Spatially explicit Bayesian clustering models in population genetics

This article reviews recent developments in Bayesian algorithms that explicitly include geographical information in the inference of population structure. Current models substantially differ in their prior distributions and background assumptions, falling into two broad categories: models with or without admixture. To aid users of this new generation of spatially explicit programs, we clarify the assumptions underlying the models, and we test these models in situations where their assumptions are not met. We show that models without admixture are not robust to the inclusion of admixed individuals in the sample, thus providing an incorrect assessment of population genetic structure in many cases. In contrast, admixture models are robust to an absence of admixture in the sample. We also give statistical and conceptual reasons why data should be explored using spatially explicit models that include admixture.     

一种有效的复杂疾病基因定位的检测法

连锁不平衡（LD）应用于某些复杂疾病基因的定位,近年来发展了许多LD定位方法,除TDT外,大多数LD定位方法须先假定无人群混和,人群混合可增大在疾病基因定位时犯Ⅰ类错误的机率,产生无效结果。此方法利用LD来检测标记位点和疾病敏感位点（DSL）的连锁（有连锁不平衡）相关（有连锁）。分析时采用不相关样本,已知其父母基因型和至少父母之一为杂合子,再将随机样本依基因型不同分类,然后对来自不同类的数据应用有力的统计方法进行单独和联合分析。此LD定位法不仅适用于患病和正常个体,而且有效消除据父母基因分类的样本定位时人群混合的影响,分析结果和模拟结果也表明此方法解决了在检测标记位点和疾病敏感位点之间的连锁和相关时人群混和的问题,但与TDT比,此法在检测的位点为DSL时丙能有效和充分地利用矫正数据,检测位点不是DSL时,此法和TDT法可相互补充更有效地检测连锁的DSL。     

Microevolution in an electronic microcosm

The evolution of microbial populations in simple environments such as chemostats is still not fully understood. The classical interpretation of adaptation involves a process of successive substitution whereby a new dominant genotype arises by mutation from the genotype previously dominant and spreads more or less rapidly through the population until it is nearly fixed. The population is, thus, nearly uniform most of the time. Some observations suggest that the process may be more complicated, but it remains formidably difficult to assemble the phylogeny of an evolving culture in sufficient detail to be sure. We report experiments with an electronic microcosm inhabited by self-replicating computer programs whose phylogeny can be rendered completely transparent. The physiology of these programs is different in many respects from that of organic creatures, but their population biology has many features in common, including a very extensive, if not unbounded, range of variation. Experimental populations evolved through point mutations (many of which were quasi-neutral when they were viable) and through rearrangements that led to a change in genome size and often had large effects on fitness. As a general rule, smaller genomes execute fewer instructions in order to replicate, the rate of replication increases as the number of instructions executed declines, and the rate of replication in pure culture is a good predictor of success in mixture. When cultured with CPU (central processing unit) time as the sole limiting resource, smaller genomes, therefore, evolve as a correlated response to natural selection for faster replication. The genetic basis of adaptation was highly contingent and always differed in replicate experiments. The pattern of evolution depends on mutation rate. At low mutation rates of 0.01 per genome per generation or less, we observed classic periodic selection, with each dominant genotype descending from the previous dominant and rising to a frequency of 0.8 or more. At higher mutation rates of about 0.1 per genome per generation, the most abundant genotypes rarely exceeded a frequency of about 0.4, and rare genotypes present in a few copies comprised a large part of the population. New dominant genotypes did not usually descend directly from previous dominants but, instead, from one of the many rare or moderately abundant genotypes. We suggest that the conventional chemostat paradigm may hold only as a special case at very low mutation rates and that the dynamics and diversity of evolving populations, even in the simplest conditions, may be more complex than is usually recognized. Artificial genetic autoadaptive systems are likely to be useful in constructing theory for situations that lie beyond the boundary of conventional population genetics.     

Screening of the Philadelphia variant of galactokinase in racially unmixed black Africans: first results.

