Samples from subdivided populations yield biased estimates of effective size that overestimate the rate of loss of genetic variation

Many empirical studies estimating effective population size apply the temporal method that provides an estimate of the variance effective size through the amount of temporal allele frequency change under the assumption that the study population is completely isolated. This assumption is frequently violated, and the magnitude of the resulting bias is generally unknown. We studied how gene flow affects estimates of effective size obtained by the temporal method when sampling from a population system and provide analytical expressions for the expected estimate under an island model of migration. We show that the temporal method tends to systematically underestimate both local and global effective size when populations are connected by gene flow, and the bias is sometimes dramatic. The problem is particularly likely to occur when sampling from a subdivided population where high levels of gene flow obscure identification of subpopulation boundaries. In such situations, sampling in a manner that prevents biased estimates can be difficult. This phenomenon might partially explain the frequently reported unexpectedly low effective population sizes of marine populations that have raised concern regarding the genetic vulnerability of even exceptionally large populations.     

Estimating pairwise relatedness from dominant genetic markers

Knowledge of the genetic relatedness between a pair of individuals is important in many research areas of quantitative genetics, conservation genetics, evolution and ecology. Many estimators have been developed to estimate such pairwise relatedness (r) using codominant markers, such as microsatellites and enzymes. In contrast, only two estimators are proposed to use dominant markers, such as random amplified polymorphic DNAs (RAPDs) and amplified fragment length polymorphisms (AFLPs), in relatedness inference. They are both biased estimators, and their statistical properties and robustness to the sampling errors in allele frequency have not been investigated. In this short paper, I propose two new pairwise relatedness estimators for dominant markers, and compare them in precision, accuracy and robustness to sampling with the two previous estimators using simulations. It was found that the new estimator based on the least squares approach is unbiased when allele frequencies are known or estimated from a sample without correcting for sampling effects. It has, however, a low precision and as a result, an intermediate overall performance among the four estimators in terms of the mean squared deviation (MSD) of estimates from actual values of r. The new estimator based on a similarity index is slightly biased but has generally the lowest MSD among the four estimators compared, regardless of the number of loci, type of actual relationships, allele frequencies known or estimated from samples. Simulations also show that the confidence intervals estimated by bootstrapping are appropriate for different estimators provided that the number of loci used in the estimation is not small.     

Short-term genetic changes: evaluating effective population size estimates in a comprehensively described brown trout (Salmo trutta) population

The effective population size (N(e)) is notoriously difficult to accurately estimate in wild populations as it is influenced by a number of parameters that are difficult to delineate in natural systems. The different methods that are used to estimate N(e) are affected variously by different processes at the population level, such as the life-history characteristics of the organism, gene flow, and population substructure, as well as by the frequency patterns of genetic markers used and the sampling design. Here, we compare N(e) estimates obtained by different genetic methods and from demographic data and elucidate how the estimates are affected by various factors in an exhaustively sampled and comprehensively described natural brown trout (Salmo trutta) system. In general, the methods yielded rather congruent estimates, and we ascribe that to the adequate genotyping and exhaustive sampling. Effects of violating the assumptions of the different methods were nevertheless apparent. In accordance with theoretical studies, skewed allele frequencies would underestimate temporal allele frequency changes and thereby upwardly bias N(e) if not accounted for. Overlapping generations and iteroparity would also upwardly bias N(e) when applied to temporal samples taken over short time spans. Gene flow from a genetically not very dissimilar source population decreases temporal allele frequency changes and thereby acts to increase estimates of N(e). Our study reiterates the importance of adequate sampling, quantification of life-history parameters and gene flow, and incorporating these data into the N(e) estimation.     

