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E-raamat: Data-driven Modelling of Structured Populations: A Practical Guide to the Integral Projection Model

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Data-driven Modelling of Structured Populations: A Practical Guide to the Integral Projection ModelSuurem pilt
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This book is a "How To" guide formodeling population dynamics using Integral Projection Models (IPM) startingfrom observational data. It is written by a leading research team in this areaand includes code in the R language (in the text and online) to carry out allcomputations. The intended audience are ecologists, evolutionary biologists,and mathematical biologists interested in developing data-driven models foranimal and plant populations. IPMs may seem hard as they involve integrals. Theaim of this book is to demystify IPMs, so they become the model of choice forpopulations structured by size or other continuously varying traits. The bookuses real examples of increasing complexity to show how the life-cycle of thestudy organism naturally leads to the appropriate statistical analysis, whichleads directly to the IPM itself. A wide range of model types and analyses arepresented, including model construction, computational methods, and theunderlying theory, with the mor

e technical material in Boxes and Appendices.Self-contained R code which replicates all of the figures and calculationswithin the text is available to readers on GitHub.Stephen P. Ellner is Horace White Professor of Ecology and Evolutionary Biology at Cornell University, USA; Dylan Z. Childs is Lecturer and NERC Postdoctoral Fellow in the Department of Animal and Plant Sciences at The University of Sheffield, UK; Mark Rees is Professor in the Department of Animal and Plant Sciences at The University of Sheffield, UK.

