Estimating population divergence time and phylogeny from single-nucleotide polymorphisms data with outgroup ascertainment bias

The inference of population divergence times and branching patterns is of fundamental importance in many population genetic analyses. Many methods have been developed for estimating population divergence times, and recently, there has been particular attention towards genome-wide single-nucleotide polymorphisms (SNP) data. However, most SNP data have been affected by an ascertainment bias caused by the SNP selection and discovery protocols. Here, we present a modification of an existing maximum likelihood method that will allow approximately unbiased inferences when ascertainment is based on a set of outgroup populations. We also present a method for estimating trees from the asymmetric dissimilarity measures arising from pairwise divergence time estimation in population genetics. We evaluate the methods by simulations and by applying them to a large SNP data set of seven East Asian populations.     

Reconstituting the frequency spectrum of ascertained single-nucleotide polymorphism data

Most of the available SNP data have eluded valid population genetic analysis because most population genetical methods do not correctly accommodate the special discovery process used to identify SNPs. Most of the available SNP data have allele frequency distributions that are biased by the ascertainment protocol. We here show how this problem can be corrected by obtaining maximum-likelihood estimates of the true allele frequency distribution. In simple cases, the ML estimate of the true allele frequency distribution can be obtained analytically, but in other cases computational methods based on numerical optimization or the EM algorithm must be used. We illustrate the new correction method by analyzing some previously published SNP data from the SNP Consortium. Appropriate treatment of SNP ascertainment is vital to our ability to make correct inferences from the data of the International HapMap Project.     

Correcting for ascertainment biases when analyzing SNP data: applications to the estimation of linkage disequilibrium

As large-scale sequencing efforts turn from single genome sequencing to polymorphism discovery, single nucleotide polymorphisms (SNPs) are becoming an increasingly important class of population genetic data. But because of the ascertainment biases introduced by many methods of SNP discovery, most SNP data cannot be analyzed using classical population genetic methods. Statistical methods must instead be developed that can explicitly take into account each method of SNP discovery. Here we review some of the current methods for analyzing SNPs and derive sampling distributions for single SNPs and pairs of SNPs for some common SNP discovery schemes. We also show that the ascertainment scheme has a large effect on the estimation of linkage disequilibrium and recombination, and describe some methods of correcting for ascertainment biases when estimating recombination rates from SNP data.     

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 Discovery of Single-Nucleotide Polymorphisms—and Inferences about Human Demographic History

A method of historical inference that accounts for ascertainment bias is developed and applied to single-nucleotide polymorphism (SNP) data in humans. The data consist of 84 short fragments of the genome that were selected, from three recent SNP surveys, to contain at least two polymorphisms in their respective ascertainment samples and that were then fully resequenced in 47 globally distributed individuals. Ascertainment bias is the deviation, from what would be observed in a random sample, caused either by discovery of polymorphisms in small samples or by locus selection based on levels or patterns of polymorphism. The three SNP surveys from which the present data were derived differ both in their protocols for ascertainment and in the size of the samples used for discovery. We implemented a Monte Carlo maximum-likelihood method to fit a subdivided-population model that includes a possible change in effective size at some time in the past. Incorrectly assuming that ascertainment bias does not exist causes errors in inference, affecting both estimates of migration rates and historical changes in size. Migration rates are overestimated when ascertainment bias is ignored. However, the direction of error in inferences about changes in effective population size (whether the population is inferred to be shrinking or growing) depends on whether either the numbers of SNPs per fragment or the SNP-allele frequencies are analyzed. We use the abbreviation "SDL," for "SNP-discovered locus," in recognition of the genomic-discovery context of SNPs. When ascertainment bias is modeled fully, both the number of SNPs per SDL and their allele frequencies support a scenario of growth in effective size in the context of a subdivided population. If subdivision is ignored, however, the hypothesis of constant effective population size cannot be rejected. An important conclusion of this work is that, in demographic or other studies, SNP data are useful only to the extent that their ascertainment can be modeled.     

Correcting Estimators of θ and Tajima's D for Ascertainment Biases Caused by the Single-Nucleotide Polymorphism Discovery Process

Most single-nucleotide polymorphism (SNP) data suffer from an ascertainment bias caused by the process of SNP discovery followed by SNP genotyping. The final genotyped data are biased toward an excess of common alleles compared to directly sequenced data, making standard genetic methods of analysis inapplicable to this type of data. We here derive corrected estimators of the fundamental population genetic parameter θ = 4N_eμ (N_e, effective population size; μ, mutation rate) on the basis of the average number of pairwise differences and on the basis of the number of segregating sites. We also derive the variances and covariances of these estimators and provide a corrected version of Tajima's D statistic. We reanalyze a human genomewide SNP data set and find substantial differences in the results with or without ascertainment bias correction.     

