Simultaneous detection of linkage disequilibrium and genetic differentiation of subdivided populations

We propose a new method for simultaneously detecting linkage disequilibrium and genetic structure in subdivided populations. Taking subpopulation structure into account with a hierarchical model, we estimate the magnitude of genetic differentiation and linkage disequilibrium in a metapopulation on the basis of geographical samples, rather than decompose a population into a finite number of random-mating subpopulations. We assume that Hardy-Weinberg equilibrium is satisfied in each locality, but do not assume independence between marker loci. Linkage states remain unknown. Genetic differentiation and linkage disequilibrium are expressed as hyperparameters describing the prior distribution of genotypes or haplotypes. We estimate related parameters by maximizing marginal-likelihood functions and detect linkage equilibrium or disequilibrium by the Akaike information criterion. Our empirical Bayesian model analyzes genotype and haplotype frequencies regardless of haploid or diploid data, so it can be applied to most commonly used genetic markers. The performance of our procedure is examined via numerical simulations in comparison with classical procedures. Finally, we analyze isozyme data of ayu, a severely exploited fish species, and single-nucleotide polymorphisms in human ALDH2.     

Analysis of multilocus zygotic associations

While nonrandom associations between zygotes at different loci (zygotic associations) frequently occur in Hardy-Weinberg disequilibrium populations, statistical analysis of such associations has received little attention. In this article, we describe the joint distributions of zygotes at multiple loci, which are completely characterized by heterozygosities at individual loci and various multilocus zygotic associations. These zygotic associations are defined in the same fashion as the usual multilocus linkage (gametic) disequilibria on the basis of gametic and allelic frequencies. The estimation and test procedures are described with details being given for three loci. The sampling properties of the estimates are examined through Monte Carlo simulation. The estimates of three-locus associations are not free of bias due to the presence of two-locus associations and vice versa. The power of detecting the zygotic associations is small unless different loci are strongly associated and/or sample sizes are large (>100). The analysis of zygotic associations not only offers an effective means of packaging numerous genic disequilibria required for a complete characterization of multilocus structure, but also provides opportunities for making inference about evolutionary and demographic processes through a comparative assessment of zygotic association vs. gametic disequilibrium for the same set of loci in nonequilibrium populations.     

Sweet drinks are made of this: conservation genetics of an endemic palm species from the Dominican Republic

Pseudophoenix ekmanii is a threatened palm species endemic to the Dominican Republic. Sap from trees is extracted to make a local drink; once they are tapped the individual usually dies. Plants are also illegally harvested for the nursery trade and destroyed by poachers hunting the endemic and threatened Hispaniolan parrot. We used 7 DNA microsatellite markers to assist land managers in developing conservation strategies for this palm. We sampled 4 populations along the known distribution range of this species (3 populations from the mainland and 1 from the small island of Isla Beata), for a total sample of n = 104. We found strong evidence for genetic drift, inbreeding, and moderate gene flow (i.e., all populations had at least 4 loci that were not in Hardy-Weinberg equilibrium, at least 9 loci pairs were in linkage disequilibrium, the pairwise F(ST) values ranged from 0.069 to 0.266, and had positive F(IS) values). Data supported an isolation-by-distance model, and cluster analyses based on genetic distances resolved 2 groups that match a north-south split. The population from Isla Beata had the lowest levels of genetic diversity and was the only one in which we found pairs of individuals with identical shared multilocus genotypes.     

Isolation and characterization of 17 microsatellite loci for the house finch (Carpodacus mexicanus)

The house finch (Carpodacus mexicanus) has emerged recently as a model species in studies of sexual selection, reproductive physiology, population genetics, and epizootic disease ecology. Here we describe 17 highly polymorphic microsatellite loci for this species. In a sample of 36 individuals, we observed an average of 16 alleles per locus and heterozygosity ranged from 0.61 to 0.97. One locus showed significant deviation from Hardy-Weinberg proportions, but no significant gametic disequilibrium was observed among any of the loci. Amplification by polymerase chain reaction was optimized under similar parameters across loci, thereby facilitating multiplexing and rapid multilocus genotyping.     

