Joint linkage and linkage disequilibrium mapping in natural populations

A new strategy for studying the genome structure and organization of natural populations is proposed on the basis of a combined analysis of linkage and linkage disequilibrium using known polymorphic markers. This strategy exploits a random sample drawn from a panmictic natural population and the open-pollinated progeny of the sample. It is established on the principle of gene transmission from the parental to progeny generation during which the linkage between different markers is broken down due to meiotic recombination. The strategy has power to simultaneously capture the information about the linkage of the markers (as measured by recombination fraction) and the degree of their linkage disequilibrium created at a historic time. Simulation studies indicate that the statistical method implemented by the Fisher-scoring algorithm can provide accurate and precise estimates for the allele frequencies, recombination fractions, and linkage disequilibria between different markers. The strategy has great implications for constructing a dense linkage disequilibrium map that can facilitate the identification and positional cloning of the genes underlying both simple and complex traits.     

Estimation of multilocus linkage disequilibria in diploid populations with dominant markers

Analysis of population structure and organization with DNA-based markers can provide important information regarding the history and evolution of a species. Linkage disequilibrium (LD) analysis based on allelic associations between different loci is emerging as a viable tool to unravel the genetic basis of population differentiation. In this article, we derive the EM algorithm to obtain the maximum-likelihood estimates of the linkage disequilibria between dominant markers, to study the patterns of genetic diversity for a diploid species. The algorithm was expanded to estimate and test linkage disequilibria of different orders among three dominant markers and can be technically extended to manipulate an arbitrary number of dominant markers. The feasibility of the proposed algorithm is validated by an example of population genetic studies of hickory trees, native to southeastern China, using dominant random amplified polymorphic DNA markers. Extensive simulation studies were performed to investigate the statistical properties of this algorithm. The precision of the estimates of linkage disequilibrium between dominant markers was compared with that between codominant markers. Results from simulation studies suggest that three-locus LD analysis displays increased power of LD detection relative to two-locus LD analysis. This algorithm is useful for studying the pattern and amount of genetic variation within and among populations.     

A haplotype-based algorithm for multilocus linkage disequilibrium mapping of quantitative trait loci with epistasis

For tightly linked loci, cosegregation may lead to nonrandom associations between alleles in a population. Because of its evolutionary relationship with linkage, this phenomenon is called linkage disequilibrium. Today, linkage disequilibrium-based mapping has become a major focus of recent genome research into mapping complex traits. In this article, we present a new statistical method for mapping quantitative trait loci (QTL) of additive, dominant, and epistatic effects in equilibrium natural populations. Our method is based on haplotype analysis of multilocus linkage disequilibrium and exhibits two significant advantages over current disequilibrium mapping methods. First, we have derived closed-form solutions for estimating the marker-QTL haplotype frequencies within the maximum-likelihood framework implemented by the EM algorithm. The allele frequencies of putative QTL and their linkage disequilibria with the markers are estimated by solving a system of regular equations. This procedure has significantly improved the computational efficiency and the precision of parameter estimation. Second, our method can detect marker-QTL disequilibria of different orders and QTL epistatic interactions of various kinds on the basis of a multilocus analysis. This can not only enhance the precision of parameter estimation, but also make it possible to perform whole-genome association studies. We carried out extensive simulation studies to examine the robustness and statistical performance of our method. The application of the new method was validated using a case study from humans, in which we successfully detected significant QTL affecting human body heights. Finally, we discuss the implications of our method for genome projects and its extension to a broader circumstance. The computer program for the method proposed in this article is available at the webpage http://www.ifasstat.ufl.edu/genome/~LD.     

Multipoint Genetic Mapping with Trisomy Data

Trisomy is the most common genetic abnormality in humans and is the leading cause of mental retardation. Although molecular studies that use a large number of highly polymorphic markers have been undertaken to understand the recombination patterns for chromosome abnormalities, there is a lack of multilocus approaches to incorporating crossover interference in the analysis of human trisomy data. In the present article, we develop two statistical methods that simultaneously use all genetic information in trisomy data. The first approach relies on a general relationship between multilocus trisomy probabilities and multilocus ordered-tetrad probabilities. Under the assumption that no more than one chiasma exists in each marker interval, we describe how to use the expectation-maximization algorithm to examine the probability distribution of the recombination events underlying meioses that lead to trisomy. One limitation of the first approach is that the amount of computation increases exponentially with the number of markers. The second approach models the crossover process as a chi(2) model. We describe how to use hidden Markov models to evaluate multilocus trisomy probabilities. Our methods are applicable when both parents are available or when only the nondisjoining parent is available. For both methods, genetic distances among a set of markers can be estimated and the pattern of overall chiasma distribution can be inspected for differences in recombination between meioses exhibiting trisomy and normal meioses. We illustrate the proposed approaches through their application to a set of trisomy 21 data.     

