Spatial autocorrelation and linkage of Mendelian RAPD markers in a population of Picea abies Karst

The spatial clustering of single- and di-locus genotypes in a natural, continuous population of Norway spruce was investigated using 69 Mendelian Random Amplified Polymorphic DNA (RAPD) markers that covered about 15 of the species genome, and whose linkage relationships were known. Spatial autocorrelation techniques and randomization tests, applied to both single- and di-locus genotypes, revealed a weak, though significant, spatial structure at the scale 0-200 m (5 of single-locus and 7 of di-locus genotypes). To assess the relative importance of isolation by distance and linkage between markers on their spatial genetic structuring, we grouped joins between sampled trees into equivalence categories expected to show similar, specific patterns of spatial distribution under isolation by distance. Results from both single- and di-locus analyses were consistent with the existence of patches of like homozygotes (about 8 and 11 of loci at the single- and di-locus level, respectively) surrounded by a mix of like heterozygotes. Similar structuring has been predicted by simulation models under isolation by distance and selective neutrality. Overall, linkage between markers accounted for an increase of spatial clumping of di-locus genotypes involving tightly linked loci with recombination fractions up to 0.1, a consequence of limited, stochastic spread of single-locus genotypes in space. Our results support the hypothesis that isolation by distance and linkage have a small, though significant, effect even within continuous forest tree populations. In general, the spatial distribution of multilocus genotypes within populations should be interpreted with caution when linkage relationships among the markers used are unknown.     

Use of restriction fragment length polymorphisms for genetic counseling: Population genetic considerations

Two-locus population genetic models are analyzed to evaluate the utility of restriction fragment length polymorphisms for purposes of genetic counseling. It is shown that the linkage disequilibrium between a neutral marker and a tightly linked overdominant mutant will increase rapidly as the mutant moves to its polymorphic equilibrium. The linkage disequilibrium decays for deleterious recessive mutants. Two measures involving the linkage disequilibrium are investigated to determine how much information the transmission of the neutral marker provides about the transmission of the selected gene. In certain kinds of matings, where the parental two-locus genotypes and linkage phases are known, it is possible to determine whether or not a progeny is homozygous for the selected gene on the basis of the fetal genotype at the marker locus. A quantity of primary interest is the fraction of matings between individuals heterozygous for the selected gene in which exact diagnosis can be made in this way. The expected proportion of such matings, taken over all two-locus matings involving heterozygotes at the selected locus, is calculated as a function of the gene frequencies at the two loci and the linkage disequilibrium between them. This expected value is maximized when the linkage disequilibrium is at its maximum in absolute value. Fewer than half of all matings are informative if the linkage disequilibrium is small in magnitude or if the gene frequencies at the two loci are quite different. Consideration is also given to various conditional measures of association that may be useful when the parental two-locus genotypes are unknown. The results suggest that the utility of tightly linked neutral marker genes in predicting the transmission of a selected gene is generally less when selection acts against a recessive gene than for overdominant selection.     

A Two-Locus Forensic Match Probability for Subdivided Populations

A two-locus match probability is presented that incorporates the effects of within-subpopulation inbreeding (consanguinity) in addition to population subdivision. The usual practice of calculating multi-locus match probabilities as the product of single-locus probabilities assumes independence between loci. There are a number of population genetics phenomena that can violate this assumption: in addition to consanguinity, which increases homozygosity at all loci simultaneously, gametic disequilibrium will introduce dependence into DNA profiles. However, in forensics the latter problem is usually addressed in part by the careful choice of unlinked loci. Hence, as is conventional, we assume gametic equilibrium here, and focus instead on between-locus dependence due to consanguinity. The resulting match probability formulae are an extension of existing methods in the literature, and are shown to be more conservative than these methods in the case of double homozygote matches. For two-locus profiles involving one or more heterozygous genotypes, results are similar to, or smaller than, the existing approaches. This revised version was published online in August 2006 with corrections to the Cover Date.     