SNP Discovery Using Next Generation Transcriptomic Sequencing in Atlantic Herring (Clupea harengus)

The introduction of Next Generation Sequencing (NGS) has revolutionised population genetics, providing studies of non-model species with unprecedented genomic coverage, allowing evolutionary biologists to address questions previously far beyond the reach of available resources. Furthermore, the simple mutation model of Single Nucleotide Polymorphisms (SNPs) permits cost-effective high-throughput genotyping in thousands of individuals simultaneously. Genomic resources are scarce for the Atlantic herring (Clupea harengus), a small pelagic species that sustains high revenue fisheries. This paper details the development of 578 SNPs using a combined NGS and high-throughput genotyping approach. Eight individuals covering the species distribution in the eastern Atlantic were bar-coded and multiplexed into a single cDNA library and sequenced using the 454 GS FLX platform. SNP discovery was performed by de novo sequence clustering and contig assembly, followed by the mapping of reads against consensus contig sequences. Selection of candidate SNPs for genotyping was conducted using an in silico approach. SNP validation and genotyping were performed simultaneously using an Illumina 1,536 GoldenGate assay. Although the conversion rate of candidate SNPs in the genotyping assay cannot be predicted in advance, this approach has the potential to maximise cost and time efficiencies by avoiding expensive and time-consuming laboratory stages of SNP validation. Additionally, the in silico approach leads to lower ascertainment bias in the resulting SNP panel as marker selection is based only on the ability to design primers and the predicted presence of intron-exon boundaries. Consequently SNPs with a wider spectrum of minor allele frequencies (MAFs) will be genotyped in the final panel. The genomic resources presented here represent a valuable multi-purpose resource for developing informative marker panels for population discrimination, microarray development and for population genomic studies in the wild.     

How do SNP ascertainment schemes and population demographics affect inferences about population history?

Background

The selection of variable sites for inclusion in genomic analyses can influence results, especially when exemplar populations are used to determine polymorphic sites. We tested the impact of ascertainment bias on the inference of population genetic parameters using empirical and simulated data representing the three major continental groups of cattle: European, African, and Indian. We simulated data under three demographic models. Each simulated data set was subjected to three ascertainment schemes: (I) random selection; (II) geographically biased selection; and (III) selection biased toward loci polymorphic in multiple groups. Empirical data comprised samples of 25 individuals representing each continental group. These cattle were genotyped for 47,506 loci from the bovine 50 K SNP panel. We compared the inference of population histories for the empirical and simulated data sets across different ascertainment conditions using F_ST and principal components analysis (PCA).

Results

Bias toward shared polymorphism across continental groups is apparent in the empirical SNP data. Bias toward uneven levels of within-group polymorphism decreases estimates of F_ST between groups. Subpopulation-biased selection of SNPs changes the weighting of principal component axes and can affect inferences about proportions of admixture and population histories using PCA. PCA-based inferences of population relationships are largely congruent across types of ascertainment bias, even when ascertainment bias is strong.

Conclusions

Analyses of ascertainment bias in genomic data have largely been conducted on human data. As genomic analyses are being applied to non-model organisms, and across taxa with deeper divergences, care must be taken to consider the potential for bias in ascertainment of variation to affect inferences. Estimates of F_ST, time of separation, and population divergence as estimated by principal components analysis can be misleading if this bias is not taken into account.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1469-5) contains supplementary material, which is available to authorized users.     

Application of single nucleotide polymorphisms to non-model species: a technical review

Single nucleotide polymorphisms (SNPs) have gained wide use in humans and model species and are becoming the marker of choice for applications in other species. Technology that was developed for work in model species may provide useful tools for SNP discovery and genotyping in non-model organisms. However, SNP discovery can be expensive, labour intensive, and introduce ascertainment bias. In addition, the most efficient approaches to SNP discovery will depend on the research questions that the markers are to resolve as well as the focal species. We discuss advantages and disadvantages of several past and recent technologies for SNP discovery and genotyping and summarize a variety of SNP discovery and genotyping studies in ecology and evolution.     

