Vertebrate body size jumps the Wright way

Abstract

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. In PNAS, Landis and Schraiber (4) put continuous-time models of anatomical evolution to the test. Although numerous studies do this using fossil data (1, 2, 5), Landis and Schraiber (4) do this using size data and phylogenetic estimates from extant taxa only. Under their model, anatomical change happens in pulses, with a probability of some time t between pulses given by a Levy process. Suppose that we simulate phylogenetic evolution and change for some continuous trait, such as size, under both continuous time and Levy processes. Under a continuous-time model, our computer generates some number between 0 and 1 for each lineage at each time step, which we then use to determine some small amount of change following, for example, a … [↵][1]1Email: pwagner16{at}unl.edu. [1]: #xref-corresp-1-1