Bayesian estimation of scaled mutation rate under the coalescent: a sequential Monte Carlo approach

Oyetunji E. Ogundijo, Xiaodong Wang

Samples of molecular sequence data of a locus obtained from random individuals in a population are often related by an unknown genealogy. More importantly, population genetics parameters, for instance, the scaled population mutation rate Θ=4N e μ for diploids or Θ=2N e μ for haploids (where N e is the effective population size and μ is the mutation rate per site per generation), which explains some of the evolutionary history and past qualities of the population that the samples are obtained from, is of significant interest. In this paper, we present the evolution of sequence data in a Bayesian framework and the approximation of the posterior distributions of the unknown parameters of the model, which include Θ via the sequential Monte Carlo (SMC) samplers for static models. Specifically, we approximate the posterior distributions of the unknown parameters with a set of weighted samples i.e., the set of highly probable genealogies out of the infinite set of possible genealogies that describe the sampled sequences. The proposed SMC algorithm is evaluated on simulated DNA sequence datasets under different mutational models and real biological sequences. In terms of the accuracy of the estimates, the proposed SMC method shows a comparable and sometimes, better performance than the state-of-the-art MCMC algorithms. We showed that the SMC algorithm for static model is a promising alternative to the state-of-the-art approach for simulating from the posterior distributions of population genetics parameters.