On the probability of loss of new mutations in the presence of linkage disequilibrium

A new selectively neutral mutation occurs in a multilocus genetic background that has achieved a stable equilibrium at which there is a linkage disequilibrium. Perturbation techniques are applied to an extension of the branching process formulation of Fisher in order to address the question of extinction probabilities. We show that under appropriate conditions the probability of extinction of the new mutant is increased by the existence of linkage disequilibrium in the genetic background.Research supported in part by NIH grant GM 28016     

Isolation by distance and vicariance drive genetic structure of a coral reef fish in the Pacific Ocean

We studied the genetic diversity of a coral reef fish species to investigate the origin of the differentiation. A total of 727 Acanthurus triostegus collected from 15 locations throughout the Pacific were analyzed for 20 polymorphic loci. The genetic structure showed limited internal disequilibrium within each population; 3.7% of the loci showed significant Hardy-Weinberg disequilibrium, mostly associated with Adh*, and we subsequently removed this locus from further analysis of geographic pattern. The genetic structure of A. triostegus throughout the tropical Pacific Ocean revealed a strong geographic pattern. Overall, there was significant population differentiation (multilocus F(ST) = 0.199), which was geographically structured according to bootstraps of neighbor-joining analysis on Nei's unbiased genetic distances and AMOVA analysis. The genetic structure revealed five geographic groups in the Pacific Ocean: western Pacific (Guam, Philippines, Palau, and Great Barrier Reef); central Pacific (Solomons, New Caledonia, and Fiji); and three groups made up of the eastern populations, namely Hawaiian Archipelago (north), Marquesas (equatorial), and southern French Polynesia (south) that incorporates Clipperton Island located in the northeastern Pacific. In addition, heterozygosity values were found to be geographically structured with higher values grouped within Polynesian and Clipperton populations, which exhibited lower population size. Finally, the genetic differentiation (F(ST)) was significantly correlated with geographic distance when populations from the Hawaiian and Marquesas archipelagos were separated from all the other locations. These results show that patterns of differentiation vary within the same species according to the spatial scale, with one group probably issued from vicariance, whereas the other followed a pattern of isolation by distance. The geographic pattern for A. triostegus emphasizes the diversity of the evolutionary processes that lead to the present genetic structure with some being more influential in certain areas or according to a particular spatial scale.     

The effects of multilocus balancing selection on neutral variability

We studied the effect of multilocus balancing selection on neutral nucleotide variability at linked sites by simulating a model where diallelic polymorphisms are maintained at an arbitrary number of selected loci by means of symmetric overdominance. Different combinations of alleles define different genetic backgrounds that subdivide the population and strongly affect variability. Several multilocus fitness regimes with different degrees of epistasis and gametic disequilibrium are allowed. Analytical results based on a multilocus extension of the structured coalescent predict that the expected linked neutral diversity increases exponentially with the number of selected loci and can become extremely large. Our simulation results show that although variability increases with the number of genetic backgrounds that are maintained in the population, it is reduced by random fluctuations in the frequencies of those backgrounds and does not reach high levels even in very large populations. We also show that previous results on balancing selection in single-locus systems do not extend to the multilocus scenario in a straightforward way. Different patterns of linkage disequilibrium and of the frequency spectrum of neutral mutations are expected under different degrees of epistasis. Interestingly, the power to detect balancing selection using deviations from a neutral distribution of allele frequencies seems to be diminished under the fitness regime that leads to the largest increase of variability over the neutral case. This and other results are discussed in the light of data from the Mhc.     

Visualization of pairwise and multilocus linkage disequilibrium structure using latent forests

Linkage disequilibrium study represents a major issue in statistical genetics as it plays a fundamental role in gene mapping and helps us to learn more about human history. The linkage disequilibrium complex structure makes its exploratory data analysis essential yet challenging. Visualization methods, such as the triangular heat map implemented in Haploview, provide simple and useful tools to help understand complex genetic patterns, but remain insufficient to fully describe them. Probabilistic graphical models have been widely recognized as a powerful formalism allowing a concise and accurate modeling of dependences between variables. In this paper, we propose a method for short-range, long-range and chromosome-wide linkage disequilibrium visualization using forests of hierarchical latent class models. Thanks to its hierarchical nature, our method is shown to provide a compact view of both pairwise and multilocus linkage disequilibrium spatial structures for the geneticist. Besides, a multilocus linkage disequilibrium measure has been designed to evaluate linkage disequilibrium in hierarchy clusters. To learn the proposed model, a new scalable algorithm is presented. It constrains the dependence scope, relying on physical positions, and is able to deal with more than one hundred thousand single nucleotide polymorphisms. The proposed algorithm is fast and does not require phase genotypic data.     

