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。     

Measuring the extent of linkage disequilibrium in commercial pig populations

To evaluate the extent of linkage disequilibrium in domestic pigs, we genotyped 33 and 44 unrelated individuals from two commercial populations for 29 and five microsatellite markers located on chromosomes 15 and 2 respectively. A high proportion of marker pairs up to 40 cM apart exhibited significant linkage disequilibrium in both populations. Pair-wise r(2) values averaged between 0.15 and 0.50 (depending on chromosome and population) for markers <1 cM apart and declined to values of 0.05 for more distant syntenic markers. Our results suggest that both populations underwent a bottleneck approximately 20 generations ago, which reduced the effective population size from thousands to <200 animals.     

The extent of linkage disequilibrium in a large cattle population of western Africa and its consequences for association studies

Several previous studies concluded that linkage disequilibrium (LD) in livestock populations from developed countries originated from the impact of strong selection. Here, we assessed the extent of LD in a cattle population from western Africa that was bred in an extensive farming system. The analyses were performed on 363 individuals in a Bos indicus x Bos taurus population using 42 microsatellite markers on BTA04, BTA07 and BTA13. A high level of expected heterozygosity (0.71), a high mean number of alleles per locus (9.7) and a mild shift in Hardy-Weinberg equilibrium were found. Linkage disequilibrium extended over shorter distances than what has been observed in cattle from developed countries. Effective population size was assessed using two methods; both methods produced large values: 1388 when considering heterozygosity (assuming a mutation rate of 10(-3)) and 2344 when considering LD on whole linkage groups (assuming a constant population size over generations). However, analysing the decay of LD as a function of marker spacing indicated a decreasing trend in effective population size over generations. This decrease could be explained by increasing selective pressure and/or by an admixture process. Finally, LD extended over small distances, which suggested that whole-genome scans will require a large number of markers. However, association studies using such populations will be effective.     

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.     

Novel measures of linkage disequilibrium that correct the bias due to population structure and relatedness

Among the several linkage disequilibrium measures known to capture different features of the non-independence between alleles at different loci, the most commonly used for diallelic loci is the r(2) measure. In the present study, we tackled the problem of the bias of r(2) estimate, which results from the sample structure and/or the relatedness between genotyped individuals. We derived two novel linkage disequilibrium measures for diallelic loci that are both extensions of the usual r(2) measure. The first one, r(S)(2), uses the population structure matrix, which consists of information about the origins of each individual and the admixture proportions of each individual genome. The second one, r(V)(2), includes the kinship matrix into the calculation. These two corrections can be applied together in order to correct for both biases and are defined either on phased or unphased genotypes.We proved that these novel measures are linked to the power of association tests under the mixed linear model including structure and kinship corrections. We validated them on simulated data and applied them to real data sets collected on Vitis vinifera plants. Our results clearly showed the usefulness of the two corrected r(2) measures, which actually captured 'true' linkage disequilibrium unlike the usual r(2) measure.     

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.     

Combined linkage disequilibrium and linkage mapping: Bayesian multilocus approach

Quantitative trait loci (QTL) affecting the phenotype of interest can be detected using linkage analysis (LA), linkage disequilibrium (LD) mapping or a combination of both (LDLA). The LA approach uses information from recombination events within the observed pedigree and LD mapping from the historical recombinations within the unobserved pedigree. We propose the Bayesian variable selection approach for combined LDLA analysis for single-nucleotide polymorphism (SNP) data. The novel approach uses both sources of information simultaneously as is commonly done in plant and animal genetics, but it makes fewer assumptions about population demography than previous LDLA methods. This differs from approaches in human genetics, where LDLA methods use LA information conditional on LD information or the other way round. We argue that the multilocus LDLA model is more powerful for the detection of phenotype–genotype associations than single-locus LDLA analysis. To illustrate the performance of the Bayesian multilocus LDLA method, we analyzed simulation replicates based on real SNP genotype data from small three-generational CEPH families and compared the results with commonly used quantitative transmission disequilibrium test (QTDT). This paper is intended to be conceptual in the sense that it is not meant to be a practical method for analyzing high-density SNP data, which is more common. Our aim was to test whether this approach can function in principle.     

Population differences in levels of linkage disequilibrium in the wild

Information about the levels of linkage disequilibrium (LD) in wild animal populations is still limited, and this is true particularly with respect to possible interpopulation variation in the levels of LD. We compared the levels and extent of LD at the genome‐wide scale in three Siberian jay (Perisoreus infaustus) populations, two of which (Kuusamo and Ylläs) represented outbred populations within the main distribution area of the species, whereas the third (Suupohja) was a semi‐isolated, partially inbred population at the margin of the species’ distribution area. Although extensive long‐range LD (>20 cM) was observed in all three populations, LD generally decayed to background levels at a distance of 1–5 cM or c. 200–600 kb. The degree and extent of LD differed markedly between populations but aligned closely with both observed levels of within‐population genetic variation and expectations based on population history. The levels of LD were highest in the most inbred population with strong population substructure (Suupohja), compared with the two outbred populations. Furthermore, the decay of LD with increasing distance was slower in Suupohja, compared with the other two populations. By demonstrating that levels of LD can vary greatly over relatively short geographical distances within a species, these results suggest that prospects for association mapping differ from population to population. In this example, the prospects are best in the Suupohja population, given that minimized marker genotyping and a minimum marker spacing of 1–5 cM (c. 200–600 kb) would be sufficient for a whole genome scan for detecting QTL.     

