Two-locus identity probabilities and identity disequilibrium in a partially selfing subdivided population

Development and characterization of microsatellite markers for population genetics of the cocoa pod borer Conopomorpha cramerella (Snellen) (Lepidoptera: Gracillaridae)

The cocoa pod borer (CPB) Conopomorpha cramerella (Snellen) (Lepidoptera: Gracillaridae) is one of the major constraints for cocoa production in South East Asia. In addition to cultural and chemical control methods, autocidal control tactics such as the Sterile Insect Technique (SIT) could be an efficient addition to the currently control strategy, however SIT implementation will depend on the population genetics of the targeted pest. The aim of the present work was to search for suitable microsatellite loci in the genome of CPB that is partially sequenced. Twelve microsatellites were initially selected and used to analyze moths collected from Indonesia, Malaysia, and the Philippines. A quality control verification process was carried out and seven microsatellites found to be suitable and efficient to distinguish differences between CPB populations from different locations. The selected microsatellites were also tested against a closely related species, i.e. the lychee fruit borer Conopomorpha sinensis (LFB) from Vietnam and eight loci were found to be suitable. The availability of these novel microsatellite loci will provide useful tools for the analysis of the population genetics and gene flow of these pests, to select suitable CPB strains to implement the SIT.

Relatedness coefficients and their applications for triplets and quartets of genetic markers

Relatedness coefficients which seek the identity-by-descent of genetic markers are described. The markers are in groups of two, three or four, and if four, can consist of two pairs. It is essential to use cumulants (not moments) for four-marker-gene probabilities, as the covariance of homozygosity, used in four-marker applications, can only be described with cumulants. A covariance of homozygosity between pairs of markers arises when populations follow a mixture distribution. Also, the probability of four markers all identical-by-descent equals the normalized fourth cumulant. In this article, a "genetic marker" generally represents either a gene locus or an allele at a locus. Applications of three marker coefficients mainly involve conditional regression, and applications of four marker coefficients can involve identity disequilibrium. Estimation of relatedness using genetic marker data is discussed. However, three- and four-marker estimators suffer from statistical and numerical problems, including higher statistical variance, complexity of estimation formula, and singularity at some intermediate allele frequencies.

Local fluctuations of genetic processes defined on two time scales, with applications to effective size estimation

In this paper we develop a general framework for how the genetic composition of a structured population with strong migration between its subunits, evolves over time. The dynamics is described in terms of a vector-valued Markov process of allele, genotype or haplotype frequencies that varies on two time scales. The more rapid changes are random fluctuations in terms of a multivariate autoregressive process, around a quasi equilibrium fix point, whereas the fix point itself varies more slowly according to a diffusion process, along a lower-dimensional subspace. Under mild regularity conditions, the fluctuations have a magnitude inversely proportional to the square root of the population size N, and hence can be used to estimate a broad class of genetically effective population sizes N_e, with genetic data from one time point only. In this way we are able to unify a number of existing notions of effective size, as well as proposing new ones, for instance one that quantifies the extent to which genotype frequencies fluctuate around Hardy-Weinberg equilibrium.

Detecting Wahlund effects together with amplification problems: Cryptic species, null alleles and short allele dominance in Glossina pallidipes populations from Tanzania

Population genetics is a convenient tool to study the population biology of non-model and hard to sample species. This is particularly true for parasites and vectors. Heterozygote deficits and/or linkage disequilibrium often occur in such studies and detecting the origin of those (Wahlund effect, reproductive system or amplification problems) is uneasy. We used new tools (correlation between the number of times a locus is found in significant linkage disequilibrium and its genetic diversity, correlations between Wright's F_IS and F_ST , F_IS and number of missing data, F_IT and allele size and standard errors comparisons) for the first time on a real data set of tsetse flies, a vector of dangerous diseases to humans and domestic animals in sub-Saharan Africa. With these new tools, and cleaning data from null allele, temporal heterogeneity and short allele dominance effects, we unveiled the coexistence of two highly divergent cryptic clades in the same sites. These results are in line with other studies suggesting that the biodiversity of many taxa still largely remain undescribed, in particular pathogenic agents and their vectors. Our results also advocate that including individuals from different cohorts tends to bias subdivision measures and that keeping loci with short allele dominance and/or too frequent missing data seriously jeopardize parameter's estimations. Finally, separated analyses of the two clades suggest very small tsetse densities and relatively large dispersal.

