A0316
Title: On the role of phase type distributions in population genetics
Authors: Andreas Futschik - JKU Linz (Austria) [presenting]
Asger Hobolth - Aarhus University (Denmark)
Mogens Bladt - University of Copenhagen (Denmark)
Iker Rivas-Gonzalez - Aarhus University (Denmark)
Abstract: A phase-type distribution describes the time to absorption in a continuous- or discrete-time Markov chain. Phase-type distributions have been successfully used in different fields of applied probability. The aim is to investigate how results from phase type theory can be applied to derive properties of the Kingman-coalescent process, which is used to model the genealogy of samples of DNA sequences in population genetics. Features such as the time to the most recent common ancestor and the total branch length are phase-type distributed. Reward transformations lead to easy calculation of covariances and correlation coefficients between, e.g., tree height, tree length, external branch length, and internal branch length. A further result is that the site frequency spectrum follows a multivariate discrete phase-type distribution. Together with properly specified rewards, phase-type distributions can also be used to derive likelihood functions for statistical inference. Providing an alternative to previous work based on the Laplace transform, likelihoods for small-size coalescent trees are derived based on phase-type theory. Their application to statistical inference is also explored.
