Monte Carlo evaluation of the likelihood for N(e) from temporally spaced samples

MLNe: Simulating and Estimating Effective Size and Migration Rate from Temporal Changes in Allele Frequencies

In studies of molecular ecology, conservation biology and evolutionary biology, the current or recent effective size (Ne) of a population is frequently estimated from the marker genotype data of two or more temporally spaced samples of individuals taken from the population. Despite the developments of numerous Bayesian, likelihood and moment estimators, only a couple of them can use both temporally and spatially spaced samples of individuals to estimate jointly the effective size (Ne) of and the migration rate (m) into a population. In this note I describe new implementations of these joint estimators of Ne and m in software MLNe which runs on multiple platforms (Windows, Mac, Linux) with or without a graphical user interface (GUI), has an integrated simulation module to simulate genotype data for investigating the impacts of various factors (such as sample size and sampling interval) on estimation precision and accuracy, exploits both Message Passing Interface (MPI) and openMP for parallel computations using multiple cores and nodes to speed up analysis. The program does not require data pre-processing and accepts multiple formats of a file of original genotype data and a file of parameters as input. The GUI facilitates data and parameter inputs and produces publication-quality output graphs, while the non-GUI version of software is convenient for batch analysis of multiple datasets as in simulations. MLNe will help advance the analysis of temporal genetic marker data for estimating Ne of and m between populations, which are important parameters that will help biologists for the conservation management of natural and managed populations. MLNe can be downloaded free from the website http://www.zsl.org/science/research/software/.

A brief history and popularity of methods and tools used to estimate micro-evolutionary forces

Population genetics is a field of research that predates the current generations of sequencing technology. Those approaches, that were established before massively parallel sequencing methods, have been adapted to these new marker systems (in some cases involving the development of new methods) that allow genome-wide estimates of the four major micro-evolutionary forces-mutation, gene flow, genetic drift, and selection. Nevertheless, classic population genetic markers are still commonly used and a plethora of analysis methods and programs is available for these and high-throughput sequencing (HTS) data. These methods employ various and diverse theoretical and statistical frameworks, to varying degrees of success, to estimate similar evolutionary parameters making it difficult to get a concise overview across the available approaches. Presently, reviews on this topic generally focus on a particular class of methods to estimate one or two evolutionary parameters. Here, we provide a brief history of methods and a comprehensive list of available programs for estimating micro-evolutionary forces. We furthermore analyzed their usage within the research community based on popularity (citation bias) and discuss the implications of this bias for the software community. We found that a few programs received the majority of citations, with program success being independent of both the parameters estimated and the computing platform. The only deviation from a model of exponential growth in the number of citations was found for the presence of a graphical user interface (GUI). Interestingly, no relationship was found for the impact factor of the journals, when the tools were published, suggesting accessibility might be more important than visibility.

Estimating virus effective population size and selection without neutral markers

By combining high-throughput sequencing (HTS) with experimental evolution, we can observe the within-host dynamics of pathogen variants of biomedical or ecological interest. We studied the evolutionary dynamics of five variants of Potato virus Y (PVY) in 15 doubled-haploid lines of pepper. All plants were inoculated with the same mixture of virus variants and variant frequencies were determined by HTS in eight plants of each pepper line at each of six sampling dates. We developed a method for estimating the intensities of selection and genetic drift in a multi-allelic Wright-Fisher model, applicable whether these forces are strong or weak, and in the absence of neutral markers. This method requires variant frequency determination at several time points, in independent hosts. The parameters are the selection coefficients for each PVY variant and four effective population sizes N_e at different time-points of the experiment. Numerical simulations of asexual haploid Wright-Fisher populations subjected to contrasting genetic drift (N_e ∈ [10, 2000]) and selection (|s| ∈ [0, 0.15]) regimes were used to validate the method proposed. The experiment in closely related pepper host genotypes revealed that viruses experienced a considerable diversity of selection and genetic drift regimes. The resulting variant dynamics were accurately described by Wright-Fisher models. The fitness ranks of the variants were almost identical between host genotypes. By contrast, the dynamics of N_e were highly variable, although a bottleneck was often identified during the systemic movement of the virus. We demonstrated that, for a fixed initial PVY population, virus effective population size is a heritable trait in plants. These findings pave the way for the breeding of plant varieties exposing viruses to stronger genetic drift, thereby slowing virus adaptation.

A growing number of experimental evolution studies are using an “evolve-and-resequence” approach to observe the within-host dynamics of pathogen variants of biomedical or ecological interest. The resulting data are particularly appropriate for studying the effects of evolutionary forces, such as selection and genetic drift, on the emergence of new pathogen variants. However, it remains challenging to unravel the effects of selection and genetic drift in the absence of neutral markers, a situation frequently encountered for microbes, such as viruses, due to their small constrained genomes. Using such an approach on a plant virus, we observed that the same set of virus variants displayed highly diverse dynamics in closely related plant genotypes. We developed and validated a method that does not require neutral markers, for estimating selection coefficients and effective population sizes from these experimental evolution data. We found that the viruses experienced considerable diversity in genetic drift regimes, depending on host genotype. Importantly, genetic drift experienced by virus populations was shown to be a heritable plant trait. These findings pave the way for the breeding of plant varieties exposing viruses to strong genetic drift, thereby slowing virus adaptation.