New explicit expressions for relative frequencies of single-nucleotide polymorphisms with application to statistical inference on population growth

We present new methodology for calculating sampling distributions of single-nucleotide polymorphism (SNP) frequencies in populations with time-varying size. Our approach is based on deriving analytical expressions for frequencies of SNPs. Analytical expressions allow for computations that are faster and more accurate than Monte Carlo simulations. In contrast to other articles showing analytical formulas for frequencies of SNPs, we derive expressions that contain coefficients that do not explode when the genealogy size increases. We also provide analytical formulas to describe the way in which the ascertainment procedure modifies SNP distributions. Using our methods, we study the power to test the hypothesis of exponential population expansion vs. the hypothesis of evolution with constant population size. We also analyze some of the available SNP data and we compare our results of demographic parameters estimation to those obtained in previous studies in population genetics. The analyzed data seem consistent with the hypothesis of past population growth of modern humans. The analysis of the data also shows a very strong sensitivity of estimated demographic parameters to changes of the model of the ascertainment procedure.     

Evaluating SNP ascertainment bias and its impact on population assignment in Atlantic cod, Gadus morhua

The increasing use of single nucleotide polymorphisms (SNPs) in studies of nonmodel organisms accentuates the need to evaluate the influence of ascertainment bias on accurate ecological or evolutionary inference. Using a panel of 1641 expressed sequence tag-derived SNPs developed for northwest Atlantic cod (Gadus morhua), we examined the influence of ascertainment bias and its potential impact on assignment of individuals to populations ranging widely in origin. We hypothesized that reductions in assignment success would be associated with lower diversity in geographical regions outside the location of ascertainment. Individuals were genotyped from 13 locations spanning much of the contemporary range of Atlantic cod. Diversity, measured as average sample heterozygosity and number of polymorphic loci, declined (c. 30%) from the western (H(e) = 0.36) to eastern (H(e) = 0.25) Atlantic, consistent with a signal of ascertainment bias. Assignment success was examined separately for pools of loci representing differing degrees of reductions in diversity. SNPs displaying the largest declines in diversity produced the most accurate assignment in the ascertainment region (c. 83%) and the lowest levels of correct assignment outside the ascertainment region (c. 31%). Interestingly, several isolated locations showed no effect of assignment bias and consistently displayed 100% correct assignment. Contrary to expectations, estimates of accurate assignment range-wide using all loci displayed remarkable similarity despite reductions in diversity. Our results support the use of large SNP panels in assignment studies of high geneflow marine species. However, our evidence of significant reductions in assignment success using some pools of loci suggests that ascertainment bias may influence assignment results and should be evaluated in large-scale assignment studies.     

Robust Demographic Inference from Genomic and SNP Data

We introduce a flexible and robust simulation-based framework to infer demographic parameters from the site frequency spectrum (SFS) computed on large genomic datasets. We show that our composite-likelihood approach allows one to study evolutionary models of arbitrary complexity, which cannot be tackled by other current likelihood-based methods. For simple scenarios, our approach compares favorably in terms of accuracy and speed with , the current reference in the field, while showing better convergence properties for complex models. We first apply our methodology to non-coding genomic SNP data from four human populations. To infer their demographic history, we compare neutral evolutionary models of increasing complexity, including unsampled populations. We further show the versatility of our framework by extending it to the inference of demographic parameters from SNP chips with known ascertainment, such as that recently released by Affymetrix to study human origins. Whereas previous ways of handling ascertained SNPs were either restricted to a single population or only allowed the inference of divergence time between a pair of populations, our framework can correctly infer parameters of more complex models including the divergence of several populations, bottlenecks and migration. We apply this approach to the reconstruction of African demography using two distinct ascertained human SNP panels studied under two evolutionary models. The two SNP panels lead to globally very similar estimates and confidence intervals, and suggest an ancient divergence (>110 Ky) between Yoruba and San populations. Our methodology appears well suited to the study of complex scenarios from large genomic data sets.     

Whole genome sequences are required to fully resolve the linkage disequilibrium structure of human populations

Background

An understanding of linkage disequilibrium (LD) structures in the human genome underpins much of medical genetics and provides a basis for disease gene mapping and investigating biological mechanisms such as recombination and selection. Whole genome sequencing (WGS) provides the opportunity to determine LD structures at maximal resolution.

