Motivation: We developed an algorithm to reconstruct ancestral sequences, taking into account the rate variation among sites of the protein sequences. Our algorithm maximizes the joint probability of the ancestral sequences, assuming that the rate is gamma distributed among sites. Our algorithm provably finds the global maximum. The use of joint reconstruction is motivated by studies that use the sequences at all the internal nodes in a phylogenetic tree, such as, for instance, the inference of patterns of amino-acid replacements, or tracing the biochemical changes that occurred during the evolution of a protein along a predefined lineage.
Results: We give an algorithm that guarantees finding the global maximum. Our method is applicable for large number of sequences, because of the efficient search method. We analyze ancestral sequences of five homologous genes, exploring the effect of the amount of among-site-rate-variation and the degree of sequence divergence on the inferred ancestral states.
Availability and supplementary information:http://evolu3.ism.ac.jp/~tal/