Modeling evolution : an introduction to numerical methods / Derek A. Roff.

Format:

Book

Author/Creator:

Roff, Derek A., 1949- author.

Series:

Oxford scholarship online.

Oxford scholarship online

Language:

English

Subjects (All):

Evolution (Biology)--Computer simulation.

Evolution (Biology).

Physical Description:

1 online resource (xii, 451 pages): illustrations (black and white).

Edition:

1st ed.

Place of Publication:

Oxford : Oxford University Press, 2023.

Summary:

Computer modeling is now an integral part of research in evolutionary biology. This book outlines how evolutionary questions are formulated and how, in practice, they can be resolved by analytical and numerical methods.

Contents:

Intro

Contents

1 Overview

1.1 Introduction

1.1.1 The aim of this book

1.1.2 Why R and MATLAB?

1.2 Operational definitions of fitness

1.2.1 Constant environment, density-independent, stable-age distribution

1.2.2 Demographic stochasticity

1.2.3 Environments of fixed length (e.g., deterministic seasonal environments)

1.2.4 Constant environment, density-dependence with a stable equilibrium

1.2.5 Constant environment, variable population dynamics

1.2.6 Temporally stochastic environments

1.2.7 Temporally variable, density-dependent environments

1.2.8 Spatially variable environments

1.2.9 Social environment

1.2.10 Frequency-dependence

1.3 Some general principles of model building

1.4 An introduction to modeling in R and MATLAB

1.4.1 General assumptions

1.4.2 Mathematical assumptions of model 1

1.4.3 Mathematical assumptions of model 2

1.4.4 Mathematical assumptions of model 3

1.4.5 Mathematical assumptions of model 4

1.4.6 Mathematical assumptions of model 5

1.4.7 Mathematical assumptions of model 6

1.5 Summary of modeling approaches described in this book

1.5.1 Fisherian optimality analysis (Chapter 2)

1.5.2 Invasibility analysis (Chapter 3)

1.5.3 Genetic models (Chapter 4)

1.5.4 Game theoretic models (Chapter 5)

1.5.5 Dynamic programming (Chapter 6)

2 Fisherian optimality models

2.1 Introduction

2.1.1 Fitness measures

2.1.2 Methods of analysis: introduction

2.1.3 Methods of analysis: W = f(&amp

#952[sub(1)], &amp

#952[sub(2}],...,&amp

#952[sub(k)], x[sub(1)], x[sub(2)],...,x[sub(n)]) and well-behaved

2.1.4 Methods of analysis: W = f(&amp

#952[sub(1)],&amp

#952[sub(2)],...,&amp

#952[sub(k)],x[sub(1)],x[sub(2)],...,x[sub(n)]) and not well-behaved

2.1.5 Methods of analysis: g(w) = f(&amp

#952[sub(1)],&amp.

#952[sub(2)],...,&amp

#952[sub(k)],x[sub(1)],x[sub(2)],...,x[sub(n)],W)