Results

We compare LD maps constructed from WGS data with LD maps produced from the array-based HapMap dataset, for representative European and African populations. WGS provides up to 5.7-fold greater SNP density than array-based data and achieves much greater resolution of LD structure, allowing for identification of up to 2.8-fold more regions of intense recombination. The absence of ascertainment bias in variant genotyping improves the population representativeness of the WGS maps, and highlights the extent of uncaptured variation using array genotyping methodologies. The complete capture of LD patterns using WGS allows for higher genome-wide association study (GWAS) power compared to array-based GWAS, with WGS also allowing for the analysis of rare variation. The impact of marker ascertainment issues in arrays has been greatest for Sub-Saharan African populations where larger sample sizes and substantially higher marker densities are required to fully resolve the LD structure.

Conclusions

WGS provides the best possible resource for LD mapping due to the maximal marker density and lack of ascertainment bias. WGS LD maps provide a rich resource for medical and population genetics studies. The increasing availability of WGS data for large populations will allow for improved research utilising LD, such as GWAS and recombination biology studies.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1854-0) contains supplementary material, which is available to authorized users.     

The effect of the Neolithic expansion on European molecular diversity

We performed extensive and realistic simulations of the colonization process of Europe by Neolithic farmers, as well as their potential admixture and competition with local Palaeolithic hunter-gatherers. We find that minute amounts of gene flow between Palaeolithic and Neolithic populations should lead to a massive Palaeolithic contribution to the current gene pool of Europeans. This large Palaeolithic contribution is not expected under the demic diffusion (DD) model, which postulates that agriculture diffused over Europe by a massive migration of individuals from the Near East. However, genetic evidence in favour of this model mainly consisted in the observation of allele frequency clines over Europe, which are shown here to be equally probable under a pure DD or a pure acculturation model. The examination of the consequence of range expansions on single nucleotide polymorphism (SNP) diversity reveals that an ascertainment bias consisting of selecting SNPs with high frequencies will promote the observation of genetic clines (which are not expected for random SNPs) and will lead to multimodal mismatch distributions. We conclude that the different patterns of molecular diversity observed for Y chromosome and mitochondrial DNA can be at least partly owing to an ascertainment bias when selecting Y chromosome SNPs for studying European populations.     

Application of SNPs for population genetics of nonmodel organisms: new opportunities and challenges

Recent improvements in the speed, cost and accuracy of next generation sequencing are revolutionizing the discovery of single nucleotide polymorphisms (SNPs). SNPs are increasingly being used as an addition to the molecular ecology toolkit in nonmodel organisms, but their efficient use remains challenging. Here, we discuss common issues when employing SNP markers, including the high numbers of markers typically employed, the effects of ascertainment bias and the inclusion of nonneutral loci in a marker panel. We provide a critique of considerations specifically associated with the application and population genetic analysis of SNPs in nonmodel taxa, focusing specifically on some of the most commonly applied methods.     

Effect of microsatellite selection on individual and population genetic inferences: an empirical study using cross‐specific and species‐specific amplifications

Although whole‐genome sequencing is becoming more accessible and feasible for nonmodel organisms, microsatellites have remained the markers of choice for various population and conservation genetic studies. However, the criteria for choosing microsatellites are still controversial due to ascertainment bias that may be introduced into the genetic inference. An empirical study of red deer (Cervus elaphus) populations, in which cross‐specific and species‐specific microsatellites developed through pyrosequencing of enriched libraries, was performed for this study. Two different strategies were used to select the species‐specific panels: randomly vs. highly polymorphic markers. The results suggest that reliable and accurate estimations of genetic diversity can be obtained using random microsatellites distributed throughout the genome. In addition, the results reinforce previous evidence that selecting the most polymorphic markers leads to an ascertainment bias in estimates of genetic diversity, when compared with randomly selected microsatellites. Analyses of population differentiation and clustering seem less influenced by the approach of microsatellite selection, whereas assigning individuals to populations might be affected by a random selection of a small number of microsatellites. Individual multilocus heterozygosity measures produced various discordant results, which in turn had impacts on the heterozygosity‐fitness correlation test. Finally, we argue that picking the appropriate microsatellite set should primarily take into account the ecological and evolutionary questions studied. Selecting the most polymorphic markers will generally overestimate genetic diversity parameters, leading to misinterpretations of the real genetic diversity, which is particularly important in managed and threatened populations.     

