Dataset Information

Complex Models of Sequence Evolution Require Accurate Estimators as Exemplified with the Invariable Site Plus Gamma Model.

ABSTRACT: The invariable site plus $\Gamma$ model (I$+\Gamma)$ is widely used to model rate heterogeneity among alignment sites in maximum likelihood and Bayesian phylogenetic analyses. The proof that the I$+$ continuous $\Gamma$ model is identifiable (model parameters can be inferred correctly given enough data) has increased the creditability of its application to phylogeny reconstruction. However, most phylogenetic software implement the I$+$ discrete $\Gamma$ model, whose identifiability is likely but unproven. How well the parameters of the I$+$ discrete $\Gamma$ model are estimated is still disputed. Especially the correlation between the fraction of invariable sites and the fractions of sites with a slow evolutionary rate is discussed as being problematic. We show that optimization heuristics as implemented in frequently used phylogenetic software (PhyML, RAxML, IQ-TREE, and MrBayes) cannot always reliably estimate the shape parameter, the proportion of invariable sites, and the tree length. Here, we propose an improved optimization heuristic that accurately estimates the three parameters. While research efforts mainly focus on tree search methods, our results signify the equal importance of verifying and developing effective estimation methods for complex models of sequence evolution.

SUBMITTER: Nguyen LT

PROVIDER: S-EPMC6204645 | biostudies-literature | 2018 May

REPOSITORIES: biostudies-literature

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Complex Models of Sequence Evolution Require Accurate Estimators as Exemplified with the Invariable Site Plus Gamma Model.

Nguyen Lam-Tung LT von Haeseler Arndt A Minh Bui Quang BQ

Systematic biology 20180501 3

The invariable site plus $\Gamma$ model (I$+\Gamma)$ is widely used to model rate heterogeneity among alignment sites in maximum likelihood and Bayesian phylogenetic analyses. The proof that the I$+$ continuous $\Gamma$ model is identifiable (model parameters can be inferred correctly given enough data) has increased the creditability of its application to phylogeny reconstruction. However, most phylogenetic software implement the I$+$ discrete $\Gamma$ model, whose identifiability is likely but ...[more]

PMID: 29186593

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Project description:BackgroundAccurate model comparison requires extensive computation times, especially for parameter-rich models of sequence evolution. In the Bayesian framework, model selection is typically performed through the evaluation of a Bayes factor, the ratio of two marginal likelihoods (one for each model). Recently introduced techniques to estimate (log) marginal likelihoods, such as path sampling and stepping-stone sampling, offer increased accuracy over the traditional harmonic mean estimator at an increased computational cost. Most often, each model's marginal likelihood will be estimated individually, which leads the resulting Bayes factor to suffer from errors associated with each of these independent estimation processes.ResultsWe here assess the original 'model-switch' path sampling approach for direct Bayes factor estimation in phylogenetics, as well as an extension that uses more samples, to construct a direct path between two competing models, thereby eliminating the need to calculate each model's marginal likelihood independently. Further, we provide a competing Bayes factor estimator using an adaptation of the recently introduced stepping-stone sampling algorithm and set out to determine appropriate settings for accurately calculating such Bayes factors, with context-dependent evolutionary models as an example. While we show that modest efforts are required to roughly identify the increase in model fit, only drastically increased computation times ensure the accuracy needed to detect more subtle details of the evolutionary process.ConclusionsWe show that our adaptation of stepping-stone sampling for direct Bayes factor calculation outperforms the original path sampling approach as well as an extension that exploits more samples. Our proposed approach for Bayes factor estimation also has preferable statistical properties over the use of individual marginal likelihood estimates for both models under comparison. Assuming a sigmoid function to determine the path between two competing models, we provide evidence that a single well-chosen sigmoid shape value requires less computational efforts in order to approximate the true value of the (log) Bayes factor compared to the original approach. We show that the (log) Bayes factors calculated using path sampling and stepping-stone sampling differ drastically from those estimated using either of the harmonic mean estimators, supporting earlier claims that the latter systematically overestimate the performance of high-dimensional models, which we show can lead to erroneous conclusions. Based on our results, we argue that highly accurate estimation of differences in model fit for high-dimensional models requires much more computational effort than suggested in recent studies on marginal likelihood estimation.

Dataset Information

Complex Models of Sequence Evolution Require Accurate Estimators as Exemplified with the Invariable Site Plus Gamma Model.

Publications

Complex Models of Sequence Evolution Require Accurate Estimators as Exemplified with the Invariable Site Plus Gamma Model.

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