An independent heterotachy model and its implications for phylogeny and divergence time estimation.

Heterotachy or variation of rates-across-sites and lineages is widespread (e.g., Fitch and Markowitz, 1970; Uzzel and Corbin, 1971; Lopez et al., 2002) and can cause biased tree estimation (Lockhart et al., 1998; Susko et al., 2004; Inagaki et al., 2004). Kolaczkowski and Thornton (2004) described an intriguing heterotachy model that lead to topological bias for likelihood-based methods. That work generated a significant amount of discussion (e.g., Spencer et al., 2005; Lockhart and Steel, 2005; Gadagkar and Kumar, 2005) and raises questions about what forms of heterotachy might create these effects. Here we consider a model that we will refer to as the random effects rate variation model (RERV) which differs from common evolutionary models only in that the rate at a site is assigned independently to each edge in the tree according to a gamma distribution. In contrast, in the commonly used gamma rates-across-sites model of Yang (1993, 1994), each site has a different rate drawn from a gamma distribution but this rate is fixed for all edge lengths. The main heterotachy model that has been implemented in practice is the covarion or covariotide model described in Huelsenbeck (2002) and Galtier (2001). The model considered here similarly allows rates to vary across sites and lineages but has computational advantages. By comparison with covarion implementations, the model does not require a two-dimensional Markov chain implementation and compared with gamma rates-across-sites models, which