The implications of stratigraphic compatibility for character integration among fossil taxa

Two characters are stratigraphically compatible if some phylogenies indicate that their combinations (state-pairs) evolved without homoplasy and in an order consistent with the fossil record. Simulations assuming independent character change indicate that we expect approximately 95% of compatible character pairs to also be stratigraphically compatible over a wide range of sampling regimes and general evolutionary models. However, two general models of rate heterogeneity elevate expected stratigraphic incompatibility: “early burst” models, where rates of change are higher among early members of a clade than among later members of that clade, and “integration” models, where the evolution of characters is correlated in some manner. Both models have important theoretical and methodological implications. Therefore, we examine 259 metazoan clades for deviations from expected stratigraphic compatibility. We do so first assuming independent change with equal rates of character change through time. We then repeat the analysis assuming independent change with separate “early” and “late” rates (with “early” = the first third of taxa in a clade), with the early and late rates chosen to maximize the probability of the observed compatibility among the early taxa and then the whole clade. We single out Cambrian trilobites as a possible “control” group because morphometric studies suggest that integration patterns are not conserved among closely related species. Even allowing for early bursts, we see excess stratigraphic incompatibility (i.e., negative deviations) in significantly more clades than expected at 0.50, 0.25, and 0.05 P values. This pattern is particularly strong in chordates, echinoderms, and arthropods. However, stratigraphic compatibility among Cambrian trilobites matches the expectations of integration studies, as they (unlike post-Cambrian trilobites) do not deviate from the expectations of independent change with no early bursts. Thus, these results suggest that processes such as integration strongly affect the data that paleontologists use to study phylogeny, disparity, and rates.