaries with the External World .179 6.5 Numerical Dispersion (* ).180 6.5.1 Example: Sediment Model .182 6.6 Case Studies in R .183 6.6.1 Implementing the Enzymatic Reaction Model .184 6.6.2 Growth of a Daphnia Individual .188 6.6.3 Zero-Dimensional Estilarme Zooplankton Model .195 6.6.4 Aphids on a Row of Plants: Numerical Solution of a Dispersion-Reaction Model . 197 6.6.5 Fate of Marine Zooplankton in an Estuary ( * ).200 6.7 Projects .206 6.7.1 Numerical Solution of the Autocatalytic Reaction in a Flow-Through Stirred Tank . 206 6.7.2 Numerical Solution of a Nutrient-Algae Chemostat Model - Euler Integration . 207 6.7.3 Rain of Organic Matter in the Ocean: Numerical Solution of the Advection-Reaction Model . 209 6.7.4 AQUAPHY Model Implementation .209 Stability and Steady-State .211 7.1 Basics .211 7.2 Stability of One First-Order Differential Equation .213 7.2.1 Equilibrium Points, Stability, Domain of Attraction .213 7.2.2 Multiple Steady States .215 7.2.3 Bifurcation .216 7.3 Stability of Two Differential Equations - Phase-Plane Analysis _218 7.3.1 Example. The Lotka- Volterra Predator-Prey Equation .220 7.4 Multiple Equations .224 7.5 Steady-State Solution of Differential Equations ().224 7.5.1 Direct Root Finding: Analytical Solution .225 7.5.2 Iterative Root Finding .225 Contents 7.5.3 From Partial to Ordinary Differential Equations .225 7.6 Formal Analysis of Stability ().226 7.7 Limit Cycles ().231 7.8 Case Studies in R .232 7.8.1 Multiple Stable States: the Spruce Budworm Model .232 7.8.2 Phase-Plane Analysis: The Lotka- Volterra Competition Equations .237 7.8.3 The Lorenz Equations - Chaos .242 7.8.4 Steady-State Solution of the Silicate Diagenetic Model () . 243 7.8.5 Fate of Marine Zooplankton in an Estuary - Equilibrium Condition () .248 7.9 Projects .250 7.9.1 The Schaefer Model of Fisheries .250 7.9.2 A Fisheries Model with Allee Effect .252 7.9.3 Ecological-Economical Fisheries Model .253 7.9.4 Predator-Prey System with Type -П Functional Response . 254 7.9.5 Succession of Nutrients, Phytoplankton and Zooplankton in a River .254 Multiple Time Scales and Equilibrium Processes .257 8.1 Simple Chemical Equilibrium Calculation: Ammonia and Ammonium .258 8.2 Chemical Equilibrium Combined with a Slow Reaction Process _259 8.3 General Approach to Equilibrium Reformulation .261 8.3.1 Enzymatic Equilibrium in a Slow Reaction Process: The Michaelis-Menten Equation () .261 8.3.2 Equilibrium Adsorption in Porous Media ().264 8.4 Examples in R .267 8.4.1 Solving pH in Aquatic Systems .267 8.4.2 A Model of pH Changes Due to Algal Growth (*).269 Discrete Time Models .273 9.1 Difference Equations .274 9.2 Discrete Logistic Models .275 9.3 Host-Parasitoid Interactions .276 9.4 Dynamic Matrix Models .278 9.4.1 Example: Age Structured Population Model .278 9.4.2 Matrix Notation .280 9.4.3 Stable Age Distribution and Rate of Increase .281 9.4.4 The Reproductive Value .282 9.5 Case Studies in R .283 9.5.1 Bifurcations in the Discrete Logistic Model .283 9.5.2 Bifurcations in the Host-Parasitoid Model .283 9.5.3 Attractors in the Host-Parasitoid Model .285 9.5.4 Population Dynamics of Teasel .287 xiv Contents 9.6 Projects .292 9.6.1 Bifurcation of the Logistic Map .292 9.6.2 Equilibrium Dynamics of a Simple Age-Class Matrix Model 292 9.6.3 Equilibrium Dynamics of a US Population .292 10 Dynamic Programming .295 10.1 Sequential Decisions .296 10.2 Finding the Optimal Solution .296 10.3 A Simple Example .297 10.4 Case Study in R: The Patch-Selection Model .301 11 Testing and Validating the Model .309 11.1 Coupled BOD-O2 Model Revisited .309 11.2 Testing the Correctness of the Model Solution .310 11.3 Testing the Internal Logic of the Model .312 11.4 Model Verification and Validity .313 11.5 Model Sensitivity .314 11.6 Case Studies in R .315 11.6.1 Time-Varying Oxygen Consumption in a Small Cylindrical Organism . 