Infinite Allele Model Research Articles

Allele excess at neutrally evolving microsatellites and the implications for tests of neutrality.

Skews in the observed allele-frequency spectrum are frequently viewed as an indication of non-neutral evolution. Recent surveys of microsatellite variability have used an excess of alleles as a statistical approach to infer positive selection. Using neutral coalescent simulations we demonstrate that the mean numbers of alleles expected under the stepwise-mutation model and infinite-allele model deviate from the observed numbers of alleles. The magnitude of this difference is dependent on the sample size, mutation rates (theta-values) and observed gene diversities. Moreover, we show that the number of observed alleles differs among loci with the same observed gene diversity but different mutation rates (theta-values). We propose that a reliable test statistic based on allele excess must determine the confidence interval by computer simulations conditional on the observed gene diversity and theta-values. As the latter are notoriously difficult to obtain for experimental data, we suggest that other statistics, such as lnRV, may be better suited to the identification of microsatellite loci subject to selection.

Isolation by distance, based on microsatellite data, tested with spatial autocorrelation (spaida) and assignment test (spassign)

Abstract spassign and spaida are two small programs useful to detect isolate by distance of microsatellite loci. The programs are written in C and are available for Linux and Windows system at http://www.hi.is/~snaebj/programs.html. spaida calculates two estimates of spatial autocorrelation, Moran's I and Geary's c, first by assuming the infinite allele model, and second by assuming a stepwise mutational model. spassign calculates the assignment probabilities of an individuals genotype to the location where it was sampled and compares probabilities of assignment to other locations. Genetic distances among regions based on the overall differences in likelihoods are calculated.

An analysis of microsatellite loci in Arabidopsis thaliana: mutational dynamics and application.

Microsatellite loci are among the most commonly used molecular markers. These loci typically exhibit variation for allele frequency distribution within a species. However, the factors contributing to this variation are not well understood. To expand on the current knowledge of microsatellite evolution, 20 microsatellite loci were examined for 126 accessions of the flowering plant, Arabidopsis thaliana. Substantial variability in mutation pattern among loci was found, most of which cannot be explained by the assumptions of the traditional stepwise mutation model or infinite alleles model. Here it is shown that the degree of locus diversity is strongly correlated with the number of contiguous repeats, more so than with the total number of repeats. These findings support a strong role for repeat disruptions in stabilizing microsatellite loci by reducing the substrate for polymerase slippage and recombination. Results of cluster analyses are also presented, demonstrating the potential of microsatellite loci for resolving relationships among accessions of A. thaliana.

Coalescence times andFSTvalues in subdivided populations with symmetric structure

The structured coalescent is a continuous-time Markov chain which describes the genealogy of a sample of homologous genes from a subdivided population. Assuming this model, some results are proved relating to the genealogy of a pair of genes and the extent of subpopulation differentiation, which are valid under certain graph-theoretic symmetry and regularity conditions on the structure of the population. We first review and extend earlier results stating conditions under which the mean time since the most recent common ancestor of a pair of genes from any single subpopulation is independent of the migration rate and equal to that of two genes from an unstructured population of the same total size. Assuming the infinite alleles model of neutral mutation with a small mutation rate, we then prove a simple relationship between the migration rate and the value of Wright's coefficientFSTfor a pair of neighbouring subpopulations, which does not depend on the precise structure of the population provided that this is sufficiently symmetric.

Coalescence times and F ST values in subdivided populations with symmetric structure

The structured coalescent is a continuous-time Markov chain which describes the genealogy of a sample of homologous genes from a subdivided population. Assuming this model, some results are proved relating to the genealogy of a pair of genes and the extent of subpopulation differentiation, which are valid under certain graph-theoretic symmetry and regularity conditions on the structure of the population. We first review and extend earlier results stating conditions under which the mean time since the most recent common ancestor of a pair of genes from any single subpopulation is independent of the migration rate and equal to that of two genes from an unstructured population of the same total size. Assuming the infinite alleles model of neutral mutation with a small mutation rate, we then prove a simple relationship between the migration rate and the value of Wright's coefficientFSTfor a pair of neighbouring subpopulations, which does not depend on the precise structure of the population provided that this is sufficiently symmetric.

Drift as a mechanism for cultural change: an example from baby names.

