Phylogenetic covariance probability: Confidence and historical associations

The correlation that exists among multiple cladograms is often taken as evidence of some underlying macroevolutionary phenomenon common to the histories of those clades and, thus, as an explanation of the patterns of association of the constituent taxa. Such studies have various forms, the most common of which are cladistic biogeography and host-parasite coevolution. The issue of confidence has periodically been a theoretical consideration of vicariance biogeographers but in practice has been largely ignored by others. Previous approaches to assessing confidence in historical associations are examined here in relation to the difference between simple-event and cumulative probabilities and in relation to the restrictiveness of joint hypothesis testing. The phylogenetic covariance probability (PCP) test, a novel approach to assessing confidence in hypotheses of historical association, employs the empirical protocol of Brooks parsimony analysis (BPA) in an iterative, computer-intensive randomization routine. The PCP value consists of the frequency with which a solution as efficient or more efficient than the observed hypothesis of correlated phylogeny is achieved with random associations (e.g., of parasites and hosts or of taxa and areas). Because only the associations, and not the contributing phylogenies, are subjected to randomization, the test is not prone to certain criticisms leveled at other cladistic randomization routines. The behavior of the PCP test is examined in relation to eight published studies of historical association. This test is appropriately sensitive to the degrees of freedom allowed by the number of contributing clades and the number of taxa in those clades, to the extent of noncorrelated associations in the observed hypothesis, and to the relative information content contributing to that hypothesis.