315 11.6.2 R for Validation and Verification .319 11.6.3 Univariate Local Sensitivity Analysis .319 11.6.4 Bivariate Local Sensitivity Analysis .325 12 Further Reading and References .329 12.1 Model Formulations .329 12.2 Spatial Pattern .330 12.3 Parameterization .331 12.4 Model Solution .331 12.5 Stability and Equilibrium Analysis .332 12.6 Discrete Time and Dynamic Programming Models .332 Appendix A About R .335 A.I bstalling R .335 A.2 A Very Short Introduction .336 A.2.1 Console Versus Scripts .336 A.2.2 Getting Help .337 A.2.3 Vectors and Matrices .337 A.2.4 More Complex Data Structures .339 A.2.5 User-defined Functions and Programming .340 A.2.6 R Packages .341 A.2.7 Graphics .341 A.2.8 Minor Things to Remember .342 A.3 Interfacing R with Low-Level Languages: The Competition in a Lattice Grid Model Revisited .343 Contents xv Appendix В Derivatives and Differential Equations .347 B.I Derivatives .347 B.2 Taxonomy of Differential Equations .348 B.3 General Solutions of Often Used Differential Equations .349 B.3.1 Simple Time-Dependent Equations .349 B.3.2 Steady-State Transport - Reaction in 1-D, Constant Surface . 350 B.3.3 Steady-State Transport - Reaction in 1-D, Cylindrical Coordinates .350 B.3.4 Steady-State Transport - Reaction in 1-D, Spherical Coordinates . 351 B.4 Particular Solutions of Dynamic Diffusion-Reaction Equation .351 B.5 Derivatives and Integrals .352 Appendix С Matrix Algebra .353 C.I Matrices .353 C.2 Linear Equations .354 C.3 Eigenvalues and Eigenvectors, Determinants .355 C.4 R-Examples .355 C.5 The Jacobian Matrix .357 Appendix D Statistical Distributions .359 D.I Probability Distribution .359 D.2 Normal Distribution .359 D.3 The Poisson Distribution .360 References .361 Index .367
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spelling	Soetaert, Karline Verfasser aut A practical guide to ecological modelling using R as a simulation platform Karline Soetaert and Peter M. J. Herman [Dordrecht] Springer 2009 XV, 372 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Ökologie Ecology Mathematical models R (Computer program language) R Programm (DE-588)4705956-4 gnd rswk-swf Biomathematik (DE-588)4139408-2 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Ökologie (DE-588)4043207-5 gnd rswk-swf Ökologie (DE-588)4043207-5 s Modellierung (DE-588)4170297-9 s DE-604 R Programm (DE-588)4705956-4 s Biomathematik (DE-588)4139408-2 s Herman, Peter M. J. Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016988572&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Soetaert, Karline Herman, Peter M. J. A practical guide to ecological modelling using R as a simulation platform Mathematisches Modell Ökologie Ecology Mathematical models R (Computer program language) R Programm (DE-588)4705956-4 gnd Biomathematik (DE-588)4139408-2 gnd Modellierung (DE-588)4170297-9 gnd Ökologie (DE-588)4043207-5 gnd
subject_GND	(DE-588)4705956-4 (DE-588)4139408-2 (DE-588)4170297-9 (DE-588)4043207-5
title	A practical guide to ecological modelling using R as a simulation platform
title_auth	A practical guide to ecological modelling using R as a simulation platform
title_exact_search	A practical guide to ecological modelling using R as a simulation platform
title_exact_search_txtP	A practical guide to ecological modelling using R as a simulation platform
title_full	A practical guide to ecological modelling using R as a simulation platform Karline Soetaert and Peter M. J. Herman
title_fullStr	A practical guide to ecological modelling using R as a simulation platform Karline Soetaert and Peter M. J. Herman
title_full_unstemmed	A practical guide to ecological modelling using R as a simulation platform Karline Soetaert and Peter M. J. Herman
title_short	A practical guide to ecological modelling
title_sort	a practical guide to ecological modelling using r as a simulation platform
title_sub	using R as a simulation platform
topic	Mathematisches Modell Ökologie Ecology Mathematical models R (Computer program language) R Programm (DE-588)4705956-4 gnd Biomathematik (DE-588)4139408-2 gnd Modellierung (DE-588)4170297-9 gnd Ökologie (DE-588)4043207-5 gnd
topic_facet	Mathematisches Modell Ökologie Ecology Mathematical models R (Computer program language) R Programm Biomathematik Modellierung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016988572&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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