Gradual or pulsed evolution: when should punctuational explanations be preferred?

The problem of gradual versus punctuated change within phyletic lineages can be understood in terms of the homogeneity of evolutionary dynamics. Hypotheses of punctuated change imply that the rules governing evolutionary change shift over time such that the normal dynamics of stasis are temporarily suspended, permitting a period of net evolutionary change. Such explanations are members of a larger class of models in which evolutionary dynamics are in some way heterogeneous over time. In this paper, I develop a likelihood-based statistical framework to evaluate the support for this kind of evolutionary model. This approach divides evolutionary sequences into nonoverlapping segments, each of which is fit to a separate evolutionary model. Models with heterogeneous dynamics are generally more complex—they require more parameters to specify— than uniform evolutionary models such as random walks and stasis. The Akaike Information Criterion can be used to judge whether the greater complexity of punctuational models is offset by a sufficient gain in log-likelihood for these models to be preferred.