D. D. Ackerly, D. S. Schwilk, and C. O. Webb. 2006. Niche evolution and adaptive radiation: testing the order of trait divergence. Ecology 87:S50–S61.

Appendix A. A discussion of alternative null models.

We have considered three approaches to testing the significance of the Divergence Order Test statistic (D), relative to the null hypothesis that D = 0. The first two are based on randomization techniques, while the third utilizes a bootstrapping approach to provide confidence intervals on D (see main text). We prefer the bootstrapping approach, but we present all three to highlight the importance of considering alternative null models when testing evolutionary hypotheses.

Method 1 - randomization of trait values: The first approach is based on the randomization of species trait values across the tips of the phylogeny. This randomization removes all phylogenetic signal from the data (Blomberg and Garland 2002), and on average it should also result in equal divergence ages (W) for the two traits. In evolutionary terms, tip randomization represents a deterministic model in which the exact same phenotypes are preserved (e.g., if a fixed set of niches were always filled), while relationships are completely randomized. A significant deviation in D, relative to this null, indicates that one or both traits violate the assumption of random distributions. Method 2 - randomization of contrasts: The second approach we consider is the randomization of contrasts across all nodes of the phylogeny. Under this method, the distribution of observed contrasts (i.e., evolutionary divergences) is treated as a fixed feature of the evolution of a group, but the age and phylogenetic position of the contrasts are randomized across the interior nodes of the tree (Ackerly and Donoghue 1998). The resulting distribution of species traits (were one to calculate it) would exhibit a degree of phylogenetic signal, as related species would derive their trait values from shared ancestors. However, the actual distribution of phenotypes among extant taxa is not preserved under this randomization. A significant value of D, relative to this null, indicates that large contrasts in one or both traits are significantly displaced towards early or late nodes. Note that under both of these null models, a significance test can be conducted for the values of W for each trait, as well as the difference between them (D). A somewhat unusual situation may also arise in which the W values diverge significantly from the null for both traits, but they are both shifted in the same direction, so D is close to 0 and not significantly different from the null hypothesis. Method 3 - bootstrapping ancestral values: The third method, presented in the paper, is based on bootstrapping the maximum likelihood estimates of ancestral states across the phylogeny. The rationale for this method is that comparative methods, particularly independent contrasts, tend to underestimate the magnitude of older divergences for rapidly evolving traits. As a simple example, consider a bifurcating tree with four species at the tips (Fig. A1). If the two pairs of sister taxa have similar trait values, reflecting rapid divergences, then the averages for their respective common ancestors will be virtually identical and the basal contrast will be nearly or exactly zero (Fig. A1c). However, given the rapid rate of evolution for this trait, it is also possible that a large divergence occurred at the first node, followed by reversals at the subsequent nodes resulting in convergence among the extant taxa. Maximum likelihood estimates of ancestral states allow for this possibility by placing confidence limits on the ancestors (Schluter et al. 1997). If a trait evolves rapidly, then the confidence limits at deeper nodes will be very large. Overall, the bootstrapping aprooach maintains the observed patterns of trait evolution, thus avoiding the problems outlined above for randomization methods. We use these ML estimates and their confidence limits to obtain bootstrap distributions of the potential magnitude of divergence events at each node (Fig. A1b, d). Hypothetical ancestral values are sampled from the distribution for each trait at each node, and from each sample the corresponding values of Cik, Cjk, Wi, Wj and D are calculated. (Note that the ancestral values and CI obtained from Schluter et al. 1997 are independent of each other, so there is no covariance in ancestral states among adjacent nodes; Ackerly 2004, D. Schluter, pers. comm.) We then examine the distribution of D values to determine whether D = 0 falls outside the 95% confidence limits on the mean, indicating significance of the observed values at p ² 0.05 (see published paper, Table 3).

LITERATURE CITED

Schluter, D., T. Price, A. Mooers, and D. Ludwig. 1997. Likelihood of ancestor states in adaptive radiation. Evolution 51:1699-1711.

TraitMean ageDN sig tips	N sig contrasts
SLA0.00657
January temperature0.004000.00257100	98
Precipitation0.004080.00249100	88

FIG. A1. Bootstrapping of contrast values based on maximum likelihood ancestral state reconstructions. A) Hypothetical four species phylogeny with values for a continuous trait. The horizontal location of points corresponds to the trait values for terminal taxa and reconstructed ancestral values for internal nodes from ANCML (Schluter et al. 1997). Error bars illustrate the 95% confidence intervals on ancestral states. B) Bootstrap distribution of the magnitude of the basal contrast for the phylogeny shown in A, based on 100 random samples of ancestral values drawn from the ML distributions at the two internal nodes. C) Hypothetical phylogeny, as in A, where the two two-species subclades exhibit convergent evolution on similar trait values. Note that the higher rate of evolution inferred from this pattern leads to wider confidence intervals at the internal nodes. D) Distribution of the basal contrast magnitude, as in B. Note that the modal contrast is 0, due to the overlapping trait values of the two subclades, but contrasts as high as 2.5 were observed in a sample of 100 random draws.