The need for a statistical approach to molecular phylogeny is stressed by emphasizing the long-branch-attraction flaw of the maximum parsimony method. The basic theory of likelihood calculation in molecular phylogeny is introduced. Widely used Markov models of nucleotide evolution are reviewed and discussed. Then, two recent advances in the field are presented. The first one has to do with molecular evolutionary modes. Standard models used in molecular phylogeny assume a constant substitution matrix between lineages. Methods become biased when this assumption is violated (e.g., when base composition varies between sequences). A non-homogeneous, non-stationary model of DNA sequence evolution is proposed to correct the bias. This model allows unexpected accurate estimation of former base compositions. The method is applied to inferences about the thermophilic nature of the universal common ancestor.
The second issue has to do with molecular evolutionary rates. Standard models of site-specific rate distribution assume that every site evolves at a single, fixed rate of evolution (either constant or variable between sites). The covarion process of molecular evolution relaxes this assumption. In such a process, the rate of a site can change in time. A markov-modulated markov chain combining a process of rate evolution and a process of nucleotide evolution is proposed to model the covarion process. It is shown that site-specific rate variation is an important feature of rRNA sequence evolutionary process. Yet inferences about rRNA ancestral GC% are little affected by taking covarion into account. Covarion modelling is also useful for the purpose of detecting adaptation at the molecular level, as illustrated by an analysis of mammalian mitochondrial proteins.