Evaluation of DNA pooling for the estimation of microsatellite allele frequencies: a case study using striped bass (Morone saxatilis)

Using striped bass (Morone saxatilis) and six multiplexed microsatellite markers, we evaluated procedures for estimating allele frequencies by pooling DNA from multiple individuals, a method suggested as cost-effective relative to individual genotyping. Using moment-based estimators, we estimated allele frequencies in experimental DNA pools and found that the three primary laboratory steps, DNA quantitation and pooling, PCR amplification, and electrophoresis, accounted for 23, 48, and 29%, respectively, of the technical variance of estimates in pools containing DNA from 2-24 individuals. Exact allele-frequency estimates could be made for pools of sizes 2-8, depending on the locus, by using an integer-valued estimator. Larger pools of size 12 and 24 tended to yield biased estimates; however, replicates of these estimates detected allele frequency differences among pools with different allelic compositions. We also derive an unbiased estimator of Hardy-Weinberg disequilibrium coefficients that uses multiple DNA pools and analyze the cost-efficiency of DNA pooling. DNA pooling yields the most potential cost savings when a large number of loci are employed using a large number of individuals, a situation becoming increasingly common as microsatellite loci are developed in increasing numbers of taxa.     

Temporal Stability of Genetic Variability and Differentiation in the Three-Spined Stickleback (Gasterosteus aculeatus)

Temporal variation in allele frequencies, whether caused by deterministic or stochastic forces, can inform us about interesting demographic and evolutionary phenomena occurring in wild populations. In spite of the continued surge of interest in the genetics of three-spined stickleback (Gasterosteus aculeatus) populations, little attention has been paid towards the temporal stability of allele frequency distributions, and whether there are consistent differences in effective size (N_e) of local populations. We investigated temporal stability of genetic variability and differentiation in 15 microsatellite loci within and among eight collection sites of varying habitat type, surveyed twice over a six-year time period. In addition, N_es were estimated with the expectation that they would be lowest in isolated ponds, intermediate in larger lakes and largest in open marine sites. In spite of the marked differences in genetic variability and differentiation among the study sites, the temporal differences in allele frequencies, as well as measures of genetic diversity and differentiation, were negligible. Accordingly, the N_e estimates were temporally stable, but tended to be lower in ponds than in lake or marine habitats. Hence, we conclude that allele frequencies in putatively neutral markers in three-spined sticklebacks seem to be temporally stable – at least over periods of few generations – across a wide range of habitat types differing markedly in levels of genetic variability, effective population size and gene flow.     

Genebank biodiversity assessments regarding optimal sample size and seed harvesting techniques for the regeneration of carrot accessions

Small, finite populations are particularly vulnerable to diversity loss during regeneration. The regeneration of a highly outbreeding open-pollinated variety relies on estimated effective population size, via the measurement of temporal change in allele frequencies. Using appropriate estimators for dominant gene markers, effective sizes were calculated for five sizes of a mating population and two seed harvesting procedures. We have shown that, in the case of carrot regeneration, 70 equally harvested plants should provide an effective size (N _e) of at least 50 plants. This value seems sufficient to limit genetic drift and to preserve an efficient level of genetic diversity within the collection. The efficiency of balanced samples (made of an equal number of seeds per plant) is compared to that of bulk samples (seeds randomly chosen among the total seed lot coming from all the plants).     

Temporal Allele Frequency Change and Estimation of Effective Size in Populations with Overlapping Generations

In this paper we study the process of allele frequency change in finite populations with overlapping generations with the purpose of evaluating the possibility of estimating the effective size from observations of temporal frequency shifts of selectively neutral alleles. Focusing on allele frequency changes between successive cohorts (individuals born in particular years), we show that such changes are not determined by the effective population size alone, as they are when generations are discrete. Rather, in populations with overlapping generations, the amount of temporal allele frequency change is dependent on the age-specific survival and birth rates. Taking this phenomenon into account, we present an estimator for effective size that can be applied to populations with overlapping generations.     

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.     

