Fig. 3. (A) Illustration of what conventional statistical analyses assume when applied to comparative data (`star' phylogeny with equal-length branches). This model implies that values at tips of the tree (phenotypic means for some trait for 10 species) are statistically independent and identically distributed. (B) Phylogenetic tree that might be inferred from taxonomic information, e.g. if five genera within a single family were represented that contained, from left to right, one, one, three, three and two species in the data set. This assumes that the genera are an unrelated series of `mini-stars' with no hierarchical structure within any of them. It also assumes that the taxa actually represent separate evolutionary lineages (monophyletic groups or clades), but such is not always the case for taxonomies. (C) Estimates of real phylogenies usually indicate hierarchical relationships and branches that do not necessarily line up along the tips of the tree. Non-contemporaneous tips can indicate that extinct taxa are included in the data set or that the rate of evolution has varied among branches. Real phylogenies like this cause various statistical problems, stemming from the non-independence of species' phenotypes, so phylogenetically based statistical methods are required for proper analyses. Modified from Garland (2001) and Rezende and Garland (2003).