Calculating Orthologous Protein-Coding Sequence Set Probability Using the Poisson Process.

Abstract

We extend the popular Jukes-Cantor evolution model and calculate the probability of an orthologous nucleotide sequence set [a reference sequence (B1) stays with the other sequences (B-1)], where the sequence evolution [from a last common ancestral sequence (ɑ)] follows the (prospective) Poisson process with the overall event rate λ prorated among mutation types (nucleotide/codon substitution, insertion, and deletion) and sites along each sequence. The corresponding retrospective process (reversing the prospective process) facilitates developing algorithms to calculate the marginal probability [Pr(B1)] (Monte Carlo integration) and sample ɑ (given B1). We calculate probability Pr(B-1|ɑ) based on the identified events (during "ɑ→B-1") from pairwise sequence alignment to implement Pr(B-1|B1) calculation (Monte Carlo integration). Event queue sampling and probability magnifiers are used to improve the computational efficiency when the number of events is large. We finally test our procedure on both simulated and recently studied hexapod transcriptome data (Brandt et al.), where each asexual lineage pairs with its closest related sexual lineage. Rate estimates (for Phasmatodea and Zygentoma) and model comparison indicate that the asexual lineages likely mutate several times faster than their sexual relatives.