Application of the Likelihood Function in Phylogenetic Analysis

The likelihood of a phylogenetic tree is proportional to the probability of observing the comparative data (such as aligned DNA sequences) conditional on the tree. The likelihood function is important because it is the vehicle that carries the observations. The likelihood function can be used in two ways to infer phylogeny. First, the tree that maximizes the likelihood can be chosen as the best estimate of phylogeny; this is the method of maximum likelihood. Second, a prior probability distribution on trees can be specified and inferences based upon the posterior probability distribution of trees; this is the approach taken by Bayesians. Although maximum likelihood and Bayesian inference are similar in that the same models of DNA substitution can be used to calculate the likelihood function, they differ in their interpretation of probability. Markov chain Monte Carlo (MCMC) can be used to approximate the posterior probabilities of trees. MCMC also makes it possible to perform comparative analyses that accommodate phylogenetic uncertainty. Keywords: Bayesian inference; Markov chain Monte Carlo; maximum likelihood; phylogeny inference; poisson process