Genetic dissection of an elite rice hybrid revealed that heterozygotes are not always advantageous for performance

We introduced an experimental design that produced an "immortalized F(2)" population allowing for complete dissection of genetic components underlying quantitative traits. Data for yield and three component traits of the immortalized F(2) were collected from replicated field trials over 2 years. Using 231 marker loci, we resolved the genetic effects into individual components and assessed relative performance of all the genotypes at both single- and two-locus levels. Single-locus analysis detected 40 QTL for the four traits. Dominance effects for about one-half of the QTL were negative, resulting in little "net" positive dominance effect. Correlation between genotype heterozygosity and trait performance was low. Large numbers of digenic interactions, including AA, AD, and DD, were detected for all the traits, with AA as the most prevalent interaction. Complementary two-locus homozygotes frequently performed the best among the nine genotypes of many two-locus combinations. While cumulative small advantages over two-locus combinations may partly explain the genetic basis of heterosis of the hybrid as double heterozygotes frequently demonstrated marginal advantages, double heterozygotes were never the best genotypes in any of the two-locus combinations. It was concluded that heterozygotes were not necessarily advantageous for trait performance even among genotypes derived from such a highly heterotic hybrid.     

The Sampling Distribution of Linkage Disequilibrium under an Infinite Allele Model without Selection

The sampling distributions of several statistics that measure the association of alleles on gametes (linkage disequilibrium) are estimated under a two-locus neutral infinite allele model using an efficient Monte Carlo method. An often used approximation for the mean squared linkage disequilibrium is shown to be inaccurate unless the proper statistical conditioning is used. The joint distribution of linkage disequilibrium and the allele frequencies in the sample is studied. This estimated joint distribution is sufficient for obtaining an approximate maximum likelihood estimate of C = 4Nc, where N is the population size and c is the recombination rate. It has been suggested that observations of high linkage disequilibrium might be a good basis for rejecting a neutral model in favor of a model in which natural selection maintains genetic variation. It is found that a single sample of chromosomes, examined at two loci cannot provide sufficient information for such a test if C less than 10, because with C this small, very high levels of linkage disequilibrium are not unexpected under the neutral model. In samples of size 50, it is found that, even when C is as large as 50, the distribution of linkage disequilibrium conditional on the allele frequencies is substantially different from the distribution when there is no linkage between the loci. When conditioned on the number of alleles at each locus in the sample, all of the sample statistics examined are nearly independent of theta = 4N mu, where mu is the neutral mutation rate.     

Likelihood Analysis of Recombinational Disequilibrium in Multiple-Locus Gametic Frequencies

Likelihood methods are developed for the estimation and testing of multiple-locus gametic disequilibria, using log-linear models of parametric effects. The estimates of disquilibrium are related to Kimura's Z-measure, and may be extended to multiple alleles and multiple loci. Likelihood ratio test criteria are constructed, which are asymptotically distributed as chi(2). The analysis is partitioned into various components corresponding to two-locus, residual three-locus, and higher order disequilibria. A four-locus example from Hordeum vulgare L. is utilized to illustrate the analysis. Most of the multiple-locus disequilibrium is accounted for by two-locus effects, and closely linked loci show considerably more disequilibrium than unlinked loci. It is shown that all possible pairwise comparisons are not statistically independent.     

Linkage Disequilibrium between Allozymes in Natural Populations of Lodgepole Pine

Pairwise linkage disequilibrium values (D) were estimated for 14 allozyme loci in two natural populations of lodgepole pine (Pinus contorta ssp. latifolia). Maternal multilocus genotypes were inferred from samples of (haploid) megagametophytic seed-endosperms. Coupling/repulsion double heterozygotes were distinguished for closely linked pairs of loci. Assays of seven of the loci in seed embryos allowed estimates of D for these loci in the outcross pollen pool (estimates of outcrossing rates indicate no significant departures from random mating in either population). No disequilibrium was observed between unlinked loci in either maternal genotypes or outcross pollen. However, significant disequilibrium was observed within and between gametes for some allelic combinations of four tightly linked loci; the assumption of random association of gamete types within individuals is thus invalid for some loci in lodgepole pine. Possible causes of the observed D were examined using the noncentrality parameter of the general noncentral chi square distribution. We concluded, from estimates of population size, linkage and measurements of population substructure, that neither drift nor population subdivision was responsible for the significant values of D which were observed and that epistatic selection was the most likely cause of the disequilibrium observed.     

