RATES OF PHENOTYPIC EVOLUTION: ARTIFACTS, TEMPORAL SCALING AND A RECOMMENDATION

Rates of phenotypic evolution are usually measured as the difference in morphology between ancestral and descendant populations, divided by elapsed time. Gingerich has shown that rates measured in this manner show a strong inverse relationship with the interval over which they are observed. Many causes have been invoked to account for this temporal scaling of rates, including: evolutionary reversals of direction, plotting a ratio versus its denominator, and limits on the minimum detectable and maximum feasible rates.

Here I discuss an alternative rate metric that is based on the single generating parameter of the unbiased random walk model. This metric, called &Delta when proposed by Lynch, has very broadly useful properties, such as being estimable from phylogenetic as well as ancestor -- descendant relationships. Perhaps most importantly, it can be shown that &Delta is independent of temporal scaling when phenotype truly evolves as a random walk.

I have used this metric to measure evolutionary rates in a large set of stratophenetic series, and in a much smaller number of phylogenetic data sets. Despite the fact that &Delta avoids or mitigates the putative causes of time-scale dependence, an inverse relationship between evolutionary rate (measured as &Delta) and elapsed time persists in these data sets. These results suggest that rates of evolution are, in a meaningful sense, faster when observed over shorter temporal scales; the inverse temporal scaling is not simply a statistical artifact. The negative temporal scaling of &Delta indicates that morphological evolution generally deviates from an unbiased random walk in showing less morphological change over longer intervals than would be predicted from shorter-term excursions, implicating stabilizing selection (or other conservative processes) in limiting long-term divergence. While it can be straightforward to devise a rate metric that is uncorrelated with elapsed time under specific modes of evolution, it is probably not possible to measure rates in a way that works equally well under different evolutionary modes (e.g., random walks, stasis, directional change). Nevertheless, because of its statistical and practical advantages over traditionally defined rates, &Delta is recommended for general use as the best of the currently available options.