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 replacement, or tracing the biochemical changes that occurred during the evolution of a given protein family. Results: We give an algorithm that guarantees finding the global maximum. The efficient search method makes our method applicable to datasets with large number sequences. We analyze ancestral sequences of five gene families, exploring the effect of the amount of among-site-rate-variation, and the degree of sequence divergence on the resulting ancestral states.
Bibliographical noteFunding Information:
T.P. was supported by a grant from the Japanese Society for the Promotion of Science (JSPS). I.P. is supported by the Clore Foundation. N.F. was supported by an Alon Fellowship. We thank Adi Stern for her contribution and help to this work.