A method to infer positive selection from marker dynamics in an asexual population

MOTIVATION: The observation of positive selection acting on a mutant indicates that the corresponding mutation has some form of functional relevance. Determining the fitness effects of mutations thus has relevance to many interesting biological questions. One means of identifying beneficial mutations in an asexual population is to observe changes in the frequency of marked subsets of the population. We here describe a method to estimate the establishment times and fitnesses of beneficial mutations from neutral marker frequency data. RESULTS: The method accurately reproduces complex marker frequency trajectories. In simulations for which positive selection is close to 5% per generation, we obtain correlations upwards of 0.91 between correct and inferred haplotype establishment times. Where mutation selection coefficients are exponentially distributed, the inferred distribution of haplotype fitnesses is close to being correct. Applied to data from a bacterial evolution experiment, our method reproduces an observed correlation between evolvability and initial fitness defect.     

Population growth of human Y chromosomes: a study of Y chromosome microsatellites

We use variation at a set of eight human Y chromosome microsatellite loci to investigate the demographic history of the Y chromosome. Instead of assuming a population of constant size, as in most of the previous work on the Y chromosome, we consider a model which permits a period of recent population growth. We show that for most of the populations in our sample this model fits the data far better than a model with no growth. We estimate the demographic parameters of this model for each population and also the time to the most recent common ancestor. Since there is some uncertainty about the details of the microsatellite mutation process, we consider several plausible mutation schemes and estimate the variance in mutation size simultaneously with the demographic parameters of interest. Our finding of a recent common ancestor (probably in the last 120,000 years), coupled with a strong signal of demographic expansion in all populations, suggests either a recent human expansion from a small ancestral population, or natural selection acting on the Y chromosome.     

Population Genetics Inference for Longitudinally-Sampled Mutants Under Strong Selection

Longitudinal allele frequency data are becoming increasingly prevalent. Such samples permit statistical inference of the population genetics parameters that influence the fate of mutant variants. To infer these parameters by maximum likelihood, the mutant frequency is often assumed to evolve according to the Wright–Fisher model. For computational reasons, this discrete model is commonly approximated by a diffusion process that requires the assumption that the forces of natural selection and mutation are weak. This assumption is not always appropriate. For example, mutations that impart drug resistance in pathogens may evolve under strong selective pressure. Here, we present an alternative approximation to the mutant-frequency distribution that does not make any assumptions about the magnitude of selection or mutation and is much more computationally efficient than the standard diffusion approximation. Simulation studies are used to compare the performance of our method to that of the Wright–Fisher and Gaussian diffusion approximations. For large populations, our method is found to provide a much better approximation to the mutant-frequency distribution when selection is strong, while all three methods perform comparably when selection is weak. Importantly, maximum-likelihood estimates of the selection coefficient are severely attenuated when selection is strong under the two diffusion models, but not when our method is used. This is further demonstrated with an application to mutant-frequency data from an experimental study of bacteriophage evolution. We therefore recommend our method for estimating the selection coefficient when the effective population size is too large to utilize the discrete Wright–Fisher model.     

Estimating the distribution of selection coefficients from phylogenetic data with applications to mitochondrial and viral DNA

The distribution of selection coefficients of new mutations is of key interest in population genetics. In this paper we explore how codon-based likelihood models can be used to estimate the distribution of selection coefficients of new amino acid replacement mutations from phylogenetic data. To obtain such estimates we assume that all mutations at the same site have the same selection coefficient. We first estimate the distribution of selection coefficients from two large viral data sets under the assumption that the viral population size is the same along all lineages of the phylogeny and that the selection coefficients vary among sites. We then implement several new models in which the lineages of the phylogeny may have different population sizes. We apply the new models to a data set consisting of the coding regions from eight primate mitochondrial genomes. The results suggest that there might be little power to determine the exact shape of the distribution of selection coefficient but that the normal and gamma distributions fit the data significantly better than the exponential distribution.     

Transition between stochastic evolution and deterministic evolution in the presence of selection: general theory and application to virology.

