A Markov model of substitution

Replacements within DNA sequences can be described and modelled by a Markov process with four states. Each state represents one base -- Adenine, Cytosine, Guanine or Thymine (see figure 2.2).

Figure 2.2: Markov model for nucleotide evolution in DNA sequences

Lots of assumptions are made in order to make phylogenetic reconstructions more computationally feasible. First, each nucleotide is supposed to evolve independently of other sites evolution and of its past history. We suppose there is no interaction between sites and we treat them independently. Further, the Markov process of substitution is assumed to be the same across all sites (spatial homogeneity). Finally, the process is assumed to remain constant over time (stationary) and time homogeneous, i.e., nucleotide frequencies and substitution rates can be assumed constant through time and across all sites in an alignment.

One might concede that assumptions made for the nucleotide evolutionary process are not strictly valid. Actual data shows some discrepancies, e.g., heterogeneous selection pressure, unequal base frequencies among species, .... We can relax these assumptions and allow for substitution rate variation across sites with the gamma model of Yang (1994). It is also possible to use multiple substitution processes simultaneously when heterogeneous data are analysed (see section 2.4.2).

In spite of their name, DNA models can naturally be used for the treatment of the loops within RNA sequences (see figure 2.3). In RNA loops, nucleotides are not subject to any structural constraints and they are assumed to evolve independently from other sites. Therefore, the use of similar Markov models for nucleotide evolution in RNA loops is appropriate.