In previous reports, it was emphasized that the gene GALKA of galactokinase was the predominant allele in white populations and that another allele, GALKP, which reduces red blood cell activity (RBC GALK), was common in black people. In a group of black Americans living in Philadelphia, the frequency of GALKA was found to be very close to values expected from independent estimation of white admixture. The authors have suggested that the ancestors of these blacks might have been virtually all GALKP homozygous. We have looked for carriers of GALKP genotypes among 73 black Africans; only 33 probands were shown to have a low RBC GALK. To detect white admixture, immunoglobulin allotypes Km and Gm were investigated in 50 individuals of the sample; 15 GALKP carriers with low RBC GALK and 30 of 35 individuals with normal RBC GALK shared Gm phenotypes exclusive to blacks. Our work demonstrates for the first time the polymorphism of GALK in black Africans in the absence of white admixture.     

Methods for high-density admixture mapping of disease genes

Admixture mapping (also known as "mapping by admixture linkage disequilibrium," or MALD) has been proposed as an efficient approach to localizing disease-causing variants that differ in frequency (because of either drift or selection) between two historically separated populations. Near a disease gene, patient populations descended from the recent mixing of two or more ethnic groups should have an increased probability of inheriting the alleles derived from the ethnic group that carries more disease-susceptibility alleles. The central attraction of admixture mapping is that, since gene flow has occurred recently in modern populations (e.g., in African and Hispanic Americans in the past 20 generations), it is expected that admixture-generated linkage disequilibrium should extend for many centimorgans. High-resolution marker sets are now becoming available to test this approach, but progress will require (a). computational methods to infer ancestral origin at each point in the genome and (b). empirical characterization of the general properties of linkage disequilibrium due to admixture. Here we describe statistical methods to estimate the ancestral origin of a locus on the basis of the composite genotypes of linked markers, and we show that this approach accurately estimates states of ancestral origin along the genome. We apply this approach to show that strong admixture linkage disequilibrium extends, on average, for 17 cM in African Americans. Finally, we present power calculations under varying models of disease risk, sample size, and proportions of ancestry. Studying approximately 2500 markers in approximately 2500 patients should provide power to detect many regions contributing to common disease. A particularly important result is that the power of an admixture mapping study to detect a locus will be nearly the same for a wide range of mixture scenarios: the mixture proportion should be 10%-90% from both ancestral populations.     

Estimation of admixture proportions: a likelihood-based approach using Markov chain Monte Carlo.

When populations are separated for long periods and then brought into contact for a brief episode in part of their range, this can result in genetic admixture. To analyze this type of event we considered a simple model under which two parental populations (P1 and P2) mix and create a hybrid population (H). After that event, the three populations evolve under pure drift without exchange during T generations. We developed a new method, which allows the simultaneous estimation of the time since the admixture event (scaled by the population size t(i) = T/N(i), where N(i) is the effective population size of population i) and the contribution of one of two parental populations (which we call p1). This method takes into account drift since the admixture event, variation caused by sampling, and uncertainty in the estimation of the ancestral allele frequencies. The method is tested on simulated data sets and then applied to a human data set. We find that (i) for single-locus data, point estimates are poor indicators of the real admixture proportions even when there are many alleles; (ii) biallelic loci provide little information about the admixture proportion and the time since admixture, even for very small amounts of drift, but can be powerful when many loci are used; (iii) the precision of the parameters' estimates increases with sample size n = 50 vs. n = 200 but this effect is larger for the t(i)'s than for p1; and (iv) the increase in precision provided by multiple loci is quite large, even when there is substantial drift (we found, for instance, that it is preferable to use five loci than one locus, even when drift is 100 times larger for the five loci). Our analysis of a previously studied human data set illustrates that the joint estimation of drift and p1 can provide additional insights into the data.     

Costs and benefits of admixture between foreign genotypes and local populations in the field

Admixture is the hybridization between populations within one species. It can increase plant fitness and population viability by alleviating inbreeding depression and increasing genetic diversity. However, populations are often adapted to their local environments and admixture with distant populations could break down local adaptation by diluting the locally adapted genomes. Thus, admixed genotypes might be selected against and be outcompeted by locally adapted genotypes in the local environments. To investigate the costs and benefits of admixture, we compared the performance of admixed and within‐population F1 and F2 generations of the European plant Lythrum salicaria in a reciprocal transplant experiment at three European field sites over a 2‐year period. Despite strong differences between site and plant populations for most of the measured traits, including herbivory, we found limited evidence for local adaptation. The effects of admixture depended on experimental site and plant population, and were positive for some traits. Plant growth and fruit production of some populations increased in admixed offspring and this was strongest with larger parental distances. These effects were only detected in two of our three sites. Our results show that, in the absence of local adaptation, admixture may boost plant performance, and that this is particularly apparent in stressful environments. We suggest that admixture between foreign and local genotypes can potentially be considered in nature conservation to restore populations and/or increase population viability, especially in small inbred or maladapted populations.     