Clear: Composition of Likelihoods for Evolve and Resequence Experiments

The advent of next generation sequencing technologies has made whole-genome and whole-population sampling possible, even for eukaryotes with large genomes. With this development, experimental evolution studies can be designed to observe molecular evolution "in action" via evolve-and-resequence (E&R) experiments. Among other applications, E&R studies can be used to locate the genes and variants responsible for genetic adaptation. Most existing literature on time-series data analysis often assumes large population size, accurate allele frequency estimates, or wide time spans. These assumptions do not hold in many E&R studies. In this article, we propose a method-composition of likelihoods for evolve-and-resequence experiments (Clear)-to identify signatures of selection in small population E&R experiments. Clear takes whole-genome sequences of pools of individuals as input, and properly addresses heterogeneous ascertainment bias resulting from uneven coverage. Clear also provides unbiased estimates of model parameters, including population size, selection strength, and dominance, while being computationally efficient. Extensive simulations show that Clear achieves higher power in detecting and localizing selection over a wide range of parameters, and is robust to variation of coverage. We applied the Clear statistic to multiple E&R experiments, including data from a study of adaptation of Drosophila melanogaster to alternating temperatures and a study of outcrossing yeast populations, and identified multiple regions under selection with genome-wide significance.

Prediction and estimation of effective population size

Effective population size (Ne) is a key parameter in population genetics. It has important applications in evolutionary biology, conservation genetics and plant and animal breeding, because it measures the rates of genetic drift and inbreeding and affects the efficacy of systematic evolutionary forces, such as mutation, selection and migration. We review the developments in predictive equations and estimation methodologies of effective size. In the prediction part, we focus on the equations for populations with different modes of reproduction, for populations under selection for unlinked or linked loci and for the specific applications to conservation genetics. In the estimation part, we focus on methods developed for estimating the current or recent effective size from molecular marker or sequence data. We discuss some underdeveloped areas in predicting and estimating Ne for future research.

Estimating the Effective Population Size from Temporal Allele Frequency Changes in Experimental Evolution

The effective population size (Ne) is a major factor determining allele frequency changes in natural and experimental populations. Temporal methods provide a powerful and simple approach to estimate short-term Ne. They use allele frequency shifts between temporal samples to calculate the standardized variance, which is directly related to Ne. Here we focus on experimental evolution studies that often rely on repeated sequencing of samples in pools (Pool-seq). Pool-seq is cost-effective and often outperforms individual-based sequencing in estimating allele frequencies, but it is associated with atypical sampling properties: Additional to sampling individuals, sequencing DNA in pools leads to a second round of sampling, which increases the variance of allele frequency estimates. We propose a new estimator of Ne, which relies on allele frequency changes in temporal data and corrects for the variance in both sampling steps. In simulations, we obtain accurate Ne estimates, as long as the drift variance is not too small compared to the sampling and sequencing variance. In addition to genome-wide Ne estimates, we extend our method using a recursive partitioning approach to estimate Ne locally along the chromosome. Since the type I error is controlled, our method permits the identification of genomic regions that differ significantly in their Ne estimates. We present an application to Pool-seq data from experimental evolution with Drosophila and provide recommendations for whole-genome data. The estimator is computationally efficient and available as an R package at https://github.com/ThomasTaus/Nest.

Natural history collections as windows on evolutionary processes

Natural history collections provide an immense record of biodiversity on Earth. These repositories have traditionally been used to address fundamental questions in biogeography, systematics and conservation. However, they also hold the potential for studying evolution directly. While some of the best direct observations of evolution have come from long-term field studies or from experimental studies in the laboratory, natural history collections are providing new insights into evolutionary change in natural populations. By comparing phenotypic and genotypic changes in populations through time, natural history collections provide a window into evolutionary processes. Recent studies utilizing this approach have revealed some dramatic instances of phenotypic change over short timescales in response to presumably strong selective pressures. In some instances, evolutionary change can be paired with environmental change, providing a context for potential selective forces. Moreover, in a few cases, the genetic basis of phenotypic change is well understood, allowing for insight into adaptive change at multiple levels. These kinds of studies open the door to a wide range of previously intractable questions by enabling the study of evolution through time, analogous to experimental studies in the laboratory, but amenable to a diversity of species over longer timescales in natural populations.

Chemical and genetic characterization of Phlomis species and wild hybrids in Crete

The genus Phlomis is represented in the island of Crete (Greece, Eastern Mediterranean) by three species Phlomis cretica C. Presl., Phlomis fruticosa L., the island endemic Phlomis lanata Willd. and three hybrids Phlomis x cytherea Rech.f. (P. cretica x P. fruticosa), Phlomis x commixta Rech.f. (P. cretica x P. lanata) and Phlomis x sieberi Vierh. (P. fruticosa x P. lanata). This work describes (a) the profile of hybrids and parental species concerning their volatile compounds, (b) the suitability of ribosomal nuclear (ITS region), chloroplast (trnH-psbA), and AFLP markers to identify hybrids and (c) their competence to characterize the different chemotypes of both hybrids and their parental species. The cluster analysis and PCA constructed from chemical data (volatile oils) suggest that there are three groups of taxa. Group IA includes P. cretica and P. fruticosa, group IB includes P. x cytherea, whereas group II consists of P. x commixta, P. x sieberi and P. lanata. Volatile compounds detected only in the hybrids P. x sieberi and P. x commixta correspond to the 3% of the total compounds, value that is much higher in P. x cytherea (21%). Neighbor-joining, statistical parsimony analysis and the observations drawn from ribotypes spectrum of ITS markers divided Phlomis species in two groups, P. lanata and the complex P. cretica/P. fruticosa. In contrast to the ITS region, the plastid DNA marker follows a geographically related pattern. Neighbor-Net, PCA and Bayesian assignment analysis performed for AFLP markers separated the genotypes into three groups corresponding to populations of P. cretica, P. fruticosa, and P. lanata, respectively, while populations of P. x commixta, P. x cytherea, and P. x sieberi presented admixed ancestry. Most of the P. x cytherea samples were identified as F1 hybrids by Bayesian assignment test, while those of P. x commixta and P. x sieberi were identified as F2 hybrids. Overall, high chemical differentiation is revealed in one of the three hybrids, which is likely related with niche variation. Moreover, molecular markers show potential to identify Phlomis taxa.

