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,...

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