Galba truncatula and Fasciola hepatica: Genetic costructures and interactions with intermediate host dispersal

Antagonistic interactions between hosts and parasites are key structuring forces in natural populations. Demographic factors like extinction, migration and the effective population size shape host-parasite metapopulational dynamics. Therefore, to understand the evolution of host-parasite systems it is necessary to study the distribution of the genetic variation of both entities simultaneously. In this paper, we investigate the population genetics co-structure of parasites and hosts within a metapopulation of the liver fluke, Fasciola hepatica, and two of its intermediate hosts, the main intermediate host in Europe, Galba truncatula, and a new intermediate host, Omphiscola glabra, in Central France. Our results reveal an absence of specificity of flukes as regard to the two alternative hosts though O. glabra shows higher prevalence of F. hepatica. Host and parasites displayed contrasting population genetics structure with very small, highly inbred (selfing) and strongly isolated G. truncatula populations and much bigger, panmictic and more dispersive F. hepatica. This could indicate a local adaptation of the parasite and a local maladaptation of the host. We also unveil a parasite-mediated biased population genetics structure suggesting that infected G. truncatula disperse more; have higher dispersal survival than uninfected snails or, more likely, that immigrant snails are infected more often than local snails (local parasites are less adapted to local hosts). Finally, an absence, or at least an ambiguous signature of isolation by distance was observed in both host and parasite population. A very weak migration rate for G. truncatula provides a reasonable explanation for this ambiguous result. Alternatively, smaller sample sizes combined with modest migration rates might explain the difficulties to unveil the signal in F. hepatica.

Effects of Interference Between Selected Loci on the Mutation Load, Inbreeding Depression, and Heterosis

A classical prediction from single-locus models is that inbreeding increases the efficiency of selection against partially recessive deleterious alleles (purging), thereby decreasing the mutation load and level of inbreeding depression. However, previous multilocus simulation studies found that increasing the rate of self-fertilization of individuals may not lead to purging and argued that selective interference among loci causes this effect. In this article, I derive simple analytical approximations for the mutation load and inbreeding depression, taking into account the effects of interference between pairs of loci. I consider two classical scenarios of nonrandomly mating populations: a single population undergoing partial selfing and a subdivided population with limited dispersal. In the first case, correlations in homozygosity between loci tend to reduce mean fitness and increase inbreeding depression. These effects are stronger when deleterious alleles are more recessive, but only weakly depend on the strength of selection against deleterious alleles and on recombination rates. In subdivided populations, interference increases inbreeding depression within demes, but decreases heterosis between demes. Comparisons with multilocus, individual-based simulations show that these analytical approximations are accurate as long as the effects of interference stay moderate, but fail for high deleterious mutation rates and low dominance coefficients of deleterious alleles.

Population genetics of autopolyploids under a mixed mating model and the estimation of selfing rate

Nowadays, the population genetics analysis of autopolyploid species faces many difficulties due to (i) limited development of population genetics tools under polysomic inheritance, (ii) difficulties to assess allelic dosage when genotyping individuals and (iii) a form of inbreeding resulting from the mechanism of 'double reduction'. Consequently, few data analysis computer programs are applicable to autopolyploids. To contribute bridging this gap, this article first derives theoretical expectations for the inbreeding and identity disequilibrium coefficients under polysomic inheritance in a mixed mating model. Moment estimators of these coefficients are proposed when exact genotypes or just markers phenotypes (i.e. allelic dosage unknown) are available. This led to the development of estimators of the selfing rate based on adult genotypes or phenotypes and applicable to any even-ploidy level. Their statistical performances and robustness were assessed by numerical simulations. Contrary to inbreeding-based estimators, the identity disequilibrium-based estimator using phenotypes is robust (absolute bias generally < 0.05), even in the presence of double reduction, null alleles or biparental inbreeding due to isolation by distance. A fairly good precision of the selfing rate estimates (root mean squared error < 0.1) is already achievable using a sample of 30-50 individuals phenotyped at 10 loci bearing 5-10 alleles each, conditions reachable using microsatellite markers. Diallelic markers (e.g. SNP) can also perform satisfactorily in diploids and tetraploids but more polymorphic markers are necessary for higher ploidy levels. The method is implemented in the software SPAGeDi and should contribute to reduce the lack of population genetics tools applicable to autopolyploids.