Estimating effective population size from temporally spaced samples with a novel, efficient maximum-likelihood algorithm

The effective population size Ne is a key parameter in population genetics and evolutionary biology, as it quantifies the expected distribution of changes in allele frequency due to genetic drift. Several methods of estimating Ne have been described, the most direct of which uses allele frequencies measured at two or more time points. A new likelihood-based estimator NB^ for contemporary effective population size using temporal data is developed in this article. The existing likelihood methods are computationally intensive and unable to handle the case when the underlying Ne is large. This article tries to work around this problem by using a hidden Markov algorithm and applying continuous approximations to allele frequencies and transition probabilities. Extensive simulations are run to evaluate the performance of the proposed estimator NB^, and the results show that it is more accurate and has lower variance than previous methods. The new estimator also reduces the computational time by at least 1000-fold and relaxes the upper bound of Ne to several million, hence allowing the estimation of larger Ne. Finally, we demonstrate how this algorithm can cope with nonconstant Ne scenarios and be used as a likelihood-ratio test to test for the equality of Ne throughout the sampling horizon. An R package “NB” is now available for download to implement the method described in this article.

Thinking too positive? Revisiting current methods of population genetic selection inference

In the age of next-generation sequencing, the availability of increasing amounts and improved quality of data at decreasing cost ought to allow for a better understanding of how natural selection is shaping the genome than ever before. However, alternative forces, such as demography and background selection (BGS), obscure the footprints of positive selection that we would like to identify. In this review, we illustrate recent developments in this area, and outline a roadmap for improved selection inference. We argue (i) that the development and obligatory use of advanced simulation tools is necessary for improved identification of selected loci, (ii) that genomic information from multiple time points will enhance the power of inference, and (iii) that results from experimental evolution should be utilized to better inform population genomic studies.

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.

Investigating population history using temporal genetic differentiation

The rapid advance of sequencing technology, coupled with improvements in molecular methods for obtaining genetic data from ancient sources, holds the promise of producing a wealth of genomic data from time-separated individuals. However, the population-genetic properties of time-structured samples have not been extensively explored. Here, we consider the implications of temporal sampling for analyses of genetic differentiation and use a temporal coalescent framework to show that complex historical events such as size reductions, population replacements, and transient genetic barriers between populations leave a footprint of genetic differentiation that can be traced through history using temporal samples. Our results emphasize explicit consideration of the temporal structure when making inferences and indicate that genomic data from ancient individuals will greatly increase our ability to reconstruct population history.

WFABC: a Wright-Fisher ABC-based approach for inferring effective population sizes and selection coefficients from time-sampled data

With novel developments in sequencing technologies, time-sampled data are becoming more available and accessible. Naturally, there have been efforts in parallel to infer population genetic parameters from these data sets. Here, we compare and analyse four recent approaches based on the Wright-Fisher model for inferring selection coefficients (s) given effective population size (N(e)), with simulated temporal data sets. Furthermore, we demonstrate the advantage of a recently proposed approximate Bayesian computation (ABC)-based method that is able to correctly infer genomewide average N(e) from time-serial data, which is then set as a prior for inferring per-site selection coefficients accurately and precisely. We implement this ABC method in a new software and apply it to a classical time-serial data set of the medionigra genotype in the moth Panaxia dominula. We show that a recessive lethal model is the best explanation for the observed variation in allele frequency by implementing an estimator of the dominance ratio (h).

Influenza virus drug resistance: a time-sampled population genetics perspective

The challenge of distinguishing genetic drift from selection remains a central focus of population genetics. Time-sampled data may provide a powerful tool for distinguishing these processes, and we here propose approximate Bayesian, maximum likelihood, and analytical methods for the inference of demography and selection from time course data. Utilizing these novel statistical and computational tools, we evaluate whole-genome datasets of an influenza A H1N1 strain in the presence and absence of oseltamivir (an inhibitor of neuraminidase) collected at thirteen time points. Results reveal a striking consistency amongst the three estimation procedures developed, showing strongly increased selection pressure in the presence of drug treatment. Importantly, these approaches re-identify the known oseltamivir resistance site, successfully validating the approaches used. Enticingly, a number of previously unknown variants have also been identified as being positively selected. Results are interpreted in the light of Fisher's Geometric Model, allowing for a quantification of the increased distance to optimum exerted by the presence of drug, and theoretical predictions regarding the distribution of beneficial fitness effects of contending mutations are empirically tested. Further, given the fit to expectations of the Geometric Model, results suggest the ability to predict certain aspects of viral evolution in response to changing host environments and novel selective pressures.

Genetic diversity, fixation and differentiation of the freshwater snail Biomphalaria pfeifferi (Gastropoda, Planorbidae) in arid lands

The freshwater snail Biomphalaria pfeifferi is the main intermediate host of human intestinal Bilharziasis. It is widely distributed in Africa, Madagascar and middle-eastern countries, and its habitat includes wetlands, and arid to semi-arid areas. Based on analysis of 18 microsatellites, we investigated reference allelic variation among 30 populations of B. pfeifferi from three drainage basins in Dhofar, Oman (the eastern limit of its distribution). This is an arid to semi-arid region, with a 9,000-year history of very low rainfall, but is subject to unpredictable and destructive flash floods. In this context we showed that genetic fixation was very high compared to genetic differentiation which was moderate and, that, relative to B. pfeifferi populations from wetlands, the populations in Dhofar show evidence of lower levels of genetic diversity, a higher degree of genetic fixation, a quasi-absence of migration, and a higher level of genetic drift. Despite the extreme conditions in the Dhofar habitat of this species, it is able to survive because of its very high self-fertilization (approaching 100 %) and fecundity rates.