A sequential coalescent algorithm for chromosomal inversions

Chromosomal inversions are common in natural populations and are believed to be involved in many important evolutionary phenomena, including speciation, the evolution of sex chromosomes and local adaptation. While recent advances in sequencing and genotyping methods are leading to rapidly increasing amounts of genome-wide sequence data that reveal interesting patterns of genetic variation within inverted regions, efficient simulation methods to study these patterns are largely missing. In this work, we extend the sequential Markovian coalescent, an approximation to the coalescent with recombination, to include the effects of polymorphic inversions on patterns of recombination. Results show that our algorithm is fast, memory-efficient and accurate, making it feasible to simulate large inversions in large populations for the first time. The SMC algorithm enables studies of patterns of genetic variation (for example, linkage disequilibria) and tests of hypotheses (using simulation-based approaches) that were previously intractable.     

Using molecular markers to map multiple quantitative trait loci: models for backcross,recombinant inbred,and doubled haploid progeny

Summary To maximize parameter estimation efficiency and statistical power and to estimate epistasis, the parameters of multiple quantitative trait loci (QTLs) must be simultaneously estimated. If multiple QTL affect a trait, then estimates of means of QTL genotypes from individual locus models are statistically biased. In this paper, I describe methods for estimating means of QTL genotypes and recombination frequencies between marker and quantitative trait loci using multilocus backcross, doubled haploid, recombinant inbred, and testcross progeny models. Expected values of marker genotype means were defined using no double or multiple crossover frequencies and flanking markers for linked and unlinked quantitative trait loci. The expected values for a particular model comprise a system of nonlinear equations that can be solved using an interative algorithm, e.g., the Gauss-Newton algorithm. The solutions are maximum likelihood estimates when the errors are normally distributed. A linear model for estimating the parameters of unlinked quantitative trait loci was found by transforming the nonlinear model. Recombination frequency estimators were defined using this linear model. Certain means of linked QTLs are less efficiently estimated than means of unlinked QTLs.     

A hidden Markov model approach to multilocus linkage analysis in a full-sib family

Statistical packages for constructing genetic linkage maps in inbred lines are well developed and applied extensively, while linkage analysis in outcrossing species faces some statistical challenges because of their complicated genetic structures. In this article, we present a multilocus linkage analysis via hidden Markov models for a linkage group of markers in a full-sib family. The advantage of this method is the simultaneous estimation of the recombination fractions between adjacent markers that possibly segregate in different ratios, and the calculation of likelihood for a certain order of the markers. When the number of markers decreases to two or three, the multilocus linkage analysis becomes traditional two-point or three-point linkage analysis, respectively. Monte Carlo simulations are performed to show that the recombination fraction estimates of multilocus linkage analysis are more accurate than those just using two-point linkage analysis and that the likelihood as an objective function for ordering maker loci is the most powerful method compared with other methods. By incorporating this multilocus linkage analysis, we have developed a Windows software, FsLinkageMap, for constructing genetic maps in a full-sib family. A real example is presented for illustrating linkage maps constructed by using mixed segregation markers. Our multilocus linkage analysis provides a powerful method for constructing high-density genetic linkage maps in some outcrossing plant species, especially in forest trees.     

Genetic differentiation of neutral markers and quantitative traits in predominantly selfing metapopulations: confronting theory and experiments with Arabidopsis thaliana

The comparison of the genetic differentiation of quantitative traits (QST) and molecular markers (FST) can inform on the strength and spatial heterogeneity of selection in natural populations, provided that markers behave neutrally. However, selection may influence the behaviour of markers in selfing species with strong linkage disequilibria among loci, therefore invalidating this test of detection of selection. We address this issue by monitoring the genetic differentiation of five microsatellite loci (FST) and nine quantitative traits (QST) in experimental metapopulations of the predominantly selfing species Arabidopsis thaliana, that evolved during eight generations. Metapopulations differed with respect to population size and selection heterogeneity. In large populations, the genetic differentiation of neutral microsatellites was much larger under heterogeneous selection than under uniform selection. Using simulations, we show that this influence of selection heterogeneity on FST can be attributable to initial linkage disequilibria among loci, creating stronger genetic differentiation of QTL than expected under a simple additive model with no initial linkage. We found no significant differences between FST and QST regardless of selection heterogeneity, despite a demonstrated effect of selection on QST values. Additional data are required to validate the role of mating system and linkage disequilibria in the joint evolution of neutral and selected genetic differentiation, but our results suggest that FST/QST comparisons can be conservative tests to detect selection in selfing species.     