In the social sciences, there is currently no consensus on the mechanism by which cultural elements come and go in human society. For elements that are value-neutral, an appropriate null model may be one of random copying between individuals in the population. We show that the frequency distributions of baby names used in the United States in each decade of the twentieth century, for both males and females, obey a power law that is maintained over 100 years even though the population is growing, names are being introduced and lost every decade and large changes in the frequencies of specific names are common. We show that these distributions are satisfactorily explained by a simple process in which individuals randomly copy names from each other, a process that is analogous to the infinite-allele model of population genetics with random genetic drift. By its simplicity, this model provides a powerful null hypothesis for cultural change. It further explains why a few elements inevitably become highly popular, even if they have no intrinsic superiority over alternatives. Random copying could potentially explain power law distributions in other cultural realms, including the links on the World Wide Web.

Detection of quantitative trait loci for growth and beef carcass fatness traits in a cross between Bos taurus (Angus) and Bos indicus (Brahman) cattle.

This study was conducted to detect quantitative trait loci (QTL) affecting growth and beef carcass fatness traits in an experimental population of Angus and Brahman crossbreds. The three-generation mapping population was generated with 602 progeny from 29 reciprocal backcross and three F2 full-sib families, and 417 genetic markers were used to produce a sex-averaged map of the 29 autosomes spanning 2,642.5 Kosambi cM. Alternative interval-mapping approaches were applied under line-cross (LC) and random infinite alleles (RA) models to detect QTL segregating between and within breeds. A total of 35 QTL (five with genomewide significant and 30 with suggestive evidence for linkage) were found on 19 chromosomes. One QTL affecting yearling weight was found with genomewide significant evidence for linkage in the interstitial region of bovine autosome (BTA) 1, and an additional 19 QTL were detected with suggestive evidence for linkage under the LC model. Many of these QTL had a dominant (complete or overdominant) mode of gene action, and only a few of the QTL were primarily additive, which reflects the fact that heterosis for growth is known to be appreciable in crosses among Brahman and British breeds. Four QTL affecting growth were detected with genomewide significant evidence for linkage under the RA model on BTA 2 and BTA 6 for birth weight, BTA 5 for yearling weight, and BTA 23 for hot carcass weight. An additional 11 QTL were detected with suggestive evidence for linkage under the RA model. None of the QTL (except for yearling weight on BTA 5) detected under the RA model were found by the LC analyses, suggesting the segregation of alternate alleles within one or both of the parental breeds. Our results reveal the utility of implementing both the LC and RA models to detect dominant QTL and also QTL with similar allele frequency distributions within parental breeds.

Microsatellite analysis of genetic diversity in four populations ofPopulus tremuloidesin Quebec

To determine overall genetic variability in aspen (Populus tremuloides Michx.) along the clay belt of northwestern Quebec, four populations were sampled at the transition zone between mixed-wood and conifer-dominated forests using a hierarchical strategy. Our objectives were (i) to estimate gene diversity among and within populations using microsatellite markers and (ii) to examine whether clonal structuring in aspen could be detected. For each population, three stands at least 1 km apart were sampled. Within each stand, five putative clones were sampled with a distance of 50 m between each clone. To examine potential genetic diversity within clones, for three of the putative clones sampled per stand, the three trees closest to this individual (potential ramets) were also sampled. All samples were analysed at four microsatellite loci. Measures of genetic variation all indicated that most of the variation occurred within rather than among the populations. Rst, based on a stepwise mutation model, was 0.0409, slightly higher than Fst, which was based on infinite allele model (0.0323). Within each stand, DNA fingerprint of five putative clones allowed the differentiation of genetically distinct individuals within these putative clones, and from 1.62 to 2.2 times more genetically distinct individuals were identified than by morphological identification. In the present study there was no correlation between the mean distance of the potential ramet to the central trunk (potential ramets were often within 2–3 m of the central trunk) and the possibility of the central trunk and ramet sharing the same genotype. The number of unique genotypes for the three putative clones sampled per stand varied from 11 genotypes per 15 samples to 14 per 15 samples. Consequently, it was not possible to identify clones by either distance from a given central trunk or morphological characteristics. Thus, after stand disturbance, suckers from different genotypes are likely to be closely mixed.Key words: genetic diversity, Populus tremuloides, microsatellites, clone size.

When can one detect overdominant selection in the infinite-alleles model?

