The Shapes of Neutral Gene Genealogies in Two Species: Probabilities of Monophyly, Paraphyly, and Polyphyly in a Coalescent Model

The genealogies of samples of orthologous regions from multiple species can be classified by their shapes. Using a neutral coalescent model of two species, I give exact probabilities of each of four possible genealogical shapes: reciprocal monophyly, two types of paraphyly, and polyphyly. After the divergence that forms two species, each of which has population size N, polyphyly is the most likely genealogical shape for the lineages of the two species. At approximately 1.300N generations after divergence, paraphyly becomes most likely, and reciprocal monophyly becomes most likely at approximately 1.665N generations. For a given species, the time at which 99% of its loci acquire monophyletic genealogies is approximately 5.298N generations, assuming all loci in its sister species are monophyletic. The probability that all lineages of two species are reciprocally monophyletic given that a sample from the two species has a reciprocally monophyletic genealogy increases rapidly with sample size, as does the probability that the most recent common ancestor (MRCA) for a sample is also the MRCA for all lineages from the two species. The results have potential applications for the testing of evolutionary hypotheses.