Comparison of microsatellites and amplified fragment length polymorphism markers for parentage analysis

This study compares the properties of dominant markers, such as amplified fragment length polymorphisms (AFLPs), with those of codominant multiallelic markers, such as microsatellites, in reconstructing parentage. These two types of markers were used to search for both parents of an individual without prior knowledge of their relationships, by calculating likelihood ratios based on genotypic data, including mistyping. Experimental data on 89 oak trees genotyped for six microsatellite markers and 159 polymorphic AFLP loci were used as a starting point for simulations and tests. Both sets of markers produced high exclusion probabilities, and among dominant markers those with dominant allele frequencies in the range 0.1-0.4 were more informative. Such codominant and dominant markers can be used to construct powerful statistical tests to decide whether a genotyped individual (or two individuals) can be considered as the true parent (or parent pair). Gene flow from outside the study stand (GFO), inferred from parentage analysis with microsatellites, overestimated the true GFO, whereas with AFLPs it was underestimated. As expected, dominant markers are less efficient than codominant markers for achieving this, but can still be used with good confidence, especially when loci are deliberately selected according to their allele frequencies.     

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.     

PPC: an algorithm for accurate estimation of SNP allele frequencies in small equimolar pools of DNA using data from high density microarrays

Robust estimation of allele frequencies in pools of DNA has the potential to reduce genotyping costs and/or increase the number of individuals contributing to a study where hundreds of thousands of genetic markers need to be genotyped in very large populations sample sets, such as genome wide association studies. In order to make accurate allele frequency estimations from pooled samples a correction for unequal allele representation must be applied. We have developed the polynomial based probe specific correction (PPC) which is a novel correction algorithm for accurate estimation of allele frequencies in data from high-density microarrays. This algorithm was validated through comparison of allele frequencies from a set of 10 individually genotyped DNA's and frequencies estimated from pools of these 10 DNAs using GeneChip 10K Mapping Xba 131 arrays. Our results demonstrate that when using the PPC to correct for allelic biases the accuracy of the allele frequency estimates increases dramatically.     

Genotype‐free estimation of allele frequencies reduces bias and improves demographic inference from RADSeq data

Restriction‐site associated DNA sequencing (RADSeq) facilitates rapid generation of thousands of genetic markers at relatively low cost; however, several sources of error specific to RADSeq methods often lead to biased estimates of allele frequencies and thereby to erroneous population genetic inference. Estimating the distribution of sample allele frequencies without calling genotypes was shown to improve population inference from whole genome sequencing data, but the ability of this approach to account for RADSeq‐specific biases remains unexplored. Here we assess in how far genotype‐free methods of allele frequency estimation affect demographic inference from empirical RADSeq data. Using the well‐studied pied flycatcher (Ficedula hypoleuca) as a study system, we compare allele frequency estimation and demographic inference from whole genome sequencing data with that from RADSeq data matched for samples using both genotype‐based and genotype free methods. The demographic history of pied flycatchers as inferred from RADSeq data was highly congruent with that inferred from whole genome resequencing (WGS) data when allele frequencies were estimated directly from the read data. In contrast, when allele frequencies were derived from called genotypes, RADSeq‐based estimates of most model parameters fell outside the 95% confidence interval of estimates derived from WGS data. Notably, more stringent filtering of the genotype calls tended to increase the discrepancy between parameter estimates from WGS and RADSeq data, respectively. The results from this study demonstrate the ability of genotype‐free methods to improve allele frequency spectrum‐ (AFS‐) based demographic inference from empirical RADSeq data and highlight the need to account for uncertainty in NGS data regardless of sequencing method.     

