Polytomies and phylogenetically independent contrasts: Examination of the bounded degrees of freedom approach

We examined the effect of soft polytomies on the performance (Type I error rate and bias) of Felsenstein's (1985; Am. Nat. 125:1-15) method of phyloge netically independent contrasts for estimating a bivariate correlation. We specifically tested the adequacy of bounding degrees of freedom, as suggest ed by Purvis and Garland (1993; Syst. Biol. 42:569-575). We simulated bivar iate character evolution under Brownian motion (assumed by independent cont rasts) and eight other models on five phylogenetic trees. For non-Brownian motion simulations, the adequacy of branch-length standardization was check ed with a simple diagnostic (Garland et al., 1992; Syst. Biol. 41: 18-32), and transformations were applied as indicated. Surprisingly soft polytomies tended to have negligible effects on Type I error rates when models other than Brownian motion were used. Overall, and irrespective of evolutionary m odel, degrees of freedom were appropriately bounded for hypothesis testing, and unbiased estimates of the correlation coefficient were obtained. Our r esults, along with those of previous simulation studies, suggest that indep endent contrasts can reliably be applied to real data, even with phylogenet ic uncertainty.