Evolutionary change of restriction cleavage sites and phylogenetic inference

Mathematical formulas are developed for the evolutionary change of restriction cleavage sites in a DNA sequence, allowing unequal rates between transitional and transversional types of nucleotide substitution. Formulas are also developed for the probability of having a particular pattern of site changes among evolutionary lineages, such as parallel gains or losses of sites, and for inferring the presence or absence of a restriction site in an ancestral sequence from data on the present-day sequences. The unordered compatibility method is proposed for inferring the phylogenetic relationships among relatively closely related organisms, treating restriction sites as cladistic characters. Formulas are derived for the probability (P+) of obtaining the correct network for a given number (N) of informative sites for the cases of four and five species. These formulas are applied to evaluate the performance of the method and to estimate the N value required for P+ to be 95% or larger. The method performs well when the branches between ancestral nodes and the branches leading to the two most recent species are more or less equal in length, but performs poorly when the latter two branches are considerably longer than the former.