Polymorphism Data Assist Estimation of the Nonsynonymous over Synonymous Fixation Rate Ratio ω for Closely Related Species.

The ratio of nonsynonymous over synonymous sequence divergence, dN/dS, is a widely used estimate of the nonsynonymous over synonymous fixation rate ratio ω, which measures the extent to which natural selection modulates protein sequence evolution. Its computation is based on a phylogenetic approach and computes sequence divergence of protein-coding DNA between species, traditionally using a single representative DNA sequence per species. This approach ignores the presence of polymorphisms and relies on the indirect assumption that new mutations fix instantaneously, an assumption which is generally violated and reasonable only for distantly related species. The violation of the underlying assumption leads to a time-dependence of sequence divergence, and biased estimates of ω in particular for closely related species, where the contribution of ancestral and lineage-specific polymorphisms to sequence divergence is substantial. We here use a time-dependent Poisson random field model to derive an analytical expression of dN/dS as a function of divergence time and sample size. We then extend our framework to the estimation of the proportion of adaptive protein evolution α. This mathematical treatment enables us to show that the joint usage of polymorphism and divergence data can assist the inference of selection for closely related species. Moreover, our analytical results provide the basis for a protocol for the estimation of ω and α for closely related species. We illustrate the performance of this protocol by studying a population data set of four corvid species, which involves the estimation of ω and α at different time-scales and for several choices of sample sizes.

Analysis of diversity-dependent species evolution using concepts in population genetics.

In this work, we consider a two-type species model with trait-dependent speciation, extinction and transition rates under an evolutionary time scale. The scaling approach and the diffusion approximation techniques which are widely used in mathematical population genetics provide modeling tools and conceptual background to assist in the study of species dynamics, and help exploring the analogy between trait-dependent species diversification and the evolution of allele frequencies in the population genetics setting. The analytical framework specified is then applied to models incorporating diversity-dependence, in order to infer effective results from processes in which the net diversification of species depends on the total number of species. In particular, the long term fate of a rare trait may be analyzed under a partly symmetric scenario, using a time-change transform technique.

Modeling a trait-dependent diversification process coupled with molecular evolution on a random species tree.

Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. In this work, we present a probabilistic modeling framework for binary trait, random species trees, in which the number of species and their traits are represented by an asymmetric, two-type, continuous time Markov branching process. The model involves a number of different parameters describing both character and molecular evolution on the so-called 'reduced' tree, consisting of only extant species at the time of observation. We expand our model by considering the impact of binary traits on dN/dS, the normalized ratio of nonsynonymous to synonymous substitutions. We also develop mechanisms which enable us to understand the substitution rates on a phylogenetic tree with regards to the observed traits. The properties obtained from the model are illustrated with a phylogeny of outcrossing and selfing plant species, which allows us to investigate not only the branching tree rates, but also the molecular rates and the intensity of selection.

Predicting pathogenicity behavior in Escherichia coli population through a state dependent model and TRS profiling.

The Binary State Speciation and Extinction (BiSSE) model is a branching process based model that allows the diversification rates to be controlled by a binary trait. We develop a general approach, based on the BiSSE model, for predicting pathogenicity in bacterial populations from microsatellites profiling data. A comprehensive approach for predicting pathogenicity in E. coli populations is proposed using the state-dependent branching process model combined with microsatellites TRS-PCR profiling. Additionally, we have evaluated the possibility of using the BiSSE model for estimating parameters from genetic data. We analyzed a real dataset (from 251 E. coli strains) and confirmed previous biological observations demonstrating a prevalence of some virulence traits in specific bacterial sub-groups. The method may be used to predict pathogenicity of other bacterial taxa.

Using the Ornstein-Uhlenbeck process to model the evolution of interacting populations.

The Ornstein-Uhlenbeck (OU) process plays a major role in the analysis of the evolution of phenotypic traits along phylogenies. The standard OU process includes random perturbations and stabilizing selection and assumes that species evolve independently. However, evolving species may interact through various ecological process and also exchange genes especially in plants. This is particularly true if we want to study phenotypic evolution among diverging populations within species. In this work we present a straightforward statistical approach with analytical solutions that allows for the inclusion of adaptation and migration in a common phylogenetic framework, which can also be useful for studying local adaptation among populations within the same species. We furthermore present a detailed simulation study that clearly indicates the adverse effects of ignoring migration. Similarity between species due to migration could be misinterpreted as very strong convergent evolution without proper correction for these additional dependencies. Finally, we show that our model can be interpreted in terms of ecological interactions between species, providing a general framework for the evolution of traits between "interacting" species or populations.

The non-equilibrium allele frequency spectrum in a Poisson random field framework.

