A MULTIVARIATE APPROACH TO RANDOM WALKS IN THE FOSSIL RECORD

One approach to the study of evolutionary time series as observed in the fossil record is to compare the observed pattern of evolutionary change to a mathematical null model of evolutionary change based on a random walk. A variety of univariate statistical tests have been proposed and used for this purpose. These tests have a high type II error rate: they frequently fail to recognize patterns known to be a result of directed selection and stabilizing selection are significantly different from a random walk. Thus, we should view with some caution finding of no significant difference from a random walk when employing these univariate tests. We present a multivariate statistical test against the null model of a random walk, utilizing landmark-based geometric morphometrics to capture information about organismal shape. Based on numerical simulation results, this multivariate Monte Carlo test has substantially higher statistical power (lower rates of Type II error) than the univariate version of the same test. The results of the application of the Multivariate Monte Carlo test to two landmark-based evolutionary time series from the fossil record, the trilobite Triarthrus becki, and the primate lineage Cantius, demonstrate the utility of the test.