An empirical exploration of data quality in DNA-based population inventories

I present data from 21 population inventory studies - 20 of them on bears - that relied on the noninvasive collection of hair, and review the methods that were used to prevent genetic errors in these studies. These methods were designed to simultaneously minimize errors (which can bias estimates of abundance) and per-sample analysis effort (which can reduce the precision of estimates by limiting sample size). A variety of approaches were used to probe the reliability of the empirical data, producing a mean, per-study estimate of no more than one undetected error in either direction (too few or too many individuals identified in the laboratory). For the type of samples considered here (plucked hair samples), the gain or loss of individuals in the laboratory can be reduced to a level that is inconsequential relative to the more universal sources of bias and imprecision that can affect mark-recapture studies, assuming that marker systems are selected according to stated guidelines, marginal samples are excluded at an early stage, similar pairs of genotypes are scrutinized, and laboratory work is performed with skill and care.     

Population admixture: detection by Hardy-Weinberg test and its quantitative effects on linkage-disequilibrium methods for localizing genes underlying complex traits

In association studies searching for genes underlying complex traits, the results are often inconsistent, and population admixture has been recognized qualitatively as one major potential cause. Hardy-Weinberg equilibrium (HWE) is often employed to test for population admixture; however, its power is generally unknown. Through analytical and simulation approaches, we quantify the power of the HWE test for population admixture and the effects of population admixture on increasing the type I error rate of association studies under various scenarios of population differentiation and admixture. We found that (1) the power of the HWE test for detecting population admixture is usually small; (2) population admixture seriously elevates type I error rate for detecting genes underlying complex traits, the extent of which depends on the degrees of population differentiation and admixture; (3) HWE testing for population admixture should be performed with random samples or only with controls at the candidate genes, or the test can be performed for combined samples of cases and controls at marker loci that are not linked to the disease; (4) testing HWE for population admixture generally reduces false positive association findings of genes underlying complex traits but the effect is small; and (5) with population admixture, a linkage disequilibrium method that employs cases only is more robust and yields many fewer false positive findings than conventional case-control analyses. Therefore, unless random samples are carefully selected from one homogeneous population, admixture is always a legitimate concern for positive findings in association studies except for the analyses that deliberately control population admixture.     

Evidence for gene flow and local clonal selection in field populations of the grain aphid (Sitobion avenae) in Britain revealed using microsatellites

Samples of the grain aphid, Sitobion avenae (F.), a major European pest of cereals, were collected in June and July 1997 from fields sown with winter wheat in a rough transect south-west of Rothamsted, UK. These aphids were genotyped at four microsatellite loci known from previous studies to be highly polymorphic. Allelic frequencies were similar between samples collected in the fields and in the 12.2 m high suction trap at Rothamsted, and there were many widespread genotypes (clones), providing evidence that the species is highly migratory. However, field samples were found to display a high level of genotypic heterogeneity (= variable clonal composition), most probably the result of clonal selection. The suction trap genotypes sample were slightly different from the field samples, indicative of the inclusion of genotypes from plant hosts (cereals and grasses, Poaceae) other than winter wheat and/or genotype-biased emigration from the field. The relevance of these data to modelling of aphid outbreaks is briefly discussed.     

