Models for Amino Acid Substitution and Gene Duplication With Roots in Molecular and Evolutionary Processes

David Liberles (February 26, 2010)

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In Darwinian evolution, mutations occur approximately at random in a gene, turned into amino acid mutations by the genetic code. Some mutations are fixed to become substitutions and some are eliminated from the population. Partitioning pairs of closely related species with complete genome sequences by population size, we look at the PAM matrices generated for these partitions and compare the substitution patterns between species. A population genetic model is generated that relates the relative fixation probabilities of different types of mutations to the selective pressure and population size. Parameterizations of the average and distribution of selective pressures for different amino acid substitution types in different population size comparisons are generated using a Bayesian framework. We find that partitions in population size as well as in substitution type are required to explain the substitution data. Mechanistic explanations of this will be discussed.

In a second line of work, models for gene duplication will be discussed, with potential extension to the Gene tree/species tree reconciliation problem. This second trajectory involves an extension of birth death models based upon an exponential distribution using a generalization based upon a Weibull distribution. Distinct parameterizations of the Weibull distribution are expected to be consistent with the neofunctionalization, subfunctionalization, and dosage compensation processes. Ongoing work involves the extension of the Weibull-based models to the gene tree/species tree reconciliation approach using a Bayesian framework, with potential utility in additionally identifying underlying evolutionary processes.