Mathematical models of social evolution : a guide for the perplexed / Richard McElreath and Robert Boyd.

Format:

Book

Author/Creator:

McElreath, Richard, 1973-

Contributor:

Boyd, Robert, 1948-

Language:

English

Subjects (All):

Social behavior in animals--Mathematical models.

Social behavior in animals.

Physical Description:

xiii, 414 pages : illustrations ; 24 cm

Place of Publication:

Chicago : University of Chicago Press, 2007.

Summary:

Over the last several decades, mathematical models have become central to the study of social evolution, both in biology and the social sciences. But students in these disciplines often lack the tools to understand them. A primer on behavioral modeling that includes both mathematics and evolutionary theory, Mathematical Models of Social Evolution aims to make the student and professional researcher in biology and the social sciences conversant in the language of the field.

Teaching biological concepts from which models can be developed, Richard McElreath and Robert Boyd introduce readers to many of the typical mathematical tools that are used to analyze evolutionary models and end each chapter with a set of problems that draw upon these techniques. Mathematical Models of Social Evolution equips behaviorists and evolutionary biologists with the mathematical knowledge to truly understand the models on which their research depends. Ultimately, McElreath and Boyd's goal is to impart the fundamental concepts that underlie modern biological understandings of the evolution of behavior so that readers will be able to more fully appreciate journal articles and scientific literature, and start building models of their own.

Contents:

1 Theoretician's Laboratory 1

1.1 The structure of evolutionary theory 3

1.2 The utility of simple models 4

1.3 Why not just simulate? 8

1.4 A model of viability selection 11

1.5 Determining long-term consequences 16

1.6 Nongenetic replication 27

2 Animal Conflict 37

2.1 The Hawk-Dove game 38

2.2 Retaliation 46

2.3 Continuous stable strategies 52

2.4 Ownership, an asymmetry 55

2.5 Resource holding power 58

2.6 Sequential play 60

3 Altruism & Inclusive Fitness 71

3.1 The prisoner's dilemma 72

3.2 Positive assortment 76

3.3 Common descent and inclusive fitness 78

3.4 Rediscovering Hamilton's rule 82

3.5 Justifying Hamilton's rule 97

3.6 Using Hamilton's rule 99

4 Reciprocity 123

4.1 The Axelrod-Hamilton model 124

4.2 Mutants and mistakes 132

4.3 Partner choice 145

4.4 Indirect reciprocity 150

4.5 Reciprocity and collective action 156

5 Animal Communication 173

5.1 Costly signaling theory 174

5.2 Cheap, honest signals 192

5.3 Signaling and altruism 201

5.4 Social learning 206

6 Selection among Groups 223

6.1 Three views of selection 225

6.2 Deriving the Price equation 228

6.3 Selection within and between groups 232

6.4 Dispersal 249

7 Sex Allocation 261

7.1 Fisher's theory of sex allocation 262

7.2 Reproductive value and Fisherian sex ratios 263

7.3 Using the Shaw-Mohler theorem 267

7.4 Biased sex ratios 271

7.5 Breaking the eigen barrier 281

8 Sexual Selection 295

8.1 Quantitative genetic models 298

8.2 Fisher's runaway process 305

8.3 Costly choice and sensory bias 309

8.4 Good genes and sexy sons 313

A Facts about Derivatives 333

B Facts about Random Variables 335

C Calculating Binomial Expectations 337

D Numerical Solution of the Kokko et al. Model 343.

Notes:

Includes bibliographical references (pages 393-407) and index.

ISBN:

9780226558264

0226558266

OCLC:

70707759

Online:

Contributor biographical information

Publisher description