A Comparison of One-Rate and Two-Rate Inference Frameworks for Site-Specific dN/ dS Estimation

Abstract

Two broad paradigms exist for inferring dN=dS; the ratio of nonsynonymous to synonymous substitution rates, from coding sequences: (i) a one-rate approach, where dN=dS is represented with a single parameter, or (ii) a two-rate approach, where d N and d S are estimated separately. The performances of these two approaches have been well studied in the specific context of proper model specification, i.e., when the inference model matches the simulation model. By contrast, the relative performances of one-rate vs. two-rate parameterizations when applied to data generated according to a different mechanism remain unclear. Here, we compare the relative merits of one-rate and two-rate approaches in the specific context of model misspecification by simulating alignments with mutation-selection models rather than with dN=dS-based models. We find that one-rate frameworks generally infer more accurate dN=dS point estimates, even when d S varies among sites. In other words, modeling d S variation may substantially reduce accuracy of dN=dS point estimates. These results appear to depend on the selective constraint operating at a given site. For sites under strong purifying selection (dN=dS ≲ 0:3), one-rate and two-rate models show comparable performances. However, one-rate models significantly outperform two-rate models for sites under moderate-to-weak purifying selection. We attribute this distinction to the fact that, for these more quickly evolving sites, a given substitution is more likely to be nonsynonymous than synonymous. The data will therefore be relatively enriched for nonsynonymous changes, and modeling d S contributes excessive noise to dN=dS estimates. We additionally find that high levels of divergence among sequences, rather than the number of sequences in the alignment, are more critical for obtaining precise point estimates.KEYWORDS dN/dS; mutation-selection models; evolutionary rate; sequence simulation; molecular evolution A variety of computational approaches have been developed to infer selection pressure from protein-coding sequences in a phylogenetically aware context. Among the most commonly used methods are those that compute the evolutionary rate ratio dN=dS; which represents the ratio of nonsynonymous to synonymous substitution rates. Beginning in the mid-1990s, this value has been calculated using maximum-likelihood (ML) approaches (Goldman and Yang 1994;Muse and Gaut 1994), and since then, a wide variety of inference frameworks have been developed to infer dN=dS at individual sites in protein-coding sequences (Nielsen and Yang 1998;Yang et al. 2000;Yang and Nielsen 2002;Yang and Swanson 2002;Lemey et al. 2012;Murrell et al. 2012bMurrell et al. , 2013.Typically, the performance of evolutionary models is examined using simulation-based approaches wherein sequences are simulated according to the model being examined, and inferences are subsequently performed on the simulated data. This approach ensures that simulated and inferred parameters correspond. Although useful, this strategy fundam...

Identification of positive selection in genes is greatly improved by using experimentally informed site-specific models

“…Therefore, in the concluding paragraph of the Discussion, I have cited [ 77 ] and added mention of how better incorporating synonymous rate variation might be one possible way to extend/improve ExpCM. Note however that the pros and cons of incorporating synonymous rate variation remain a topic of active debate [ 92 ], although I tend to side with the reviewer [ 77 ] and others [ 27 ] that incorporating such variation is beneficial. …”

Measuring evolutionary rates of proteins in a structural context

“…The model infers one dN value per site and one dS value per the entire sequence 21 . The one-rate FEL model has been found to infer more accurate dN/dS values than other HyPhy methods 22 .…”

“…For codon data, we consider site-specific dN/dS values. These are site-specific rates of nonsynonymous variation normalized by (whole-gene) rates of synonymous variation 21, 22 . At step (iii), we discuss two related but somewhat distinct structural measures.…”

Calculating site-specific evolutionary rates at the amino-acid or codon level yields similar rate estimates

“…We ran HyPhy using the FEL1 script provided in Spielman, Wan & Wilke (2016). After running the dN ∕ dS inference, we explicitly set dN ∕ dS  = 0 at all sites that did not experience any amino-acid changes.…”