We present here a self-contained analytic review of the role of stochastic factors acting on a virus population. We develop a simple one-locus, two-allele model of a haploid population of constant size including the factors of random drift, purifying selection, and random mutation. We consider different virological experiments: accumulation and reversion of deleterious mutations, competition between mutant and wild-type viruses, gene fixation, mutation frequencies at the steady state, divergence of two populations split from one population, and genetic turnover within a single population. In the first part of the review, we present all principal results in qualitative terms and illustrate them with examples obtained by computer simulation. In the second part, we derive the results formally from a diffusion equation of the Wright-Fisher type and boundary conditions, all derived from the first principles for the virus population model. We show that the leading factors and observable behavior of evolution differ significantly in three broad intervals of population size, N. The "neutral limit" is reached when N is smaller than the inverse selection coefficient. When N is larger than the inverse mutation rate per base, selection dominates and evolution is "almost" deterministic. If the selection coefficient is much larger than the mutation rate, there exists a broad interval of population sizes, in which weakly diverse populations are almost neutral while highly diverse populations are controlled by selection pressure. We discuss in detail the application of our results to human immunodeficiency virus population in vivo, sampling effects, and limitations of the model.     

Transition between Stochastic Evolution and Deterministic Evolution in the Presence of Selection: General Theory and Application to Virology

We present here a self-contained analytic review of the role of stochastic factors acting on a virus population. We develop a simple one-locus, two-allele model of a haploid population of constant size including the factors of random drift, purifying selection, and random mutation. We consider different virological experiments: accumulation and reversion of deleterious mutations, competition between mutant and wild-type viruses, gene fixation, mutation frequencies at the steady state, divergence of two populations split from one population, and genetic turnover within a single population. In the first part of the review, we present all principal results in qualitative terms and illustrate them with examples obtained by computer simulation. In the second part, we derive the results formally from a diffusion equation of the Wright-Fisher type and boundary conditions, all derived from the first principles for the virus population model. We show that the leading factors and observable behavior of evolution differ significantly in three broad intervals of population size, N. The “neutral limit” is reached when N is smaller than the inverse selection coefficient. When N is larger than the inverse mutation rate per base, selection dominates and evolution is “almost” deterministic. If the selection coefficient is much larger than the mutation rate, there exists a broad interval of population sizes, in which weakly diverse populations are almost neutral while highly diverse populations are controlled by selection pressure. We discuss in detail the application of our results to human immunodeficiency virus population in vivo, sampling effects, and limitations of the model.     

Environmental variation, fluctuating selection and genetic drift in subdivided populations

Although there have many studies of the population genetical consequences of environmental variation, little is known about the combined effects of genetic drift and fluctuating selection in structured populations. Here we use diffusion theory to investigate the effects of temporally and spatially varying selection on a population of haploid individuals subdivided into a large number of demes. Using a perturbation method for processes with multiple time scales, we show that as the number of demes tends to infinity, the overall frequency converges to a diffusion process that is also the diffusion approximation for a finite, panmictic population subject to temporally fluctuating selection. We find that the coefficients of this process have a complicated dependence on deme size and migration rate, and that changes in these demographic parameters can determine both the balance between the dispersive and stabilizing effects of environmental variation and whether selection favors alleles with lower or higher fitness variance.     

Haplotype-based inference of the distribution of fitness effects

Recent genome sequencing studies with large sample sizes in humans have discovered a vast quantity of low-frequency variants, providing an important source of information to analyze how selection is acting on human genetic variation. In order to estimate the strength of natural selection acting on low-frequency variants, we have developed a likelihood-based method that uses the lengths of pairwise identity-by-state between haplotypes carrying low-frequency variants. We show that in some nonequilibrium populations (such as those that have had recent population expansions) it is possible to distinguish between positive or negative selection acting on a set of variants. With our new framework, one can infer a fixed selection intensity acting on a set of variants at a particular frequency, or a distribution of selection coefficients for standing variants and new mutations. We show an application of our method to the UK10K phased haplotype dataset of individuals.     

A method for inferring the rate of occurrence and fitness effects of advantageous mutations

The distribution of fitness effects (DFE) of new mutations is of fundamental importance in evolutionary genetics. Recently, methods have been developed for inferring the DFE that use information from the allele frequency distributions of putatively neutral and selected nucleotide polymorphic variants in a population sample. Here, we extend an existing maximum-likelihood method that estimates the DFE under the assumption that mutational effects are unconditionally deleterious, by including a fraction of positively selected mutations. We allow one or more classes of positive selection coefficients in the model and estimate both the fraction of mutations that are advantageous and the strength of selection acting on them. We show by simulations that the method is capable of recovering the parameters of the DFE under a range of conditions. We apply the method to two data sets on multiple protein-coding genes from African populations of Drosophila melanogaster. We use a probabilistic reconstruction of the ancestral states of the polymorphic sites to distinguish between derived and ancestral states at polymorphic nucleotide sites. In both data sets, we see a significant improvement in the fit when a category of positively selected amino acid mutations is included, but no further improvement if additional categories are added. We estimate that between 1% and 2% of new nonsynonymous mutations in D. melanogaster are positively selected, with a scaled selection coefficient representing the product of the effective population size, N(e), and the strength of selection on heterozygous carriers of ～2.5.     

