Phylogenetic Covariance Probability: Confidence and Historical Associations

Abstract

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 coevo- lution. 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 as- sessing 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 confi- dence 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 his- torical 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 noncor- related associations in the observed hypothesis, and to the relative information content contrib- uting to that hypothesis. (Biogeography; BPA; coevolution; confidence; historical associations; ran- domization.) Although biogeography and host-para- site association studies are relatively com- mon, rarely is there an attempt to quantify the strength of the support for historical association. Borrowing from correlation analysis, an r value provides an estimate of the goodness of fit of a function. Con- fidence in the relationship is expressed in terms of a P value, the probability that an equally efficient result could be achieved by chance. In questions of historical asso- ciation, the notion that congruence be- tween independently derived cladograms is fundamentally a probabilistic issue has been widely acknowledged (Metcalf, 1929: 4; Rosen, 1978:160; Brooks, 1979:303, 1981: 229; Nelson, 1979:8; Nelson and Platnick, 1981:312; Mitter and Brooks, 1983:85), as is the notion that discovering the extent of historical association is fundamentally an exercise in determining the degree of cor- relation between the associates' phyloge- netic histories (Kellogg, 1913:158; Brooks, 1979:300, 1981:235, 1988:249; Nelson and