A practical guide to ecological modelling: using R as a simulation platform
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Dordrecht]
Springer
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 372 S. Ill., graph. Darst. |
| ISBN: | 9781402086236 9781402086243 |
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| 020 | |a 9781402086236 |c Gb. : ca. EUR 74.85 (freier Pr.), ca. sfr 116.50 (freier Pr.) |9 978-1-4020-8623-6 | ||
| 020 | |a 9781402086243 |9 978-1-402-08624-3 | ||
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| 100 | 1 | |a Soetaert, Karline |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A practical guide to ecological modelling |b using R as a simulation platform |c Karline Soetaert and Peter M. J. Herman |
| 264 | 1 | |a [Dordrecht] |b Springer |c 2009 | |
| 300 | |a XV, 372 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Ökologie | |
| 650 | 4 | |a Ecology |x Mathematical models | |
| 650 | 4 | |a R (Computer program language) | |
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| 700 | 1 | |a Herman, Peter M. J. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016988572 | ||
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| _version_ | 1804138355380715520 |
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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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Soetaert, Karline Herman, Peter M. J. |
| author_facet | Soetaert, Karline Herman, Peter M. J. |
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| building | Verbundindex |
| bvnumber | BV035181830 |
| callnumber-first | Q - Science |
| callnumber-label | QH541 |
| callnumber-raw | QH541.15.M3 |
| callnumber-search | QH541.15.M3 |
| callnumber-sort | QH 3541.15 M3 |
| callnumber-subject | QH - Natural History and Biology |
| classification_rvk | AR 12450 WC 5300 |
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| dewey-full | 577.015118 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 577 - Ecology |
| dewey-raw | 577.015118 |
| dewey-search | 577.015118 |
| dewey-sort | 3577.015118 |
| dewey-tens | 570 - Biology |
| discipline | Allgemeines Biologie Umwelt |
| discipline_str_mv | Allgemeines Biologie Umwelt |
| format | Book |
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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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