Effects of branch length errors on the performance of phylogenetically independent contrasts.

We examined Type I error rates of Felsenstein's (1985; Am. Nat. 125:1-15) comparative method of phylogenetically independent contrasts when branch lengths are in error and the model of evolution is not Brownian motion. We used seven evolutionary models, six of which depart strongly from Brownian motion, to simulate the evolution of two continuously valued characters along two different phylogenies (15 and 49 species). First, we examined the performance of independent contrasts when branch lengths are distorted systematically, for example, by taking the square root of each branch segment. These distortions often caused inflated Type I error rates, but performance was almost always restored when branch length transformations were used. Next, we investigated effects of random errors in branch lengths. After the data were simulated, we added errors to the branch lengths and then used the altered phylogenies to estimate character correlations. Errors in the branches could be of two types: fixed, where branch lengths are either shortened or lengthened by a fixed fraction; or variable, where the error is a normal variate with mean zero and the variance is scaled to the length of the branch (so that expected error relative to branch length is constant for the whole tree). Thus, the error added is unrelated to the microevolutionary model. Without branch length checks and transformations, independent contrasts tended to yield extremely inflated and highly variable Type I error rates. Type I error rates were reduced, however, when branch lengths were checked and transformed as proposed by Garland et al. (1992; Syst. Biol. 41:18-32), and almost never exceeded twice the nominal P-value at alpha = 0.05. Our results also indicate that, if branch length transformations are applied, then the appropriate degrees of freedom for testing the significance of a correlation coefficient should, in general, be reduced to account for estimation of the best branch length transformation. These results extend those reported in Díaz-Uriarte and Garland (1996; Syst. Biol. 45:27-47), and show that, even with errors in branch lengths and evolutionary models different from Brownian motion, independent contrasts are a robust method for testing hypotheses of correlated evolution.