One of the goals of this paper is to show that the infinite-alleles model with overdominant selection looks the neutral infinite-alleles model when the selection intensity and mutation rate get large together. This rather surprising behavior was noticed by Gillespie (1999) in simulations. To make rigorous and refine Gillespie's observations, we analyze the limiting behavior of the likelihood ratio of the stationary distributions for the model under selection and neutrality, as the mutation rate and selection intensity go to $\infty$ together in a specified manner. In particular, we show that the likelihood ratio tends to 1 as the mutation rate goes to $\infty$, provided the selection intensity is a multiple of the mutation rate raised to a power less than $3/2$. (Gillespie's simulations correspond to the power 1.) This implies that we cannot distinguish between the two models in this setting. Conversely, if the selection intensity grows like a multiple of the mutation rate raised to a power greater than $3/2$, selection can be detected; that is, the likelihood ratio tends to 0 under neutrality and $\infty$ under selection. We also determine the nontrivial limit distributions in the case of the critical exponent $3/2$. We further analyze the limiting behavior when the exponent is less than $3/2$ by determining the rate at which the likelihood ratio converges to 1 and by developing results for the distributions of finite samples.

Metapopulation genetic structure and migration pathways in the land snail Helix aspersa: influence of landscape heterogeneity

The spatial genetic structuring of the land snail Helix aspersa was investigated for 32 colonies within an intensive agricultural area, the polders of the Bay of Mont-Saint-Michel (France). Given the habitat patchiness and environmental instability, the setting of H. aspersa colonies meets the broader view of a metapopulation structure. The identification of extrinsic barriers to migration and their impact on the genetic distribution was addressed through the genotyping of 580 individuals using a combined set of enzyme and microsatellite loci. To evaluate the distance as well as the direction over which the spatial genetic arrangement occurs, two-dimensional spatial autocorrelation analyses, Mantel tests of association and multivariate Mantel correlograms were used. Different connectivity networks and geographical distances based on landscape features were constructed to evaluate the effect of environmental heterogeneity and to test the adequacy of an isolation by distance model on the distribution of the genetic variability. Genetic divergence was assessed using either classical IAM-based statistics, or SMM-based genetic distances specifically designed to accommodate the mutational processes thought to fit microsatellite evolution (IAM: Infinite Allele Model; SMM: Stepwise Mutation Model). Genetic distances based only on genetic drift yielded the most plausible biologically meaningful interpretation of the observed spatial structure. Applying a landscape-based geographical distance which postulates that migration arises along roadside verges, hedges or irrigation canal embankments gave a better fit to an isolation by distance model than did a simple Euclidean distance. The progressive decline of genetic similarity with physical distance appeared to be environmentally induced, leading to functional migration pathways.

Genetic structure of the contemporary Cuban population for nine STR loci

Short tandem repeats (STR) are, at the moment, the most convenient and powerful way to infer personal identification out of genome data obtained from scarce and highly degraded DNA. In the forensic context, personal identification from bones and other human remains is one of the most challenging tasks to solve in cases where traditional anthropology is insufficient to achieve that goal. In order to assess the usefulness of a set of microsatellites containing the loci HUMTH01, HUMTPOX, HUMCSF1PO, HUMvWA, HUMFESFPS, HUMF13A01, HUMF13B, HUMHPRTB and HUMLPL, reference databases were constructed for the three main racial groups of the contemporary Cuban population (Caucasoids, Mestizos and Negroids). Minimal allele frequencies were estimated following the expression described by Budowle [1] based on the predictions of the Infinite Alleles Model to avoid negative bias when rare alleles are considered. The distributions of allele frequencies were found to be similar to the ones reported by other authors at closely related population groups. A rare allele 5 was found, sequenced and characterized in Mestizo group at the HUMCSF1PO locus. Private alleles were found for the three groups. The three Cubans databases were validated for the presence of Hardy– Weinberg equilibrium and linkage disequilibrium using Markov Chain Monte Carlo methods. A few significant P-values were eliminated when Bonferoni-type corrections were done for the control of type I error, indicating both the validity of the sampling scheme done and the possibility of using the standard formulae to estimate the frequency of a multilocus profile in the Cuban population. The way genetic variation is distributed in

Chilean Tetraploid Cultivated Potato,Solanum tuberosum, is Distinct from the Andean Populations

This study tests the genetic difference between landrace populations of Solanum tuberosum L. subsp. tuberosum and subsp. andigenum (Juz. & Bukasov) Hawkes using nuclear DNA microsatellites. Microsatellite loci were amplified in subsp. andigenum (35 accessions), subsp. tuberosum (35 accessions), and other cultivated and wild species (22 accessions). A total of 208 alleles were scored from 18 microsatellite loci spread throughout all 12 chromosomes of potato. Using an infinite allele model and a least squares method of analysis, microsatellite loci separated subsp. tuberosum from subsp. andigenum, and cultivated and wild species. These results support the genetic difference of these two populations and their recognition at some classification level.

