The information content of a character under a Markov model of evolution

The rate of evolutionary change associated with a character determines its utility for the reconstruction of phylogenetic history. For a given age of lineage splits, we examine the information content of a character to assess the magnitude and range of an optimal rate of substitution. On the one hand an optimal transition rate must provide sufficiently many character changes to distinguish subclades, whereas on the other hand changes must be sufficiently rare that reversals on a single branch (and hence homoplasy) are uncommon. In this study, we evolve binary characters over three tree topologies with fixed branch lengths, while varying transition rate as a parameter. We use the character state distribution obtained to measure the "information content" of a character given a transition rate. This is done with respect to several criteria-the probability of obtaining the correct tree using parsimony, the probability of infering the correct ancestral state, and Shannon-Weaver and Fisher information measures on the configuration of probability distributions. All of the information measures suggest the intuitive result of the existence of optimal rates for phylogeny reconstruction. This nonzero optimum is less pronounced if one conditions on there having been a change, in which case the parsimony-based results of minimum change being the most informative tends to hold.