Marginal Likelihoods in Phylogenetics: A Review of Methods and Applications

Abstract

By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to increase in complexity to better capture micro- and macroevolutionary processes. In a Bayesian framework, the marginal likelihood is how data update our prior beliefs about models, which gives us an intuitive measure of comparing model fit that is grounded in probability theory. Given the rapid increase in the number and complexity of phylogenetic models, methods for approximating marginal likelihoods are increasingly important. Here, we try to provide an intuitive description of marginal likelihoods and why they are important in Bayesian model testing. We also categorize and review methods for estimating marginal likelihoods of phylogenetic models, highlighting several recent methods that provide well-behaved estimates. Furthermore, we review some empirical studies that demonstrate how marginal likelihoods can be used to learn about models of evolution from biological data. We discuss promising alternatives that can complement marginal likelihoods for Bayesian model choice, including posterior-predictive methods. Using simulations, we find one alternative method based on approximate-Bayesian computation to be biased. We conclude by discussing the challenges of Bayesian model choice and future directions that promise to improve the approximation of marginal likelihoods and Bayesian phylogenetics as a whole.

The comparative biogeography of Philippine geckos challenges predictions from a paradigm of climate‐driven vicariant diversification across an island archipelago

“…Because the marginal likelihoods are averaged with respect to the priors on all the parameters of the model, they can be sensitive to those priors regardless of the informativeness the data (Oaks et al. ).…”

The comparative biogeography of Philippine geckos challenges predictions from a paradigm of climate-driven vicariant diversification across an island archipelago

“…Because the marginal likelihoods are averaged with respect to the priors on all the parameters of the model, they can be sensitive to those priors regardless of the informativeness the data (Oaks et al, 2019).…”

An Annealed Sequential Monte Carlo Method for Bayesian Phylogenetics

“…More specifically, the ratio r = p 1 (y)/p 2 (y) of two marginal likelihoods based on two evolutionary models, p 1 (·), p 2 (·), can be used to assess the strength of evidence y provides for p 1 (when r > 1) or p 2 (when r < 1). The ratio r is called the Bayes factor (Jeffreys 1935;Lartillot et al 2006;Oaks et al 2018). In the context of phylogenetics, the Bayes factor assesses how much support a set of sequencing data provides for one evolutionary model against another one.…”