Papers in the Biological Sciences


Date of this Version



13068–13070 | PNAS | December 12, 2017 | vol. 114 | no. 50


the Papers in the Biological Sciences at DigitalCommons@University of Nebraska - Lincoln


Fossil data provide copious evidence that anatomical (morphological) change within individual lineages is not constant: short bursts of great change commonly separate long durations of little change (1, 2). Despite this, most models of morphological change assume that probabilities of morphological character change are the same from one generation to the next: even if rates change over time—such as in “Cambrian explosion” or “early burst” models, where high disparity among anatomies evolves early—then it is still assumed that fast rates of continuous character change gave way to slow rates of continuous change (3). In statistical parlance, early bursts usually are modeled as nonstationary processes (usually lognormal for continuous data such as size, or Poisson for discrete characters, such as presence/absence of structures) in which some instantaneous rate of change declines over time. In contrast, null hypotheses are modeled as stationary processes in which the instantaneous rate does not shift over time. However, both null and test models assume that the processes underlying anatomical change are continuous-time processes, with instantaneous probabilities of change or amounts of change.

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