Recombination and linkage disequilibrium among mitochondrial genes in structured populations of the gynodioecious plant Silene vulgaris

The impact of intergenic recombination on the population genetics of plant mitochondrial genomes is unknown. In an effort to study this in the gynodioecious plant Silene vulgaris three-locus PCR/RFLP genotypes (based on the mitochondrial genes atpA, cox1, and cob) were determined for 239 individuals collected from 20 North American populations. Seventeen three-locus PCR/RFLP genotypes were found. Recombination was indicated by observation of each of the four two-locus genotypes possible when the two most common alleles are considered for each of two loci. Based on these common alleles the absolute values of standardized linkage disequilibrium |D'| between pairs of loci range from 0.17 to 0.78. This indicates modest disequilibrium, rather than the maximum value expected in the absence of recombination |D'=1|, or the linkage equilibrium expected if recombination is pervasive (D'=0). Values of D' did not depend on which pair of loci contributed alleles to the analysis. The direction of D' obtained for the common atpA and cox1 alleles was comparable in sign and magnitude to that obtained by examining similar information obtained in a prior study of European samples. All three loci indicated a high degree of population structure (average FST=0.63), which would limit the within-population genetic diversity required for intergenic recombination to create novel genotypes, if most mating is local. Thus, population structure acts as a constraint on the approach to linkage equilibrium.     

Dynamics of linkage disequilibrium in bacterial genomes undergoing transformation and/or conjugation

Bacteria may undergo recombinational exchange either by conjugation followed by crossing over, or by transformation of small segments of DNA into the cell followed by incorporation into the chromosome by gene conversion. These two forms of recombination may have very different consequences on the patterns of linkage disequilibrium seen within bacterial genomes. In this paper deterministic recursions are obtained for three linked loci in populations having these two forms of recombination. Both neutral genetic variation and the case of one selected gene are considered. It is shown that the two forms of exchange have identical consequences on two-locus linkage disequilibria, but that three-locus disequilibria can have different behaviors. Hitchhiking also has different consequences on the pattern of disequilibrium seen between linked neutral genes in the region of the selected locus. Inference of the relative importance of these two modes of recombination from static samples of DNA sequences will hinge on the relationship between linkage map distance and disequilibria.     

Spatial Autocorrelation of Genotypes under Directional Selection

The spatial distributions of genetic variation under selection-mutation equilibrium within populations that have limited dispersal are investigated. The results show that directional selection with moderate strength rapidly reduces the amount of genetic structure and spatial autocorrelations far below that predicted for selectively neutral loci. For the latter, homozygotes are spatially clustered into separate areas or patches, each consisting of several hundred homozygotes. When selection is added the patches of the deleterious homozygotes are much smaller, in the range of 25 to 50 individuals. Selection also reduces temporal correlations. Also investigated are the effects of random replacement processes, such as mutation, immigration, and long-distance migration, on spatial and temporal correlations. The detection of natural selection through spatial pattern analysis is discussed, and applied to data from populations of the morning glory, Ipomoea purpurea.     

Population structure in admixed populations: effect of admixture dynamics on the pattern of linkage disequilibrium

Gene flow between genetically distinct populations creates linkage disequilibrium (admixture linkage disequilibrium [ALD]) among all loci (linked and unlinked) that have different allele frequencies in the founding populations. We have explored the distribution of ALD by using computer simulation of two extreme models of admixture: the hybrid-isolation (HI) model, in which admixture occurs in a single generation, and the continuous-gene-flow (CGF) model, in which admixture occurs at a steady rate in every generation. Linkage disequilibrium patterns in African American population samples from Jackson, MS, and from coastal South Carolina resemble patterns observed in the simulated CGF populations, in two respects. First, significant association between two loci (FY and AT3) separated by 22 cM was detected in both samples. The retention of ALD over relatively large (>10 cM) chromosomal segments is characteristic of a CGF pattern of admixture but not of an HI pattern. Second, significant associations were also detected between many pairs of unlinked loci, as observed in the CGF simulation results but not in the simulated HI populations. Such a high rate of association between unlinked markers in these populations could result in false-positive linkage signals in an admixture-mapping study. However, we demonstrate that by conditioning on parental admixture, we can distinguish between true linkage and association resulting from shared ancestry. Therefore, populations with a CGF history of admixture not only are appropriate for admixture mapping but also have greater power for detection of linkage disequilibrium over large chromosomal regions than do populations that have experienced a pattern of admixture more similar to the HI model, if methods are employed that detect and adjust for disequilibrium caused by continuous admixture.     

