Maximum likelihood reconstruction of ancestral amino-acid sequences

Maximum-likelihood methods are used extensively in phylogenetic studies [3]. In particular, aminoacid sequences of ancestral species have been inferred using these methods [7]. Such ancestral reconstruction tasks aim at identifying either the most likely sequence in a specific ancestor species (marginal reconstruction), or the most likely set of ancestral states corresponding to all the ancestral taxa in a given phylogeny (joint reconstruction [6]). Joint reconstruction is motivated by studies of phenomena involving several independent lineages, like [8], and is implemented in [6]. However, existing algorithms for this task are exhaustive, and take exponential time. Furthermore, these algorithms assume a naive model of evolution, i.e., a constant substitution rate, whereas [5] shows that models incorporating rate variation among sites are statistically superior. In this work we: (a) Devise a dynamic programming algorithm for joint reconstruction. The complexity of this algorithm is linear in the number of sequences, but assumes no rate variation among sites.1 (b) Present a greedy heuristic for joint reconstruction assuming rate variation among sites. (c) Introduce a speed-up for calculating the replacement probabilities between any two states.