Disturbance of the indigenous gene pool of the threatened brook lamprey Lethenteron sp. S by intraspecific introgression and habitat fragmentation

Artificial introduction and habitat fragmentation affect the indigenous gene pools of fluvial animals. To investigate the effect of human activities on the genetic population structure of vulnerable brook lamprey Lethenteron sp. S in a single river system, samples from 12 tributaries of the Jinzu River, Japan, were analyzed using mitochondrial and microsatellite DNA markers. Exogenous Lake Biwa (Japan) haplotypes and alleles were detected in lampreys from several Jinzu River tributaries. Since Lake Biwa is the source of the commercial ayu fish Plecoglossus altivelis that is introduced in the Jinzu River, the exogenous Lake Biwa lamprey genotypes in the Jinzu River probably originated from the Lake Biwa lampreys that were unintentionally introduced along with the ayu fish. Bayesian admixture and mitochondrial DNA analyses revealed various genetic disturbance phases of the exogenous genotypes in the Jinzu River, such as the six indigenous populations, four admixed populations with low frequencies (average admixture proportion = 0.02–0.04; exogenous haplotype proportion <0.01), one introgressed population (0.71 and 0.57) and one population almost displaced by exogenous genotypes (0.93 and 0.96). Samples from three tributaries with weirs were genetically differentiated from the others by using pairwise F _ST and Bayesian analyses; the results suggested isolation by the weirs. Reduced mitochondrial DNA diversity was observed in 1 of the 3 samples probably due to reduced population size. These findings indicate that the indigenous lamprey populations in the Jinzu River are seriously affected by introgression with exogenous genotypes via unintentional introduction and habitat fragmentation by weirs.     

Genetic structure of an aphid studied using microsatellites: cyclic parthenogenesis, differentiated lineages and host specialization

In a previous study, samples of the grain aphid Sitobion avenae (F.) were collected from wheat and adjacent cocksfoot hosts in a population thought to be primarily parthenogenetic, and DNA from individual aphids was analysed with a multilocus technique. Here we have applied single-locus microsatellites and a mitochondrial DNA marker to a subset of the same DNA extracts, and have made several additional inferences about important genetic and population processes in S. avenae . Microsatellite analysis indicated very high levels of genic and genotypic variation. S. avenae fell into three genotypic groups inferred to be almost noninterbreeding, while analysis of linkage and Hardy-Weinberg equilibria suggested high levels of sexual recombination within each genotypic group. Host specialization was evident: one lineage was found only on wheat, and one (bearing many alleles inferred to be introgressed from the blackberry-grass aphid S. fragariae (Walker)) was found only on cocksfoot. The third group of interrelated genotypes was found commonly on both hosts. Although most genotypes were found only once, some were much more numerous in the sample than expected from the frequency of the alleles they contained. This, and rapid temporal changes in genotypic composition of samples, indicates strong selective differences between genotypes and lineages. In the major genotypic group, the commonest genotypes were significantly more homozygous than were rare ones: thus these data may help to explain the frequent observation of homozygous excess in aphid allozymes. The genotype group showing S. avenae -like as well as S. fragariae -like alleles also carried S. fragariae -like mitochondrial DNA in at least 25/31 cases, indicating gender-asymmetrical hybridization.     

Estimating the long-term effects of stocking domesticated trout into wild brown trout (Salmo trutta) populations: an approach using microsatellite DNA analysis of historical and contemporary samples

Indigenous salmonid fish gene pools are affected by domesticated conspecifics, derived from aquaculture escapes and deliberate releases. Variability was examined at nine microsatellite loci in order to assess the long-term impact of stocking domesticated trout in two brown trout populations. The study was based on analysis of two historical samples (1945-56), represented by old scale collections, and seven contemporary samples (1986-2000). In one population historical and contemporary samples were remarkably genetically similar despite more than a decade of intense stocking. Estimation of admixture proportions showed a small genetic contribution from domesticated trout (approximately 6%), and individual admixture analysis demonstrated a majority of nonadmixed individuals. The expected genetic contribution by domesticated trout was 64%, assessed from the number of stocked trout and assuming equal survival and reproductive performance of wild and domesticated trout. This demonstrates poor performance and low fitness of domesticated trout in the wild. In another population there was a strong genetic contribution from domesticated trout (between 57% and 88% in different samples), both in samples from a broodstock thought to represent the indigenous population and in a sample of wild spawners. Survival of domesticated trout and admixture with indigenous fish in the broodstock and subsequent stocking into the river, combined with a low population size of native trout relative to the number of stocked trout, could explain the observed introgression. Few nonadmixed individuals remained in the introgressed population, and I discuss how individual admixture analysis can be used to identify and conserve nonintrogressed remains of the population.     