CYCLICAL ENVIRONMENTAL CHANGES AS A FACTOR MAINTAINING GENETIC POLYMORPHISM. 2. DIPLOID SELECTION FOR AN ADDITIVE TRAIT

The subject of this paper is polymorphism maintenance due to stabilizing selection with a moving optimum. It was shown that in case of two-locus additive control of the selected trait, global polymorphism is possible only when the geometric mean fitnesses of double homozygotes averaged over the period are lower than that of the single heterozygotes and of the double heterozygote (with a multiplier [1 – r]^p, which depends on recombination rate r and period length p). But local stability of polymorphism cannot be excluded even if geometric mean fitnesses of all double homozygotes are higher than that of all heterozygotes. We proved, that for logarithmically convex fitness functions, cyclical changes of the optimum cannot help in polymorphism maintenance in case of additive control of the selected trait by two equal loci. However, within the same class of fitness functions, nonequal gene action and/or dominance effect for one or both loci may lead to local polymorphism stability with large enough polymorphism attracting domain. The higher the intensity of selection and closer the linkage between selected loci the larger is this domain. Note that even simple cyclical selection could result in two forms of polymorphic limiting behavior: (a) usually expected forced cycle with a period equal to that of environmental changes; and (b) “supercycles,” nondumping auto-oscillations with a period comprising of hundreds of forced oscillation periods.     

CIS-TRANS Effects Induced by Linkage Disequilibrium

This note concerns theoretical and experimental studies of multifactorial traits, especially fitness and its components, in which (1) the loci studied are only a subset of those relevant to the character of interest and (2) the genotypes at the loci studied are in nonrandom association (linkage disequilibrium) with genotypes at the loci ignored. In these cases, phenotypic differences between cis and trans double heterozygotes can occur even though no linkage phase effects are inherent in the genetic determination of the trait. Examples are drawn from both theoretical and experimental work, and implications in both areas are discussed.     

MALADAPTED GENE COMPLEXES WITHIN POPULATIONS OF THE INTERTIDAL COPEPOD TIGRIOPUS CALIFORNICUS?

The prevalence of F2 hybrid breakdown in interpopulation crosses of the marine copepod Tigriopus californicus can be explained by disruption of coadapted gene complexes. This study further dissects the nature of hybrid gene interactions, revealing that parental populations may also harbor maladapted gene complexes. Diagnostic molecular markers (14) were assayed in reciprocal F2 hybrids to test for gene interactions affecting viability. Results showed some evidence of nuclear–nuclear coadaptation. Although there were no significant examples of pairwise linkage disequilibrium between physically unlinked loci, one of the two reciprocal crosses did show an overall excess of parental double homozygotes and an overall dearth of nonparental double homozygotes. In contrast, the nuclear–cytoplasmic data showed a stronger tendency toward maladaptation within the specific inbred lines used in this study. For three out of four loci with significant frequency differences between reciprocal F2, homozygotes were favored on the wrong cytoplasmic background. A separate study of reciprocal backcross hybrids between the same two populations (but different inbred lines) revealed faster development time when the full haploid nuclear genome did not match the cytoplasm. The occurrence of such suboptimal gene complexes may be attributable to effects of genetic drift in small, isolated populations.     

Limits to the Relationship among Recombination, Disequilibrium and Epistasis in Two-Locus Models

I determine limits to the equilibrium relationship among epistasis, recombination and disequilibrium in two-locus, two-allele models using linear programming techniques. I show that when allele frequencies are one-half at each locus, the symmetric model is the fitness pattern that generates the most disequilibrium for the smallest level of epistasis. When allele frequencies deviate from one-half much larger levels of epistasis are required to generate similar levels of disequilibrium. I determine the level of epistasis required to generate observed significant levels of disequilibrium in natural populations. The overall implication is that disequilibrium will be large at equilibrium only between strongly interacting, closely linked loci.     

Three-Locus Systems Impose Additional Constraints on Pairwise Disequilibria

Combinations of allele frequencies and pairwise linkage disequilibrium terms, each of which is permissible at the two-locus level, may not always be permissible at the three-locus level. These additional constraints on the possible maximum and minimum values for the pairwise disequilibrium terms are formally determined and numerically analyzed. In some cases, the three-locus constraints on a pairwise disequilibrium (D) may be equivalent to the usual two-locus constraints, while in others, the positive or negative range may be restricted. This can result in situations where the allowable values of D are limited to only positive or only negative values up to the extreme case where there is only a single admissible value. No additional restrictions are placed on pairwise disequilibrium values when four loci are considered, other than those imposed by the three-way combinations containing the two loci of interest. A new measure of normalized pairwise linkage disequilibrium, allowing for the three-locus constraints, is defined and illustrated by an application to data from the human histocompatibility antigen (HLA) system. An analogous normalized three-way disequilibrium measure is also formulated.     

