REVOLUTIONARY INVASION ANALYSES

Abstract

Review of: Dercole, F. and S. Rinaldi. 2008. Analysis of Evo lutionary Processes: The Adaptive Dynamics Approach and its Applications. Princeton University Press. 333 pp. ISBN: 978-0 691-12006-5. $65.00 (cloth) Recent years have witnessed an explosion of interest among evolutionary biologists in a modeling technique known as adap tive dynamics. In some ways this modeling technique has raised considerable controversy (see Waxman and Gavrilets 2005 and re lated replies in the same issue). In my view, the controversy is not over its utility, because there can be little doubt that it has provided interesting and important new insights into a variety of topics in evolutionary biology. Rather, some of the controversy has cen tered on the assumptions made in this modeling approach (e.g., separation of timescales, rates of mutation, etc.). Although these criticisms have some validity, they are really no more damning to the technique of adaptive dynamics than are analogous criticisms to the techniques of game theory, population genetics, and other modeling approaches. A somewhat more nebulous source of controversy over adap tive dynamics stems from the question of its novelty. Does adap tive dynamics really represent something new, and if so, how does it fit within the broader framework of other modeling techniques? Here there appear to be as many answers as there are practicing theoretical evolutionary biologists. To appreciate and use adaptive dynamics techniques effectively, however, it is essential that some perspective on this question be reached. Only then can adaptive dynamics be properly understood as being one of several model ing approaches in evolutionary biology. And, like other modeling approaches, adaptive dynamics has both its advantages and dis advantages. An important new book by Fabio Dercole and Sergio Rinaldi aim to help newcomers to the field sort through these complex issues. Their book, Analysis of Evolutionary Processes: The Adap tive Dynamics Approach and its Applications, provides a general overview of evolutionary modeling, and presents a detailed math ematical treatment of what adaptive dynamics is, and how it can be profitably applied. The book is aimed primarily at students and researchers in applied mathematics and evolutionary biology, a d could well be used as the basis of a graduate course on this subject. The authors state that readers will require only an un dergraduate skill in mathematics. In practical terms this means that most readers will benefit from having some prior knowledge of dynamical systems and its related terminology, in addition to a basic knowledge of calculus. The book is structured in a simple and pleasing way, consist ing of two main sections. The first section (Chapters 1-3) contains the main treatment of adaptive dynamics, whereas the second sec tion (Chapters 4-10) contains applications. Chapter 1 gives a very well-crafted historical and conceptual overview of evolutionary biology, and it will provide an excellent introduction for non specialists. On the whole it is very well-balanced, although there is naturally the occasional point where one might quibble. For instance, it is suggested that a separation of evolutionary and eco logical timescales is typically reasonable on biological grounds, and that [m]ost mutations affect a small portion of a single gene and thus have small phenotypic effects (p. 9). Although both are sometimes true, evidence from a variety of biological systems cer tainly questions the generality of these statements. This is perhaps a minor issue, but these aspects of timescale and mutation size are central assumptions of the adaptive dynamics approach. My