Reconstructing the Prior Probabilities of Allelic Phylogenies

In general when a phylogeny is reconstructed from DNA or protein sequence data, it makes use only of the probabilities of obtaining some phylogeny given a collection of data. It is also possible to determine the prior probabilities of different phylogenies. This information can be of use in analyzing the biological causes for the observed divergence of sampled taxa. Unusually "rare" topologies for a given data set may be indicative of different biological forces acting. A recursive algorithm is presented that calculates the prior probabilities of a phylogeny for different allelic samples and for different phylogenies. This method is a straightforward extension of Ewens' sample distribution. The probability of obtaining each possible sample according to Ewens' distribution is further subdivided into each of the possible phylogenetic topologies. These probabilities depend not only on the identity of the alleles and on 4N(mu) (four times the effective population size times the neutral mutation rate) but also on the phylogenetic relationships among the alleles. Illustrations of the algorithm are given to demonstrate how different phylogenies are favored under different conditions.