Horizontal transmission rapidly erodes disequilibria between organelle and symbiont genomes

We investigate the generation and decay of interspecific disequilibrium (ID) between organelle and symbiont genomes as a function of the rate of horizontal transmission. We show that rare horizontal transmission greatly diminishes the covariance between organelle and symbiont genomes. This result has two important implications. First, a low level of ID does not indicate low levels of vertical transmission. Second, even with low levels of horizontal transmission, the additive effects of host and symbiont loci will determine the response to selection, while epistatic effects will not be selectable.

Heterozygosity-fitness correlations: a time for reappraisal

Owing to the remarkable progress of molecular techniques, heterozygosity-fitness correlations (HFCs) have become a popular tool to study the impact of inbreeding in natural populations. However, their underlying mechanisms are often hotly debated. Here we argue that these "debates" rely on verbal arguments with no basis in existing theory and inappropriate statistical testing, and that it is time to reconcile HFC with its historical and theoretical fundaments. We show that available data are quantitatively and qualitatively consistent with inbreeding-based theory. HFC can be used to estimate the impact of inbreeding in populations, although such estimates are bound to be imprecise, especially when inbreeding is weak. Contrary to common belief, linkage disequilibrium is not an alternative to inbreeding, but rather comes with some forms of inbreeding, and is not restricted to closely linked loci. Finally, the contribution of local chromosomal effects to HFC, while predicted by inbreeding theory, is expected to be small, and has rarely if ever proven statistically significant using adequate tests. We provide guidelines to safely interpret and quantify HFCs, and present how HFCs can be used to quantify inbreeding load and unravel the structure of natural populations.

Macroecological patterns of genetic structure and diversity in the aquatic moss Platyhypnidium riparioides

Genetic diversity and structure are described in the aquatic moss Platyhypnidium riparioides to assess its dispersal ability at a regional scale and to determine whether patterns of genetic differentiation correlate with environmental variation. Variation at six nuclear microsatellite loci from 50 populations in southern Belgium was investigated through Mantel tests, partial Mantel tests and spatial analysis of molecular variance. Overall patterns of genotypic variation showed strong differentiation among populations at a regional scale (F(ST) = 0.57). The high values of F(IS) observed within populations at both the ramet and genet levels, and the higher proportion of ramets with the same genotype than expected by chance, all point to a strongly clonal or selfing mating system. A genetic discontinuity was identified between northern and southern groups of populations. Within each group, F(ST) and geographical distances were significantly correlated. Partial Mantel tests suggest that genetic and ecological distances are significantly correlated in the southern group. The results point to strong dispersal limitation at the landscape scale and suggest that the southern and northern groups experienced different histories. Within the former, the correlation between genetic and ecological variation is suggestive of reproductive isolation among ecotypes.

Population structure of Glossina palpalis gambiensis (Diptera: Glossinidae) between river basins in Burkina Faso: consequences for area-wide integrated pest management

African animal trypanosomosis is a major obstacle to the development of more efficient and sustainable livestock production systems in West Africa. Riverine tsetse species such as Glossina palpalis gambiensis Vanderplank are their major vectors. A wide variety of control tactics is available to manage these vectors, but their elimination will only be sustainable if control is exercised following area-wide integrated pest management (AW-IPM) principles, i.e. the control effort is targeting an entire tsetse population within a circumscribed area. In the present study, genetic variation at microsatellite DNA loci was used to examine the population structure of G. p. gambiensis inhabiting two adjacent river basins, i.e. the Comoé and the Mouhoun River basins in Burkina Faso. A remote sensing analysis revealed that the woodland savannah habitats between the river basins have remained unchanged during the last two decades. In addition, genetic variation was studied in two populations that were separated by a man-made lake originating from a dam built in 1991 on the Comoé. Low genetic differentiation was observed between the samples from the Mouhoun and the Comoé River basins and no differentiation was found between the samples separated by the dam. The data presented indicate that the overall genetic differentiation of G. p. gambiensis populations inhabiting two adjacent river basins in Burkina Faso is low (F(ST)=0.016). The results of this study suggest that either G. p. gambiensis populations from the Mouhoun are not isolated from those of the Comoé, or that the isolation is too recent to be detected. If elimination of the G. p. gambiensis population from the Mouhoun River basin is the selected control strategy, re-invasion from adjacent river basins may need to be prevented by establishing a buffer zone between the Mouhoun and the other river basin(s).

