An introduction to phylogenetically based statistical methods, with a new method for confidence intervals on ancestral values

American Zoologist, Apr 1999 by Garland, Theodore Jr, Midford, Peter E, Ives, Anthony R

As developed by Martins and Hansen (1997), estimates of trait values at the basal node can also be obtained using generalized least-squares models (Judge et al., 1985). As will be shown in detail elsewhere (Garland and Ives, in preparation), generalized least-squares estimators produce identical results to the explicit equations derived by use of the independent contrasts formalism. Although the generalized least-squares approach gives estimates only for the basal node, estimates of trait values at other internal nodes can be obtained by reconfiguring the phylogenetic tree to place the node in question at the base, as with the independent contrasts approach presented here.

Populations, species, and higher taxa as data points

A typical comparative data set consists of estimates of the average values for one or more phenotypic traits for each of several species. Sometimes data are available for multiple subspecies or populations within a species. If the phylogenetic relationships of these are known (or assumed) and gene flow is low, then the populations can add to the overall sample size just as if they were separate "species" (Garland et al., 1992; Garland and Adolph, 1994; Foster and Cameron, 1996; Bauwens and Diaz-Uriarte, 1997; Pierce and Crawford, 1997). If gene flow occurs in a complicated fashion across the multiple populations, then difficulties arise because most analytical methods presume that phylogenetic relationships are divergent rather than reticulate (but see below on the phylogenetic autocorrelation approach). In the simplest case of two populations from a given species, gene flow between them only (potentially) shortens the branch lengths that should be used for analyses. Thus, we have suggested that a good design for a comparative study might be to include pairs of populations from each of a series of species (Garland et al., 1992). The population differences would then provide information on microevolutionary (withinspecies) phenomena, whereas differences among species and higher nodes would inform about macroevolutionary phenomena.

When data sets are derived from the literature, it may only be possible to obtain a composite estimate of the average value for a species. That is, information from several different references, often involving different populations, may be averaged or otherwise combined to yield a single value that is then used to represent the species (e.g., Clobert et al., 1998). Obviously, this sort of procedure must be undertaken cautiously, because population differences are common both at the level of genotype and phenotype (Garland and Adolph, 1991). At higher taxonomic levels, and under the assumption that the taxa are monophyletic, data for different species are sometimes combined to yield an estimate of the average value for, say, a genus (e.g., Moreno and Carrascal, 1993). In any case, a typical comparative data set consists of "average" values for a set of populations, subspecies, species or even higher taxa. For simplicity, we have referred to all such data points as "species."