Testing for concordant equilibria between population samples

A substantial body of theory has been developed to assess the effect of evolutionary forces on the distribution of genotypes, both single and multilocus, within populations. One area where the potential for application of this theory has not been fully appreciated concerns the extent to which population samples differ. Within populations, the divergence of genotype or haplotype frequencies from that expected under Hardy-Weinberg (HW) or linkage equilibrium can be measured as disequilibria coefficients. To assess population samples for concordant equilibria, an analytical framework for comparing disequilibria coefficients between populations is necessary. Here we present log-linear models to evaluate such hypotheses. These models have broad utility ranging from conventional population genetics to genetic epidemiology. We demonstrate the use of these log-linear models (1) as a test for genetic association with disease and (2) as a test for different levels of linkage disequilibria between human populations.     

A general framework for statistical linkage analysis in multivalent tetraploids

In multivalent polyploids, simultaneous pairings among homologous chromosomes at meiosis result in a unique cytological phenomenon-double reduction. Double reduction casts an impact on chromosome evolution in higher plants, but because of its confounded effect on the pattern of gene cosegregation, it complicates linkage analysis and map construction with polymorphic molecular markers. In this article, we have proposed a general statistical model for simultaneously estimating the frequencies of double reduction, the recombination fraction, and optimal parental linkage phases between any types of markers, both fully and partially informative, or dominant and codominant, for a tetraploid species that undergoes only multivalent pairing. This model provides an in-depth extension of our earlier linkage model that was built upon Fisher's classifications for different gamete formation modes during the polysomic inheritance of a multivalent polyploid. By implementing a two-stage hierarchical EM algorithm, we derived a closed-form solution for estimating the frequencies of double reduction through the estimation of gamete mode frequencies and the recombination fraction. We performed different settings of simulation studies to demonstrate the statistical properties of our model for estimating and testing double reduction and the linkage in multivalent tetraploids. As shown by a comparative analysis, our model provides a general framework that covers existing statistical approaches for linkage mapping in polyploids that are predominantly multivalent. The model will have great implications for understanding the genome structure and organization of polyploid species.     

Implications of life-history transitions on the population genetic structure of the toxigenic marine dinoflagellate Alexandrium tamarense

Genotypic or phenotypic markers for characterization of natural populations of marine microalgae have typically addressed questions regarding differentiation among populations, usually with reference to a single or few clonal isolates. Based upon a large number of contemporaneous isolates from the same geographical population of the toxigenic species Alexandrium tamarense from the North Sea, we uncovered significant genetic substructure and low but significant multilocus linkage disequilibrium (LD) within the planktonic population. Between the alternative molecular genotyping approaches, only amplified fragment length polymorphism (AFLP) revealed cryptic genetic population substructure by Bayesian clustering, whereas microsatellite markers failed to yield concordant patterns. Both markers, however, gave evidence for genetic differentiation of population subgroups as defined by AFLP. A considerable portion of multilocus LD could be attributed to population subdivision. The remaining LD within population subgroups is interpreted as an indicator of frequency shifts of clonal lineages during vegetative growth of planktonic populations. Phenotypic characters such as cellular content and composition of neurotoxins associated with paralytic shellfish poisoning (PSP) and allelochemical properties may contribute to intra- or inter-annual differentiation of planktonic populations, if clonal lineages that express these characters are selectively favoured. Nevertheless, significant phenotypic differentiation for these characters among the genetically differentiated subgroups was only detected for PSP toxin content in two of the four population subgroups. By integrating the analysis of phenotypic and genotypic characteristics, we developed a conceptual population genetic model to explain the importance of life-cycle dynamics and transitions in the evolutionary ecology of these dinoflagellates.     

