Congruence between phylogeny and stratigraphy: Randomization tests and thegap excess ratio

Stratigraphic congruence indices (e.g., stratigraphic consistency index [SC I] of Huelsenbeck, 1994, Paleobiology 40:563-569; relative completeness ind ex [RCI] of Benton, 1994, Trends Ecol. Evol. 9:181-185 [not to be confused with the rescaled consistency index of Farris, 1989, Cladistics 5:417-419]) are increasingly being quoted for cladograms containing fossil taxa. Howev er, like the character consistency index (CI, summed over all characters), these values cannot be compared for trees derived from different data sets. Just as the number of characters and taxa in data matrices affects typical CI values, so tree balance and the distribution of stratigraphic ranges la nd indirectly tree size) delimit the range of congruence indices that can b e obtained. Because investigators often seek to compare the performance of cladograms from different sources (e.g., different taxa, habitats, periods in history), indices of fit insensitive to these factors are desirable. Two approaches are proposed here: (1) The gap excess ratio (GER) is a new metr ic that controls for the distribution of range data but is sensitive to dif ferences in tree balance. The GER expresses the difference between the mini mum implied gap (MIG; the total ghost range implied by a given set of strat igraphic ranges on a given tree) and G(min) (the minimum possible ghost ran ge for those data on any tree) as a fraction of the range of values possibl e for those stratigraphic data on any tree. Rather than reflecting inferred completeness of the fossil record las does the RCI, which is only partiall y determined by cladistic constraints), the GER indicates congruence alone. (2) Randomization tests hold most potentially conflated parameters constan t and compare the observed RCI or GER index with the distribution of indice s obtained by randomly reassigning range data over the tree. This enables u s to deduce whether the MIG is significantly less (i.e., shows greater cong ruence) than for random permutations of the same range data. Stratigraphic congruence indices have been invoked as an ancillary criterion for assessin g competing hypotheses of relationships derived from different sources or f or choosing between equally parsimonous trees derived from the same charact er matrix. The first application is illustrated with comparisons of actinop terygian and eutherian phylogenies, and the second is illustrated with a st udy of trees for fossil and Recent arthropods.