The limitations of adaptive dynamics as a model of evolution

Adaptive dynamics describes the evolution of an asexual population through the successive substitution of mutations of small effect. Waxman & Gavrilets (2005) give an excellent overview of the method and its applications. In this note, we focus on the plausibility of the key assumption that mutations have small effects, and the consequences of relaxing that assumption. We argue that: (i) successful mutations often have large effects; (ii) such mutations generate a qualitatively different evolutionary pattern, which is inherently stochastic; and (iii) in models of competition for a continuous resource, selection becomes very weak once several phenotypes are established. This makes the effects of introducing new mutations unpredictable using the methods of adaptive dynamics. We should make clear at the outset that our criticism is of methods that rely on local analysis of fitness gradients (eqn 2 of Waxman & Gavrilets, 2005), and not of the broader idea that evolution can be understood by examining the invasion of successive mutations. We use the term ‘adaptive dynamics’ to refer to the former technique, and contrast it with a more general population genetic analysis of probabilities of invasion.