2014 GSA Annual Meeting in Vancouver, British Columbia (19–22 October 2014)

Paper No. 144-7
Presentation Time: 2:45 PM


GINGERICH, Philip D., Museum of Paleontology and Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI 48109, gingeric@umich.edu

Paleontologists have classically viewed adaptive radiations as involving an early burst of diversification from an ancestral stock, with rapid divergence in morphology followed by slower diversification and divergence. A recent study of many extant animal groups published by Harmon et al. in Evolution found that adaptive radiations are rare compared to random walk models. Here I compare an early burst model for the evolution of size to a random walk model. The Harmon et al. evidence included (1) clade age; and (2) net ‘variance’ in trait means per million years (m.y.) in units of within-population standard deviations (s.d.). Forty-two clades were found to have a mean rate of divergence in body size of 0.74 s.d./m.y.; an average time depth (time scale) of 24 m.y.; and consequently a mean divergence of 17.8 s.d. units. Average generation (gen.) time is 1.71 years, so the average rate of divergence corrected from Harmon et al. is D7.15 = 4.33 × 10-7 s.d./gen. on a time scale of 1.40 × 107 gen.

The dispersion of a random-walk evolutionary time series increases in proportion to the square root of time. For most lineages (95%) to lie within 8.9 s.d. of the starting value (a range of 17.8 s.d.), a rate of dispersion, D0 on a time scale of one generation, is required. Here 1.96 × D0 × √(1.40 × 107) = 17.8 s.d. Solving, D0 can be as small as 2.42 × 10-3 s.d./gen. (a much higher rate than the Harmon et al. 4.33 × 10-7 s.d./gen.). If D0 is as high as 0.10 s.d./gen., a rate commonly found in scaling studies, then the time required to fill a range of 17.8 s.d. is 8.25 × 103 gen. (much less than 1.40 × 107 gen.).

What happens when the range of possible variation is filled? When a range is filled, diversification is necessarily much slower for the remaining 1.40 × 107 generations. We can quibble about details, but any reasonable rates will yield an early burst of diversification with rapid evolution, followed by a long interval of much slower diversification to yield what we see today. Harmon et al.’s average rate of divergence D7.15 = 4.33 × 10-7 s.d./gen. is a rate on a time scale irrelevant to the evolutionary process. D7.15 = 4.33 × 10-7 s.d./gen. is also a rate averaged when it should have been scaled: average rates are meaningless when their time scales are different.