The Impact of Modelling Rate Heterogeneity among Sites on Phylogenetic Estimates of Intraspecific Evolutionary Rates and Timescales

Abstract

Phylogenetic analyses of DNA sequence data can provide estimates of evolutionary rates and timescales. Nearly all phylogenetic methods rely on accurate models of nucleotide substitution. A key feature of molecular evolution is the heterogeneity of substitution rates among sites, which is often modelled using a discrete gamma distribution. A widely used derivative of this is the gamma-invariable mixture model, which assumes that a proportion of sites in the sequence are completely resistant to change, while substitution rates at the remaining sites are gamma-distributed. For data sampled at the intraspecific level, however, biological assumptions involved in the invariable-sites model are commonly violated. We examined the use of these models in analyses of five intraspecific data sets. We show that using 6–10 rate categories for the discrete gamma distribution of rates among sites is sufficient to provide a good approximation of the marginal likelihood. Increasing the number of gamma rate categories did not have a substantial effect on estimates of the substitution rate or coalescence time, unless rates varied strongly among sites in a non-gamma-distributed manner. The assumption of a proportion of invariable sites provided a better approximation of the asymptotic marginal likelihood when the number of gamma categories was small, but had minimal impact on estimates of rates and coalescence times. However, the estimated proportion of invariable sites was highly susceptible to changes in the number of gamma rate categories. The concurrent use of gamma and invariable-site models for intraspecific data is not biologically meaningful and has been challenged on statistical grounds; here we have found that the assumption of a proportion of invariable sites has no obvious impact on Bayesian estimates of rates and timescales from intraspecific data.

Limits and patterns of cytomegalovirus genomic diversity in humans

“…These values differ from those estimated for other species. The number of conserved sites in the human genome is ∼8% (48), and, in other viruses, the proportion is much higher, including 66% for HIV (49), 63% for influenza A virus (50), and 78% for rubella virus (51). These trends suggest that the number of invariant sites is inversely correlated with genome size.…”

Evolution of lacewings and allied orders using anchored phylogenomics (Neuroptera, Megaloptera, Raphidioptera)

“…The best‐fitting substitution model across all partitions for the nucleotide dataset was a general time‐reversible substitution model (GTR; Tavaré, ) with rate heterogeneity described by a gamma distribution discretized into four bins (+G; Yang, ) and a proportion of invariant sites (+I, Fitch & Margoliash, ). We did not use the GTR + I + G mixture model (Gu et al ., ; Waddell & Steel, ) because this approach has been highly criticized on both empirical and theoretical grounds (Yang, , , ; Sullivan et al ., ; Mayrose et al ., ; Jia et al ., ). Studies indicate that some of the parameters of the +I and +G models cannot be optimized independently of each other (Yang, , ; Jia et al ., ); indeed, the estimated proportion of invariable sites was demonstrated to be highly susceptible to changes in the number of gamma rate categories of the +G model (Jia et al ., ).…”

“…We did not use the GTR + I + G mixture model (Gu et al ., ; Waddell & Steel, ) because this approach has been highly criticized on both empirical and theoretical grounds (Yang, , , ; Sullivan et al ., ; Mayrose et al ., ; Jia et al ., ). Studies indicate that some of the parameters of the +I and +G models cannot be optimized independently of each other (Yang, , ; Jia et al ., ); indeed, the estimated proportion of invariable sites was demonstrated to be highly susceptible to changes in the number of gamma rate categories of the +G model (Jia et al ., ). Furthermore, it has been suggested that the assumption of a proportion of invariable sites has no obvious impact on Bayesian estimates of rates, and little to no biological meaning, especially at the intraspecific level (Jia et al ., ).…”

“…Studies indicate that some of the parameters of the +I and +G models cannot be optimized independently of each other (Yang, , ; Jia et al ., ); indeed, the estimated proportion of invariable sites was demonstrated to be highly susceptible to changes in the number of gamma rate categories of the +G model (Jia et al ., ). Furthermore, it has been suggested that the assumption of a proportion of invariable sites has no obvious impact on Bayesian estimates of rates, and little to no biological meaning, especially at the intraspecific level (Jia et al ., ). Thus, we employed a GTR + G mixture model separately for each metapartition.…”

Phylogenomics — principles, opportunities and pitfalls of big‐data phylogenetics

“…This implies that the standard practice of model selection before phylogeny inference is unnecessary when a complex and parameter-rich model is applied to nucleotide data (Abadi et al, 2019). However, it is worth mentioning that combining a gamma distribution (+G; Yang, 1993) with a proportion of invariant sites (+I; Fitch & Margoliash, 1967) to account for among-site rate heterogeneity has been highly criticized, mainly because some of the parameters of the +I and + G models cannot be optimized independently of each other (Yang, 2006;Sullivan, 1999;Mayrose, 2005;Jia et al, 2014). Thus, it is more advisable to apply a GTR + G mixture model for each partition, as opposed to a GTR + I + G.…”