In population genetic studies, the allele frequency spectrum (AFS) efficiently summarizes genome-wide polymorphism data and shapes a variety of allele frequency-based summary statistics. While existing theory typically features equilibrium conditions, emerging methodology requires an analytical understanding of the build-up of the allele frequencies over time. In this work, we use the framework of Poisson random fields to derive new representations of the non-equilibrium AFS for the case of a Wright-Fisher population model with selection. In our approach, the AFS is a scaling-limit of the expectation of a Poisson stochastic integral and the representation of the non-equilibrium AFS arises in terms of a fixation time probability distribution. The known duality between the Wright-Fisher diffusion process and a birth and death process generalizing Kingman's coalescent yields an additional representation. The results carry over to the setting of a random sample drawn from the population and provide the non-equilibrium behavior of sample statistics. Our findings are consistent with and extend a previous approach where the non-equilibrium AFS solves a partial differential forward equation with a non-traditional boundary condition. Moreover, we provide a bridge to previous coalescent-based work, and hence tie several frameworks together. Since frequency-based summary statistics are widely used in population genetics, for example, to identify candidate loci of adaptive evolution, to infer the demographic history of a population, or to improve our understanding of the underlying mechanics of speciation events, the presented results are potentially useful for a broad range of topics.

Why time matters: codon evolution and the temporal dynamics of dN/dS.

The ratio of divergence at nonsynonymous and synonymous sites, dN/dS, is a widely used measure in evolutionary genetic studies to investigate the extent to which selection modulates gene sequence evolution. Originally tailored to codon sequences of distantly related lineages, dN/dS represents the ratio of fixed nonsynonymous to synonymous differences. The impact of ancestral and lineage-specific polymorphisms on dN/dS, which we here show to be substantial for closely related lineages, is generally neglected in estimation techniques of dN/dS. To address this issue, we formulate a codon model that is firmly anchored in population genetic theory, derive analytical expressions for the dN/dS measure by Poisson random field approximation in a Markovian framework and validate the derivations by simulations. In good agreement, simulations and analytical derivations demonstrate that dN/dS is biased by polymorphisms at short time scales and that it can take substantial time for the expected value to settle at its time limit where only fixed differences are considered. We further show that in any attempt to estimate the dN/dS ratio from empirical data the effect of the intrinsic fluctuations of a ratio of stochastic variables, can even under neutrality yield extreme values of dN/dS at short time scales or in regions of low mutation rate. Taken together, our results have significant implications for the interpretation of dN/dS estimates, the McDonald-Kreitman test and other related statistics, in particular for closely related lineages.

A Nearly Neutral Model of Molecular Signatures of Natural Selection after Change in Population Size.

The nearly neutral theory is a common framework to describe natural selection at the molecular level. This theory emphasizes the importance of slightly deleterious mutations by recognizing their ability to segregate and eventually get fixed due to genetic drift in spite of the presence of purifying selection. As genetic drift is stronger in smaller than in larger populations, a correlation between population size and molecular measures of natural selection is expected within the nearly neutral theory. However, this hypothesis was originally formulated under equilibrium conditions. As most natural populations are not in equilibrium, testing the relationship empirically may lead to confounded outcomes. Demographic nonequilibria, for instance following a change in population size, are common scenarios that are expected to push the selection-drift relationship off equilibrium. By explicitly modeling the effects of a change in population size on allele frequency trajectories in the Poisson random field framework, we obtain analytical solutions of the nonstationary allele frequency spectrum. This enables us to derive exact results of measures of natural selection and effective population size in a demographic nonequilibrium. The study of their time-dependent relationship reveals a substantial deviation from the equilibrium selection-drift balance after a change in population size. Moreover, we show that the deviation is sensitive to the combination of different measures. These results therefore constitute relevant tools for empirical studies to choose suitable measures for investigating the selection-drift relationship in natural populations. Additionally, our new modeling approach extends existing population genetics theory and can serve as foundation for methodological developments.

Positive selection on human gamete-recognition genes.

Coevolution of genes that encode interacting proteins expressed on the surfaces of sperm and eggs can lead to variation in reproductive compatibility between mates and reproductive isolation between members of different species. Previous studies in mice and other mammals have focused in particular on evidence for positive or diversifying selection that shapes the evolution of genes that encode sperm-binding proteins expressed in the egg coat or zona pellucida (ZP). By fitting phylogenetic models of codon evolution to data from the 1000 Genomes Project, we identified candidate sites evolving under diversifying selection in the human genes ZP3 and ZP2. We also identified one candidate site under positive selection in C4BPA, which encodes a repetitive protein similar to the mouse protein ZP3R that is expressed in the sperm head and binds to the ZP at fertilization. Results from several additional analyses that applied population genetic models to the same data were consistent with the hypothesis of selection on those candidate sites leading to coevolution of sperm- and egg-expressed genes. By contrast, we found no candidate sites under selection in a fourth gene (ZP1) that encodes an egg coat structural protein not directly involved in sperm binding. Finally, we found that two of the candidate sites (in C4BPA and ZP2) were correlated with variation in family size and birth rate among Hutterite couples, and those two candidate sites were also in linkage disequilibrium in the same Hutterite study population. All of these lines of evidence are consistent with predictions from a previously proposed hypothesis of balancing selection on epistatic interactions between C4BPA and ZP3 at fertilization that lead to the evolution of co-adapted allele pairs. Such patterns also suggest specific molecular traits that may be associated with both natural reproductive variation and clinical infertility.