Modelling the Variability of Evolutionary Processes

The evolutionary processes that act at the molecular level are highly variable. For example, the substitution rates and the natural selection regimes vary extensively during the course of evolution and across sequence sites. This chapter describes the mathematical tools and concepts to describe and understand these variations. We show how the standard Markov models of sequence evolution are extended through mixture models to account for variability among sites, and how the mixture approach is further generalised by Markov-modulated Markov models (MMM) to incorporate variability among lineages. We illustrate these models using data sets from plants and human immunodeficiency virus type 1 (HIV-1). Both data sets are processed under the 3-component mixture codon-based model of Nielsen and Yang (1998) and its MMM extension (Guindon, 2004). We show that these models allow to get insight into important biological features such as positively selected sites at the surface of the envelope protein of HIV-1 and site-specific changes within selection regimes correlated to duplication events in plant genes.