Significant cross-species gene flow detected in the Tamias quadrivittatus group of North American chipmunks

In the past two decades genomic data have been widely used to detect historical gene flow between species in a variety of plants and animals. The Tamias quadrivittatus group of North America chipmunks, which originated through a series of rapid speciation events, are known to undergo massive amounts of mitochondrial introgression. Yet in a recent analysis of targeted nuclear loci from the group, no evidence for cross-species introgression was detected, indicating widespread cytonuclear discordance. The study used heuristic methods that analyze summaries of the multilocus sequence data to detect gene flow, which may suffer from low power. Here we use the full likelihood method implemented in the Bayesian program BPP to reanalyze these data. We take a stepwise approach to constructing an introgression model by adding introgression events onto a well-supported binary species tree. The analysis detected robust evidence for multiple ancient introgression events affecting the nuclear genome, with introgression probabilities reaching 65%. We estimate population parameters and highlight the fact that species divergence times may be seriously underestimated if ancient cross-species gene flow is ignored in the analysis. Our analyses highlight the importance of using adequate statistical methods to reach reliable biological conclusions concerning cross-species gene flow.

Estimation of Cross-Species Introgression Rates using Genomic Data Despite Model Unidentifiability

The multispecies coalescent with introgression (MSci) model accommodates both the coalescent process and cross-species introgression/ hybridization events, two major processes that create genealogical fluctuations across the genome and gene-tree-species-tree discordance. Full likelihood implementations of the MSci model take such fluctuations as a major source of information about the history of species divergence and gene flow, and provide a powerful tool for estimating the direction, timing and strength of cross-species introgression using multilocus sequence data. However, introgression models, in particular those that accommodate bidirectional introgression (BDI), are known to cause unidentifiability issues of the label-switching type, whereby different models or parameters make the same predictions about the genomic data and thus cannot be distinguished by the data. Nevertheless, there has been no systematic study of unidentifiability when full likelihood methods are applied. Here we characterize the unidentifiability of arbitrary BDI models and derive simple rules for its identification. In general, an MSci model with k BDI events has 2^k unidentifiable towers in the posterior, with each BDI event between sister species creating within-model unidentifiability and each BDI between non-sister species creating cross-model unidentifiability. We develop novel algorithms for processing Markov chain Monte Carlo (MCMC) samples to remove label switching and implement them in the BPP program. We analyze genomic sequence data from Heliconius butterflies as well as synthetic data to illustrate the utility of the BDI models and the new algorithms.

Assessing the utility of CASP14 models for molecular replacement

The assessment of CASP models for utility in molecular replacement is a measure of their use in a valuable real-world application. In CASP7, the metric for molecular replacement assessment involved full likelihood-based molecular replacement searches; however, this restricted the assessable targets to crystal structures with only one copy of the target in the asymmetric unit, and to those where the search found the correct pose. In CASP10, full molecular replacement searches were replaced by likelihood-based rigid-body refinement of models superimposed on the target using the LGA algorithm, with the metric being the refined likelihood (LLG) score. This enabled multi-copy targets and very poor models to be evaluated, but a significant further issue remained: the requirement of diffraction data for assessment. We introduce here the relative-expected-LLG (reLLG), which is independent of diffraction data. This reLLG is also independent of any crystal form, and can be calculated regardless of the source of the target, be it X-ray, NMR or cryo-EM. We calibrate the reLLG against the LLG for targets in CASP14, showing that it is a robust measure of both model and group ranking. Like the LLG, the reLLG shows that accurate coordinate error estimates add substantial value to predicted models. We find that refinement by CASP groups can often convert an inadequate initial model into a successful MR search model. Consistent with findings from others, we show that the AlphaFold2 models are sufficiently good, and reliably so, to surpass other current model generation strategies for attempting molecular replacement phasing.

Assessing the utility of CASP14 models for molecular replacement

The assessment of CASP models for utility in molecular replacement is a measure of their use in a valuable real-world application. In CASP7, the metric for molecular replacement assessment involved full likelihood-based molecular replacement searches; however, this restricted the assessable targets to crystal structures with only one copy of the target in the asymmetric unit, and to those where the search found the correct pose. In CASP10, full molecular replacement searches were replaced by likelihood-based rigid-body refinement of models superimposed on the target using the LGA algorithm, with the metric being the refined likelihood (LLG) score. This enabled multi-copy targets and very poor models to be evaluated, but a significant further issue remained: the requirement of diffraction data for assessment. We introduce here the relative-expected-LLG (reLLG), which is independent of diffraction data. This reLLG is also independent of any crystal form, and can be calculated regardless of the source of the target, be it X-ray, NMR or cryo-EM. We calibrate the reLLG against the LLG for targets in CASP14, showing that it is a robust measure of both model and group ranking. Like the LLG, the reLLG shows that accurate coordinate error estimates add substantial value to predicted models. We find that refinement by CASP groups can often convert an inadequate initial model into a successful MR search model. Consistent with findings from others, we show that the AlphaFold2 models are sufficiently good, and reliably so, to surpass other current model generation strategies for attempting molecular replacement phasing.

