The Maximum Likelihood Approach to Reconstructing Ancestral Character States of Discrete Characters on Phylogenies

A phylogeny describes the hierarchical pattern of descent of some group of species from a common ancestor. If information is available on the character states of the contemporary species, thepossibility is raised of using that information in combination with the phylogeny to reconstruct the historical events of evolution. These reconstructions can be used to retrieve a picture of theworld as the species evolved alongwhatwould become the branches of the phylogeny. This, in turn, provides a way to test hypotheses about evolution and adaptation. Methods based on the principle of parsimony reconstruct the ancestral character states to minimize the number of historical character changes required to produce the diversity observed among the contemporary species (seeMaddison et al., 1984, for a general account). An alternative to parsimony approaches makes use of the principle of maximum likelihood. Maximum likelihood solutions make the observed data most likely given somemodel of the process under investigation (see Edwards, 1972). In a phylogenetic context this means reconstructing the ancestral character states to make the character states observed among the contemporary species most probable, given some statistical model of the way evolution proceeds. Maximum likelihood solutions may or may not be the mostparsimonious solution. I restrict myself here to using maximum likelihood models to infer ancestral character states for binary discrete characters, that is, for characters that can adopt only two states, although the generalization to more than two states requires no new concepts.My approach to reconstructing ancestral states makes use of a Markov model of binary character evolution on phylogenies (Pagel, 1994). Sanderson (1993) describes a related model for investigating rates of gains and losses of characters for which the ancestral states are assumed to be known. Schluter (1995), Yang et al. (1995), and Koshi and Goldstein (1996) derive methods that are similar to the procedures I will describe here. However, Yang et al. (1995) and Koshi and Goldstein (1996) use what I shall term “global” methods for estimating ancestral characters, I argue for a “local” approach on grounds that the global method does not produce a maximum-likelihood estimate of the hypothesis of interest. Schluter (1995) reported global and local estimators in his investigation of artiodactyl ribonucleases, and Schluter et al. (1997) reported global estimators. In several recent papers, Schluter (1995; Schluter et al., 1997) called attention to the usefulness of reconstructing ancestral character states for testing ideas about adaptation and evolution, and much of what I say here owes its inspiration to these investigations. Mooers and Schluter (1999) now provide important additional examples of how maximum likelihood methods can return both more information about ancestral character states thanparsimony approaches, as well as information that is at odds with parsimony reconstructions. I intend this article to act as a primer to thosewhoare interested in usingmaximumlikelihood methods but who may not be familiar with the mathematics of the approach. Accordingly, I begin with the simplest case of estimating the ancestral state of two species.