Polytomies and Phylogenetically Independent Contrasts: Examination of the Bounded Degrees of Freedom Approach

Abstract

Abstract.-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 phylogenetically independent contrasts for estimating a bivariate correlation. We speci cally tested the adequacy of bounding degrees of freedom, as suggested by Purvis and Garland (1993; Syst. Biol. 42:569-575). We simulated bivariate character evolution under Brownian motion (assumed by independent contrasts) and eight other models on ve phylogenetic trees. For non-Brownian motion simulations, the adequacy of branchlength standardization was checked 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 model, degrees of freedom were appropriately bounded for hypothesis testing, and unbiased estimates of the correlation coef cient were obtained. Our results, along with those of previous simulation studies, suggest that independent contrasts can reliably be applied to real data, even with phylogenetic uncertainty.

Laboratory endurance capacity predicts variation in field locomotor behaviour among lizard species

“…1) contained some polytomies (unresolved nodes), indicating branches whose phylogenetic placement is uncertain (one for PTM, two for MPM, and one for DMD). Therefore, to be maximally conservative in the analyses with independent contrasts (see Purvis & Garland 1993;Garland & Díaz-Uriarte, in press), degrees of freedom for hypothesis testing were reduced by one, two and one, respectively, yielding 12, 9 and 8. All tests for associations between movement variables and endurance were one tailed, consistent with the directional hypothesis (see Introduction), and statistical significance was judged at P<0.05.…”

The smallest avian genomes are found in hummingbirds

“…One degree of freedom was subtracted for each branch in the single polytomy (Purvis & Garland 1993;Garland & Díaz-Uriarte 1999). Mass-corrected PICs were conducted in MESQUITE by first performing independent contrast correlations between parameter 1 (e.g.…”

Genome size and wing parameters in passerine birds

“…However, all significant relationships were repeated following each of the branch length methods of Grafen, Nee and Pagel as given in MESQUITE (Maddison & Maddison 2008). One degree of freedom was subtracted for each branch in soft polytomies (Purvis & Garland 1993;Garland & Díaz-Uriarte 1999). Mass-corrected PICs were conducted in MESQUITE by first performing independent contrast correlations between parameter 1 (e.g.…”