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Oxford University Press, Molecular Biology and Evolution, 2(22), p. 223-234, 2004

DOI: 10.1093/molbev/msi009

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A Simple Hierarchical Approach to Modeling Distributions of Substitution Rates

Journal article published in 2004 by Sergei L. Kosakovsky Pond, Simon D. W. Frost ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Data provided by SHERPA/RoMEO

Abstract

Genetic sequence data typically exhibit variability in substitution rates across sites. In practice, there is often too little variation to fit a different rate for each site in the alignment, but the distribution of rates across sites may not be well modeled using simple parametric families. Mixtures of different distributions can capture more complex patterns of rate variation, but are often parameter-rich and difficult to fit. We present a simple hierarchical model in which a baseline rate distribution, such as a gamma distribution, is discretized into several categories, the quantiles of which are estimated using a discretized beta distribution. Although this approach involves adding only two extra parameters to a standard distribution, a wide range of rate distributions can be captured. Using simulated data, we demonstrate that a "beta-" model can reproduce the moments of the rate distribution more accurately than the distribution used to simulate the data, even when the baseline rate distribution is misspecified. Using hepatitis C virus and mammalian mitochondrial sequences, we show that a beta- model can fit as well or better than a model with multiple discrete rate categories, and compares favorably with a model which fits a separate rate category to each site. We also demonstrate this discretization scheme in the context of codon models specifically aimed at identifying individual sites undergoing adaptive or purifying evolution.