Branch lengths and support.

Although technical definitions exist for various support metrics, the notion of support per se has received little explicit attention. Thus, despite its widespread use in phylogenetics, “support” is absent from the glossaries and/or indices of several recent texts (e.g., Kitching et al., 1998; Page and Holmes, 1998; Schuh, 2001). Farris et al. (2001) recently argued that interpreting branch lengths of trees as indicative of support for corresponding groups is both common and unfortunate. To support their claim, they presented two contrived examples in which “long branches do not indicate support and in fact create a highly misleading impression if so interpreted” (Farris et al., 2001:298). Here, we argue that Farris et al.’s claim presupposes a particular view of support and that their conclusions do not hold under an alternative and reasonable perspective that they did not discuss. Farris et al.’s first example is very simple. Consider four species, A–D, and data comprising 500 characters, “of which half split the terminals AB/CD and the rest AC/BD” (Farris et al., 2001:298). There are two mostparsimonious trees, AB/CD and AC/BD. Farris et al. pointed out that the consensus of these trees is unresolved and that the decay indices (=Bremer support) of the single internal branch of each tree are therefore 0 despite these branches having a parsimony length of 250 steps. Farris et al. offered no explicit definition of support, but we assume that they view relationships as supported only if they are present in all the optimal trees and therefore in the consensus. In the context of parsimony analysis, this view corresponds to Nixon and Carpenter’s (1996) notion of strictly supported relationships, under which it is not possible for data to support alternative incompatible phylogenetic hypotheses (see also Farris, 2001). However, support need not be construed in this way. Our preferred interpretation of Farris et al.’s first example is that the data support two alternative hypotheses equally. To say that half the characters split the terminals AB/CD and the rest split AC/BD is to say that half the characters support AB/CD and half support AC/BD. This seems to be a natural way to talk about the relationship between characters and hypotheses, without which the statement that characters “split the terminals” (upon which their example depends) requires some further explication. The alternative view that data may contain multiple signals that support a complex mix of incompatible hypotheses is not uncommon (e.g., Hendy and Penny, 1993; Lento et al., 1995; Wagele, 1996; Frohlich and Estabrook, 2000; Pisani and Wilkinson, 2002). Farris et al.’s “support” also appears to be a differential or relative concept. In their example, there is no differential support provided by the complete data set for AB/CD over AC/BD or vice versa, so they contend that neither hypothesis is supported. We agree that there is no differential support for one hypothesis over the other, but this is precisely because both hypotheses are equally (and nonnegatively) supported and equally contradicted. A problem with Farris et al.’s view becomes clear as soon as the third possible resolved tree, AD/BC, is also considered. In Farris et al.’s view, none of the hypothesis AB/CD, AC/BD, or AD/BC (Fig. 1a–c) is supported (none appears in the consensus tree, Fig. 1d), but this as a misleading and therefore unfortunate view of the relationship between the data and the hypotheses. Only for AD/BC is there no support, in the sense that there are no supporting characters. Further, there is extensive evidence against this hypothesis (the decay index of which is −500). Thus, using Farris et al.’s preferred measure, the data provide considerable evidence against AD/BC (or equivalently they support the hypothesis “not AD/BC”). This interpretation makes sense only if the data support the equivalent composite hypothesis, AB/CD or AC/BD, which does not seem coherent under Farris et al.’s conception of support. By focusing only on relationships in the consensus, Farris et al.’s view of support promotes a simplistic representation of potentially complex patterns of support and conflict that phylogeneticists might be better encouraged to explore than ignore. Split decomposition graphs, or