Perfect simulation from population genetic models with selection

We consider using the ancestral selection graph (ASG) to simulate samples from population genetic models with selection. Currently the use of the ASG to simulate samples is limited. This is because the computational requirement for simulating samples increases exponentially with the selection rate and also due to needing to simulate a sample of size one from the population at equilibrium. For the only case where the distribution of a sample of size one is known, that of parent-independent mutations, more efficient simulation algorithms exist. We will show that by applying the idea of coupling from the past to the ASG, samples can be simulated from a general K-allele model without knowledge of the distribution of a sample of size one. Furthermore, the computation involved in generating such samples appears to be less than that of simulating the ASG until its ultimate ancestor. In particular, in the case of genic selection with parent-independent mutations, the computational requirement increases only quadratically with the selection rate. The algorithm is demonstrated by simulating samples at a microsatellite locus.     

Effects of sample size on the performance of species distribution models

A wide range of modelling algorithms is used by ecologists, conservation practitioners, and others to predict species ranges from point locality data. Unfortunately, the amount of data available is limited for many taxa and regions, making it essential to quantify the sensitivity of these algorithms to sample size. This is the first study to address this need by rigorously evaluating a broad suite of algorithms with independent presence–absence data from multiple species and regions. We evaluated predictions from 12 algorithms for 46 species (from six different regions of the world) at three sample sizes (100, 30, and 10 records). We used data from natural history collections to run the models, and evaluated the quality of model predictions with area under the receiver operating characteristic curve (AUC). With decreasing sample size, model accuracy decreased and variability increased across species and between models. Novel modelling methods that incorporate both interactions between predictor variables and complex response shapes (i.e. GBM, MARS-INT, BRUTO) performed better than most methods at large sample sizes but not at the smallest sample sizes. Other algorithms were much less sensitive to sample size, including an algorithm based on maximum entropy (MAXENT) that had among the best predictive power across all sample sizes. Relative to other algorithms, a distance metric algorithm (DOMAIN) and a genetic algorithm (OM-GARP) had intermediate performance at the largest sample size and among the best performance at the lowest sample size. No algorithm predicted consistently well with small sample size ( n  < 30) and this should encourage highly conservative use of predictions based on small sample size and restrict their use to exploratory modelling.     

SNP arrays in heterogeneous tissue: highly accurate collection of both germline and somatic genetic information from unpaired single tumor samples

SNP arrays provide reliable genotypes and can detect chromosomal aberrations at a high resolution. However, tissue heterogeneity is currently a major limitation for somatic tissue analysis. We have developed SOMATICs, an original program for accurate analysis of heterogeneous tissue samples. Fifty-four samples (42 tumors and 12 normal tissues) were processed through Illumina Beadarrays and then analyzed with SOMATICs. We demonstrate that tissue heterogeneity-related limitations not only can be overcome but can also be turned into an advantage. First, admixture of normal cells with tumor can be used as an internal reference, thereby enabling highly sensitive detection of somatic deletions without having corresponding normal tissue. Second, the presence of normal cells allows for discrimination of somatic from germline aberrations, and the proportion of cells in the tissue sample that are harboring the somatic events can be assessed. Third, relatively early versus late somatic events can also be distinguished, assuming that late events occur only in subsets of cancer cells. Finally, admixture by normal cells allows inference of germline genotypes from a cancer sample. All this information can be obtained from any cancer sample containing a proportion of 40-75% of cancer cells. SOMATICs is a ready-to-use open-source program that integrates all of these features into a simple format, comprehensively describing each chromosomal event.     

Distribution of common genotypes of Myzus persicae (Hemiptera: Aphididae) in Greece, in relation to life cycle and host plant

