A new method for estimating the effective population size from allele frequency changes

A new procedure is proposed for estimating the effective population size, given that information is available on changes in frequencies of the alleles at one or more independently segregating loci and the population is observed at two or more separate times. Approximate expressions are obtained for the variances of the new statistic, as well as others, also based on allele frequency changes, that have been discussed in the literature. This analysis indicates that the new statistic will generally have a smaller variance than the others. Estimates of effective population sizes and of the standard errors of the estimates are computed for data on two fly populations that have been discussed in earlier papers. In both cases, there is evidence that the effective population size is very much smaller than the minimum census size of the population.     

Likelihood-based estimation of the effective population size using temporal changes in allele frequencies: a genealogical approach

A new genetic estimator of the effective population size (N(e)) is introduced. This likelihood-based (LB) estimator uses two temporally spaced genetic samples of individuals from a population. We compared its performance to that of the classical F-statistic-based N(e) estimator (N(eFk)) by using data from simulated populations with known N(e) and real populations. The new likelihood-based estimator (N(eLB)) showed narrower credible intervals and greater accuracy than (N(eFk)) when genetic drift was strong, but performed only slightly better when genetic drift was relatively weak. When drift was strong (e.g., N(e) = 20 for five generations), as few as approximately 10 loci (heterozygosity of 0.6; samples of 30 individuals) are sufficient to consistently achieve credible intervals with an upper limit <50 using the LB method. In contrast, approximately 20 loci are required for the same precision when using the classical F-statistic approach. The N(eLB) estimator is much improved over the classical method when there are many rare alleles. It will be especially useful in conservation biology because it less often overestimates N(e) than does N(eLB) and thus is less likely to erroneously suggest that a population is large and has a low extinction risk.     

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.     

Using maximum likelihood to estimate population size from temporal changes in allele frequencies.

We develop a maximum-likelihood framework for using temporal changes in allele frequencies to estimate the number of breeding individuals in a population. We use simulations to compare the performance of this estimator to an F-statistic estimator of variance effective population size. The maximum-likelihood estimator had a lower variance and smaller bias. Taking advantage of the likelihood framework, we extend the model to include exponential growth and show that temporal allele frequency data from three or more sampling events can be used to test for population growth.     

Maximum-likelihood and markov chain monte carlo approaches to estimate inbreeding and effective size from allele frequency changes

Maximum-likelihood and Bayesian (MCMC algorithm) estimates of the increase of the Wright-Malécot inbreeding coefficient, F(t), between two temporally spaced samples, were developed from the Dirichlet approximation of allelic frequency distribution (model MD) and from the admixture of the Dirichlet approximation and the probabilities of fixation and loss of alleles (model MDL). Their accuracy was tested using computer simulations in which F(t) = 10% or less. The maximum-likelihood method based on the model MDL was found to be the best estimate of F(t) provided that initial frequencies are known exactly. When founder frequencies are estimated from a limited set of founder animals, only the estimates based on the model MD can be used for the moment. In this case no method was found to be the best in all situations investigated. The likelihood and Bayesian approaches give better results than the classical F-statistics when markers exhibiting a low polymorphism (such as the SNP markers) are used. Concerning the estimations of the effective population size all the new estimates presented here were found to be better than the F-statistics classically used.     

Temporal changes in allele frequencies and low effective population size in greater prairie-chickens

The number of greater prairie-chickens in Wisconsin has decreased by 91% since 1932. The current population of approximately 1500 birds exists primarily in four isolated management areas. In previous studies of the Wisconsin populations we documented low levels of genetic variation at microsatellite loci and the mitochondrial DNA control region. Here we investigate changes in genetic structure between the four management areas in Wisconsin over the last 50 years. We estimated the harmonic mean effective population size (Ne) over the last 50 years by comparing allele frequencies from the early 1950s with those from contemporary samples. Using a pseudo-likelihood approach that accounted for migration, estimates of Ne (15-32 prairie-chickens within each management area) were 10 times lower than census numbers from booming-ground counts. These low estimates of Ne are consistent with increased habitat fragmentation and an increase in genetic isolation between management areas over the last 50 years. The reduction of gene flow between areas has reduced Ne, increased genetic drift and, consequently, reduced genetic variation. These results have immediate consequences for the conservation of the prairie-chicken, and highlight the importance of how mating systems and limited dispersal may exacerbate the loss of genetic variation in fragmented populations.     