The degeneration of asexual haploid populations and the speed of Muller's ratchet

The accumulation of deleterious mutations due to the process known as Muller's ratchet can lead to the degeneration of nonrecombining populations. We present an analytical approximation for the rate at which this process is expected to occur in a haploid population. The approximation is based on a diffusion equation and is valid when N exp(-u/s) > 1, where N is the population size, u is the rate at which deleterious mutations occur, and s is the effect of each mutation on fitness. Simulation results are presented to show that the approximation estimates the rate of the process better than previous approximations for values of mutation rates and selection coefficients that are compatible with the biological data. Under certain conditions, the ratchet can turn at a biologically significant rate when the deterministic equilibrium number of individuals free of mutations is substantially >100. The relevance of this process for the degeneration of Y or neo-Y chromosomes is discussed.     

Estimating the strength of selective sweeps from deep population diversity data

Selective sweeps are typically associated with a local reduction of genetic diversity around the adaptive site. However, selective sweeps can also quickly carry neutral mutations to observable population frequencies if they arise early in a sweep and hitchhike with the adaptive allele. We show that the interplay between mutation and exponential amplification through hitchhiking results in a characteristic frequency spectrum of the resulting novel haplotype variation that depends only on the ratio of the mutation rate and the selection coefficient of the sweep. On the basis of this result, we develop an estimator for the selection coefficient driving a sweep. Since this estimator utilizes the novel variation arising from mutations during a sweep, it does not rely on preexisting variation and can also be applied to loci that lack recombination. Compared with standard approaches that infer selection coefficients from the size of dips in genetic diversity around the adaptive site, our estimator requires much shorter sequences but sampled at high population depth to capture low-frequency variants; given such data, it consistently outperforms standard approaches. We investigate analytically and numerically how the accuracy of our estimator is affected by the decay of the sweep pattern over time as a consequence of random genetic drift and discuss potential effects of recombination, soft sweeps, and demography. As an example for its use, we apply our estimator to deep sequencing data from human immunodeficiency virus populations.     

Estimating Selection Coefficients in Spatially Structured Populations from Time Series Data of Allele Frequencies

Inferring the nature and magnitude of selection is an important problem in many biological contexts. Typically when estimating a selection coefficient for an allele, it is assumed that samples are drawn from a panmictic population and that selection acts uniformly across the population. However, these assumptions are rarely satisfied. Natural populations are almost always structured, and selective pressures are likely to act differentially. Inference about selection ought therefore to take account of structure. We do this by considering evolution in a simple lattice model of spatial population structure. We develop a hidden Markov model based maximum-likelihood approach for estimating the selection coefficient in a single population from time series data of allele frequencies. We then develop an approximate extension of this to the structured case to provide a joint estimate of migration rate and spatially varying selection coefficients. We illustrate our method using classical data sets of moth pigmentation morph frequencies, but it has wide applications in settings ranging from ecology to human evolution.     

Components of Selection in the Evolution of the Influenza Virus: Linkage Effects Beat Inherent Selection

The influenza virus is an important human pathogen, with a rapid rate of evolution in the human population. The rate of homologous recombination within genes of influenza is essentially zero. As such, where two alleles within the same gene are in linkage disequilibrium, interference between alleles will occur, whereby selection acting upon one allele has an influence upon the frequency of the other. We here measured the relative importance of selection and interference effects upon the evolution of influenza. We considered time-resolved allele frequency data from the global evolutionary history of the haemagglutinin gene of human influenza A/H3N2, conducting an in-depth analysis of sequences collected since 1996. Using a model that accounts for selection-caused interference between alleles in linkage disequilibrium, we estimated the inherent selective benefit of individual polymorphisms in the viral population. These inherent selection coefficients were in turn used to calculate the total selective effect of interference acting upon each polymorphism, considering the effect of the initial background upon which a mutation arose, and the subsequent effect of interference from other alleles that were under selection. Viewing events in retrospect, we estimated the influence of each of these components in determining whether a mutant allele eventually fixed or died in the global viral population. Our inherent selection coefficients, when combined across different regions of the protein, were consistent with previous measurements of dN/dS for the same system. Alleles going on to fix in the global population tended to be under more positive selection, to arise on more beneficial backgrounds, and to avoid strong negative interference from other alleles under selection. However, on average, the fate of a polymorphism was determined more by the combined influence of interference effects than by its inherent selection coefficient.     

