A bias correction for estimates of effective population size based on linkage disequilibrium at unlinked gene loci*

Analysis of linkage disequilibrium (=mean squared correlation of allele frequencies at different gene loci) provides a means of estimating effective population size (N _e) from a single sample, but this method has seen much less use than the temporal method (which requires at least two samples). It is shown that for realistic numbers of loci and alleles, the linkage disequilibrium method can provide precision comparable to that of the temporal method. However, computer simulations show that estimates of N _e based on for unlinked, diallelic gene loci are sharply biased downwards ( in some cases) if sample size (S) is less than true N _e. The bias is shown to arise from inaccuracies in published formula for when S and/or N _e are small. Empirically derived modifications to for two mating systems (random mating and lifetime monogamy) effectively eliminate the bias (residual bias in % in most cases). The modified method also performs well in estimating N _e in non-ideal populations with skewed sex ratio or non-random variance in reproductive success. Recent population declines are not likely to seriously affect , but if N has recently increased from a bottleneck can be biased downwards for a few generations. These results should facilitate application of the disequilibrium method for estimating contemporary N _e in natural populations. However, a comprehensive assessment of performance of with highly polymorphic markers such as microsatellites is needed.The US Governmentȁ9s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Estimates of linkage disequilibrium and effective population size in rainbow trout

Background

Mitochondrial DNA (mtDNA) is widely used in population genetic and phylogenetic studies in animals. However, such studies can generate misleading results if the species concerned contain nuclear copies of mtDNA (Numts) as these may amplify in addition to, or even instead of, the authentic target mtDNA. The aim of this study was to determine if Numts are present in Aedes aegypti mosquitoes, to characterise any Numts detected, and to assess the utility of using mtDNA for population genetics studies in this species.

Results

BLAST searches revealed large numbers of Numts in the Ae. aegypti nuclear genome on 146 supercontigs. Although the majority are short (80% < 300 bp), some Numts are almost full length mtDNA copies. These long Numts are not due to misassembly of the nuclear genome sequence as the Numt-nuclear genome junctions could be recovered by amplification and sequencing. Numt evolution appears to be a complex process in Ae. aegypti with ongoing genomic integration, fragmentation and mutation and the secondary movement of Numts within the nuclear genome. The PCR amplification of the putative mtDNA nicotinamide adenine dinucleotide dehydrogenase subunit 4 (ND4) gene from 166 Southeast Asian Ae. aegypti mosquitoes generated a network with two highly divergent lineages (clade 1 and clade 2). Approximately 15% of the ND4 sequences were a composite of those from each clade indicating Numt amplification in addition to, or instead of, mtDNA. Clade 1 was shown to be composed at least partially of Numts by the removal of clade 1-specific bases from composite sequences following enrichment of the mtDNA. It is possible that all the clade 1 sequences in the network were Numts since the clade 2 sequences correspond to the known mitochondrial genome sequence and since all the individuals that produced clade 1 sequences were also found to contain clade 2 mtDNA-like sequences using clade 2-specific primers. However, either or both sets of clade sequences could have Numts since the BLAST searches revealed two long Numts that match clade 2 and one long Numt that matches clade 1. The substantial numbers of mutations in cloned ND4 PCR products also suggest there are both recently-derived clade 1 and clade 2 Numt sequences.

Conclusion

We conclude that Numts are prevalent in Ae. aegypti and that it is difficult to distinguish mtDNA sequences due to the presence of recently formed Numts. Given this, future population genetic or phylogenetic studies in Ae. aegypti should use nuclear, rather than mtDNA, markers.     

Early detection of population fragmentation using linkage disequilibrium estimation of effective population size

Population subdivision due to habitat loss and modification, exploitation of wild populations and altered spatial population dynamics is of increasing concern in nature. Detecting population fragmentation is therefore crucial for conservation management. Using computer simulations, we show that a single sample estimator of N _e based on linkage disequilibrium is a highly sensitive and promising indicator of recent population fragmentation and bottlenecks, even with some continued gene flow. For example, fragmentation of a panmictic population of N _e = 1,000 into demes of N _e = 100 can be detected with high probability after a single generation when estimates from this method are compared to prefragmentation estimates, given data for ~20 microsatellite loci in samples of 50 individuals. We consider a range of loci (10–40) and individuals (25–100) typical of current studies of natural populations and show that increasing the number of loci gives nearly the same increase in precision as increasing the number of individuals sampled. We also evaluated effects of incomplete fragmentation and found this N _e-reduction signal is still apparent in the presence of considerable migration (m ~ 0.10–0.25). Single-sample genetic estimates of N _e thus show considerable promise for early detection of population fragmentation and decline.     