Microsatellite genotyping was used to identify common clones in populations of the Myzus persicae group from various hosts and regions in mainland Greece and southern Italy and to compare their distribution and occurrence on tobacco and other crops. Common clones were defined as genotypes collected at more than one time or in more than one population; and, therefore, unlikely to be participating in the annual sexual phase on peach. Sixteen common genotypes were found, accounting for 49.0% of the 482 clonal lineages examined. Eight of these genotypes were subjected, in the laboratory, to short days and found to continue parthenogenetic reproduction, i.e. they were anholocyclic. Four of the six commonest genotypes were red, and one of these accounted for 29.6% of the samples from tobacco and 29.4% of those from overwintering populations on weeds. All six commonest genotypes were found on weeds and five of them both on tobacco and on other field crops. In mainland Greece, the distribution of common clones corresponded closely with that of anholocyclic lineages reported in a previous study of life cycle variation. Common genotypes were in the minority in the commercial peach-growing areas in the north, except on weeds in winter and in tobacco seedbeds in early spring, but predominated further south, away from peach trees. This contrasts with the situation in southern Italy, reported in a previous paper, where peaches were available for the sexual phase, yet all samples from tobacco were of common genotypes.     

Expectation maximization algorithm based haplotype relative risk (EM-HRR): test of linkage disequilibrium using incomplete case-parents trios

The Haplotype Relative Risk (HRR) was first proposed [Falk et al., Ann Hum Genet 1987] to test for Linkage Disequilibrium (LD) between a marker and a putative disease locus using case-parent trios. Spurious association does not appear in such family-based studies under population admixture. In this paper, we extend the HRR to accommodate incomplete trios via the Expectation-Maximization (EM) algorithm [Dempster et al., J R Stat Soc Ser B, 1977]. In addition to triads and dyads (parent-offspring pair), the EM-HRR easily incorporates individuals with no parental genotype information available, which is excluded from the one parent Transmission/Disequilibrium Test (1-TDT) [Sun et al., Am J Epidemiol 1999]. Due to the data structure of EM-HRR, transmitted alleles are always available regardless of the number of missing parental genotypes. As a result of having a larger sample size, computer simulations reveal that the EM-HRR is more powerful in detecting LD than the 1-TDT in a population under Hardy-Weinberg Equilibirum (HWE). If admixture is not extreme, the EM-HRR remains more powerful. When a large degree of admixture exists, the EM-HRR performs better the 1-TDT when the association is strong, though not as well when the association is weak. We illustrate the proposed method with an application to the Framingham Heart Study.     

Population size estimation in Yellowstone wolves with error-prone noninvasive microsatellite genotypes

Determining population sizes can be difficult, but is essential for conservation. By counting distinct microsatellite genotypes, DNA from noninvasive samples (hair, faeces) allows estimation of population size. Problems arise because genotypes from noninvasive samples are error-prone, but genotyping errors can be reduced by multiple polymerase chain reaction (PCR). For faecal genotypes from wolves in Yellowstone National Park, error rates varied substantially among samples, often above the 'worst-case threshold' suggested by simulation. Consequently, a substantial proportion of multilocus genotypes held one or more errors, despite multiple PCR. These genotyping errors created several genotypes per individual and caused overestimation (up to 5.5-fold) of population size. We propose a 'matching approach' to eliminate this overestimation bias.     

Fast and accurate population admixture inference from genotype data from a few microsatellites to millions of SNPs

Model-based (likelihood and Bayesian) and non-model-based (PCA and K-means clustering) methods were developed to identify populations and assign individuals to the identified populations using marker genotype data. Model-based methods are favoured because they are based on a probabilistic model of population genetics with biologically meaningful parameters and thus produce results that are easily interpretable and applicable. Furthermore, they often yield more accurate structure inferences than non-model-based methods. However, current model-based methods either are computationally demanding and thus applicable to small problems only or use simplified admixture models that could yield inaccurate results in difficult situations such as unbalanced sampling. In this study, I propose new likelihood methods for fast and accurate population admixture inference using genotype data from a few multiallelic microsatellites to millions of diallelic SNPs. The methods conduct first a clustering analysis of coarse-grained population structure by using the mixture model and the simulated annealing algorithm, and then an admixture analysis of fine-grained population structure by using the clustering results as a starting point in an expectation maximisation algorithm. Extensive analyses of both simulated and empirical data show that the new methods compare favourably with existing methods in both accuracy and running speed. They can analyse small datasets with just a few multiallelic microsatellites but can also handle in parallel terabytes of data with millions of markers and millions of individuals. In difficult situations such as many and/or lowly differentiated populations, unbalanced or very small samples of individuals, the new methods are substantially more accurate than other methods.Subject terms: Population genetics, Evolutionary ecology