The impact of ancestral population size and incomplete lineage sorting on Bayesian estimation of species divergence times

Abstract

Although the effects of the coalescent process on sequence divergence and genealogies are well understood, the virtual majority of studies that use molecular sequences to estimate times of divergence among species have failed to account for the coalescent process. Here we study the impact of ancestral population size and incomplete lineage sorting on Bayesian estimates of species divergence times under the molecular clock when the inference model ignores the coalescent process. Using a combination of mathematical analysis, computer simulations and analysis of real data, we find that the errors on estimates of times and the molecular rate can be substantial when ancestral populations are large and when there is substantial incomplete lineage sorting. For example, in a simple three-species case, we find that if the most precise fossil calibration is placed on the root of the phylogeny, the age of the internal node is overestimated, while if the most precise calibration is placed on the internal node, then the age of the root is underestimated. In both cases, the molecular rate is overestimated. Using simulations on a phylogeny of nine species, we show that substantial errors in time and rate estimates can be obtained even when dating ancient divergence events. We analyse the hominoid phylogeny and show that estimates of the neutral mutation rate obtained while ignoring the coalescent are too high. Using a coalescent-based technique to obtain geological times of divergence, we obtain estimates of the mutation rate that are within experimental estimates and we also obtain substantially older divergence times within the phylogeny.

Geogenetic patterns in mouse lemurs (genus Microcebus ) reveal the ghosts of Madagascar's forests past

“…The program BPP (52), which implements the multispecies coalescent, was used to estimate the species tree topology, branch lengths (τ), and nucleotide diversity (θ = 4Nμ) using whole ddRAD loci (as opposed to SNP data). The posterior of τ and θ can be converted to geological times of divergence and effective population sizes by using priors on the per-generation mutation rate and the generation time (68). Bayesian analysis using the multispecies coalescent is computationally expensive, so here we used a small dataset to estimate the tree topology and a large dataset to estimate τ and θ values more precisely by fixing the topology to that obtained with the small dataset.…”

“…To convert τ and θ values to divergence times (t) and population sizes (N), we sampled values for the mutation rate (μ) and generation time (g) from priors and used these values to calculate posterior estimates of t and N (see ref. 68 for details). The prior on μ was Gamma (27.80, 31.96), which roughly has a 95% prior credible interval (CI) between 0.5 and 1.2 × 10 −8 substitutions per site per generation.…”

Climatic niche evolution in the Andean genus Menonvillea (Cremolobeae: Brassicaceae)

“…Nucleotide substitution models selected in jModeltest2 2.1.6 based on (AIC) scores were SYM + G (ITS), TPM1uf + G (trnL-F), TPM1uf + G (trnH-psbA), and TIM1 + G (rps16 intron). Because coalescent-based methods have demonstrated to be more accurate for species tree topology estimation (Heled and Drummond 2010), and divergence times can be overestimated with gene-tree-based approaches that do not correct for genetic divergence that predates speciation (especially for recent divergence events) (McCormack et al 2011;Angelis and Dos Reis 2015), we estimated the species tree of Menonvillea using the coalescent-based method implemented in *BEAST extension (Heled and Drummond 2010) of BEAST v2.3.0 (Bouckaert et al 2014). All nucleotide substitution models were unlinked across loci, and an uncorrelated log-normal clock model (UCLN) was assigned to each sampled locus.…”

Incomplete lineage sorting impacts the inference of macroevolutionary regimes from molecular phylogenies when concatenation is employed: An analysis based on Cetacea

“…Theoretically, employing gene trees rather than the species tree to estimate macroevolutionary parameters may lead to significant bias; especially in shallow divergences, where incomplete lineage sorting (ILS) has a relatively larger impact on species divergence times (Angelis & Dos Reis, ; Leaché, Harris, Rannala, & Yang, ). This issue is not ameliorated using the tree built from concatenating genes into a supermatrix because even if the phylogeny is correctly determined, the biological meaning of branch lengths in such trees is elusive, as the age of nodes do not mirror speciation times (Angelis & Dos Reis, ; Edwards & Beerli, ).…”

“…Theoretically, employing gene trees rather than the species tree to estimate macroevolutionary parameters may lead to significant bias; especially in shallow divergences, where incomplete lineage sorting (ILS) has a relatively larger impact on species divergence times (Angelis & Dos Reis, ; Leaché, Harris, Rannala, & Yang, ). This issue is not ameliorated using the tree built from concatenating genes into a supermatrix because even if the phylogeny is correctly determined, the biological meaning of branch lengths in such trees is elusive, as the age of nodes do not mirror speciation times (Angelis & Dos Reis, ; Edwards & Beerli, ). Population‐level phenomena, such as ILS, gene duplication and loss, and hybridization will increase the probability of gene tree/species tree mismatch (Degnan & Rosenberg, ; Liu, Yu, Pearl, & Edwards, ; Schrago, Menezes, Furtado, Bonvicino, & Seuanez, ; Song et al., ; Tonini, Moore, Stern, Shcheglovitova, & Ortí, ).…”