利用全基因组连锁不平衡估计中国荷斯坦牛有效群体大小

有效群体大小是群体遗传学研究的一个重要内容,有助于我们更清楚地了解群体的遗传变异、进化和复杂性状的遗传机制等。随着高密度SNP标记的出现,越来越多的研究利用SNP标记间连锁不平衡估计有效群体大小。文章采集北京地区中国荷斯坦牛2 093个样本,并利用牛SNP芯片(Illumina BovineSNP50,含5 4001 SNPs)进行基因型测定,估计不同世代中国荷斯坦牛的有效群体大小。质量控制标准设定为SNP检出率0.95,最小等位基因频率>0.05,样本检出率0.95,哈代温伯格平衡检验显著性水平P<0.0001。经过质量控制,共1 968个样本和38 796个SNPs用于连锁不平衡分析。文章选取SNP间距0.1、0.2、0.5、1、2、5、10、15(Mb),估计中国荷斯坦牛在4世代之前有效群体大小。结果表明,中国荷斯坦牛的有效群体呈逐代下降趋势,至4世代前,中国荷斯坦牛平均有效群体为45头左右。     

ldne: a program for estimating effective population size from data on linkage disequilibrium

ldne is a program with a Visual Basic interface that implements a recently developed bias correction for estimates of effective population size (N(e) ) based on linkage disequilibrium data. The program reads genotypic data in standard formats and can accommodate an arbitrary number of samples, individuals, loci, and alleles, as well as two mating systems: random and lifetime monogamy. ldne calculates separate estimates using different criteria for excluding rare alleles, which facilitates evaluation of data for highly polymorphic markers such as microsatellites. The program also introduces a jackknife method for obtaining confidence intervals that appears to perform better than parametric methods currently in use.     

Estimating effective population size from linkage disequilibrium: severe bias in small samples

Effective population size (N _e) is a central concept in evolutionary biology and conservation genetics. It predicts rates of loss of neutral genetic variation, fixation of deleterious and favourable alleles, and the increase of inbreeding experienced by a population. A method exists for the estimation of N _e from the observed linkage disequilibrium between unlinked loci in a population sample. While an increasing number of studies have applied this method in natural and managed populations, its reliability has not yet been evaluated. We developed a computer program to calculate this estimator of N _e using the most widely used linkage disequilibrium algorithm and used simulations to show that this estimator is strongly biased when the sample size is small (<‰100) and below the true N _e. This is probably due to the linkage disequilibrium generated by the sampling process itself and the inadequate correction for this phenomenon in the method. Results suggest that N _e estimates derived using this method should be regarded with caution in many cases. To improve the method’s reliability and usefulness we propose a way to determine whether a given sample size exceeds the population N _e and can therefore be used for the computation of an unbiased estimate.     

Estimating contemporary effective population size on the basis of linkage disequilibrium in the face of migration

Effective population size (Ne) is an important genetic parameter because of its relationship to loss of genetic variation, increases in inbreeding, accumulation of mutations, and effectiveness of selection. Like most other genetic approaches that estimate contemporary Ne, the method based on linkage disequilibrium (LD) assumes a closed population and (in the most common applications) randomly recombining loci. We used analytical and numerical methods to evaluate the absolute and relative consequences of two potential violations of the closed-population assumption: (1) mixture LD caused by occurrence of more than one gene pool, which would downwardly bias Ne and (2) reductions in drift LD (and hence upward bias in Ne) caused by an increase in the number of parents responsible for local samples. The LD method is surprisingly robust to equilibrium migration. Effects of mixture LD are small for all values of migration rate (m), and effects of additional parents are also small unless m is high in genetic terms. LD estimates of Ne therefore accurately reflect local (subpopulation) Ne unless m>～5-10%. With higher m, Ne converges on the global (metapopulation) Ne. Two general exceptions were observed. First, equilibrium migration that is rare and hence episodic can occasionally lead to substantial mixture LD, especially when sample size is small. Second, nonequilibrium, pulse migration of strongly divergent individuals can also create strong mixture LD and depress estimates of local Ne. In both cases, assignment tests, Bayesian clustering, and other methods often will allow identification of recent immigrants that strongly influence results. In simulations involving equilibrium migration, the standard LD method performed better than a method designed to jointly estimate Ne and m. The above results assume loci are not physically linked; for tightly linked loci, the LD signal from past migration events can persist for many generations, with consequences for Ne estimates that remain to be evaluated.     