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.

Estimating allele age and selection coefficient from time-serial data

Recent advances in sequencing technologies have made available an ever-increasing amount of ancient genomic data. In particular, it is now possible to target specific single nucleotide polymorphisms in several samples at different time points. Such time-series data are also available in the context of experimental or viral evolution. Time-series data should allow for a more precise inference of population genetic parameters and to test hypotheses about the recent action of natural selection. In this manuscript, we develop a likelihood method to jointly estimate the selection coefficient and the age of an allele from time-serial data. Our method can be used for allele frequencies sampled from a single diallelic locus. The transition probabilities are calculated by approximating the standard diffusion equation of the Wright-Fisher model with a one-step process. We show that our method produces unbiased estimates. The accuracy of the method is tested via simulations. Finally, the utility of the method is illustrated with an application to several loci encoding coat color in horses, a pattern that has previously been linked with domestication. Importantly, given our ability to estimate the age of the allele, it is possible to gain traction on the important problem of distinguishing selection on new mutations from selection on standing variation. In this coat color example for instance, we estimate the age of this allele, which is found to predate domestication.

Microsatellite genotyping reveals end-Pleistocene decline in mammoth autosomal genetic variation

The last glaciation was a dynamic period with strong impact on the demography of many species and populations. In recent years, mitochondrial DNA sequences retrieved from radiocarbon-dated remains have provided novel insights into the history of Late Pleistocene populations. However, genotyping of loci from the nuclear genome may provide enhanced resolution of population-level changes. Here, we use four autosomal microsatellite DNA markers to investigate the demographic history of woolly mammoths (Mammuthus primigenius) in north-eastern Siberia from before 60 000 years ago up until the species' final disappearance c.4000 years ago. We identified two genetic groups, implying a marked temporal genetic differentiation between samples with radiocarbon ages older than 12 thousand radiocarbon years before present (ka) and those younger than 9ka. Simulation-based analysis indicates that this dramatic change in genetic composition, which included a decrease in individual heterozygosity of approximately 30%, was due to a multifold reduction in effective population size. A corresponding reduction in genetic variation was also detected in the mitochondrial DNA, where about 65% of the diversity was lost. We observed no further loss in genetic variation during the Holocene, which suggests a rapid final extinction event.

Catastrophic floods may pave the way for increased genetic diversity in endemic artesian spring snail populations

The role of disturbance in the promotion of biological heterogeneity is widely recognised and occurs at a variety of ecological and evolutionary scales. However, within species, the impact of disturbances that decimate populations are neither predicted nor known to result in conditions that promote genetic diversity. Directly examining the population genetic consequences of catastrophic disturbances however, is rarely possible, as it requires both longitudinal genetic data sets and serendipitous timing. Our long-term study of the endemic aquatic invertebrates of the artesian spring ecosystem of arid central Australia has presented such an opportunity. Here we show a catastrophic flood event, which caused a near total population crash in an aquatic snail species (Fonscochlea accepta) endemic to this ecosystem, may have led to enhanced levels of within species genetic diversity. Analyses of individuals sampled and genotyped from the same springs sampled both pre (1988–1990) and post (1995, 2002–2006) a devastating flood event in 1992, revealed significantly higher allelic richness, reduced temporal population structuring and greater effective population sizes in nearly all post flood populations. Our results suggest that the response of individual species to disturbance and severe population bottlenecks is likely to be highly idiosyncratic and may depend on both their ecology (whether they are resilient or resistant to disturbance) and the stability of the environmental conditions (i.e. frequency and intensity of disturbances) in which they have evolved.

Bayesian inference of a historical bottleneck in a heavily exploited marine mammal

Emerging Bayesian analytical approaches offer increasingly sophisticated means of reconstructing historical population dynamics from genetic data, but have been little applied to scenarios involving demographic bottlenecks. Consequently, we analysed a large mitochondrial and microsatellite dataset from the Antarctic fur seal Arctocephalus gazella, a species subjected to one of the most extreme examples of uncontrolled exploitation in history when it was reduced to the brink of extinction by the sealing industry during the late eighteenth and nineteenth centuries. Classical bottleneck tests, which exploit the fact that rare alleles are rapidly lost during demographic reduction, yielded ambiguous results. In contrast, a strong signal of recent demographic decline was detected using both Bayesian skyline plots and Approximate Bayesian Computation, the latter also allowing derivation of posterior parameter estimates that were remarkably consistent with historical observations. This was achieved using only contemporary samples, further emphasizing the potential of Bayesian approaches to address important problems in conservation and evolutionary biology.

Historical sampling reveals dramatic demographic changes in western gorilla populations

BACKGROUND

Today many large mammals live in small, fragmented populations, but it is often unclear whether this subdivision is the result of long-term or recent events. Demographic modeling using genetic data can estimate changes in long-term population sizes while temporal sampling provides a way to compare genetic variation present today with that sampled in the past. In order to better understand the dynamics associated with the divergences of great ape populations, these analytical approaches were applied to western gorillas (Gorilla gorilla) and in particular to the isolated and Critically Endangered Cross River gorilla subspecies (G. g. diehli).