High throughput automated allele frequency estimation by pyrosequencing

Pyrosequencing is a DNA sequencing method based on the principle of sequencing-by-synthesis and pyrophosphate detection through a series of enzymatic reactions. This bioluminometric, real-time DNA sequencing technique offers unique applications that are cost-effective and user-friendly. In this study, we have combined a number of methods to develop an accurate, robust and cost efficient method to determine allele frequencies in large populations for association studies. The assay offers the advantage of minimal systemic sampling errors, uses a general biotin amplification approach, and replaces dTTP for dATP-apha-thio to avoid non-uniform higher peaks in order to increase accuracy. We demonstrate that this newly developed assay is a robust, cost-effective, accurate and reproducible approach for large-scale genotyping of DNA pools. We also discuss potential improvements of the software for more accurate allele frequency analysis.     

Effective population size associated with self-fertilization: lessons from temporal changes in allele frequencies in the selfing annual Medicago truncatula

Despite its significance in evolutionary and conservation biology, few estimates of effective population size (N(e)) are available in plant species. Self-fertilization is expected to affect N(e), through both its effect on homozygosity and population dynamics. Here, we estimated N(e) using temporal variation in allele frequencies for two contrasted populations of the selfing annual Medicago truncatula: a large and continuous population and a subdivided population. Estimated N(e) values were around 5-10% of the population census size suggesting that other factors than selfing must contribute to variation in allele frequencies. Further comparisons between monolocus allelic variation and changes in the multilocus genotypic composition of the populations show that the local dynamics of inbred lines can play an important role in the fluctuations of allele frequencies. Finally, comparing N(e) estimates and levels of genetic variation suggest that H(e) is a poor estimator of the contemporaneous variance effective population size.     

Investigating the causes of changes in allele frequency during evolution

The use of models as teaching aids in the study of the causes of changes of gene frequency during evolution is now a well established practice in school and degree courses. The effects of migration, selection and genetic drift may all be investigated. This paper extends the range of procedures which may be used with sixth form and more advanced students by discussing possible migration models, by describing an improved selection model where selection is applied unconsciously and the selection coefficient can be calculated from the data and by comparing single and multiple generation models.

In each case there is a brief discussion of points to be extracted from class results.

An overall teaching programme is suggested which should enable the students to investigate all three factors while spending a minimum of time on repetitive manual procedures.

Finally, there is a brief discussion of the roles of migration, drift and selection in evolution.     

Allele-sharing methods for estimation of population size

Genetic data are becoming increasingly important in ecology and conservation biology. This article presents a novel method for estimating population size from DNA profiles obtained from a random sample of individuals. The underlying idea is that the degree of biological relationship between individuals in the sample reflects the size of the population and that DNA profiles provide information about relatedness. A pseudolikelihood approach is taken, involving pairwise comparison of individuals. The main field of applications is seen to be catch data, and as an example, the method is applied to DNA profiles (10 microsatellite loci) from 334 North Atlantic minke whales. It is concluded that the sample size is too small for the method to give useful results. The question about the required sample size is investigated by simulation.     

Plant-capture estimation of the size of a homogeneous population

We consider maximum likelihood estimation of the size of a targetpopulation to which has been added a known number of plantedindividuals. The standard equal-catchability model used in mark-recaptureis assumed to be applicable to the augmented population. Afterproving the unimodality of the profile likelihood for the targetpopulation size, we obtain both the maximum likelihood estimatorof this size and interval estimators based on its asymptoticdistribution.     

SNP calling, genotype calling, and sample allele frequency estimation from new-generation sequencing data

We present a statistical framework for estimation and application of sample allele frequency spectra from New-Generation Sequencing (NGS) data. In this method, we first estimate the allele frequency spectrum using maximum likelihood. In contrast to previous methods, the likelihood function is calculated using a dynamic programming algorithm and numerically optimized using analytical derivatives. We then use a Bayesian method for estimating the sample allele frequency in a single site, and show how the method can be used for genotype calling and SNP calling. We also show how the method can be extended to various other cases including cases with deviations from Hardy-Weinberg equilibrium. We evaluate the statistical properties of the methods using simulations and by application to a real data set.     