An evaluation of the methods to estimate effective population size from measures of linkage disequilibrium

In 1971, John Sved derived an approximate relationship between linkage disequilibrium (LD) and effective population size for an ideal finite population. This seminal work was extended by Sved and Feldman (Theor Pop Biol 4, 129, 1973) and Weir and Hill (Genetics 95, 477, 1980) who derived additional equations with the same purpose. These equations yield useful estimates of effective population size, as they require a single sample in time. As these estimates of effective population size are now commonly used on a variety of genomic data, from arrays of single nucleotide polymorphisms to whole genome data, some authors have investigated their bias through simulation studies and proposed corrections for different mating systems. However, the cause of the bias remains elusive. Here, we show the problems of using LD as a statistical measure and, analogously, the problems in estimating effective population size from such measure. For that purpose, we compare three commonly used approaches with a transition probability‐based method that we develop here. It provides an exact computation of LD. We show here that the bias in the estimates of LD and effective population size are partly due to low‐frequency markers, tightly linked markers or to a small total number of crossovers per generation. These biases, however, do not decrease when increasing sample size or using unlinked markers. Our results show the issues of such measures of effective population based on LD and suggest which of the method here studied should be used in empirical studies as well as the optimal distance between markers for such estimates.     

Genome‐wide linkage disequilibrium and past effective population size in three Korean cattle breeds

The routine collection and use of genomic data are useful for effectively managing breeding programs for endangered populations. Linkage disequilibrium (LD) using high‐density DNA markers has been widely used to determine population structures and predict the genomic regions that are associated with economic traits in beef cattle. The extent of LD also provides information about historical events, including past effective population size (N_e), and it allows inferences on the genetic diversity of breeds. The objective of this study was to estimate the LD and N_e in three Korean cattle breeds that are genetically similar but have different coat colors (Brown, Brindle and Jeju Black Hanwoo). Brindle and Jeju Black are endangered breeds with small populations, whereas Brown Hanwoo is the main breeding population in Korea. DNA samples from these cattle breeds were genotyped using the Illumina BovineSNP50 Bead Chip. We examined 13 cattle breeds, including European taurines, African taurines and indicines, and hybrids to compare their LD values. Brown Hanwoo consistently had the lowest mean LD compared to Jeju Black, Brindle and the other 13 cattle breeds (0.13, 0.19, 0.21 and 0.15–0.22 respectively). The high LD values of Brindle and Jeju Black contributed to small N_e values (53 and 60 respectively), which were distinct from that of Brown Hanwoo (531) for 11 generations ago. The differences in LD and N_e for each breed reflect the breeding strategy applied. The N_e for these endangered cattle breeds remain low; thus, effort is needed to bring them back to a sustainable tract.     

Sex-specific population structure,natural selection,and linkage disequilibrium in a wild bird population as revealed by genome-wide microsatellite analyses

Background  

Sexual dimorphism in ecologically important traits is widespread, yet the differences in the genomic architecture between the two sexes are largely unexplored. We employed a genome-wide multilocus approach to examine the sexual differences in population subdivision, natural selection and linkage disequilibrium (LD) in a wild Siberian jay (Perisoreus infaustus) population, using genotypes at a total of 107 autosomal and Z-chromosomal microsatellites.     

Effects of population size and linkage on optimal selection intensity

Following Robertson (1970a) it is generally considered that for mass selection the selected proportion that maximises ultimate response is 0.5. This prediction has been partly tested by different authors. Here we explicitly address the question using computer simulations of selection in finite populations with linkage. The results show that the response achieved is always lower than the one predicted by standard methods, and that optimum selection intensity may be much lower than predicted unless population size is small.     