RESULTS

We used microsatellite genotypes from museum specimens and contemporary samples of Cross River gorillas to infer both the long-term and recent population history. We find that Cross River gorillas diverged from the ancestral western gorilla population ~17,800 years ago (95% HDI: 760, 63,245 years). However, gene flow ceased only ~420 years ago (95% HDI: 200, 16,256 years), followed by a bottleneck beginning ~320 years ago (95% HDI: 200, 2,825 years) that caused a 60-fold decrease in the effective population size of Cross River gorillas. Direct comparison of heterozygosity estimates from museum and contemporary samples suggests a loss of genetic variation over the last 100 years.

CONCLUSIONS

The composite history of western gorillas could plausibly be explained by climatic oscillations inducing environmental changes in western equatorial Africa that would have allowed gorilla populations to expand over time but ultimately isolate the Cross River gorillas, which thereafter exhibited a dramatic population size reduction. The recent decrease in the Cross River population is accordingly most likely attributable to increasing anthropogenic pressure over the last several hundred years. Isolation of diverging populations with prolonged concomitant gene flow, but not secondary admixture, appears to be a typical characteristic of the population histories of African great apes, including gorillas, chimpanzees and bonobos.

Estimation of 2Nes from temporal allele frequency data

We develop a new method for estimating effective population sizes, Ne, and selection coefficients, s, from time-series data of allele frequencies sampled from a single diallelic locus. The method is based on calculating transition probabilities, using a numerical solution of the diffusion process, and assuming independent binomial sampling from this diffusion process at each time point. We apply the method in two example applications. First, we estimate selection coefficients acting on the CCR5-delta 32 mutation on the basis of published samples of contemporary and ancient human DNA. We show that the data are compatible with the assumption of s = 0, although moderate amounts of selection acting on this mutation cannot be excluded. In our second example, we estimate the selection coefficient acting on a mutation segregating in an experimental phage population. We show that the selection coefficient acting on this mutation is approximately 0.43.

Unbiased estimator for genetic drift and effective population size

Amounts of genetic drift and the effective size of populations can be estimated from observed temporal shifts in sample allele frequencies. Bias in this so-called temporal method has been noted in cases of small sample sizes and when allele frequencies are highly skewed. We characterize bias in commonly applied estimators under different sampling plans and propose an alternative estimator for genetic drift and effective size that weights alleles differently. Numerical evaluations of exact probability distributions and computer simulations verify that this new estimator yields unbiased estimates also when based on a modest number of alleles and loci. At the cost of a larger standard deviation, it thus eliminates the bias associated with earlier estimators. The new estimator should be particularly useful for microsatellite loci and panels of SNPs, representing a large number of alleles, many of which will occur at low frequencies.

The genetic effective and adult census size of an Australian population of tiger prawns (Penaeus esculentus)

This study compares estimates of the census size of the spawning population with genetic estimates of effective current and long-term population size for an abundant and commercially important marine invertebrate, the brown tiger prawn (Penaeus esculentus). Our aim was to focus on the relationship between genetic effective and census size that may provide a source of information for viability analyses of naturally occurring populations. Samples were taken in 2001, 2002 and 2003 from a population on the east coast of Australia and temporal allelic variation was measured at eight polymorphic microsatellite loci. Moments-based and maximum-likelihood estimates of current genetic effective population size ranged from 797 to 1304. The mean long-term genetic effective population size was 9968. Although small for a large population, the effective population size estimates were above the threshold where genetic diversity is lost at neutral alleles through drift or inbreeding. Simulation studies correctly predicted that under these experimental conditions the genetic estimates would have non-infinite upper confidence limits and revealed they might be overestimates of the true size. We also show that estimates of mortality and variance in family size may be derived from data on average fecundity, current genetic effective and census spawning population size, assuming effective population size is equivalent to the number of breeders. This work confirms that it is feasible to obtain accurate estimates of current genetic effective population size for abundant Type III species using existing genetic marker technology.

Demographic and genetic estimates of effective population and breeding size in the amphibian Rana temporaria

Genetic methods for estimating effective population size ( Ne) or the effective number of breeders ( Nb) have become popular, but comparisons of these estimates with demographic estimates of Ne and Nb are rare, especially in anurans. We used three genetic (linkage disequilibrium, temporal moments, Bayesian coalescent-based method) and three demographic models, the latter considering number of breeding individuals, sex ratio, reproductive skew, and other demographic data, to estimate Ne and Nb in two subarctic populations (T and P) of the common frog Rana temporaria, subject to long-term capture-recapture studies. Demographic estimates of Ne based on total population size ( Ne ([T])= 44.5-56.9; Ne ([P])= 68.8-93.7) deviated markedly from the genetic estimates obtained using the linkage disequilibrium method ( Ne ([T])= 97.1; Ne ([P])= 13.2). The demographic estimates of Nb, taking into consideration sex ratio and variance in reproductive success ( Nb ([T])= 10.1-39.7; Nb ([P])= 3.9-21.3), were higher than the genetic estimates ( Nb ([T])= 3.7-5.4; Nb ([P])= 3.5-3.9). The main factors affecting the effective size estimates were sex ratio and reproductive skew. The discrepancies between corresponding Ne and Nb estimates highlight the sensitivity of both demographic and genetic estimates on their underlying assumptions. Yet the ratios of effective or breeding effective size to the census population size were similar to those reported earlier for anurans, reinforcing the view that the discrepancy between actual and effective breeding sizes in anuran populations is typically very large.