Correlation measures for linkage disequilibrium within and between populations

Correlation statistics can be used to measure the amount of linkage disequilibrium (LD) between two loci in subdivided populations. Within populations, the square of the correlation of gene frequencies, r2, is a convenient measure of LD. Between populations, the statistic rirj, for populations i and j, measures the relatedness of LD. Recurrence relationships for these two parameters are derived for the island model of population subdivision, under the assumptions of the linked identity-by-descent (LIBD) model in which correlation measures are equated to probability measures. The recurrence relationships closely predict the build-up of r2 and rirj following population subdivision in computer simulations. The LIBD model predicts that a steady state will be reached with r2 equal to 1/[1+4Nec(1+(k-1)rho)], where k is the number of island populations, Ne is the effective local population (island) size, and rho measures the ratio of migration (m) to recombination (c) and is equal to m/[c(k-1)+m]. For low values of m/c, rho=0, and E(r2) is equal to 1/(1+4Nec). For high values of m/c, rho=1, and E(r2) is equal to 1/(1+4kNec). The value of rirj following separation eventually settles down to a steady state whose expectation, E(rirj), is equal to E(r2) multiplied by rho. Equations predicting the change in rirj values are applied to the separation of African (Yoruba - YRI) and non-African (European - CEU) populations, using data from Hapmap. The primary data lead to an estimate of separation time of less than 1000 generations if there has been no migration, which is around one-third of minimum current estimates. Ancient rather than recent migration can explain the form of the data.

The population structure of Glossina palpalis gambiensis from island and continental locations in Coastal Guinea

Background

We undertook a population genetics analysis of the tsetse fly Glossina palpalis gambiensis, a major vector of sleeping sickness in West Africa, using microsatellite and mitochondrial DNA markers. Our aims were to estimate effective population size and the degree of isolation between coastal sites on the mainland of Guinea and Loos Islands. The sampling locations encompassed Dubréka, the area with the highest Human African Trypanosomosis (HAT) prevalence in West Africa, mangrove and savannah sites on the mainland, and two islands, Fotoba and Kassa, within the Loos archipelago. These data are discussed with respect to the feasibility and sustainability of control strategies in those sites currently experiencing, or at risk of, sleeping sickness.

Principal Findings

We found very low migration rates between sites except between those sampled around the Dubréka area that seems to contain a widely dispersed and panmictic population. In the Kassa island samples, various effective population size estimates all converged on surprisingly small values (10<N_e<30) that suggest either a recent bottleneck, and/or other biological or ecological factors such as strong variance in the reproductive success of individuals.

Conclusion/Significance

Whatever their origin, the small effective population sizes suggest high levels of inbreeding in tsetse flies within the island samples in marked contrast to the large diffuse deme in Dubréka zones. We discuss how these genetic results suggest that different tsetse control strategies should be applied on the mainland and islands.

Guinea is the country with the highest prevalence of sleeping sickness in West Africa, and we undertook a population genetics analysis there of the most dangerous tsetse fly species of West Africa, Glossina palpalis gambiensis. Our aims were to estimate effective population size and the degree of isolation between coastal sites on the mainland of Guinea (including Dubréka, a highly prevalent sleeping sickness focus) and Loos Islands in order to get the most possible accurate vision of feasibility and sustainability of anti-tsetse strategies of these sites. We found very low migration rates of tsetse between sites except between those situated in the Dubréka area, which seems to contain a widely distributed panmictic tsetse population (i.e. a population where mating occurs at random). Effective population sizes on Loos islands estimated with various techniques all converged to surprisingly small values. These values might be explained by a recent decrease in tsetse numbers on Kassa Island due to bauxite mining activities. But on the other sites, other explanations have to be found, including possible variance in reproductive success. Our genetic results suggest that different control strategies should be advised on the mainland (reduction in tsetse densities, no elimination) compared to the islands (total elimination feasible). This approach could be extended to many areas where vector control of Human and Animal Trypanosomoses is contemplated.

