Mathematical Models of Social Evolution: A Guide for the Perplexed »

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.

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 Evolution aims 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 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.

Science

"Mathematical Models of Social Evolution will no doubt reward psychologists, sociologists, and economists interested in evolutionary theory. Anyone desiring a thorough, yet down-to-Earth, introduction to modeling in social evolution couldn’t do much better than to read this book. Using little more than high school mathematics, McElreath and Boyd show how one can take a big step toward understanding many perplexing evolutionary processes."—Daniel J. Rankin, Science

— Daniel J. Rankin

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