Temporal estimates of effective population size in species with overlapping generations

The standard temporal method for estimating effective population size (N(e)) assumes that generations are discrete, but it is routinely applied to species with overlapping generations. We evaluated bias in the estimates N(e) caused by violation of this assumption, using simulated data for three model species: humans (type I survival), sparrow (type II), and barnacle (type III). We verify a previous proposal by Felsenstein that weighting individuals by reproductive value is the correct way to calculate parametric population allele frequencies, in which case the rate of change in age-structured populations conforms to that predicted by discrete-generation models. When the standard temporal method is applied to age-structured species, typical sampling regimes (sampling only newborns or adults; randomly sampling the entire population) do not yield properly weighted allele frequencies and result in biased N(e). The direction and magnitude of the bias are shown to depend on the sampling method and the species' life history. Results for populations that grow (or decline) at a constant rate paralleled those for populations of constant size. If sufficient demographic data are available and certain sampling restrictions are met, the Jorde-Ryman modification of the temporal method can be applied to any species with overlapping generations. Alternatively, spacing the temporal samples many generations apart maximizes the drift signal compared to sampling biases associated with age structure.

Simultaneous estimation of mixing rates and genetic drift under successive sampling of genetic markers with application to the mud crab (Scylla paramamosain) in Japan

In stock enhancement programs, it is important to assess mixing rates of released individuals in stocks. For this purpose, genetic stock identification has been applied. The allele frequencies in a composite population are expressed as a mixture of the allele frequencies in the natural and released populations. The estimation of mixing rates is possible, under successive sampling from the composite population, on the basis of temporal changes in allele frequencies. The allele frequencies in the natural population may be estimated from those of the composite population in the preceding year. However, it should be noted that these frequencies can vary between generations due to genetic drift. In this article, we develop a new method for simultaneous estimation of mixing rates and genetic drift in a stock enhancement program. Numerical simulation shows that our procedure estimates the mixing rate with little bias. Although the genetic drift is underestimated when the amount of information is small, reduction of the bias is possible by analyzing multiple unlinked loci. The method was applied to real data on mud crab stocking, and the result showed a yearly variation in the mixing rate.

High genetic diversity and no inbreeding in the endangered copper redhorse, Moxostoma hubbsi (Catostomidae, Pisces): the positive sides of a long generation time

The evolutionary potential of a species is determined by its genetic diversity. Thus, management plans should integrate genetic concerns into active conservation efforts. The copper redhorse (Moxostoma hubbsi) is an endangered species, with an endemic distribution limited to the Richelieu River and a short section of the St Lawrence River in Quebec, Canada. The population, gradually fragmented since 1849, is characterized by a decline in population size and a lack of recruitment. A total of 269 samples were collected between 1984 and 2004 and genotyped using 22 microsatellite loci, which indicated that these fish comprise a single population, with a global F(ST) value of only 0.0038. Despite a small census size ( approximately 500), a high degree of genetic diversity was observed compared to common values for freshwater fishes (average number of 12.5 alleles/locus and average HO of 0.77 +/- 0.08). No difference was observed between expected and observed pairwise values of relatedness (r(xy): -0.00013 +/- 0.11737), suggesting an outbred population. Long-term Ne was estimated at 4476 whereas contemporary Ne values ranged from 107 to 568, suggesting a pronounced yet gradual demographic decline of the population, as no bottleneck could be detected for the recent past. By means of simulations, we estimated Ne would need to remain at more than approximately 400 to retain 90% of the genetic diversity over 100 years. Overall, these observations corroborate other recent empirical studies confirming that long generation times may act as a buffering effect contributing to a reduction in the pace of genetic diversity erosion in threatened species.

Genetic diversity, population structure, effective population size and demographic history of the Finnish wolf population

The Finnish wolf population (Canis lupus) was sampled during three different periods (1996-1998, 1999-2001 and 2002-2004), and 118 individuals were genotyped with 10 microsatellite markers. Large genetic variation was found in the population despite a recent demographic bottleneck. No spatial population subdivision was found even though a significant negative relationship between genetic relatedness and geographic distance suggested isolation by distance. Very few individuals did not belong to the local wolf population as determined by assignment analyses, suggesting a low level of immigration in the population. We used the temporal approach and several statistical methods to estimate the variance effective size of the population. All methods gave similar estimates of effective population size, approximately 40 wolves. These estimates were slightly larger than the estimated census size of breeding individuals. A Bayesian model based on Markov chain Monte Carlo simulations indicated strong evidence for a long-term population decline. These results suggest that the contemporary wolf population size is roughly 8% of its historical size, and that the population decline dates back to late 19th century or early 20th century. Despite an increase of over 50% in the census size of the population during the whole study period, there was only weak evidence that the effective population size during the last period was higher than during the first. This may be caused by increased inbreeding, diminished dispersal within the population, and decreased immigration to the population during the last study period.

Impact of insecticide-treated bed nets implementation on the genetic structure of Anopheles arabiensis in an area of irrigated rice fields in the Sahelian region of Cameroon

Variation at 12 microsatellite loci was investigated to assess the impact of the implementation of insecticide-treated bed nets (ITNs) on the genetic structure of Anopheles arabiensis in Simatou, a village surrounded by irrigated rice fields in the Sahelian area of Cameroon. The An. arabiensis population of Simatou was sampled twice before ITN implementation, and twice after. Effective population size estimates (N(e)) were similar across each time point, except for the period closely following ITN introduction where a nonsignificant reduction was recorded. Hence, we believe that ITN implementation resulted in a temporary bottleneck, rapidly followed by a demographic expansion. The genetic diversity of the population was not significantly affected since different genetic parameters (allele number, observed and expected heterozygosities) remained stable. Low estimates of genetic differentiation between the populations from Simatou and Lagdo, separated by 300 km, suggested extensive gene flow among populations of An. arabiensis in the Sahelian region of Cameroon. A decrease in the susceptibility to deltamethrin was observed following ITN introduction, but no kdr mutation was detected and a metabolic resistance mechanism is probably involved. The temporary effect of ITNs on the genetic structure of An. arabiensis population suggests that, to optimize the success of any control programme of this species based on ITNs, the control area should be very large and the programme should be implemented for a long period of time.

