The Mathematics of Nepotism: A Review of Foundations of Social Evolution by Steven A. Frank

The theory of natural selection suggests that animals will do their best to maximize their number of offspring. So why do some young Florida scrub jays stay at the nest and help their parents to raise next year’s brood, instead of striking out on their own? Why do most ants, bees and termites remain childless, working tirelessly for the good of their colony? Ever since the landmark work of Hamilton (1964), we have understood such social phenomena in terms of kin selection. This is the idea that an organism has two ways of perpetuating its genetic material: firstly, by direct reproduction, and secondly, by assisting relatives in their reproductive efforts, thereby promoting the survival of copies of at least some of its genes. Hamilton quantified kin selection by noting that assisting a relative would be selected for if rB − C > 0, that is, if the benefit of being helped out (B), scaled by the degree to which the two parties were related (r), was greater than the cost of being nice (C). Steven A. Frank, in his recent book Foundations of Social Evolution (1998), is not out to capsize this orthodox Hamiltonian view. However, he argues that the appealing simplicity of Hamilton’s formulation can be misleading, and that it does not always help us to solve the problems we’re interested in. For example, specifying exactly what is meant by relatedness has caused much confusion in the literature—Hamilton himself later revised his original definition (Hamilton, 1970; Michod & Hamilton, 1980). It is also difficult to be clear and consistent about the units with which B and C should be measured. Frank’s goal is to clear up exactly these ambiguities. His book is about the proper measures of success or fitness needed to study social evolution. It is intended as both a practical guide to constructing mathematical models, and as a summary of the kin selection literature. The book also features original models and arguments. Frank focuses on three evolutionary currencies: marginal value, reproductive value, and inclusive fitness. The first two of these have familiar economic interpretations.