COMPARISON OF NON‐GAUSSIAN QUANTITATIVE GENETIC MODELS FOR MIGRATION AND STABILIZING SELECTION

The balance between stabilizing selection and migration of maladapted individuals has formerly been modeled using a variety of quantitative genetic models of increasing complexity, including models based on a constant expressed genetic variance and models based on normality. The infinitesimal model can accommodate nonnormality and a nonconstant genetic variance as a result of linkage disequilibrium. It can be seen as a parsimonious one‐parameter model that approximates the underlying genetic details well when a large number of loci are involved. Here, the performance of this model is compared to several more realistic explicit multilocus models, with either two, several or a large number of alleles per locus with unequal effect sizes. Predictions for the deviation of the population mean from the optimum are highly similar across the different models, so that the non‐Gaussian infinitesimal model forms a good approximation. It does, however, generally estimate a higher genetic variance than the multilocus models, with the difference decreasing with an increasing number of loci. The difference between multilocus models depends more strongly on the effective number of loci, accounting for relative contributions of loci to the variance, than on the number of alleles per locus.     

Allozymic Variation and Linkage Disequilibrium in Some Laboratory Populations of DROSOPHILA MELANOGASTER

Nine laboratory populations of D. melanogaster were surveyed by starch gel electrophoresis for variation at 17 enzyme loci. A single-fly extract could be assayed for all 17 enzymes, so that the data consist of 17-locus genotypes.--Pairwise linkage disequilibria were estimated from the multilocus genotypic frequencies, using both Burrows' and Hill's methods. Large amounts of linkage disequilibrium were found, in contrast to the results reported for natural populations.-Knowledge of the approximate sizes of these populations was used to compare the observed heterozygosities and linkage disequilibria with predictions of the neutral allele hypothesis. The relatively large amount of linkage disequilibrium is consistent with the small sizes of the populations. However, the levels of heterozygosity in at least some populations suggest that some mechanism has been operating to retard the rate of decay by random drift. Several examples of significant deviation from Hardy-Weinberg frequencies and the large amount of linkage disequilibrum present in these populations indicate that a likely mechanism is selective effects associated with neutral alleles because of linkage disequilibrium with selected loci (e.g., "associative overdominance"). The results are therefore consistent with both neutralist, and selectionist hypotheses, but suggest the importance of considering linkage disequilibrium between neutral and selected loci when attempting to explain the dynamics of enzyme polymorphisms.     

Global convergence properties in multilocus viability selection models: the additive model and the Hardy-Weinberg law

A natural coordinate system is introduced for the analysis of the global stability of the Hardy-Weinberg (HW) polymorphism under the general multilocus additive viability model. A global convergence criterion is developed and used to prove that the HW polymorphism is globally stable when each of the loci is diallelic, provided the loci are overdominant and the multilocus recombination is positive. As a corollary the multilocus Hardy-Weinberg law for neutral selection is derived.Research supported in part by NIH grants GM 39907-01, GM 10452-26 and NSF Grant DMS 86-06244Research supported in part by a US-Israel Binational Science Foundation grant 85-00021 and NIH grant GM 28016     

Analysis of genetic structure in soil populations of Rhizobium leguminosarum recovered from the USA and the UK