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.     

GONe: software for estimating effective population size in species with generational overlap

GONe is a user-friendly, Windows-based program for estimating effective size (N(e) ) in populations with overlapping generations. It uses the Jorde-Ryman modification to the temporal method to account for age structure in populations. This method requires estimates of age-specific survival and birth rate and allele frequencies measured in two or more consecutive cohorts. Allele frequencies are acquired by reading in genotypic data from files formatted for either GENEPOP or TEMPOFS. For each interval between consecutive cohorts, N(e) is estimated at each locus and over all loci. Furthermore, N(e) estimates are output for three different genetic drift estimators (F(s) , F(c) and F(k) ). Confidence intervals are derived from a chi-square distribution with degrees of freedom equal to the number of independent alleles. GONe has been validated over a wide range of N(e) values, and for scenarios where survival and birth rates differ between sexes, sex ratios are unequal and reproductive variances differ. GONe is freely available for download at https://bcrc.bio.umass.edu/pedigreesoftware/.     

Dissecting linkage disequilibrium in African-American genomes: roles of markers and individuals

Substantial increases of linkage disequilibrium (LD) both in magnitude and in range have been observed in recently admixed populations such as African-American (AfA). On the other hand, it has also been shown that LD in AfAs was very similar to that of African. In this study, we attempted to resolve these contradicting observations by conducting a systematic examination of the LD structure in AfAs by genotyping a sample of AfA individuals at 24,341 single nucleotide polymorphisms (SNPs) spanning almost the entire chromosome 21, with an average density of 1.5 kb/SNP. The overall LD in AfAs is similar to that in African populations and much less than that in European populations. Even when the ancestry-informative markers (AIMs) were used, extended LD in AfA was found to be limited to certain magnitude range (0.2 < or = r(2) < or = 0.8) and certain distance range, that is, between-marker distance more than 200 kb. Furthermore, the inclusion of AfA individuals with predominant African ancestry was found to reduce the overall magnitude of LD. Elevation of LD in the AfA population, compared with its parental populations, can only be observed at the markers with large allele frequency differences between 2 parental populations at limited scenario. AfA individuals of wholly African ancestry contribute little to the extended LD in the AfA population, and further genotyping or association analysis conducted using only admixed individuals may lead to higher statistical power and possibly reduced cost.     

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.     

Generation time and effective population size in Polar Eskimos

North Greenland Polar Eskimos are the only hunter-gatherer population, to our knowledge, who can offer precise genealogical records spanning several generations. This is the first report from Eskimos on two key parameters in population genetics, namely, generation time (T) and effective population size (Ne). The average mother-daughter and father-son intervals were 27 and 32 years, respectively, roughly similar to the previously published generation times obtained from recent agricultural societies across the world. To gain an insight for the generation time in our distant ancestors, we calculated maternal generation time for two wild chimpanzee populations. We also provide the first comparison among three distinct approaches (genealogy, variance and life table methods) for calculating Ne, which resulted in slightly differing values for the Eskimos. The ratio of the effective to the census population size is estimated as 0.6-0.7 for autosomal and X-chromosomal DNA, 0.7-0.9 for mitochondrial DNA and 0.5 for Y-chromosomal DNA. A simulation of alleles along the genealogy suggested that Y-chromosomal DNA may drift a little faster than mitochondrial DNA in this population, in contrast to agricultural Icelanders. Our values will be useful not only in prehistoric population inference but also in understanding the shaping of our genome today.     

Inbreeding effective population size under some artificial selection schemes

Summary It is well known that truncation selection is the most efficient form of directional selection in terms of changing gene frequency. In this paper we show circumstances where truncation selection followed by a balanced mating generates inbreeding effective population size smaller than that generated by a selection that assigns mating frequencies to individuals according to their breeding values, where both selection schemes give the same expected performance of selected individuals (selection differential). Breeding values of selected individuals and the weight used to determine mating frequencies are assumed to be linearly distributed on a performance scales, x. To assign mating frequencies to the individuals in the weighting system, the selected individuals are grouped using a constant , and ith group in the interval x_i, x_i + . With small number of groups, say 2 or 3, the weighting system in general generates inbreeding effective population size that is larger than that generated by a truncation selection. As the number of the groups increases, truncation selection generates larger effective numbers.     

Estimating the ratio of effective to actual size of an age‐structured population from individual demographic data

The effective population size is a central concept for understanding evolutionary processes in a finite population. We employ Fisher's reproductive value to estimate the ratio of effective to actual population size for an age‐structured population with two sexes using random samples of individual vital rates. The population may be subject to environmental stochasticity affecting the vital rates. When the mean sex ratio at birth is known, improved efficiency is obtained by utilizing the records of total number of offspring rather than considering separately female and male offspring. We also show how to incorporate uncertain paternity.     