Prediction of multilocus identity-by-descent

Previous studies have enabled exact prediction of probabilities of identity-by-descent (IBD) in random-mating populations for a few loci (up to four or so), with extension to more using approximate regression methods. Here we present a precise predictor of multiple-locus IBD using simple formulas based on exact results for two loci. In particular, the probability of non-IBD X(ABC) at each of ordered loci A, B, and C can be well approximated by X(ABC) = X(AB)X(BC)/X(B) and generalizes to X(123...k) = X(12)X(23...)X(k)(-1,k)/X(k-2), where X is the probability of non-IBD at each locus. Predictions from this chain rule are very precise with population bottlenecks and migration, but are rather poorer in the presence of mutation. From these coefficients, the probabilities of multilocus IBD and non-IBD can also be computed for genomic regions as functions of population size, time, and map distances. An approximate but simple recurrence formula is also developed, which generally is less accurate than the chain rule but is more robust with mutation. Used together with the chain rule it leads to explicit equations for non-IBD in a region. The results can be applied to detection of quantitative trait loci (QTL) by computing the probability of IBD at candidate loci in terms of identity-by-state at neighboring markers.

Beyond the point of no return? A comparison of genetic diversity in captive and wild populations of two nearly extinct species of Goodeid fish reveals that one is inbred in the wild

The relative importance of genetic and non-genetic factors in extinction liability has been extensively debated. Here, we examine the levels of genetic variability at 13 (seven informative) loci in wild and captive populations of two endangered species of Mexican Goodeid fish, Ameca splendens and Zoogoneticus tequila. Allelic diversity was higher in the wild populations, and F(IS) lower. Values of theta (=4Nemu) were estimated using a coalescent approach. These implied that the effective population size of all captive populations of A. splendens were smaller than that of the wild population; qualitatively similar results were obtained using an analytical method based on within-population gene identity disequilibrium. However, the wild population of Z. tequila did not show a significantly greater estimate of theta. We used the Beaumont approach to infer population declines, and found that both species showed clear evidence of a decline in effective population size, although this was stronger and probably occurred over a longer period of time in Z. tequila than in A. splendens. The decline in Z. tequila probably occurred before captive populations were established. We discuss implications for the conservation of critically endangered populations.

Sampling properties of homozygosity-based statistics for linkage disequilibrium

Homozygosity-based statistics such as Ohta's identity-in-state (IIS) excess offer the potential to measure linkage disequilibrium for multiallelic loci in small samples. However, previous observations have suggested that for independent loci, in small samples these statistics might produce values that more frequently lie on one side rather than on the other side of zero. Here we investigate the sampling properties of the IIS excess. We find that for any pair of independent polymorphic loci, as sample size n approaches infinity, the sampling distribution of the IIS excess approaches a normal distribution. For large samples, the IIS excess tends towards symmetry around zero, and the probabilities of positive and of negative IIS excess both approach 1/2. Surprisingly, however, we also find that for sufficiently large n, independent loci can be chosen so that the probability of a sample having positive IIS excess is arbitrarily close to either 0 or 1. The results are applied to interpretation of data from human populations, and we conclude that before employing homozygosity-based statistics to measure LD in a particular sample, especially for loci with either very small or very large homozygosities, it is useful to verify that loci with the observed homozygosity values are not likely to produce a large bias in IIS excess in samples of the given size.

Inbreeding Depression and the Evolution of Dispersal Rates: A Multilocus Model

Inbreeding depression is one of the possible reasons organisms disperse. In this article, we present a two-locus model for the evolution of dispersal in the presence of inbreeding depression. The first locus codes for a modifier of the migration rate, while the second locus is a selected locus generating inbreeding depression. We express the change in frequency of the migration modifier as a function of allele frequencies and genetic associations and then use a quasi-equilibrium assumption to express genetic associations as functions of allele frequencies. Our model disentangles two effects of inbreeding depression: it gives an advantage to migrant individuals because their offspring are on average less homozygous, but it also decreases the degree of population structure, thus decreasing the strength of kin selection for dispersal. We then extend our model to include an infinite number of selected loci. When the cost of dispersal is not too high, the model predictions are confirmed by multilocus simulation results and show that inbreeding depression can have a substantial effect on the dispersal rate. For high costs of dispersal, we observe discrepancies between the model and the simulations, probably caused by associations among selected loci, which are neglected in the analysis.