Although many studies have shown that animal-associated bacterial species exhibit linkage disequilibrium at chromosomal loci, recent studies indicate that both animal-associated and soil-borne bacterial species can display a nonclonal genetic structure in which alleles at chromosomal loci are in linkage equilibrium. To examine the situation in soil-borne species further, we compared genetic structure in two soil populations of Rhizobium leguminosarum bv. trifolii and two populations of R. leguminosarum bv. viciae from two sites in Oregon, with genetic structure in R. leguminosarum bv. viciae populations recovered from peas grown at a site in Washington, USA, and at a site in Norfolk, UK. A total of 234 chromosomal types (ET) were identified among 682 strains analysed for allelic variation at 13 enzyme-encoding chromosomal loci by multilocus enzyme electrophoresis (MLEE). Chi-square tests for heterogeneity of allele frequencies showed that the populations were not genetically uniform. A comparison of the genetic diversity within combined and individual populations confirmed that the Washington population was the primary cause of genetic differentiation between the populations. Each individual population exhibited linkage disequilibrium, with the magnitude of the disequilibrium being greatest in the Washington population and least in the UK population of R. leguminosarum bv. viciae. Linkage disequilibrium in the UK population was created between two clusters of 9 and 23 ETs, which, individually, were in linkage equilibrium. Strong linkage disequilibrium between the two major clusters of 8 and 12 ETs in the Washington population was caused by the low genetic diversity of the ETs within each cluster relative to the inter-cluster genetic distance. Because neither the magnitude of genetic diversity nor of linkage disequilibrium increased as hierarchical combinations of the six local populations were analysed, we conclude that the populations have not been isolated from each other for sufficient time, nor have they been exposed to enough selective pressure to develop unique multilocus genetic structure.     

Reticulated and epidemic population genetic structure of Rhizobium etli biovar phaseoli in a traditionally managed locality in Mexico

We conducted a multilocus enzyme electrophoresis (MLEE) study to assess the genetic structure of the nitrogen-fixing bacteria Rhizobium etli bv. phaseoli . We analysed the genetic variation at 10 enzyme-encoding chromosomal loci of 482 isolates from root nodules of Phaseolus vulgaris and P. coccineus bean plants. The isolates were obtained from six traditionally managed agricultural plots in two localities in the State of Puebla, in Central Mexico. The total mean genetic diversity ( H _E) for the six plots was 0.531. Among the 482 isolates collected, 126 distinctive multilocus genotypes (electrophoretic types [Ets]) were obtained, and approximately half of the isolates are represented by five widespread ETs. A significant degree of genetic differentiation among the six plots ( G _ST = 0.072) and between the two localities ( G _ST = 0.022) was detected. The main part of the observed variability (70%) was found among the isolates within the plants. The cluster analysis revealed two deeply diverging lineages, separated at a genetic distance of 0.7. When a multilocus linkage disequilibrium analysis was performed at different hierarchical levels, we found significant linkage disequilibrium, but when the analysis was performed for the genotypes within the two diverging lineages, we found evidence of recombination. We propose for R. etli bv. phaseoli a reticulated and epidemic genetic structure, in which few genotypes increase in frequency to produce numerically dominant clones, and genetic exchange occurs mainly among genotypes within each lineage.     

Inter-locus interactions: A review of experimental evidence

In quantitative genetics, experiments designed to elucidate the nature of gene action and hence the importance of epistasis, have included analysis of genetic differences among individuals in random mating populations (partitioning of genetic variation, analysis of selection responses), of differences among inbred lines or selected populations (variance components in crosses among lines, chromosome analysis using genetic markers and crossover suppression), of the effects of inbreeding, and of population structure. Evidence in population genetic studies has come from studies of linkage disequilibrium and co-adaptation in natural populations, and of multilocus fitness estimation and linkage disequilibrium and associative overdominance in experimental populations. While it is clear that epistasis does contribute to the genetic variation in some quantitative characters, and in particular reproductive fitness, much of the evidence is equivocal and unsatisfying.     

On Models of Quantitative Genetic Variability: A Stabilizing Selection-Balance Model

A model of stabilizing selection on a multilocus character is proposed that allows the maintenance of stable allelic polymorphism and linkage disequilibrium. The model is a generalization of Lerner's model of homeostasis in which heterozygotes are less susceptible to environmental variation and hence are superior to homozygotes under phenotypic stabilizing selection. The analysis is carried out for weak selection with a quadratic-deviation model for the stabilizing selection. The stationary state is characterized by unequal allele frequencies, unequal proportions of complementary gametes, and a reduction of the genetic (and phenotypic) variance by the linkage disequilibrium. The model is compared with Mather's polygenic balance theory, with models that include mutation-selection balance, and others that have been proposed to study the role of linkage disequilibrium in quantitative inheritance.     