2.2 Summary of scenarios (Table 2.1)

2.3 Scenario 1: A simple trade-off model

2.3.1 General assumptions

2.3.2 Mathematical assumptions

2.3.3 Plotting the fitness function

2.3.4 Finding the maximum using the calculus

2.3.5 Finding the maximum using a numerical approach

2.4 Scenario 2: Adding age structure may not affect the optimum

2.4.1 General assumptions

2.4.2 Mathematical assumptions

2.5 Scenario 3: Adding age-specific mortality that affects the optimum

2.5.1 General assumptions

2.5.2 Mathematical assumptions

2.5.3 Plotting the fitness function

2.5.4 Finding the maximum using the calculus

2.5.5 Finding the maximum using a numerical approach

2.6 Scenario 4: Adding age-specific mortality that affects the optimum and using integration rather than summation

2.6.1 General assumptions

2.6.2 Mathematical assumptions

2.6.3 Plotting the fitness function

2.6.4 Finding the maximum using the calculus

2.6.5 Finding the maximum using a numerical approach

2.7 Scenario 5: Maximizing the Malthusian parameter, r, rather than expected lifetime reproductive success, R[sub(o)]

2.7.1 General assumptions

2.7.2 Mathematical assumptions

2.7.3 Plotting the fitness function

2.7.4 Finding the maximum using the calculus

2.7.5 Finding the maximum using a numerical approach

2.8 Scenario 6: Stochastic variation in parameters

2.8.1 General assumptions

2.8.2 Mathematical assumptions

2.8.3 Plotting the fitness function

2.8.4 Finding the maximum using the calculus

2.8.5 Finding the maximum using a numerical approach

2.9 Scenario 7: Discrete temporal variation in parameters

2.9.1 General assumptions

2.9.2 Mathematical assumptions

2.9.3 Plotting the fitness function.

2.9.4 Finding the maximum using the calculus

2.9.5 Finding the maximum using numerical methods

2.10 Scenario 8: Continuous temporal variation in parameters

2.10.1 General assumptions

2.10.2 Mathematical assumptions

2.10.3 Plotting the fitness function

2.10.4 Finding the maximum using a numerical approach

2.11 Scenario 9: Maximizing two traits simultaneously

2.11.1 General assumptions

2.11.2 Mathematical assumptions

2.11.3 Plotting the fitness function

2.11.4 Finding the maximum using the calculus

2.11.5 Finding the maximum using a numerical approach

2.12 Scenario 10: Two traits may covary but optima are independent

2.12.1 General assumptions

2.12.2 Mathematical assumptions

2.13 Scenario 11: Two traits may be resolved into a single trait

2.13.1 General assumptions

2.13.2 Mathematical assumptions

2.13.3 Plotting the fitness function

2.13.4 Finding the optimum using the calculus

2.13.5 Finding the optimum using a numerical approach

2.14 Scenario 12: The importance of plotting and the utility of brute force

2.14.1 General assumptions

2.14.2 Mathematical assumptions

2.14.3 Plotting the fitness function

2.14.4 Finding the maximum using the calculus

2.14.5 Finding the maximum using a numerical approach

2.15 Scenario 13: Dealing with recursion by brute force

2.15.1 General assumptions

2.15.2 Mathematical assumptions

2.15.3 Plotting the fitness function

2.15.4 Finding the maximum using the calculus

2.15.5 Finding the maximum using a numerical approach

2.16 Scenario 14: Adding a third variable and more

2.16.1 General assumptions

2.16.2 Mathematical assumptions

2.16.3 Plotting the fitness function

2.16.4 Finding the maximum using the calculus

2.16.5 Finding the maximum using a numerical approach

2.17 Some exemplary papers

2.18 MATLAB code.

2.18.1 Scenario 1: Plotting the fitness function

2.18.2 Scenario 1: Finding the maximum using the calculus

2.18.3 Scenario 1: Finding the maximum using a numerical approach

2.18.4 Scenario 3: Plotting the fitness function

2.18.5 Scenario 3: Finding the maximum by the calculus

2.18.6 Scenario 3: Finding the maximum using a numerical approach

2.18.7 Scenario 4: Plotting the fitness function

2.18.8 Scenario 4: Finding the maximum using the calculus

2.18.9 Scenario 4: Finding the maximum using a numerical approach

2.18.10 Scenario 5: Plotting the fitness function

2.18.11 Scenario 5: Finding the maximum using the calculus

2.18.12 Scenario 5: Finding the maximum using a numerical approach

2.18.13 Scenario 6: Plotting the fitness function

2.18.14 Scenario 6: Finding the maximum using the calculus

2.18.15 Scenario 6: Finding the maximum using a numerical approach

2.18.16 Scenario 7: Plotting the fitness function

2.18.17 Scenario 7: Finding the maximum using the calculus

2.18.18 Scenario 7: Finding the maximum using numerical methods

2.18.19 Scenario 8: Plotting the fitness function

2.18.20 Scenario 8: Finding the maximum using a numerical approach

2.18.21 Scenario 9: The derivative can also be determined using MATLAB

2.18.22 Scenario 9: Plotting the fitness function

2.18.23 Scenario 9: Finding the maximum using the calculus

2.18.24 Scenario 9: Finding the maximum using a numerical approach

2.18.25 Scenario 11: Plotting the fitness function

2.18.26 Scenario 11: Finding the optimum using the calculus

2.18.27 Scenario 11: Finding the optimum using a numerical approach

2.18.28 Scenario 12: Plotting the fitness function

2.18.29 Scenario 12: Finding the maximum using the calculus

2.18.30 Scenario 12: Finding the maximum using a numerical approach.

2.18.31 Scenario 13: Plotting the fitness function

2.18.32 Scenario 13: Finding the maximum using a numerical approach

2.18.33 Scenario 14: Finding the maximum using a numerical approach

3 Invasibility analysis

3.1 Introduction

3.1.1 Age-or stage-structured models

3.1.2 Modeling evolution using the Leslie matrix

3.1.3 Stage-structured models

3.1.4 Adding density-dependence

3.1.5 Estimating fitness

3.1.6 Pairwise invasibility analysis

3.1.7 Elasticity analysis

3.1.8 Multiple invasibility analysis

3.2 Summary of scenarios

3.3 Scenario 1: Comparing approaches

3.3.1 General assumptions

3.3.2 Mathematical assumptions

3.3.3 Solving using the methods of Chapter 2

3.3.4 Solving using the eigenvalue of the Leslie matrix

3.4 Scenario 2: Adding density-dependence

3.4.1 General assumptions

3.4.2 Mathematical assumptions

3.4.3 Solving using R[sub(o)] as the fitness measure

3.4.4 Pairwise invasibility analysis

3.4.5 Elasticity analysis

3.5 Scenario 3: Functional dependence in the Ricker model

3.5.1 General assumptions

3.5.2 Mathematical assumptions

3.5.3 Pairwise invasibility analysis

3.5.4 Elasticity analysis

3.5.5 Multiple invasibility analysis

3.6 Scenario 4: The evolution of reproductive effort

3.6.1 General assumptions

3.6.2 Mathematical assumptions

3.6.3 Pairwise invasibility analysis

3.6.4 Elasticity analysis

3.7 Scenario 5: A two stage model

3.7.1 General assumptions

3.7.2 Mathematical assumptions

3.7.3 Elasticity analysis

3.7.4 Pairwise invasibility analysis

3.8 Scenario 6: A case in which the putative ESS is not stable

3.8.1 General assumptions

3.8.2 Mathematical assumptions

3.8.3 Pairwise invasibility analysis

3.8.4 Elasticity analysis

3.8.5 Multiple invasibility analysis

3.9 Some exemplary papers.

4 Genetic models.

Notes:

Formerly CIP.

Previously issued in print: 2009.

Includes bibliographical references and index.

Derived record based on print version record and publisher information.

ISBN:

1-383-04658-1

0-19-157668-9

9786612383731

1-282-38373-6

OCLC:

1406785342