SnIPRE: Selection Inference Using a Poisson Random Effects Model

We present an approach for identifying genes under natural selection using polymorphism and divergence data from synonymous and non-synonymous sites within genes. A generalized linear mixed model is used to model the genome-wide variability among categories of mutations and estimate its functional consequence. We demonstrate how the model''s estimated fixed and random effects can be used to identify genes under selection. The parameter estimates from our generalized linear model can be transformed to yield population genetic parameter estimates for quantities including the average selection coefficient for new mutations at a locus, the synonymous and non-synynomous mutation rates, and species divergence times. Furthermore, our approach incorporates stochastic variation due to the evolutionary process and can be fit using standard statistical software. The model is fit in both the empirical Bayes and Bayesian settings using the lme4 package in R, and Markov chain Monte Carlo methods in WinBUGS. Using simulated data we compare our method to existing approaches for detecting genes under selection: the McDonald-Kreitman test, and two versions of the Poisson random field based method MKprf. Overall, we find our method universally outperforms existing methods for detecting genes subject to selection using polymorphism and divergence data.     

Anisotropic diffusion of fluorescently labeled ATP in rat cardiomyocytes determined by raster image correlation spectroscopy

A series of experimental data points to the existence of profound diffusion restrictions of ADP/ATP in rat cardiomyocytes. This assumption is required to explain the measurements of kinetics of respiration, sarcoplasmic reticulum loading with calcium, and kinetics of ATP-sensitive potassium channels. To be able to analyze and estimate the role of intracellular diffusion restrictions on bioenergetics, the intracellular diffusion coefficients of metabolites have to be determined. The aim of this work was to develop a practical method for determining diffusion coefficients in anisotropic medium and to estimate the overall diffusion coefficients of fluorescently labeled ATP in rat cardiomyocytes. For that, we have extended raster image correlation spectroscopy (RICS) protocols to be able to discriminate the anisotropy in the diffusion coefficient tensor. Using this extended protocol, we estimated diffusion coefficients of ATP labeled with the fluorescent conjugate Alexa Fluor 647 (Alexa-ATP). In the analysis, we assumed that the diffusion tensor can be described by two values: diffusion coefficient along the myofibril and that across it. The average diffusion coefficients found for Alexa-ATP were as follows: 83 +/- 14 microm(2)/s in the longitudinal and 52 +/- 16 microm(2)/s in the transverse directions (n = 8, mean +/- SD). Those values are approximately 2 (longitudinal) and approximately 3.5 (transverse) times smaller than the diffusion coefficient value estimated for the surrounding solution. Such uneven reduction of average diffusion coefficient leads to anisotropic diffusion in rat cardiomyocytes. Although the source for such anisotropy is uncertain, we speculate that it may be induced by the ordered pattern of intracellular structures in rat cardiomyocytes.     

Estimation of deleterious genomic mutation parameters in natural populations by accounting for variable mutation effects across loci

The genomes of all organisms are subject to continuous bombardment of deleterious genomic mutations (DGM). Our ability to accurately estimate various parameters of DGM has profound significance in population and evolutionary genetics. The Deng-Lynch method can estimate the parameters of DGM in natural selfing and outcrossing populations. This method assumes constant fitness effects of DGM and hence is biased under variable fitness effects of DGM. Here, we develop a statistical method to estimate DGM parameters by considering variable mutation effects across loci. Under variable mutation effects, the mean fitness and genetic variance for fitness of parental and progeny generations across selfing/outcrossing in outcrossing/selfing populations and the covariance between mean fitness of parents and that of their progeny are functions of DGM parameters: the genomic mutation rate U, average homozygous effect s, average dominance coefficient h, and covariance of selection and dominance coefficients cov(h, s). The DGM parameters can be estimated by the algorithms we developed herein, which may yield improved estimation of DGM parameters over the Deng-Lynch method as demonstrated by our simulation studies. Importantly, this method is the first one to characterize cov(h, s) for DGM.     

