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# Mathematical Models of Social Evolution

## A Guide for the Perplexed

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.

432 pages | 55 line drawings, 99 tables, 41 boxes | 6 x 9 | © 2007

Biological Sciences: Behavioral Biology, Evolutionary Biology

Economics and Business: Economics--General Theory and Principles

## Reviews

"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

Preface: How to use this book

1 Theoretician’s Laboratory
1.1 Structure of evolutionary theory
1.2 The utility of simple models
1.3 Why not just simulate?
1.4 A model of viability selection
1.5 Determining long-term consequences
1.6 Non-genetic replication

2 Animal Conflict
2.1 The Hawk-Dove game
2.2 Retaliation
2.3 Continuous stable strategies
2.4 Ownership
2.5 Resource holding power
2.6 Sequential play

3 Altruism & Inclusive Fitness
3.1 The prisoner’s dilemma
3.2 Positive assortment
3.3 Common descent and inclusive fitness
3.4 Rediscovering Hamilton’s rule
3.5 Justifying Hamilton’s rule
3.6 Using Hamilton’s rule

4 Reciprocity
4.1 The Axelrod-Hamilton model
4.2 Mutants and mistakes
4.3 Partner Choice
4.4 Indirect Reciprocity
4.5 Reciprocity & Collective Action

5 Animal Communication
5.1 Costly signaling theory
5.2 Cheap honest signals
5.3 Signaling and altruism
5.4 Social learning

6 Selection Among Groups
6.1 Three views of selection
6.2 Deriving the Price equation
6.3 Selection within & between groups
6.4 Dispersal

7 Sex Allocation
7.1 Fisher’s theory of sex allocation
7.2 Reproductive value & sex ratio
7.3 Using the Shaw-Mohler Theorem
7.4 Biased sex ratios
7.5 Breaking the Eigen Barrier

8 Sexual Selection
8.1 Quantitative genetic models
8.2 Fisher’s runaway process
8.3 Costly choice & sensory bias
8.4 Good genes and sexy sons