Estimating the correlation of pairwise relatedness along chromosomes

The 'spatial' pattern of the correlation of pairwise relatedness among loci within a chromosome is an important aspect for an insight into genomic evolution in natural populations. In this article, a statistical genetic method is presented for estimating the correlation of pairwise relatedness among linked loci. The probabilities of identity-in-state (IIS) are related to the probabilities of identity-by-descent (IBS) for the two- and three-loci cases. By decomposing the joint probabilities of two- or three-loci IBD, the probability of pairwise relatedness at a single locus and its correlation among linked loci can be simultaneously estimated. To provide effective statistical methods for estimation, weighted least square (LS) and maximum likelihood (ML) methods are evaluated through extensive Monte Carlo simulations. Results show that the ML method gives a better performance than the weighted LS method with haploid genotypic data. However, there are no significant differences between the two methods when two- or three-loci diploid genotypic data are employed. Compared with the optimal size for haploid genotypic data, a smaller optimal sample size is predicted with diploid genotypic data.

Joint effects of self-fertilization and population structure on mutation load, inbreeding depression and heterosis

Both the spatial distribution of organisms and their mode of reproduction have important effects on the change in allele frequencies within populations. In this article, we study the combined effect of population structure and the rate of partial selfing of organisms on the efficiency of selection against recurrent deleterious mutations. Assuming an island model of population structure and weak selection, we express the mutation load, the within- and between-deme inbreeding depression, and heterosis as functions of the frequency of deleterious mutants in the metapopulation; we then use a diffusion model to calculate an expression for the equilibrium probability distribution of this frequency of deleterious mutants. This allows us to derive approximations for the average mutant frequency, mutation load, inbreeding depression, and heterosis, the simplest ones being Equations 35-39 in the text. We find that population structure can help to purge recessive deleterious mutations and reduce the load for some parameter values (in particular when the dominance coefficient of these mutations is <0.2-0.3), but that this effect is reversed when the selfing rate is above a given value. Conversely, within-deme inbreeding depression always decreases, while heterosis always increases, with the degree of population subdivision, for all selfing rates.

Polyploid and multilocus extensions of the Wahlund inequality

Wahlund's inequality informally states that if a structured and an unstructured population have the same allele frequencies at a locus, the structured population contains more homozygotes. We show that this inequality holds generally for ploidy level P, that is, the structured population has more P-polyhomozygotes. Further, for M randomly chosen loci (M >or= 2), the structured population is also expected to contain more M-multihomozygotes than an unstructured population with the same single-locus homozygosities. The extended inequalities suggest multilocus identity coefficients analogous to F(ST). Using microsatellite genotypes from human populations, we demonstrate that the multilocus Wahlund inequality can explain a positive bias in "identity-in-state excess".

Metapopulation models for historical inference

The genealogical process for a sample from a metapopulation, in which local populations are connected by migration and can undergo extinction and subsequent recolonization, is shown to have a relatively simple structure in the limit as the number of populations in the metapopulation approaches infinity. The result, which is an approximation to the ancestral behaviour of samples from a metapopulation with a large number of populations, is the same as that previously described for other metapopulation models, namely that the genealogical process is closely related to Kingman's unstructured coalescent. The present work considers a more general class of models that includes two kinds of extinction and recolonization, and the possibility that gamete production precedes extinction. In addition, following other recent work, this result for a metapopulation divided into many populations is shown to hold both for finite population sizes and in the usual diffusion limit, which assumes that population sizes are large. Examples illustrate when the usual diffusion limit is appropriate and when it is not. Some shortcomings and extensions of the model are considered, and the relevance of such models to understanding human history is discussed.

Small effective population sizes in a widespread selfing species, Lymnaea truncatula (Gastropoda: Pulmonata)

We present here a spatial and temporal population genetic survey of a common freshwater snail, also a predominantly selfing species, Lymnaea truncatula. The rate of genetic diversity loss was quantified by estimating the effective size (Ne) of the snail populations, using two different methods. A temporal survey allowed estimation of a variance effective size of the populations, and a spatial survey allowed the estimation of an inbreeding effective size, from two-locus identity disequilibria estimates. Both methods were consistent and provided low Ne values. Drift due to (i) high amounts of selfing and (ii) fluctuations in population sizes because of temporary habitats, and also selection coupled to genome-wide linkage disequilibria, could explain such reductions in Ne. The loss of genetic diversity appears to be counterbalanced only very partially by low apparent rates of gene flow.