Introduction.- Simple Deterministic IPM.- Basic Analysis 1: Demographic Measures and Events in the Life Cycle.- Basic Analysis 2: Prospective Perturbation Analysis.- Density Dependence.- General Deterministic IPM.- Environmental Stochasticity.- Spatial Models.- Evolutionary Demography.- Future Directions and Advanced Topics.
1 Introduction
1(8)
1.1 Linking individuals, traits, and population dynamics
1(1)
1.2 Survey of research applications
2(1)
1.3 About this book
3(3)
1.3.1 Mathematical prerequisites
4(1)
1.3.2 Statistical prerequisites and data requirements
5(1)
1.3.3 Programming prerequisites
5(1)
1.4 Notation and nomenclature
6(3)
2 Simple Deterministic IPM
9(48)
2.1 The individual-level state variable
9(1)
2.2 Key assumptions and model structure
10(2)
2.3 From life cycle to model: specifying a simple IPM
12(5)
2.3.1 Changes
15(2)
2.4 Numerical implementation
17(2)
2.5 Case study 1A: A monocarpic perennial
19(13)
2.5.1 Summary of the demography
19(2)
2.5.2 Individual-based model (IBM)
21(1)
2.5.3 Demographic analysis using lm and glm
22(2)
2.5.4 Implementing the IPM
24(2)
2.5.5 Basic analysis: projection and asymptotic behavior
26(4)
2.5.6 Always quantify your uncertainty!
30(2)
2.6 Case study 2A: Ungulate
32(9)
2.6.1 Summary of the demography
33(1)
2.6.2 Individual-based model
34(1)
2.6.3 Demographic analysis
35(1)
2.6.4 Implementing the IPM
36(3)
2.6.5 Basic analysis
39(2)
2.7 Model diagnostics
41(8)
2.7.1 Model structure
42(1)
2.7.2 Demographic rate models
42(3)
2.7.3 Implementation: choosing the size range
45(3)
2.7.4 Implementation: the number of mesh points
48(1)
2.8 Looking ahead
49(1)
2.9 Appendix: Probability Densities and the Change of Variables Formula
49(3)
2.10 Appendix: Constructing IPMs when more than one census per time year is available
52(5)
3 Basic Analyses 1: Demographic Measures and Events in the Life Cycle
57(30)
3.1 Demographic quantities
57(8)
3.1.1 Population growth
58(4)
3.1.2 Age-specific vital rates
62(1)
3.1.3 Generation time
63(2)
3.2 Life cycle properties and events
65(9)
3.2.1 Mortality: age and size at death
66(4)
3.2.2 Reproduction: who, when, and how much?
70(3)
3.2.3 And next
73(1)
3.3 Case study 1B: Monocarp life cycle properties and events
74(8)
3.3.1 Population growth
74(1)
3.3.2 Mortality: age and size at death calculations
75(3)
3.3.3 Reproduction: who, when, and how much?
78(4)
3.4 Appendix: Derivations
82(5)
4 Basic Analyses 2: Prospective Perturbation Analysis
87(24)
4.1 Introduction
87(1)
4.2 Sensitivity and elasticities
88(1)
4.3 Sensitivity analysis of population growth rate
88(8)
4.3.1 Kernel-level perturbations
89(4)
4.3.2 Vital rate functions
93(1)
4.3.3 Parameters and lower-level functions
94(2)
4.4 Case Study 2B: Ungulate population growth rate
96(10)
4.4.1 Kernel-level perturbations
96(2)
4.4.2 Vital rate functions
98(5)
4.4.3 Parameters and lower-level functions
103(3)
4.5 Sensitivity analysis of life cycle properties and events
106(2)
4.6 Case Study 2B (continued): Ungulate life cycle
108(3)
5 Density Dependence
111(28)
5.1 Introduction
111(1)
5.2 Modeling density dependence: recruitment limitation
112(3)
5.3 Modeling density dependence: Idaho steppe
115(6)
5.4 Theory
121(7)
5.4.1 Persistence or extinction?
122(4)
5.4.2 Local stability of equilibria
126(1)
5.4.3 Equilibrium perturbation analysis
127(1)
5.4.4 Density dependence and environmental stochasticity
128(1)
5.5 Case study 2C: ungulate competition
128(8)
5.6 Coda
136(1)
5.7 Appendix: Mean field approximations for neighborhood competition
136(3)
6 General Deterministic IPM
139(48)
6.1 Overview
139(1)
6.2 Case study 2D: ungulate age-size structure
140(8)
6.2.1 Structure of an age-size IPM
141(1)
6.2.2 Individual-based model and demographic analysis
142(2)
6.2.3 Implementing the model
144(4)
6.3 Specifying a general IPM
148(2)
6.4 Examples
150(5)
6.4.1 Seeds and plants
150(1)
6.4.2 Susceptible and Infected
151(1)
6.4.3 Time delays
152(1)
6.4.4 Individual quality and size
152(2)
6.4.5 Stage structure with variable stage durations
154(1)
6.5 Stable population growth
155(5)
6.5.1 Assumptions for stable population growth
156(3)
6.5.2 Alternate stable states
159(1)
6.5.3 Time delay models
159(1)
6.6 Numerical implementation
160(7)
6.6.1 Computing eigenvalues and eigenvectors
160(2)
6.6.2 Implementing a size-quality model
162(5)
6.7 Case Study 2D: Age-size structured ungulate, further calculations
167(4)
6.7.1 Population growth rate
167(2)
6.7.2 Other demographic measures
169(1)
6.7.3 Consequences of age-structure
170(1)
6.8 Other ways to compute integrals
171(9)
6.9 Appendix: the details
180(7)
6.9.1 Derivations
183(4)
7 Environmental Stochasticity
187(42)
7.1 Why environmental stochasticity matters
187(2)
7.1.1 Kernel selection versus parameter selection
188(1)
7.2 Case Study 1C: Another monocarpic perennial
189(6)
7.2.1 Building an IPM
191(2)
7.2.2 Basic analyses by projection
193(2)
7.3 Modeling temporal variation
195(6)
7.3.1 Fixed versus random effects
195(6)
7.4 Long-run growth rate
201(5)
7.4.1 Implementation
204(2)
7.5 Sensitivity and elasticity analysis
206(12)
7.5.1 Kernel perturbations
209(2)
7.5.2 Function perturbations
211(3)
7.5.3 Parameter perturbations
214(4)
7.6 Life Table Response Experiment (LTRE) Analysis
218(3)
7.7 Events in the life cycle
221(2)
7.8 Appendix: the details
223(6)
7.8.1 Derivations
227(2)
8 Spatial Models
229(26)
8.1 Overview of spatial IPMs
229(2)
8.2 Building a dispersal kernel
231(6)
8.2.1 Descriptive movement modeling
232(4)
8.2.2 Mechanistic movement models
236(1)
8.3 Theory: bounded spatial domain
237(2)
8.4 Theory: unbounded spatial domain
239(4)
8.5 Some applications of purely spatial IPMs
243(1)
8.6 Combining space and demography: invasive species
244(7)
8.7 Invasion speed in fluctuating environments
251(4)
9 Evolutionary Demography
255(28)
9.1 Introduction
255(2)
9.2 Motivation
257(1)
9.3 Evolution: Dynamics
257(3)
9.3.1 Approximating Evolutionary Dynamics
259(1)
9.4 Evolution: Statics
260(5)
9.4.1 Evolutionary Endpoints
261(2)
9.4.2 Finding ESSs using an optimization principle
263(2)
9.5 Evolution: Stochastic Environments
265(7)
9.6 Function-valued traits
272(8)
9.6.1 Solving the ESS conditions for function-valued strategies
277(3)
9.7 Prospective evolutionary models
280(1)
9.8 Appendix: Approximating evolutionary change
281(2)
10 Future Directions and Advanced Topics
283(32)
10.1 More flexible kernels
283(8)
10.1.1 Transforming variables
284(1)
10.1.2 Nonconstant variance
284(2)
10.1.3 Nonlinear growth: modeling the mean
286(1)
10.1.4 Nonlinear growth: parametric variance models
287(1)
10.1.5 Nonparametric models for growth variation
288(3)
10.2 High-dimensional kernels
291(2)
10.3 Demographic stochasticity
293(11)
10.3.1 Population growth rate
297(4)
10.3.2 Extinction
301(3)
10.4 IPM meets DEB: deterministic trait dynamics or constraints
304(2)
10.5 Different kinds of data
306(6)
10.5.1 Mark-recapture-recovery data
306(4)
10.5.2 Count data
310(2)
10.6 Coda
312(1)
10.7 Appendix: Covariance with demographic stochasticity
312(3)
References 315(12)
Index 327
Stephen Ellner is a Horace White Professor of EEB at Cornell University, Department of Ecology and Evolutionary Biology. His general interests are in theoretical population biology and evolutionary ecology.





Dylan Childs is an NERC Postdoctoral Fellow at the University of Sheffield. His key research interests include life history theory, evolutionary demography, structured population modeling, and host-parasite dynamics. 





Mark Rees is a Professor in the Department of Animal and Plant Sciences at the University of Sheffield. His key research interests include evolution of plant reproductive strategies, modeling and management strategies for weed populations, population biology of invasive plants, and modeling structured populations using integral projection models.
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