Detecting past population bottlenecks using temporal genetic data

Population bottlenecks wield a powerful influence on the evolution of species and populations by reducing the repertoire of responses available for stochastic environmental events. Although modern contractions of wild populations due to human-related impacts have been documented globally, discerning historic bottlenecks for all but the most recent and severe events remains a serious challenge. Genetic samples dating to different points in time may provide a solution in some cases. We conducted serial coalescent simulations to assess the extent to which temporal genetic data are informative regarding population bottlenecks. These simulations demonstrated that the power to reject a constant population size hypothesis using both ancient and modern genetic data is almost always higher than that based solely on modern data. The difference in power between the modern and temporal DNA approaches depends significantly on effective population size and bottleneck intensity and less significantly on sample size. The temporal approach provides more power in cases of genetic recovery (via migration) from a bottleneck than in cases of demographic recovery (via population growth). Choice of genetic region is critical, as mutation rate heavily influences the extent to which temporal sampling yields novel information regarding the demographic history of populations.

Population structure within lineages of Wheat streak mosaic virus derived from a common founding event exhibits stochastic variation inconsistent with the deterministic quasi-species model

Structure of Wheat streak mosaic virus (WSMV) populations derived from a common founding event and subjected to serial passage at high multiplicity of infection (MOI) was evaluated. The founding population was generated by limiting dilution inoculation. Lineages of known pedigree were sampled at passage 9 (two populations) and at passage 15, with (three populations) or without mixing (four populations) of lineages at passage 10. Polymorphism within each population was assessed by sequencing 17-21 clones containing a 1371 nt region (WSMV-Sidney 81 nts 8001-9371) encompassing the entire coat protein cistron and flanking regions. Mutation frequency averaged approximately 5.0 x 10(-4)/nt across all populations and ranged from 2.4 to 11.6 x 10(-4)/nt within populations, but did not consistently increase or decrease with the number of passages removed from the founding population. Shared substitutions (19 nonsynonymous, 10 synonymous, and 3 noncoding) occurred at 32 sites among 44 haplotypes. Only four substitutions became fixed (frequency = 100%) within a population and nearly one third (10/32) never achieved a frequency of 10% or greater in any sampled population. Shared substitutions were randomly distributed with respect to genome position, with transitions outnumbering transversions 5.4:1 and a clear bias for A to G and U to C substitutions. Haplotype composition of each population was unique with complexity of each population varying unpredictably, in that the number and frequency of haplotypes within a lineage were not correlated with number of passages removed from the founding population or whether the population was derived from a single or mixed lineage. The simplest explanation is that plant virus lineages, even those propagated at high MOI, are subject to frequent, narrow genetic bottlenecks during systemic movement that result in low effective population size and stochastic changes in population structure upon serial passage.

Estimation of effective population sizes from data on genetic markers

The effective population size (Ne) is an important parameter in ecology, evolutionary biology and conservation biology. It is, however, notoriously difficult to estimate, mainly because of the highly stochastic nature of the processes of inbreeding and genetic drift for which Ne is usually defined and measured, and because of the many factors (such as time and spatial scales, systematic forces) confounding such processes. Many methods have been developed in the past three decades to estimate the current, past and ancient effective population sizes using different information extracted from some genetic markers in a sample of individuals. This paper reviews the methodologies proposed for estimating Ne from genetic data using information on heterozygosity excess, linkage disequilibrium, temporal changes in allele frequency, and pattern and amount of genetic variation within and between populations. For each methodology, I describe mainly the logic and genetic model on which it is based, the data required and information used, the interpretation of the estimate obtained, some results from applications to simulated or empirical datasets and future developments that are needed.

Comparative evaluation of a new effective population size estimator based on approximate bayesian computation

We describe and evaluate a new estimator of the effective population size (N(e)), a critical parameter in evolutionary and conservation biology. This new "SummStat" N(e) estimator is based upon the use of summary statistics in an approximate Bayesian computation framework to infer N(e). Simulations of a Wright-Fisher population with known N(e) show that the SummStat estimator is useful across a realistic range of individuals and loci sampled, generations between samples, and N(e) values. We also address the paucity of information about the relative performance of N(e) estimators by comparing the SummStat estimator to two recently developed likelihood-based estimators and a traditional moment-based estimator. The SummStat estimator is the least biased of the four estimators compared. In 32 of 36 parameter combinations investigated using initial allele frequencies drawn from a Dirichlet distribution, it has the lowest bias. The relative mean square error (RMSE) of the SummStat estimator was generally intermediate to the others. All of the estimators had RMSE > 1 when small samples (n = 20, five loci) were collected a generation apart. In contrast, when samples were separated by three or more generations and N(e) < or = 50, the SummStat and likelihood-based estimators all had greatly reduced RMSE. Under the conditions simulated, SummStat confidence intervals were more conservative than the likelihood-based estimators and more likely to include true N(e). The greatest strength of the SummStat estimator is its flexible structure. This flexibility allows it to incorporate any potentially informative summary statistic from population genetic data.