Using genetic markers to estimate the pollen dispersal curve

Pollen dispersal is a critical process that shapes genetic diversity in natural populations of plants. Estimating the pollen dispersal curve can provide insight into the evolutionary dynamics of populations and is essential background for making predictions about changes induced by perturbations. Specifically, we would like to know whether the dispersal curve is exponential, thin-tailed (decreasing faster than exponential), or fat-tailed (decreasing slower than the exponential). In the latter case, rare events of long-distance dispersal will be much more likely. Here we generalize the previously developed TWOGENER method, assuming that the pollen dispersal curve belongs to particular one- or two-parameter families of dispersal curves and estimating simultaneously the parameters of the dispersal curve and the effective density of reproducing individuals in the population. We tested this method on simulated data, using an exponential power distribution, under thin-tailed, exponential and fat-tailed conditions. We find that even if our estimates show some bias and large mean squared error (MSE), we are able to estimate correctly the general trend of the curve - thin-tailed or fat-tailed - and the effective density. Moreover, the mean distance of dispersal can be correctly estimated with low bias and MSE, even if another family of dispersal curve is used for the estimation. Finally, we consider three case studies based on forest tree species. We find that dispersal is fat-tailed in all cases, and that the effective density estimated by our model is below the measured density in two of the cases. This latter result may reflect the difficulty of estimating two parameters, or it may be a biological consequence of variance in reproductive success of males in the population. Both the simulated and empirical findings demonstrate the strong potential of TWOGENER for evaluating the shape of the dispersal curve and the effective density of the population (d(e)).

Theory of the effects of population structure and sampling on patterns of linkage disequilibrium applied to genomic data from humans

We develop predictions for the correlation of heterozygosity and for linkage disequilibrium between two loci using a simple model of population structure that includes migration among local populations, or demes. We compare the results for a sample of size two from the same deme (a single-deme sample) to those for a sample of size two from two different demes (a scattered sample). The correlation in heterozygosity for a scattered sample is surprisingly insensitive to both the migration rate and the number of demes. In contrast, the correlation in heterozygosity for a single-deme sample is sensitive to both, and the effect of an increase in the number of demes is qualitatively similar to that of a decrease in the migration rate: both increase the correlation in heterozygosity. These same conclusions hold for a commonly used measure of linkage disequilibrium (r(2)). We compare the predictions of the theory to genomic data from humans and show that subdivision might account for a substantial portion of the genetic associations observed within the human genome, even though migration rates among local populations of humans are relatively large. Because correlations due to subdivision rather than to physical linkage can be large even in a single-deme sample, then if long-term migration has been important in shaping patterns of human polymorphism, the common practice of disease mapping using linkage disequilibrium in "isolated" local populations may be subject to error.

Dependency effects in multi-locus match probabilities

For finite populations, differences in individual histories can cause between-locus allelic dependencies even for unlinked loci. The main motivation for this study is to quantify the effect of such dependencies on genotypic match probabilities. We compare the two-locus match probability, the probability that two individuals (four gametes) chosen at random will have the same genotype at both loci, with the probability computed as the product of the one-locus match probabilities. It is demonstrated that the product rule probability always underestimates the two-locus match probability. For highly mutable minisatellite loci, these probabilities can differ by an order of magnitude or more. A simplified three-locus problem is explored, providing evidence that the degree of under-estimation worsens for more loci.

Estimation of effective population size and migration rate from one- and two-locus identity measures

Standard methods for inferring demographic parameters from genetic data are based mainly on one-locus theory. However, the association of genes at different loci (e.g., two-locus identity disequilibrium) may also contain some information about demographic parameters of populations. In this article, we define one- and two-locus parameters of population structure as functions of one- and two-locus probabilities for the identity in state of genes. Since these parameters are known functions of demographic parameters in an infinite island model, we develop moment-based estimators of effective population size and immigration rate from one- and two-locus parameters. We evaluate this method through simulation. Although variance and bias may be quite large, increasing the number of loci on which the estimates are derived improves the method. We simulate an infinite allele model and a K allele model of mutation. Bias and variance are smaller with increasing numbers of alleles per locus. This is, to our knowledge, the first attempt of a joint estimation of local effective population size and immigration rate.