Patterns of differentiation in a colour polymorphism and in neutral markers reveal rapid genetic changes in natural damselfly populations

The existence and mode of selection operating on heritable adaptive traits can be inferred by comparing population differentiation in neutral genetic variation between populations (often using F(ST) values) with the corresponding estimates for adaptive traits. Such comparisons indicate if selection acts in a diversifying way between populations, in which case differentiation in selected traits is expected to exceed differentiation in neutral markers [F(ST )(selected) > F(ST )(neutral)], or if negative frequency-dependent selection maintains genetic polymorphisms and pulls populations towards a common stable equilibrium [F(ST) (selected) < F(ST) (neutral)]. Here, we compared F(ST) values for putatively neutral data (obtained using amplified fragment length polymorphism) with estimates of differentiation in morph frequencies in the colour-polymorphic damselfly Ischnura elegans. We found that in the first year (2000), population differentiation in morph frequencies was significantly greater than differentiation in neutral loci, while in 2002 (only 2 years and 2 generations later), population differentiation in morph frequencies had decreased to a level significantly lower than differentiation in neutral loci. Genetic drift as an explanation for population differentiation in morph frequencies could thus be rejected in both years. These results indicate that the type and/or strength of selection on morph frequencies in this system can change substantially between years. We suggest that an approach to a common equilibrium morph frequency across all populations, driven by negative frequency-dependent selection, is the cause of these temporal changes. We conclude that inferences about selection obtained by comparing F(ST) values from neutral and adaptive genetic variation are most useful when spatial and temporal data are available from several populations and time points and when such information is combined with other ecological sources of data.     

Moment estimation of population diversity and genetic distance from data on recessive markers

A moment-based method for estimating a measure of population diversity, theta or Wright's FST, is given for dominant markers such as amplified fragment length polymorphisms (AFLPs) or RAPDs in noninbred populations. Basic assumptions are that there is random mating, Hardy-Weinberg equilibrium, linkage equilibrium, no mutation from common ancestor and equally distant populations. It is based on the variances between and within populations of genotype frequencies, whereas previously moment methods for dominant markers have been indirect in that they have been based on first estimating allele frequencies and then using the variances of those frequencies. The use of genotype frequencies directly appears to be more robust. Approximate sampling errors of the estimates are given. Methods are extended to estimate genetic distances and their sampling errors. The AFLP data from samples of breeds of pig are used for illustration.     

Empirical Bayes procedure for estimating genetic distance between populations and effective population size

We developed an empirical Bayes procedure to estimate genetic distances between populations using allele frequencies. This procedure makes it possible to describe the skewness of the genetic distance while taking full account of the uncertainty of the sample allele frequencies. Dirichlet priors of the allele frequencies are specified, and the posterior distributions of the various composite parameters are obtained by Monte Carlo simulation. To avoid overdependence on subjective priors, we adopt a hierarchical model and estimate hyperparameters by maximizing the joint marginal-likelihood function. Taking advantage of the empirical Bayesian procedure, we extend the method to estimate the effective population size using temporal changes in allele frequencies. The method is applied to data sets on red sea bream, herring, northern pike, and ayu broodstock. It is shown that overdispersion overestimates the genetic distance and underestimates the effective population size, if it is not taken into account during the analysis. The joint marginal-likelihood function also estimates the rate of gene flow into island populations.     

Precision and accuracy of divergence time estimates from STR and SNPSTR variation

Inference of intraspecific population divergence patterns typically requires genetic data for molecular markers with relatively high mutation rates. Microsatellites, or short tandem repeat (STR) polymorphisms, have proven informative in many such investigations. These markers are characterized, however, by high levels of homoplasy and varying mutational properties, often leading to inaccurate inference of population divergence. A SNPSTR is a genetic system that consists of an STR polymorphism closely linked (typically < 500 bp) to one or more single-nucleotide polymorphisms (SNPs). SNPSTR systems are characterized by lower levels of homoplasy than are STR loci. Divergence time estimates based on STR variation (on the derived SNP allele background) should, therefore, be more accurate and precise. We use coalescent-based simulations in the context of several models of demographic history to compare divergence time estimates based on SNPSTR haplotype frequencies and STR allele frequencies. We demonstrate that estimates of divergence time based on STR variation on the background of a derived SNP allele are more accurate (3% to 7% bias for SNPSTR versus 11% to 20% bias for STR) and more precise than STR-based estimates, conditional on a recent SNP mutation. These results hold even for models involving complex demographic scenarios with gene flow, population expansion, and population bottlenecks. Varying the timing of the mutation event generating the SNP revealed that estimates of divergence time are sensitive to SNP age, with more recent SNPs giving more accurate and precise estimates of divergence time. However, varying both mutational properties of STR loci and SNP age demonstrated that multiple independent SNPSTR systems provide less biased estimates of divergence time. Furthermore, the combination of estimates based separately on STR and SNPSTR variation provides insight into the age of the derived SNP alleles. In light of our simulations, we interpret estimates from data for human populations.     

