EVALUATING THE COMPATIBILITY BETWEEEN MORPHOLOGICAL CHARACTERS AND STRATIGRAPHY

Phylogenetic analyses require assumptions about rates of character change. Here we discuss using compatibility between stratigraphic data and morphological character states as a means of evaluating characters prior to phylogenetic analyses. Two characters are compatible if the observed combinations of character states do not necessarily imply homoplasy (e.g., a binary pair showing only 00, 01 and 11). Simulations demonstrate that character compatibility decreases as rates of change and homoplasy increase. A compatible pair of characters is also compatible with stratigraphy if there are no gaps in the state pairs for each character (e.g., continuous ranges for all taxa with 00, 01, etc.). Simulations indicate that at sampling levels typical of marine invertebrates, stratigraphic incompatibility typically reflects homoplasy rather than sampling error. However, at rates typical of some terrestrial taxa, stratigraphic incompatibility reflect gaps in sampling as often as it reflect homoplasy. Variable sampling compounds this, especially when we frequently sample only one taxon in a time interval. Analyses of numerous groups show that stratigraphic compatibility is fairly high in many molluscan and echinoderm groups as well as among many mammals. Stratigraphic compatibility tends to be low among trilobites. However, this reflects very low character compatibility that typifies trilobites. Simulations show that given the high rates of homoplasy needed to achieve such low compatibility among trilobite morphological characters. Trilobite sampling rates must be fairly high to achieve observed stratigraphic compatibility. Unsurprisingly, stratigraphic compatibility tends to be fairly low among many dinosaur clades. For many taxa, stratigraphic compatibility can add power to compatibility tests for assessing relative rates among characters. Likelihood curves for rates of character change often are much steeper given stratigraphic compatibility than they are when given just character compatibility. Such tests can evaluate ideas about character evolution (such as rejecting “equal weights”) before making them models and should further improve tests and inferences of phylogeny.