Detecting and Measuring Selection from Gene Frequency Data

The recent advent of high-throughput sequencing and genotyping technologies makes it possible to produce, easily and cost effectively, large amounts of detailed data on the genotype composition of populations. Detecting locus-specific effects may help identify those genes that have been, or are currently, targeted by natural selection. How best to identify these selected regions, loci, or single nucleotides remains a challenging issue. Here, we introduce a new model-based method, called SelEstim, to distinguish putative selected polymorphisms from the background of neutral (or nearly neutral) ones and to estimate the intensity of selection at the former. The underlying population genetic model is a diffusion approximation for the distribution of allele frequency in a population subdivided into a number of demes that exchange migrants. We use a Markov chain Monte Carlo algorithm for sampling from the joint posterior distribution of the model parameters, in a hierarchical Bayesian framework. We present evidence from stochastic simulations, which demonstrates the good power of SelEstim to identify loci targeted by selection and to estimate the strength of selection acting on these loci, within each deme. We also reanalyze a subset of SNP data from the Stanford HGDP–CEPH Human Genome Diversity Cell Line Panel to illustrate the performance of SelEstim on real data. In agreement with previous studies, our analyses point to a very strong signal of positive selection upstream of the LCT gene, which encodes for the enzyme lactase–phlorizin hydrolase and is associated with adult-type hypolactasia. The geographical distribution of the strength of positive selection across the Old World matches the interpolated map of lactase persistence phenotype frequencies, with the strongest selection coefficients in Europe and in the Indus Valley.     

Statistical inference of selection and divergence from a time-dependent Poisson random field model

We apply a recently developed time-dependent Poisson random field model to aligned DNA sequences from two related biological species to estimate selection coefficients and divergence time. We use Markov chain Monte Carlo methods to estimate species divergence time and selection coefficients for each locus. The model assumes that the selective effects of non-synonymous mutations are normally distributed across genetic loci but constant within loci, and synonymous mutations are selectively neutral. In contrast with previous models, we do not assume that the individual species are at population equilibrium after divergence. Using a data set of 91 genes in two Drosophila species, D. melanogaster and D. simulans, we estimate the species divergence time t(div) = 2.16 N(e) (or 1.68 million years, assuming the haploid effective population size N(e) = 6.45 x 10(5) years) and a mean selection coefficient per generation μ(γ) = 1.98/N(e). Although the average selection coefficient is positive, the magnitude of the selection is quite small. Results from numerical simulations are also presented as an accuracy check for the time-dependent model.     

Intrasexual selection in Verreaux's sifaka (Propithecus verreauxi verreauxi)

Studies of sexual selection show that both female choice and male-male competition can influence the evolution and expression of male phenotypes. In this regard, it is important to determine the functional basis through which male traits influence variation in male reproductive success. In this study, we estimate the strength and type of sexual selection acting on adult males in a population of wild lemur, Verreaux's sifaka (Propithecus verreauxi verreauxi). The data used in this study were collected at Beza Mahafaly Special Reserve, southwest Madagascar. We conducted paternity analyses on 70 males in order to estimate the distribution of reproductive success in this population. Paternity data were combined with morphometric data in order to determine which morphological traits covary with male fitness. Five morphological traits were defined in this analysis: body size, canine size, torso shape, arm shape, and leg shape. We utilized phenotypic selection models in order to determine the strength and type of selection acting directly on each trait. Our results show that directional selection acts on leg shape (a trait that is functionally related to locomotor performance), stabilizing selection acts on body mass and torso shape, and negative correlational selection acts on body mass and leg shape. We draw from biomechanical and kinematic studies of sifaka locomotion to provide a functional context for how these traits influence male mating competition within an arboreal environment. Verreaux's sifaka and many other gregarious lemurs are sexually monomorphic in body mass and canine size, despite a high frequency and intensity of male-male aggressive competition. Our results provide some insight into this paradox: in our population, there is no directional selection acting on body mass or canine size in males. The total pattern of selection implicates that behaviors relating to locomotor performance are more important than behaviors relating to fighting ability during intrasexual contests.