Complex introgression history of the erato-sara clade of Heliconius butterflies

Introgression plays a key role in adaptive evolution and species diversification in many groups of species including Heliconius butterflies. However, frequent hybridization and subsequent gene flow between species makes estimation of the species phylogeny challenging. Here, we infer species phylogeny and introgression events from whole-genome sequence data of six members of the erato-sara clade of Heliconius using a multispecies coalescent model with introgression (MSci) and an isolation-with-migration (IM) model. These approaches probabilistically capture the genealogical heterogeneity across the genome due to introgression and incomplete lineage sorting in a full likelihood framework. We detect robust signals of introgression across the genome, and estimate the direction, timing and magnitude of each introgression event. The results clarify several processes of speciation and introgression in the erato-sara group. In particular, we confirm ancestral gene flow between the sara clade and an ancestral population of H. telesiphe, a hybrid origin of H. hecalesia, and gene flow between the sister species H. erato and H. himera. The ability to confidently infer the presence, timing and magnitude of introgression events using genomic sequence data is helpful for understanding speciation in the presence of gene flow and will be useful for understanding the adaptive consequences of introgressed regions of the genome. Our analysis serves to highlight the power of full likelihood methods under the MSci model to the history of species divergence and cross-species introgression from genome-scale data.

Complexity of the simplest species tree problem

The multispecies coalescent (MSC) model provides a natural framework for species tree estimation accounting for gene-tree conflicts. While a number of species tree methods under the MSC have been suggested and evaluated using simulation, their statistical properties remain poorly understood. Here we use mathematical analysis aided by computer simulation to examine the identifiability, consistency, and efficiency of different species tree methods in the case of three species and three sequences under the molecular clock. We consider four major species-tree methods including concatenation, two-step, independent-sites maximum likelihood (ISML) and maximum likelihood (ML). We develop approximations that predict that the probit transform of the species tree estimation error decreases linearly with the square root of the number of loci. Even in this simplest case major differences exist among the methods. Fulllikelihood methods are considerably more efficient than summary methods such as concatenation and two-step. They also provide estimates of important parameters such as species divergence times and ancestral population sizes while these parameters are not identifiable by summary methods. Our results highlight the need to improve the statistical efficiency of summary methods and the computational efficiency of full likelihood methods of species tree estimation.

Assessing the fit of the multi-species network coalescent to multi-locus data

Motivation With growing genome-wide molecular datasets from next-generation sequencing, phylogenetic networks can be estimated using a variety of approaches. These phylogenetic networks include events like hybridization, gene flow or horizontal gene transfer explicitly. However, the most accurate network inference methods are computationally heavy. Methods that scale to larger datasets do not calculate a full likelihood, such that traditional likelihood-based tools for model selection are not applicable to decide how many past hybridization events best fit the data. We propose here a goodness-of-fit test to quantify the fit between data observed from genome-wide multi-locus data, and patterns expected under the multi-species coalescent model on a candidate phylogenetic network. Results We identified weaknesses in the previously proposed TICR test, and proposed corrections. The performance of our new test was validated by simulations on real-world phylogenetic networks. Our test provides one of the first rigorous tools for model selection, to select the adequate network complexity for the data at hand. The test can also work for identifying poorly inferred areas on a network. Availability and implementation Software for the goodness-of-fit test is available as a Julia package at https://github.com/cecileane/QuartetNetworkGoodnessFit.jl. Supplementary information Supplementary data are available at Bioinformatics online.

COAL_PHYRE: A Composite Likelihood Method for Estimating Species Tree Parameters from Genomic Data Using Coalescent Theory

2AbstractGenome-scale data are increasingly being used to infer phylogenetic trees. A major challenge in such inferences is that different regions of the genome may have local topologies that differ from the species tree due to incomplete lineage sorting (ILS). Another source of gene tree discrepancies is estimation errors arising from the randomness of the mutational process during sequence evolution. There are two major groups of methods for estimating species tree from whole-genome data: a set of full likelihood methods, which model both sources of variance, but do not scale to large numbers of independent loci, and a class of faster approximation methods which do not model the mutational variance.To bridge the gap between these two classes of methods, we present COAL_PHYRE (COmposite Approximate Likelihood for PHYlogenetic REconstruction), a composite likelihood based method for inferring population size and divergence time estimates of rooted species trees from aligned gene sequences. COAL_PHYRE jointly models coalescent variation across loci using the MSC and variation in local gene tree reconstruction using a normal approximation. To evaluate the accuracy and speed of the method, we compare against BPP, a powerful MCMC full-likelihood method, as well as ASTRAL-III, a fast approximate method. We show that COAL_PHYRE’s divergence time and population size estimates are more accurate than ASTRAL, and comparable to those obtained using BPP, with an order of magnitude decrease in computational time. We also present results on previously published data from a set of Gibbon species to evaluate the accuracy in topology and parameter inference on real data, and to illustrate the method’s ability to analyze data sets which are prohibitively large for MCMC methods.