Abstract:
When comparative biologists observe that animal species living in caves also tend to have reduced eyes, they may see such correlation as evidence that the traits are adaptively or functionally linked: for instance, selection to maintain eye function is relaxed when light is unavailable. Such cross-species correlations cannot give definitive tests of evolutionary mechanisms, but nonetheless offer important insights into biological relationships among traits in realms as diverse as ecology (e.g., Paradis et al. 1998; Purvis et al. 2000) and genomics (e.g., von Mering et al. 2002; Barker and Pagel 2005). However, the last few decades have taught us that among-species correlative tests should take into account evolutionary relationships (Felsenstein 1985; Ridley 1989; Harvey and Pagel 1991). If phylogeny is not taken into account, an interpreted correlation may have a trivial explanation different from the biological relationship we claim. There is a correlation among species in the distribution of fur and bones in the middle ear—species with fur also have three bones in the middle ear, and vice versa. These two traits are characteristics of mammals, and absent outside the mammals. Using their shared distribution as evidence of an interesting biological relationship between fur and middle ear bones would be considered a mistake, however, for reasons understood long ago by Darwin (1872): We may often falsely attribute to correlated variation structures which are common to whole groups of species, and which in truth are simply due to inheritance; for an ancient progenitor may have acquired through natural selection some one modification in structure, and, after thousands of generations, some other and independent modification; and these two modifications, having been transmitted to a whole group of descendants with diverse habits, would naturally be thought to be in some necessary manner correlated. In modern vocabulary, we would say that the thousands of species of mammals are not statistically independent because of their shared history (Felsenstein 1985; Ridley 1989), instead being pseudoreplicates. Many methods have been developed to avoid pseudoreplication while assessing cross-species correlations by accounting for phylogenetic relationships (e.g., Felsenstein 1985; Maddison 1990; Harvey and Pagel 1991; Garland et al. 1992;Pagel 1994;ReadandNee 1995;MartinsandHansen 1997; Huelsenbeck et al. 2003; Hadfield and Nakagawa 2010). These phylogenetically aware correlation methods have been applied with enthusiasm, although there have been skeptics questioning their need (Westoby 1999) and cautions expressed over their use (Ricklefs and Starck 1996; Freckleton 2009). Not all is healthy with the paradigm, however. For categorical characters a special concern has been raised: commonly used and well-respected methods (e.g., Pagel 1994), do not eliminate pseudoreplication, as they are susceptible to an effect from a single evolutionary event (Maddison 1990, 2000; Read and Nee 1995; Ridley and Grafen 1996; Grafen and Ridley 1997). As a result, a significant statistical association between traits inferred by these methods can mean very little in some circumstances, misleading biologists about the relationship between traits. Although this concern has been raised, there has been little effect on the practice of comparative studies, we think because the issue has not been well understood. We do not, alas, have a solution. Our purpose here is to explore the issue in depth in part to bring caution to comparative studies, in part to characterize how our methods should behave in hopes of provoking appropriate solutions.