Microsatellite genetic variation in small and isolated populations of Magnolia sieboldii ssp. japonica.

Magnolia sieboldii ssp. japonica, distributed mainly in western Japan, is restricted to high elevation areas (1000-2000 m above sea level) and usually forms small isolated populations. Four microsatellite loci were assayed for 19 populations from six regions spanning the range of distribution, and the levels and distribution of genetic variation were estimated. All four loci were variable, with a total of 39 alleles, but the overall level of microsatellite genetic variation was low, especially compared with a related species, M. obovata. Genetic structure in M. sieboldii was characterised by low intrapopulational genetic variation (A = 3.74 and H(o) = 0.366 on average) and high genetic differentiation even among regional populations. Highly significant isolation-by-distance (IBD) models at the short distance were detected. Genetic drift and limited gene flow was considered to be important in determining the genetic structure within regions. Total genetic differentiation was remarkably high (F(ST) = 0.488 and R(ST) = 0.538), suggesting genetic barriers among regions. Neighbour-joining dendrograms relating the 19 populations, and further analysis on the IBD models, revealed that a stepwise mutation model was more suited than an infinite allele model to explain the genetic differentiation among regions. It is suggested that mutation at microsatellite loci might be influential in generating the genetic differentiation among regions. These results showed the potential of hypervariable microsatellite loci to evaluate the effects of genetic drift and population isolation within regions, and to detect genetic distinctiveness, in spite of the loss of overall genetic variation in M. sieboldii.

Population genetics ofIntsia palembanica(Leguminosae) and genetic conservation of Virgin Jungle Reserves in Peninsular Malaysia

A field survey of Virgin Jungle Reserve (VJR) compartments in Peninsular Malaysia allowed us to identify six populations of Intsia palembanica for this study. These were Pasoh Forest Reserve (FR) (Pasoh), Sungai Lalang FR (Lalang), Bukit Lagong FR (Lagong), Bubu FR (Bubu), Bukit Kinta FR (Kinta), and Bukit Perangin FR (Perangin). About 40 adult individuals were sampled in each population. In addition, progeny arrays were collected from nine mother plants at Lagong for a mating system study. A total of nine allozymes, encoded by 14 putative gene loci, were consistently resolved in I. palembanica. The mating system study showed that the species exhibited a mixed-mating system, with multilocus outcrossing rate of 0.766. The levels of diversity were comparably high (mean number of alleles per polymorphic locus = 2.4, mean effective number of alleles per polymorphic locus = 1.64, and mean expected heterozygosity (H(e)) = 0.242), and the majority of the diversity was partitioned within population (G(ST) = 0.040 and F(ST) = 0.048). Significant levels of inbreeding were detected in Bubu and Perangin. Probability tests of recent effective population size reduction using the Infinite Allele Model showed the occurrence of genetic bottlenecks on Lalang and Kinta. Two genetically unique populations (Pasoh and Perangin) were inferred using jackknife analysis. By using the neutral mutation rates, effective population size (N(e)) to maintain the H(e) was 80-800 000 individuals. A simulation study based on pooled samples, however, circumscribed the N(e) to 200 and 210 individuals. Implications of the study for managing the species and the VJRs are discussed.

Microsatellites in Zea - variability, patterns of mutations, and use for evolutionary studies.

To evaluate the performance of microsatellites or simple sequence repeats (SSRs) for evolutionary studies in Zea, 46 microsatellite loci originally derived from maize were applied to diverse arrays of populations that represent all the diploid species of Zea and 101 maize inbreds. Although null phenotypes and amplification of more than two alleles per plant were observed at modest rates, no practical obstacle was encountered for applying maize microsatellites to other Zea species. Sequencing of microsatellite alleles revealed complex patterns of mutation including frequent indels in the regions flanking microsatellite repeats. In one case, all variation at a microsatellite locus came from indels in the flanking region rather than in the repeat motif. Maize microsatellites show great variability within populations and provide a reliable means to measure intraspecific variation. Phylogeographic relationships of Zea populations were successfully reconstructed with good resolution using a genetic distance based on the infinite allele model, indicating that microsatellite loci are useful in evolutionary studies in Zea. Microsatellite loci show a principal division between tropical and temperate inbred lines, and group inbreds within these two broad germplasm groups in a manner that is largely consistent with their known pedigrees.

