Mathematical Models of Social Evolution

by McElreath, Richard

• ISBN13: 9780226558264
• ISBN10: 0226558266
• Format: Hardcover
• Copyright: 2007-03-15
• Publisher: Univ of Chicago Pr

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 seriously lack the tools to understand them. A primer on behavioral modeling that includes both mathematics and evolutionary theory,Mathematical Models of Social Evolutionaims to make the student and professional researcher in biology and the social sciences fully 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 Evolutionequips 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.

Author Biography

Richard McElreath is associate professor of anthropology at the University of California, Davis. Robert Boyd is professor of anthropology at the University of California, Los Angeles, and coauthor of Not by Genes Alone, also published by the University of Chicago Press.

Table of Contents

Preface	p. ix
Theoretician's Laboratory	p. 1
The structure of evolutionary theory	p. 3
The utility of simple models	p. 4
Why not just simulate?	p. 8
A model of viability selection	p. 11
Determining long-term consequences	p. 16
Nongenetic replication	p. 27
Animal Conflict	p. 37
The Hawk-Dove game	p. 38
Retaliation	p. 46
Continuous stable strategies	p. 52
Ownership, an asymmetry	p. 55
Resource holding power	p. 58
Sequential play	p. 60
Altruism & Inclusive Fitness	p. 71
The prisoner's dilemma	p. 72
Positive assortment	p. 76
Common descent and inclusive fitness	p. 78
Rediscovering Hamilton's rule	p. 82
Justifying Hamilton's rule	p. 97
Using Hamilton's rule	p. 99
Reciprocity	p. 123
The Axelrod-Hamilton model	p. 124
Mutants and mistakes	p. 132
Partner choice	p. 145
Indirect reciprocity	p. 150
Reciprocity and collective action	p. 156
Animal Communication	p. 173
Costly signaling theory	p. 174
Cheap, honest signals	p. 192
Signaling and altruism	p. 201
Social learning	p. 206
Selection among Groups	p. 223
Three views of selection	p. 225
Deriving the Price equation	p. 228
Selection within and between groups	p. 232
Dispersal	p. 249
Sex Allocation	p. 261
Fisher's theory of sex allocation	p. 262
Reproductive value and Fisherian sex ratios	p. 263
Using the Shaw-Mohler theorem	p. 267
Biased sex ratios	p. 271
Breaking the eigen barrier	p. 281
Sexual Selection	p. 295
Quantitative genetic models	p. 298
Fisher's runaway process	p. 305
Costly choice and sensory bias	p. 309
Good genes and sexy sons	p. 313
Appendixes	p. 333
Facts about Derivatives	p. 333
Facts about Random Variables	p. 335
Calculating Binomial Expectations	p. 337
Numerical Solution of the Kokko et al. Model	p. 343
Solutions to Problems	p. 349
Bibliography	p. 393
Index	p. 409
Table of Contents provided by Ingram. All Rights Reserved.