Accounting for unequal variances in evolutionary trend mechanisms

Abstract

Evolutionary trends seemingly abound throughout the history of life. Perhaps the best-known example is Cope's rule, the tendency for lineages to increase in size over time. Other examples include hypothesized trends toward increasing complexity and fitness. What kinds of mechanisms cause such large-scale trends—trends occurring in higher taxa over geological time spans—and how can we effectively visualize them? In a seminal paper, Stanley (1973) proposed that apparent directional trends such as Cope's rule can result from unbiased change away from small initial values, analogous to diffusion away from a lower bound. Fisher (1986) generalized this idea, and Gould (1988, 1996) argued that such trends are properly viewed as increases in variance rather than trends in the average. These types of trend mechanisms were labeled by McShea (1994) as passive, in contrast to driven mechanisms in which change is biased in a particular direction because of (for instance) adaptive benefit or ontogenic constraint. In McShea's usage (McShea 1994, 1998b, 2000), the passive and driven categories include a broad range of evolutionary dynamics, of which unbiased diffusion and biased change are the simplest. More generally, McShea defines a driven trend mechanism as one resulting from an unstructured state space in which rates of change, speciation, and extinction are constant for all lineages. In contrast, a passive trend mechanism is one in which change among lineages follows a state space in which the rates vary in a structured way (McShea 2000). A similar distinction is the passive/active classification proposed by Wagner (1996), although Wagner's active trends constitute a broader category than McShea's driven trends. Much empirical and methodological work has been devoted to distinguishing passive and driven trends. Some recent papers in the paleontological literature include those of Carlson (1992), Boyajian and Lutz (1992), McShea (1993, …