Gaussian Limits Associated with the Poisson-Dirichlet Distribution and the Ewens Sampling Formula

In this paper we consider large $\theta$ approximations for the stationary distribution of the neutral infinite alleles model as described by the the Poisson–Dirichlet distribution with parameter $\theta$. We prove a variety of Gaussian limit theorems for functions of the population frequencies as the mutation rate $\theta$ goes to infinity. In particular, we show that if a sample of size $n$ is drawn from a population described by the Poisson–Dirichlet distribution, then the conditional probability of a particular sample configuration is asymptotically normal with mean and variance determined by the Ewens sampling formula. The asymptotic normality of the conditional sampling distribution is somewhat surprising since it is a fairly complicated function of the population frequencies. Along the way, we also prove an invariance principle giving weak convergence at the process level for powers of the size-biased allele frequencies.

Genetic monitoring of brackish-water populations: the Mediterranean toothcarp Aphanius fasciatus (Cyprinodontidae) as a model

The measurement of genetic variability and assessment of population genetic losses are important components of environmental management programs. Twenty-three natural populations of the Mediterranean brackish-water toothcarp Aphanius fasciatus were investigated using different statistical approaches based on genetic data at 13 polymorphic allozyme loci. In general, no differ- ences between values of within-population genetic variability estimates occurred. The Wilcoxon sign-rank test for heterozygosity excess due to a recent bottleneck was conducted on the array of populations. In addition, a qualitative descriptor of allele frequency distribution was used to infer bottlenecks. Only populations from the Orbetello lagoon and La Salina at Elba Island revealed sig- nificant heterozygosity excess under both the infinite allele model (IAM) and stepwise mutation model (SMM). A recent dystrophic crisis may account for the genetic loss detected in the population of A. fasciatus from the Orbetello lagoon, whereas exceptionally high predation pressure and/or the increased mortality rate created by local hydrological conditions could be responsible for the bottle- neck in the population at La Salina. Tests for bottlenecks have proved effective tools for genetic monitoring of A. fasciatus populations.

Estimating the total number of alleles using a sample coverage method.

Previously reported methods for estimating the number of different alleles at a single locus in a population have not described a useful general result. Using the number of alleles observed in a sample gives an underestimate for the true number of alleles. The similar problem of estimating the number of species in a population was first investigated in 1943. In this article we use the sample coverage method proposed by Chao and Lee in 1992 to estimate the number of alleles in a population when there are unequal allele frequencies. Simulation studies under the recurrent mutation model show that, for reasonable sample sizes, a significantly better estimate of the true number can be obtained than that using only the observed alleles. Results under the stepwise mutation model and infinite-allele model are presented. Possible applications include improving the characterization of the prior distribution for the allele frequencies, adjusting the estimates of genetic diversity, and estimating the range of microsatellite alleles.

The validity of genetic models underlying quantitative traits

This paper reviews the validity of the assumptions and predictions of genetic models used for the analysis of quantitative traits. When data on phenotypes and pedigrees but not individual genes are available, the traditional, additive, infinitesimal model makes satisfactory predictions of short-term response to selection despite the incorrectness of its assumptions. Improvements can made in the model such as the inclusion of non-additive variance components or major genes but gains in the accuracy of prediction have seldom been demonstrated. When data are available on individual genes or markers, two models are in common use — a two allele and an infinite allele model. The two models differ in a number of respects such as assumptions about segregation variance, estimation of fixed or random effects and number of parameters to be estimated when multiple traits are used. There is little information on the accuracy with which either model predicts the performance of future animals.

Likelihoods and simulation methods for a class of nonneutral population genetics models.

Methods for simulating samples and sample statistics, under mutation-selection-drift equilibrium for a class of nonneutral population genetics models, and for evaluating the likelihood surface, in selection and mutation parameters, are developed and applied for observed data. The methods apply to large populations in settings in which selection is weak, in the sense that selection intensities, like mutation rates, are of the order of the inverse of the population size. General diploid selection is allowed, but the approach is currently restricted to models, such as the infinite alleles model and certain K-models, in which the type of a mutant allele does not depend on the type of its progenitor allele. The simulation methods have considerable advantages over available alternatives. No other methods currently seem practicable for approximating likelihood surfaces.