Making sense of genetic estimates of effective population size

The last decade has seen an explosion of interest in use of genetic markers to estimate effective population size, N_e. Effective population size is important both theoretically (N_e is a key parameter in almost every aspect of evolutionary biology) and for practical application (N_e determines rates of genetic drift and loss of genetic variability and modulates the effectiveness of selection, so it is crucial to consider in conservation). As documented by Palstra & Fraser ( 2012 ), most of the recent growth in N_e estimation can be attributed to development or refinement of methods that can use a single sample of individuals (the older temporal method requires at least two samples separated in time). As with other population genetic methods, performance of new N_e estimators is typically evaluated with simulated data for a few scenarios selected by the author(s). Inevitably, these initial evaluations fail to fully consider the consequences of violating simplifying assumptions, such as discrete generations, closed populations of constant size and selective neutrality. Subsequently, many researchers studying natural or captive populations have reported estimates of N_e for multiple methods; often these estimates are congruent, but that is not always the case. Because true N_e is rarely known in these empirical studies, it is difficult to make sense of the results when estimates differ substantially among methods. What is needed is a rigorous, comparative analysis under realistic scenarios for which true N_e is known. Recently, Gilbert & Whitlock ( 2015 ) did just that for both single‐sample and temporal methods under a wide range of migration schemes. In the current issue of Molecular Ecology, Wang ( 2016 ) uses simulations to evaluate performance of four single‐sample N_e estimators. In addition to assessing effects of true N_e, sample size, and number of loci, Wang also evaluated performance under changing abundance, physical linkage and genotyping errors, as well as for some alternative life histories (high rates of selfing; haplodiploids). Wang showed that the sibship frequency (SF) and linkage disequilibrium (LD) methods perform dramatically better than the heterozygote excess and molecular coancestry methods under most scenarios (see Fig. 1, modified from figure 2 in Wang 2016 ), and he also concluded that SF is generally more versatile than LD. This article represents a truly Herculean effort, and results should be of considerable value to researchers interested in applying these methods to real‐world situations.     

Using multilocus sequence data to assess population structure, natural selection, and linkage disequilibrium in wild tomatoes

We employed a multilocus approach to examine the effects of population subdivision and natural selection on DNA polymorphism in 2 closely related wild tomato species (Solanum peruvianum and Solanum chilense), using sequence data for 8 nuclear loci from populations across much of the species' range. Both species exhibit substantial levels of nucleotide variation. The species-wide level of silent nucleotide diversity is 18% higher in S. peruvianum (pi(sil) approximately 2.50%) than in S. chilense (pi(sil) approximately 2.12%). One of the loci deviates from neutral expectations, showing a clinal pattern of nucleotide diversity and haplotype structure in S. chilense. This geographic pattern of variation is suggestive of an incomplete (ongoing) selective sweep, but neutral explanations cannot be entirely dismissed. Both wild tomato species exhibit moderate levels of population differentiation (average F(ST) approximately 0.20). Interestingly, the pooled samples (across different demes) exhibit more negative Tajima's D and Fu and Li's D values; this marked excess of low-frequency polymorphism can only be explained by population (or range) expansion and is unlikely to be due to population structure per se. We thus propose that population structure and population/range expansion are among the most important evolutionary forces shaping patterns of nucleotide diversity within and among demes in these wild tomatoes. Patterns of population differentiation may also be impacted by soil seed banks and historical associations mediated by climatic cycles. Intragenic linkage disequilibrium (LD) decays very rapidly with physical distance, suggesting high recombination rates and effective population sizes in both species. The rapid decline of LD seems very promising for future association studies with the purpose of mapping functional variation in wild tomatoes.     

The effective size of a natural drosophila subobscura population.

The effective size of a natural Drosophila subobscura population has been computed by drawing together various pieces of ecological information. The value, for both variance and inbreeding effective numbers, is approximately 400. This is largely due to reductions caused by a winter bottleneck and non-random distributions of family sizes. Areas where such estimates might be refined further are pointed out, and the implications of the results are discussed.     

