Mathematical sociobiology: A problem-centered textbook

Herbert Gintis

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From the book : Evolutionary Psychology 6 issue 3 : 480-481.

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• Publié par: evolutionary-psychology
• Publié le: 01 janvier 2008
• Nombre de lectures: 5
• Licence : En savoir +
  Paternité, pas d'utilisation commerciale, partage des conditions initiales à l'identique
• Langue: English

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Evolutionary Psychology

www.epjournal.net – 2008. 6(3): 480-481

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Book Review

Mathematical Sociobiology: A Problem-Centered Textbook

A review of Richard McElreath and Robert Boyd,Mathematical Models of Social Evolution: Guide for the Perplexed, of Chicago Press, 2007, 432 pp., University US$62.50, ISBN 9780226558264

Herbert Gintis, Santa Fe Institute, Santa Fe, NM 87501, USA. Email:ast.netit@soccmghni 

 Robert Boyd is a professor of anthropology at UCLA, and McElreath is his former student, now professor of Anthropology at UC Davis. Boyd, together with Peter Richerson, were early contributors to a dynamic (and correct, I believe) version of sociobiology known as gene-culture coevolution. The theory developed in this book is relevant for anyone interested in social behavior, whether they are biologists, anthropologists, or have their training in another behavioral discipline.  “Imagine a field in which nearly all important theory is written in Latin, but most researchers can barely read Latin and certainly cannot speak it.” This is the first sentence in the Preface of this exciting book. Of course, “Latin” translates into “mathematics,” and the field is evolutionary biology. The use of mathematical models in explaining animal behavior has advanced enormously since the seminal contributions of William Hamilton on inclusive fitness and John Maynard Smith on the use of game theory in modeling strategic interaction. However, there remains a lamentable tendency for researchers to be either mathematical idiot savants or mathematical illiterates. Unlike physics or chemistry, one can have a brilliant career in the behavioral sciences without engaging in model-building (think of Ernst Mayr, E.O. Wilson, and Stephen Jay Gould). However, there is an unfortunate tendency for whole branches of social theory to lack any division of labor in which some do model building and others formulate and test theory in a less formal way. For instance, I think there is a good possibility that evolutionary psychologists, who do not do model- building, reject gene-culture coevolutionary theory (which the authors of this volume espouse) not because of any deficiency in the theory, but merely because it is inherently mathematical, and hence fear-inducing.  This volume will not turn students of animal behavior into mathematical sociobiologists, but it might help bridge the gap between the “two worlds” of sociobiology- --the mathematical and the verbal.  The central commitment of this textbook is that learning mathematical biology requires lots of problem-solving and lots of attention to understanding and being able to

 Mathematical sociobiology

derive formulas. Every chapter has a problem set at the end, and full answers are provided at the back of the book. The student who peeks at the answers rather than sweating through the problems might just as well throw the book away. Worse than not learning the material, the student will likely have a false sense of confidence concerning his achievements.  The book has only algebra as a mathematical prerequisite, but the math becomes more challenging as the student moves from chapter to chapter. Whatever concepts are needed are developed in the book, but students must give themselves time to assimilate new material. It might be necessary to reread a chapter five or more times, over a period of days or weeks, before the material will feel natural and intuitive.  InGame Theory Evolving (in press), I approach the same body of theory as McElreath and Boyd, but in a math-driven rather than a topic-drive manner: such topics as cooperation, reciprocity, and sexual selection are treated as illustrating particular game- theoretic techniques rather than as substantive biological topics. McElreath and Boyd present the material in a topic-driven fashion, which has clear advantages for students who mainly want to master sociobiological theory. I suggest that those who really enjoy this book follow it up with a math-driven approach that stresses the mathematical theory and subordinates the biological. But, for most students, the math will, and should, never be more than a tool for understanding animal behavior.  The topics dealt with in this book include animal conflict (e.g., the Hawk-Dove game and its variants), altruism and inclusive fitness (prisoner's dilemma), reciprocity (repeated prisoner's dilemma), communication and signaling (signaling games), group selection (Price's equation), sexual selection (the Darwin-Fisher theory), and the theory of sex ratios. Curiously, given that the authors are anthropologists who work mainly with humans, there is little material specifically devoted to humans, although the books treatment of group selection is powerful and lucid. The authors do not develop evolutionary dynamics and do not present the replicator equations of evolutionary game theory, but one might argue that the level of mathematical sophistication required for this body of material is simply more than most students possess (it requires at least multivariate calculus, some linear algebra, and basic point-set topology). The book comes close to these issues in dealing with sex allocation (“breaking the eigen barrier”), however.  References  Gintis, H. (in press).Game theory evolving: A problem-centered introduction to modeling strategic interaction. Princeton: Princeton University Press.

Evolutionary Psychology – ISSN 1474-7049 – Volume 6(3). 2008. -481-