Genotype-Imputation Accuracy across Worldwide Human Populations

A current approach to mapping complex-disease-susceptibility loci in genome-wide association (GWA) studies involves leveraging the information in a reference database of dense genotype data. By modeling the patterns of linkage disequilibrium in a reference panel, genotypes not directly measured in the study samples can be imputed and tested for disease association. This imputation strategy has been successful for GWA studies in populations well represented by existing reference panels. We used genotypes at 513,008 autosomal single-nucleotide polymorphism (SNP) loci in 443 unrelated individuals from 29 worldwide populations to evaluate the “portability” of the HapMap reference panels for imputation in studies of diverse populations. When a single HapMap panel was leveraged for imputation of randomly masked genotypes, European populations had the highest imputation accuracy, followed by populations from East Asia, Central and South Asia, the Americas, Oceania, the Middle East, and Africa. For each population, we identified “optimal” mixtures of reference panels that maximized imputation accuracy, and we found that in most populations, mixtures including individuals from at least two HapMap panels produced the highest imputation accuracy. From a separate survey of additional SNPs typed in the same samples, we evaluated imputation accuracy in the scenario in which all genotypes at a given SNP position were unobserved and were imputed on the basis of data from a commercial “SNP chip,” again finding that most populations benefited from the use of combinations of two or more HapMap reference panels. Our results can serve as a guide for selecting appropriate reference panels for imputation-based GWA analysis in diverse populations.     

Matching strategies for genetic association studies in structured populations

Association studies in populations that are genetically heterogeneous can yield large numbers of spurious associations if population subgroups are unequally represented among cases and controls. This problem is particularly acute for studies involving pooled genotyping of very large numbers of single-nucleotide-polymorphism (SNP) markers, because most methods for analysis of association in structured populations require individual genotyping data. In this study, we present several strategies for matching case and control pools to have similar genetic compositions, based on ancestry information inferred from genotype data for approximately 300 SNPs tiled on an oligonucleotide-based genotyping array. We also discuss methods for measuring the impact of population stratification on an association study. Results for an admixed population and a phenotype strongly confounded with ancestry show that these simple matching strategies can effectively mitigate the impact of population stratification.     

The effect of SNP discovery method and sample size on estimation of population genetic data for Chinese and Indian rhesus macaques (<Emphasis Type="Italic">Macaca mulatta</Emphasis>)

This study was designed to address issues regarding sample size and marker location that have arisen from the discovery of SNPs in the genomes of poorly characterized primate species and the application of these markers to the study of primate population genetics. We predict the effect of discovery sample size on the probability of discovering both rare and common SNPs and then compare this prediction with the proportion of common and rare SNPs discovered when different numbers of individuals are sequenced. Second, we examine the effect of genomic region on estimates of common population genetic data, comparing markers from both coding and non-coding regions of the rhesus macaque genome and the population genetic data calculated from these markers, to measure the degree and direction of bias introduced by SNPs located in coding versus non-coding regions of the genome. We found that both discovery sample size and genomic region surveyed affect SNP marker attributes and population genetic estimates, even when these are calculated from an expanded data set containing more individuals than the original discovery data set. Although none of the SNP detection methods or genomic regions tested in this study was completely uninformative, these results show that each has a different kind of genetic variation that is suitable for different purposes, and each introduces specific types of bias. Given that each SNP marker has an individual evolutionary history, we calculated that the most complete and unbiased representation of the genetic diversity present in the individual can be obtained by incorporating at least 10 individuals into the discovery sample set, to ensure the discovery of both common and rare polymorphisms.     

The effects of conditioning on probands to correct for multiple ascertainment.

Cannings and Thompson suggested conditioning on the phenotypes of the probands to correct for ascertainment in the analysis of pedigree data. The method assumes single ascertainment and can be expected to yield asymptotically biased parameter estimates except in this specific case. However, because the method is easy to apply, we investigated the degree of bias in the more typical situation of multiple ascertainment, in the hope that the bias might be small and that the method could be applied more generally. To explore the utility of conditioning on probands to correct for multiple ascertainment, we calculated the asymptotic value of the segregation ratio for two versions of the simple Mendelian segregation model on sibship data. For both versions, we found that this asymptotic value decreased approximately linearly as the ascertainment probability increased. When ascertainment was complete, the segregation-ratio estimates were zero, not just asymptotically but for finite sample size as well. In some cases, conditioning on probands actually resulted in greater parameter bias than no ascertainment correction at all. These results hold for a variety of sibship-size distributions, several modes of inheritance, and a wide range of population prevalences of affected individuals.