Linkage disequilibrium and historical effective population size in the Thoroughbred horse

Many genomic methodologies rely on the presence and extent of linkage disequilibrium (LD) between markers and genetic variants underlying traits of interest, but the extent of LD in the horse has yet to be comprehensively characterized. In this study, we evaluate the extent and decay of LD in a sample of 817 Thoroughbreds. Horses were genotyped for over 50,000 single nucleotide polymorphism (SNP) markers across the genome, with 34,848 autosomal SNPs used in the final analysis. Linkage disequilibrium, as measured by the squared correlation coefficient (r(2)), was found to be relatively high between closely linked markers (>0.6 at 5 kb) and to extend over long distances, with average r(2) maintained above non-syntenic levels for single nucleotide polymorphisms (SNPs) up to 20 Mb apart. Using formulae which relate expected LD to effective population size (N(e)), and assuming a constant actual population size, N(e) was estimated to be 100 in our population. Values of historical N(e), calculated assuming linear population growth, suggested a decrease in N(e) since the distant past, reaching a minimum twenty generations ago, followed by a subsequent increase until the present time. The qualitative trends observed in N(e) can be rationalized by current knowledge of the history of the Thoroughbred breed, and inbreeding statistics obtained from published pedigree analyses are in agreement with observed values of N(e). Given the high LD observed and the small estimated N(e), genomic methodologies such as genomic selection could feasibly be applied to this population using the existing SNP marker set.     

The effect of single nucleotide polymorphism identification strategies on estimates of linkage disequilibrium

At present there is tremendous interest in characterizing the magnitude and distribution of linkage disequilibrium (LD) throughout the human genome, which will provide the necessary foundation for genome-wide LD analyses and facilitate detailed evolutionary studies. To this end, a human high-density single-nucleotide polymorphism (SNP) marker map has been constructed. Many of the SNPs on this map, however, were identified by sampling a small number of chromosomes from a single population, and inferences drawn from studies using such SNPs may be influenced by ascertainment bias (AB). Through extensive simulations, we have found that AB is a potentially significant problem in estimating and comparing LD within and between populations. Specifically, the magnitude of AB is a function of the SNP discovery strategy, number of chromosomes used for SNP discovery, population genetic characteristics of the particular genomic region considered, amount of gene flow between populations, and demographic history of the populations. We demonstrate that a balanced SNP discovery strategy (where equal numbers of chromosomes are sampled from multiple subpopulations) is the optimal study design for generating broadly applicable SNP resources. Finally, we validate our theoretical predictions by comparing our results to publicly available data from ten genes sequenced in 24 African American and 23 European American individuals.     

The extent of linkage disequilibrium caused by selection on G6PD in humans

The gene coding for glucose-6-phosphate dehydrogenase (G6PD) is subject to positive selection by malaria in some human populations. The G6PD A- allele, which is common in sub-Saharan Africa, is associated with deficient enzyme activity and protection from severe malaria. To delimit the impact of selection on patterns of linkage disequilibrium (LD) and nucleotide diversity, we resequenced 5.1 kb at G6PD and approximately 2-3 kb at each of eight loci in a 2.5-Mb region roughly centered on G6PD in a diverse sub-Saharan African panel of 51 unrelated men (including 20 G6PD A-, 11 G6PD A+, and 20 G6PD B chromosomes). The signature of selection is evident in the absence of genetic variation at G6PD and at three neighboring loci within 0.9 Mb from G6PD among all individuals bearing G6PD A- alleles. A genomic region of approximately 1.6 Mb around G6PD was characterized by long-range LD associated with the A- alleles. These patterns of nucleotide variability and LD suggest that G6PD A- is younger than previous age estimates and has increased in frequency in sub-Saharan Africa due to strong selection (0.1 < s < 0.2). These results also show that selection can lead to nonrandom associations among SNPs over great physical and genetic distances, even in African populations.     

Assignment of chromosomal locations for unassigned SNPs/scaffolds based on pair-wise linkage disequilibrium estimates

Background  

Recent developments of high-density SNP chips across a number of species require accurate genetic maps. Despite rapid advances in genome sequence assembly and availability of a number of tools for creating genetic maps, the exact genome location for a number of SNPs from these SNP chips still remains unknown. We have developed a locus ordering procedure based on linkage disequilibrium (LODE) which provides estimation of the chromosomal positions of unaligned SNPs and scaffolds. It also provides an alternative means for verification of genetic maps. We exemplified LODE in cattle.     

The effects of finite population size and selection on the correlation between gene frequency changes at two different loci and on the amount of linkage disequilibrium

Summary A potentially infinite random-mating population of monoecious diploid individuals is subjected to a single cycle of sampling and selection based on the values of a quantitative character. In the absence of epistatic interactions, expressions are obtained for the correlation between the gene frequencies at two linked loci and for the mean and variance of linkage disequilibrium after one cycle of selection. Numerical results are presented for a range of population sizes and for various values of the genetic parameters.