Genetic monitoring reveals temporal stability over 30 years in a small, lake-resident brown trout population

Knowledge of the degree of temporal stability of population genetic structure and composition is important for understanding microevolutionary processes and addressing issues of human impact of natural populations. We know little about how representative single samples in time are to reflect population genetic constitution, and we explore the temporal genetic variability patterns over a 30-year period of annual sampling of a lake-resident brown trout (Salmo trutta) population, covering 37 consecutive cohorts and five generations. Levels of variation remain largely stable over this period, with no indication of substructuring within the lake. We detect genetic drift, however, and the genetically effective population size (N(e)) was assessed from allele-frequency shifts between consecutive cohorts using an unbiased estimator that accounts for the effect of overlapping generation. The overall mean N(e) is estimated as 74. We find indications that N(e) varies over time, but there is no obvious temporal trend. We also estimated N(e) using a one-sample approach based on linkage disequilibrium (LD) that does not account for the effect of overlapping generations. Combining one-sample estimates for all years gives an N(e) estimate of 76. This similarity between estimates may be coincidental or reflecting a general robustness of the LD approach to violations of the discrete generations assumption. In contrast to the observed genetic stability, body size and catch per effort have increased over the study period. Estimates of annual effective number of breeders (N(b)) correlated with catch per effort, suggesting that genetic monitoring can be used for detecting fluctuations in abundance.     

Gene genealogies when the sample size exceeds the effective size of the population

We study the properties of gene genealogies for large samples using a continuous approximation introduced by R. A. Fisher. We show that the major effect of large sample size, relative to the effective size of the population, is to increase the proportion of polymorphisms at which the mutant type is found in a single copy in the sample. We derive analytical expressions for the expected number of these singleton polymorphisms and for the total number of polymorphic, or segregating, sites that are valid even when the sample size is much greater than the effective size of the population. We use simulations to assess the accuracy of these predictions and to investigate other aspects of large-sample genealogies. Lastly, we apply our results to some data from Pacific oysters sampled from British Columbia. This illustrates that, when large samples are available, it is possible to estimate the mutation rate and the effective population size separately, in contrast to the case of small samples in which only the product of the mutation rate and the effective population size can be estimated.     

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.     

The pattern of linkage disequilibrium in German Holstein cattle

This study presents a second generation of linkage disequilibrium (LD) map statistics for the whole genome of the Holstein–Friesian population, which has a four times higher resolution compared with that of the maps available so far. We used DNA samples of 810 German Holstein–Friesian cattle genotyped by the Illumina Bovine SNP50K BeadChip to analyse LD structure. A panel of 40 854 (75.6%) markers was included in the final analysis. The pairwise r² statistic of SNPs up to 5 Mb apart across the genome was estimated. A mean value of r² = 0.30 ± 0.32 was observed in pairwise distances of <25 kb and it dropped to 0.20 ± 0.24 at 50–75 kb, which is nearly the average inter‐marker space in this study. The proportion of SNPs in useful LD (r² ≥ 0.25) was 26% for the distance of 50 and 75 kb between SNPs. We found a lower level of LD for SNP pairs at the distance ≤100 kb than previously thought. Analysis revealed 712 haplo‐blocks spanning 4.7% of the genome and containing 8.0% of all SNPs. Mean and median block length were estimated as 164 ± 117 kb and 144 kb respectively. Allele frequencies of the SNPs have a considerable and systematic impact on the estimate of r². It is shown that minimizing the allele frequency difference between SNPs reduces the influence of frequency on r² estimates. Analysis of past effective population size based on the direct estimates of recombination rates from SNP data showed a decline in effective population size to N_e = 103 up to ～4 generations ago. Systematic effects of marker density and effective population size on observed LD and haplotype structure are discussed.     

Genome-wide linkage disequilibrium in two Japanese beef cattle breeds

There is little knowledge about the degree of linkage disequilibrium (LD) in beef cattle. This study aims to perform a genome-wide search for LD in Japanese Black and Japanese Brown beef cattle and to compare the level of LD between these two breeds. Parameter D' (the LD coefficient) was used as a measure of LD, and LD was tested for significance of allelic associations between syntenic and between non-syntenic marker pairs. Effects of breed, chromosome, genetic map distance and their interactions with D' were tested based on least squares analyses. Both breeds showed high levels of LD, which ranged over several tens of cM and declined as the marker distance increased for syntenic marker pairs. A rapid decline of the D' value was observed between markers that were spaced 5 and 20 cM apart. LD was significant in most cases for marker pairs <40 cM apart but was not significant between non-syntenic loci. The pattern of LD found in these two breeds was similar to that previously published for dairy cattle. The D' value between breeds was not significantly different (P > 0.05), but the interaction between breed and chromosome was highly significant (P < 0.001). Genetic selection seems to have caused the heterogeneity of the D' values among chromosomes within breed. These results indicate that LD mapping is a useful tool for fine-mapping quantitative trait loci of economically important traits in Japanese beef cattle.