A central resource for accurate allele frequency estimation from pooled DNA genotyped on DNA microarrays

Analysing pooled DNA on microarrays is an efficient way to genotype hundreds of individuals for thousands of markers for genome-wide association. Although direct comparison of case and control fluorescence scores is possible, correction for differential hybridization of alleles is important, particularly for rare single nucleotide polymorphisms. Such correction relies on heterozygous fluorescence scores and requires the genotyping of hundreds of individuals to obtain sufficient estimates of the correction factor, completely negating any benefit gained by pooling samples. We explore the effect of differential hybridization on test statistics and provide a solution to this problem in the form of a central resource for the accumulation of heterozygous fluorescence scores, allowing accurate allele frequency estimation at no extra cost.     

Redistribution of gene frequency and changes of genetic variation following a bottleneck in population size

Although the distribution of frequencies of genes influencing quantitative traits is important to our understanding of their genetic basis and their evolution, direct information from laboratory experiments is very limited. In theory, different models of selection and mutation generate different predictions of frequency distributions. When a large population at mutation-selection balance passes through a rapid bottleneck in size, the frequency distribution of genes is dramatically altered, causing changes in observable quantities such as the mean and variance of quantitative traits. We investigate the gene frequency distribution of a population at mutation-selection balance under a joint-effect model of real stabilizing and pleiotropic selection and its redistribution and thus changes of the genetic properties of metric and fitness traits after the population passes a rapid bottleneck and expands in size. If all genes that affect the trait are neutral with respect to fitness, the additive genetic variance (VA) is always reduced by a bottleneck in population size, regardless of their degree of dominance. For genes that have been under selection, VA increases following a bottleneck if they are (partially) recessive, while the dominance variance increases substantially for any degree of dominance. With typical estimates of mutation parameters, the joint-effect model can explain data from laboratory experiments on the effect of bottlenecking on fitness and morphological traits, providing further support for it as a plausible mechanism for maintenance of quantitative genetic variation.     

Robust estimation of population size in closed animal populations from capture-recapture experiments

In this paper the problem of finding robust estimators of population size in closed K-sample capture-recapture experiments is considered. Particular attention is paid to models where heterogeneity of capture probabilities is allowed. First, a general estimation procedure is given which does not depend on any assumptions about the form of the distribution of capture probabilities. This is followed by a detailed discussion of the usefulness of the generalized jackknife technique to reduce bias. Numerical comparisons of the bias and variance of various estimators are given. Finally, a general discussion is given with several recommendations on estimators to be used in practice.     

SNP allele frequency estimation in DNA pools and variance components analysis

The estimation of single nucleotide polymorphism (SNP) allele frequency in pooled DNA samples has been proposed as a cost-effective approach to whole genome association studies. However, the key issue is the allele frequency window in which a genotyping method operates and provides a statistically reliable answer. We assessed the homogeneous mass extend assay and estimated the variance associated with each experimental stage. We report that a relationship between estimated allele frequency and variance might exist, suggesting that high statistical power can be retained at low, as well as high, allele frequencies. Assuming this relationship, the formation of subpools consisting of 100 samples retains an effective sample size greater than 70% of the true sample size, with a savings of 11-fold the cost of an individual genotyping study, regardless of allele frequency.     

Genetic drift and estimation of effective population size

The statistical properties of the standardized variance of gene frequency changes (a quantity equivalent to Wright's inbreeding coefficient) in a random mating population are studied, and new formulae for estimating the effective population size are developed. The accuracy of the formulae depends on the ratio of sample size to effective size, the number of generations involved (t), and the number of loci or alleles used. It is shown that the standardized variance approximately follows the chi(2) distribution unless t is very large, and the confidence interval of the estimate of effective size can be obtained by using this property. Application of the formulae to data from an isolated population of Dacus oleae has shown that the effective size of this population is about one tenth of the minimum census size, though there was a possibility that the procedure of sampling genes was improper.