Empirical evaluation of cytonuclear models incorporating genetic drift and tests for neutrality of mtDNA variants: data from experimental Gambusia hybrid zones

Statistical tests of genetic drift and of the neutrality of mtDNA are presented using empirical time‐series data on multi‐generational changes in cytonuclear disequilibria within replicated experimental hybrid populations of two species of live‐bearing Poeciliid fishes (Gambusia holbrooki and G.affinis) which were monitored over a period of two years (three generations). Cytonuclear disequilibria D and D (which measure departures from random associations of cytoplasmic and nuclear genotypes) over the three generations of the experiment were non‐zero for all replicate populations. For each of five nuclear loci, the observed measures of D and D were highly concordant between replicates during each generation. Significant departures from expectations were observed after one and two generations. A statistical measure of goodness of fit of observed changes in cytonuclear disequilibria (and implicitly of the neutrality of the mtDNA markers) was calculated for each nuclear locus. When the results for the replicates were combined into an overall test of neutrality, the fit to the random union of zygotes (RUZ) model was rejected for four of the five nuclear loci (P < 0.05). A simple genetic drift model does not explain the temporal changes in composite cytonuclear genotypic frequencies. Frequencies of parental G. holbrooki mitochondrial alleles and nuclear genotypes exceeded expected values during most time periods, implying some selective advantage of offspring produced by G. holbrooki females. Expansion of cytonuclear models to explicitly address questions of genetic drift and neutrality have general relevance to studies of natural populations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Population genetic analysis of Enterocytozoon bieneusi in humans

Genotyping based on sequence analysis of the ribosomal internal transcribed spacer has revealed significant genetic diversity in Enterocytozoonbieneusi. Thus far, the population genetics of E. bieneusi and its significance in the epidemiology of microsporidiosis have not been examined. In this study, a multilocus sequence typing of E. bieneusi in AIDS patients in Lima, Peru was conducted, using 72 specimens previously genotyped as A, D, IV, EbpC, WL11, Peru7, Peru8, Peru10 and Peru11 at the internal transcribed spacer locus. Altogether, 39 multilocus genotypes were identified among the 72 specimens. The observation of strong intragenic linkage disequilibria and limited genetic recombination among markers were indicative of an overall clonal population structure of E. bieneusi. Measures of pair-wise intergenic linkage disequilibria and a standardised index of association (IAS) based on allelic profile data further supported this conclusion. Both sequence-based and allelic profile-based phylogenetic analyses showed the presence of two genetically isolated groups in the study population, one (group 1) containing isolates of the anthroponotic internal transcribed spacer genotype A, and the other (group 2) containing isolates of multiple internal transcribed spacer genotypes (mainly genotypes D and IV) with zoonotic potential. The measurement of linkage disequilibria and recombination indicated group 2 had a clonal population structure, whereas group 1 had an epidemic population structure. The formation of the two sub-populations was confirmed by STRUCTURE and Wright's fixation index (FST) analyses. The data highlight the power of MLST in understanding the epidemiology of E. bieneusi.     

The importance of sexual and asexual reproduction in the recent evolution of Allium vineale

In the weedy plant species Allium vineale (wild garlic), individuals may simultaneously produce sexually and asexually derived offspring, by seed and bulbils, respectively. In this study, genetic and genotypic diversity was determined in samples from 14 European A. vineale populations using nuclear (RAPD) and cytoplasmic (PCR-RFLP of cpDNA) markers to investigate the importance of the different reproductive modes. In the whole sample, 77 nuclear multilocus genotypes and four chloroplast haplotypes (chlorotypes) were found. Populations exhibited a high degree of subdivision for nuclear and cytoplasmic markers as estimated from hierarchical F-statistics; at the same time, identical chlorotypes could be found in populations separated by large distances. Genotypic diversity was significantly lower than expected under free recombination in almost all populations, indicating that recruitment into populations is mostly by asexually produced offspring. Nevertheless, within each chlorotype, the distribution of markers from pairs of nuclear loci was incompatible with a purely clonal structure, suggesting that many multilocus genotypes have originated by sexual recombination rather than by mutation within asexual lineages. It is argued that the weedy habit of A. vineale is likely to have favored bulbil reproduction, whereas sexually generated genotypes may have facilitated local adaptation during the species' expansion across Europe.     

hybridlab (version 1.0): a program for generating simulated hybrids from population samples

We present the computer program hybridlab 1.0 for simulating intraspecific hybrids from population samples of nuclear genetic markers such as microsatellites, allozymes or SNPs (single nucleotide polymorphisms). The program generates a user‐specified number of multilocus F1 hybrid genotypes between any pair of potentially hybridizing populations included in a standard input‐file of multilocus genotypes for population genetic analysis. This simple, user‐friendly program has a wide range of applications for studying natural and artificial hybridization; in particular, for evaluating the statistical power for individual assignment of parental and hybrid individuals. An example of application for Atlantic cod populations is given.     