Ecological components and evolution of selfing in the freshwater snail Galba truncatula

The reproductive assurance hypothesis emphasizes that self-fertilization should evolve in species with reduced dispersal capability, low population size or experiencing recurrent bottlenecks. Our work investigates the ecological components of the habitats colonized by the snail, Galba truncatula, that may influence the evolution of selfing. Galba truncatula is a preferential selfer inhabiting freshwater habitats, which vary with respect to the degree of permanence. We considered with a population genetic approach the spatial and the temporal degree of isolation of populations of G. truncatula. We showed that patches at distances of only a few meters are highly structured. The effective population sizes appear quite low, in the order of 10 individuals or less. This study indicates that individuals of the species G. truncatula are likely to be alone in a site and have a low probability of finding a partner from a nearby site to reproduce. These results emphasize the advantage of selfing in this species.

An efficient Monte Carlo method for estimating Ne from temporally spaced samples using a coalescent-based likelihood

This article presents an efficient importance-sampling method for computing the likelihood of the effective size of a population under the coalescent model of Berthier et al. Previous computational approaches, using Markov chain Monte Carlo, required many minutes to several hours to analyze small data sets. The approach presented here is orders of magnitude faster and can provide an approximation to the likelihood curve, even for large data sets, in a matter of seconds. Additionally, confidence intervals on the estimated likelihood curve provide a useful estimate of the Monte Carlo error. Simulations show the importance sampling to be stable across a wide range of scenarios and show that the N(e) estimator itself performs well. Further simulations show that the 95% confidence intervals around the N(e) estimate are accurate. User-friendly software implementing the algorithm for Mac, Windows, and Unix/Linux is available for download. Applications of this computational framework to other problems are discussed.

On the distribution of temporal variations in allele frequency: consequences for the estimation of effective population size and the detection of loci undergoing selection

The effective population size (Ne) is frequently estimated using temporal changes in allele frequencies at neutral markers. Such temporal changes in allele frequencies are usually estimated from the standardized variance in allele frequencies (Fc). We simulate Wright-Fisher populations to generate expected distributions of Fc and of Fc (Fc averaged over several loci). We explore the adjustment of these simulated Fc distributions to a chi-square distribution and evaluate the resulting precision on the estimation of Ne for various scenarios. Next, we outline a procedure to test for the homogeneity of the individual Fc across loci and identify markers exhibiting extreme Fc-values compared to the rest of the genome. Such loci are likely to be in genomic areas undergoing selection, driving Fc to values greater (or smaller) than expected under drift alone. Our procedure assigns a P-value to each locus under the null hypothesis (drift is homogeneous throughout the genome) and simultaneously controls the rate of false positive among loci declared as departing significantly from the null. The procedure is illustrated using two published data sets: (i) an experimental wheat population subject to natural selection and (ii) a maize population undergoing recurrent selection.

Estimation of genetically effective breeding numbers using a rejection algorithm approach

Polygynous mating results in nonrandom sampling of the adult male gamete pool in each generation, thereby increasing the rate of genetic drift. In principle, genetic paternity analysis can be used to infer the effective number of breeding males (Nebm). However, this requires genetic data from an exhaustive sample of candidate males. Here we describe a new approach to estimate Nebm using a rejection algorithm in association with three statistics: Euclidean distance between the frequency distributions of maternally and paternally inherited alleles, average number of paternally inherited alleles and average gene diversity of paternally inherited alleles. We quantify the relationship between these statistics and Nebm using an individual-based simulation model in which the male mating system varied continuously between random mating and extreme polygyny. We evaluate this method using genetic data from a natural population of highly polygynous fruit bats (Cynopterous sphinx). Using data in the form of mother-offspring genotypes, we demonstrate that estimates of Nebm are very similar to independent estimates based on a direct paternity analysis that included data on candidate males. Our method also permits an evaluation of uncertainty in estimates of Nebm and thus facilitates inferences about the mating system from genetic data. Finally, we investigate the sensitivity of our method to sample size, model assumptions, adult population size and the mating system. These analyses demonstrate that the rejection algorithm provides accurate estimates of Nebm across a broad range of demographic scenarios, except when the true Nebm is high.

Effective population sizes and temporal stability of genetic structure in Rana pipiens, the northern leopard frog

Although studies of population genetic structure are very common, whether genetic structure is stable over time has been assessed for very few taxa. The question of stability over time is particularly interesting for frogs because it is not clear to what extent frogs exist in dynamic metapopulations with frequent extinction and recolonization, or in stable patches at equilibrium between drift and gene flow. In this study we collected tissue samples from the same five populations of leopard frogs, Rana pipiens, over a 22-30 year time interval (11-15 generations). Genetic structure among the populations was very stable, suggesting that these populations were not undergoing frequent extinction and colonization. We also estimated the effective size of each population from the change in allele frequencies over time. There exist few estimates of effective size for frog populations, but the data available suggest that ranid frogs may have much larger ratios of effective size (Ne) to census size (Nc) than toads (bufonidae). Our results indicate that R. pipiens populations have effective sizes on the order of hundreds to at most a few thousand frogs, and Ne/Nc ratios in the range of 0.1-1.0. These estimates of Ne/Nc are consistent with those estimated for other Rana species. Finally, we compared the results of three temporal methods for estimating Ne. Moment and pseudolikelihood methods that assume a closed population gave the most similar point estimates, although the moment estimates were consistently two to four times larger. Wang and Whitlock's new method that jointly estimates Ne and the rate of immigration into a population (m) gave much smaller estimates of Ne and implausibly large estimates of m. This method requires knowing allele frequencies in the source of immigrants, but was thought to be insensitive to inexact estimates. In our case the method may have failed because we did not know the true source of immigrants for each population. The method may be more sensitive to choice of source frequencies than was previously appreciated, and so should be used with caution if the most likely source of immigrants cannot be identified clearly.