Estimating levels of inbreeding using AFLP markers

In the absence of detailed pedigree records, researchers have attempted to estimate individuals' levels of inbreeding using molecular markers, generally making use of heterozygosity measures based on microsatellite markers. Here we report and validate a method for estimating an individual's inbreeding coefficient, f, using amplified fragment length polymorphism (AFLP) markers. We use simulations to confirm that our measure scales appropriately with f when allele frequencies can be estimated from a subset of outbred individuals. We also present an approach for obtaining satisfactory estimates even in the absence of an independent set of known outbred individuals from which to estimate allele frequencies. We then test our method against empirical data from 179 wild and captive-bred old-field mice, Peromyscus polionotus subgriseus, comprising pedigree-based estimates of f, along with genetic data from 94 AFLP markers and 12 microsatellites. Inbreeding estimates based on both AFLP and microsatellite markers were found to correlate strongly with pedigree-based inbreeding coefficients. Owing to their ease of amplification in any species, AFLP markers may prove to be a valuable new tool for estimating f in natural populations and for examining correlations between heterozygosity and fitness.     

TEMPORAL CHANGE OF MITOCHONDRIAL DNA HAPLOTYPE FREQUENCIES AND FEMALE EFFECTIVE SIZE IN A BROWN TROUT (SALMO TRUTTA) POPULATION

We report data on genetic drift of mitochondrial DNA (mtDNA) haplotypes in a natural brown trout (Salmo trutta) population in Sweden. Large temporal frequency shifts were observed over the 14 consecutive year classes studied. The observed rate of drift was used to estimate the effective size of the population. This effective size applies to the female segment of the population as mtDNA is maternally inherited. The magnitude of mtDNA haplotype frequency change is compared with the corresponding allele frequency changes at 14 allozyme loci in the same population. The female effective size is estimated as 58, which is approximately half the effective size of 97 for the total population (both sexes) previously obtained from the shifts of allozyme allele frequencies.     

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.     

微卫星标记在种群生物学研究中的应用

微卫星是以几个碱基 (一般为 1～ 6个 )为重复单位组成的简单的串联重复序列 ,具有丰度高、多态性高、共显性标记、选择中性、可自动检测等优点。本文着重介绍了微卫星在种群生物学研究中的应用。微卫星位点可以提供具高分辨率的遗传信息 ,这一特点使微卫星既适合于个体水平上的研究 ,又适合于种群水平上的研究。在个体水平上包括个体识别、交配系统和亲本分析、基因流等研究。微卫星是常用的个体识别手段 ,但在克隆植物遗传结构研究方面的应用还很有限 ;微卫星提高了交配系统和亲本分析、基因流等研究的准确性。在种群水平上微卫星可用于遗传结构、有效种群大小、种群的系统发育重建等研究。微卫星在很多物种 (包括珍稀物种 )的遗传结构研究中得到应用 ;利用微卫星标记确定有效种群大小、检测有效种群大小的波动可以促使我们正确理解种群遗传结构动态和种群进化过程 ;微卫星在种群的系统发育重建研究方面有很大的应用潜力。然而微卫星并不是研究所有问题的唯一选择。文中还讨论了在实际工作中应如何正确利用分子标记等问题