The Genetical Response to Natural Selection by Varied Environments. IV. Gametic Disequilibrium in Spatially Varied Environments

Gametic disequilibria between allozyme loci were related to spatial variation of the environment in caged populations of Drosophila melanogaster . Two experiments, one with flies collected at "Chateau Tahbilk," South Australia, and the other with flies from "Groningen," The Netherlands, were sampled at generations 16 and 32. Spatial variation of the environment was stimulated using three food media. Eight polymorphic allozyme loci were used to estimate gametic disequilibria from digenic combinations of allotypes. All populations were duplicated within an environment and maintained at about 2500 adults. Standardized gametic disequilibria were compared by a weighted least squares analysis of the z-transformed statistical correlation of allele frequencies. Gametic disequilibria were strongly dependent upon food niche and food-niche interactions. The effects also varied with sampling time and were similar in duplicate populations. Gametic disequilibria were most often detected in the "Groningen"-derived populations and their strength was not strongly associated with recombination fraction. Many of the disequilibria concerned unlinked loci. The strength of selection was probably considerable and populations were evolving genetic architectures which reflected niche selection by the different foods without marked genetic isolation between foods; gene frequencies did not vary between niches within a population cage.     

Genetic structure and linkage disequilibrium in landrace populations of barley in Sardinia

Multilocus digenic linkage disequilibria (LD) and their population structure were investigated in eleven landrace populations of barley (Hordeum vulgare ssp. vulgare L.) in Sardinia, using 134 dominant simple-sequence amplified polymorphism markers. The analysis of molecular variance for these markers indicated that the populations were partially differentiated (F(ST) = 0.18), and clustered into three geographic areas. Consistent with this population pattern, STRUCTURE analysis allocated individuals from a bulk of all populations into four genetic groups, and these groups also showed geographic patterns. In agreement with other molecular studies in barley, the general level of LD was low (13% of locus pairs, with P < 0.01) in the bulk of 337 lines, and decayed steeply with map distance between markers. The partitioning of multilocus associations into various components indicated that genetic drift and founder effects played a major role in determining the overall genetic makeup of the diversity in these landrace populations, but that epistatic homogenising or diversifying selection was also present. Notably, the variance of the disequilibrium component was relatively high, which implies caution in the pooling of barley lines for association studies. Finally, we compared the analyses of multilocus structure in barley landrace populations with parallel analyses in both composite crosses of barley on the one hand and in natural populations of wild barley on the other. Neither of these serves as suitable mimics of landraces in barley, which require their own study. Overall, the results suggest that these populations can be exploited for LD mapping if population structure is controlled.     

PATTERNS OF VARIATION AND LINKAGE DISEQUILIBRIUM IN A FIELD CRICKET HYBRID ZONE

The distribution of multilocus genotypes found within a natural hybrid zone is determined by the sample of genotypes present when the hybrid zone first formed, by subsequent patterns of genetic exchange between the hybridizing taxa, and by drift and selection within each of the hybrid zone populations. We have used anonymous nuclear DNA restriction fragment polymorphisms (RFLPs) to characterize the array of multilocus genotypes present within a well-studied hybrid zone between two eastern North American field crickets, Gryllus pennsylvanicus and Gryllus firmus. These crickets hybridize along a zone of contact that extends from New England to Virginia. Previous studies have shown that both premating and postmating barriers exist between the two cricket species, but the absence of diagnostic morphological and allozyme markers has made it difficult to assess the consequences of these barriers for genetic exchange. Analyses based on four diagnostic anonymous nuclear markers indicate that hybrid zone populations in Connecticut contain few F₁ hybrids, and that nonrandom associations persist among nuclear gene markers, between nuclear and cytoplasmic markers, and between molecular markers and morphology. Field cricket populations within the hybrid zone are not “hybrid swarms” but consist primarily of crickets that are very much like one or the other of the parental species. Despite ample opportunity for genetic exchange and evidence for introgression at some loci, the two species remain quite distinct. Such a pattern appears to be characteristic of many natural hybrid zones.     

Recombination shapes the natural population structure of the hyperthermophilic archaeon Sulfolobus islandicus

Although microorganisms make up the preponderance of the biodiversity on Earth, the ecological and evolutionary factors that structure microbial populations are not well understood. We investigated the genetic structure of a thermoacidophilic crenarchaeal species, Sulfolobus islandicus, using multilocus sequence analysis of six variable protein-coding loci on a set of 60 isolates from the Mutnovsky region of Kamchatka, Russia. We demonstrate significant incongruence among gene genealogies and a lack of association between alleles consistent with recombination rates greater than the rate of mutation. The observation of high relative rates of recombination suggests that the structure of this natural population does not fit the periodic selection model often used to describe populations of asexual microorganisms. We propose instead that frequent recombination among closely related individuals prevents periodic selection from purging diversity and provides a fundamental cohesive mechanism within this and perhaps other archaeal species.