Edited by Neil H. Shubin, The University of Chicago, Chicago, IL, and approved October 6, 2017 (received for review June 18, 2017)
The diversity of forms found among animals on Earth is striking. Despite decades of study, it has been difficult to reconcile the patterns of diversity seen between closely related species with those observed when studying single species on ecological timescales. We propose a set of models, called Lévy processes, to attempt to reconcile rapid evolution between species with the relatively stable distributions of phenotypes seen within species. These models, which have been successfully used to model stock market data, allow for long periods of stasis followed by bursts of rapid change. We find that many vertebrate groups are well fitted by Lévy models compared with models for which traits evolve toward a stationary optimum or evolve in an incremental and wandering manner.
The relative importance of different modes of evolution in shaping phenotypic diversity remains a hotly debated question. Fossil data suggest that stasis may be a common mode of evolution, while modern data suggest some lineages experience very fast rates of evolution. One way to reconcile these observations is to imagine that evolution proceeds in pulses, rather than in increments, on geological timescales. To test this hypothesis, we developed a maximum-likelihood framework for fitting Lévy processes to comparative morphological data. This class of stochastic processes includes both an incremental and a pulsed component. We found that a plurality of modern vertebrate clades examined are best fitted by pulsed processes over models of incremental change, stationarity, and adaptive radiation. When we compare our results to theoretical expectations of the rate and speed of regime shifts for models that detail fitness landscape dynamics, we find that our quantitative results are broadly compatible with both microevolutionary models and observations from the fossil record.
Author contributions: M.J.L. and J.G.S. designed research, performed research, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
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