EARLY BURSTS OF EVOLUTION ARE RARE? LET'S GET THE RATES RIGHT!
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.