厚壳桂新微卫星体分子标记的开发与应用

生境破碎化是导致全球生物多样性危机的主要原因,即使常见物种也会受到很大影响.厚壳桂(Cryptocarya chinensis)是我国南亚热带季风常绿阔叶林群落演替顶极物种,由于这一森林植被的破坏而呈片断化分布.在以往的研究中,我们利用筛选到的一些微卫星体对其遗传多样性研究后发现其可能以无性生殖为主.为进一步证实这一发...     

Properties of the multiallelic trend test

Disease genes can be mapped on the basis of associations between genetic markers and disease status, with the case-control design having the advantage of not requiring individuals from different generations. When the marker loci have multiple alleles, there has been debate on whether the power of tests for association increases or decreases. We show here that the multiple-allele version of Armitage's trend test has increased power over the two-allele version under the requirement of equifrequent alleles, but not in general. The trend test has the advantage of remaining valid even when the sampled population is not in Hardy-Weinberg equilibrium. A departure from Hardy-Weinberg means that association tests depend on gametic and nongametic linkage disequilibrium between marker and disease loci, and we illustrate the magnitude of these effects with simulated data.     

MIGRATION PATTERNS AND THE DEVELOPMENT OF MULTILOCUS ASSOCIATIONS IN A SELFING ANNUAL,TRITICUM DICOCCOIDES

Migration patterns in wild emmer wheat, Triticum dicoccoides, were inferred from single-locus and multilocus genetic distributions based primarily on expectations derived from single-locus and multilocus cline theory. Populations from five collections displayed a large amount of multilocus structuring, as indicated by high values of gametic-phase disequilibrium between pairs of loci and by high values of multilocus associations. Analyses of the distributions of individual alleles, however, indicated that alleles had apparent independent centers of origin and that at least some independent dispersal within regions occupied by ecotypes or races of wild emmer had occurred. The distribution of the degrees of multilocus association suggests that there has been a net migration of the northern or Qazrin race south and west into the pocket occupied by the Yehudiyya race. The results suggest that ecotypic differentiation may be independent and may antedate electrophoretically determined differentiation in these populations. There is no convincing evidence that the multilocus associations represent coadapted complexes; rather they appear to involve associations of mutant alleles that have been accentuated and preserved by low recombination rates and gene-flow barriers within previously differentiated ecotypes.     

QUANTITATIVE GENETIC VARIANCE MAINTAINED BY FLUCTUATING SELECTION WITH OVERLAPPING GENERATIONS: VARIANCE COMPONENTS AND COVARIANCES

The quantitative genetic variance-covariance that can be maintained in a random environment is studied, assuming overlapping generations and Gaussian stabilizing selection with a fluctuating optimum. The phenotype of an individual is assumed to be determined by additive contributions from each locus on paternal and maternal gametes (i.e., no epistasis and no dominance). Recurrent mutation is ignored, but linkage between loci is arbitrary. The genotype distribution in the evolutionarily stable population is generically discrete: only a finite number of polymorphic alleles with distinctly different effects are maintained, even though we allow a continuum of alleles with arbitrary phenotypic contributions to invade. Fluctuating selection maintains nonzero genetic variance in the evolutionarily stable population if the environmental heterogeneity is larger than a certain threshold. Explicit asymptotic expressions for the standing variance-covariance components are derived for the population near the threshold, or for large generational overlap, as a function of environmental variability and genetic parameters (i.e., number of loci, recombination rate, etc.), using the fact that the genotype distribution is discrete. Above the threshold, the population maintains considerable genetic variance in the form of positive linkage disequilibrium and positive gamete covariance (Hardy-Weinberg disequilibrium) as well as allelic variance. The relative proportion of these disequilibrium variances in the total genetic variance increases with the environmental variability.     

Fully informative microsatellite markers for the tetraploid plant Eritrichium nanum (Boraginaceae)

We characterized eight polymorphic, codominant nuclear microsatellite loci in the tetraploid plant Eritrichium nanum. The different allelic configurations occurring under tetrasomic inheritance were fully resolved at all loci. Two natural populations showed high observed heterozygosities, which were in agreement with Hardy-Weinberg expectations. There was no evidence of genetic linkage disequilibrium for any pair of loci. The results suggest that these microsatellite markers are useful for mating system and population genetic analyses in high-alpine E. nanum.