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

Measures of association of genes at different loci (linkage disequilibrium) are widely used to determine whether the structure of natural populations is clonal or not, to map genes from population data, or to test for the homogeneity of response of molecular markers to background selection, for example. However, the usual definitions of parameters for gametic associations may not be suitable for all these purposes. In this paper, we derive the recursion equations for one- and two-locus identity probabilities in an infinite island model. We study the role of drift, gene flow, partial selfing and mutation model on the expected association of genes across loci. We define the 'within-subpopulation identity disequilibrium' as the difference between the joint two-locus probability of identity in state and the expected product of one-locus identity probabilities. We evaluate this parameter as a function of recombination rate, effective size, gene flow and selfing rate. Within-subpopulation identity disequilibrium attains maximum values for intermediate immigration rates, whatever the selfing rate. Moreover, identity disequilibrium may be very small, even for high selfing rates. We discuss the implications of these findings for the analysis of data from natural populations.     

Quantitative predictions for patch occupancy of capercaillie in fragmented habitats

A major conclusion of studying metapopulation biology is that species conservation should favor regional rather than local population persistence. Regional persistence is tightly linked to size, spatial configuration and quality of habitat patches. Hence it is important for the management of endangered species that priority patches can be identified. We developed a predictive model of patch occupancy by capercaillie, a threatened grouse species, based on a single snapshot of data. We used logistic regression to predict patch occupancy as a function of patch size, isolation, connectivity, relative altitude, and biogeographical area. The probability of a patch being occupied increased with patch size and increasing altitude, and decreased with increasing distance to the next occupied patch. Patch size was the most important predictor although occupied patches varied considerably in size. Our model only uses data on the number, size and spatial configuration of habitat patches. It is a useful tool to designate priority areas for conservation, i.e. large core patches with high resilience in habitat quality, smaller island‐patches that still have high probability of being inhabited or becoming recolonised, and patches functioning as “stepping stones”. If capercaillie is to be preserved, habitat suitability needs to be maintained in a functional network of patches that account for size and inter‐patch distance thresholds as found in this study. We suggest that similar area‐isolation relationships are valid for almost any region within the distribution range of capercaillie. The thresholds for occupancy are however likely to depend on characteristics of the respective landscape. The outcome of our study emphasises the need for future investigations that explore the relationship between patch occupancy, matrix quality and its resistance to dispersing individuals.     

SimPed: a simulation program to generate haplotype and genotype data for pedigree structures

With the widespread availability of SNP genotype data, there is great interest in analyzing pedigree haplotype data. Intermarker linkage disequilibrium for microsatellite markers is usually low due to their physical distance; however, for dense maps of SNP markers, there can be strong linkage disequilibrium between marker loci. Linkage analysis (parametric and nonparametric) and family-based association studies are currently being carried out using dense maps of SNP marker loci. Monte Carlo methods are often used for both linkage and association studies; however, to date there are no programs available which can generate haplotype and/or genotype data consisting of a large number of loci for pedigree structures. SimPed is a program that quickly generates haplotype and/or genotype data for pedigrees of virtually any size and complexity. Marker data either in linkage disequilibrium or equilibrium can be generated for greater than 20,000 diallelic or multiallelic marker loci. Haplotypes and/or genotypes are generated for pedigree structures using specified genetic map distances and haplotype and/or allele frequencies. The simulated data generated by SimPed is useful for a variety of purposes, including evaluating methods that estimate haplotype frequencies for pedigree data, evaluating type I error due to intermarker linkage disequilibrium and estimating empirical p values for linkage and family-based association studies.     

Dynamics of cytonuclear disequilibria in finite populations and comparison with a two-locus nuclear system.

We study the behavior of cytonuclear disequilibria in a finite monoecious population due to (1) random drift alone, (2) random drift and mutation, and (3) random drift and migration, using exact results on the RUZ (Random Union of Zygotes) model and diffusion approximations. We also show that the RUG (Random Union of Gametes) model is not suitable for a cytonuclear system. The study is also accompanied by a comparison with a two-locus nuclear system. We show that in a finite population of size N without mutation, the rate of decrease of the cytonuclear allelic disequilibrium is the same as that in the corresponding unlinked two-locus nuclear system. The principal rate of decrease of variance in allelic disequilibrium in a cytonuclear system is slightly faster than that in the corresponding nuclear system. However, the expected value of the variance in cytonuclear disequilibria is larger than that in a two-locus nuclear system for at least the first N generations. With mutation, the expected value of steady state variances of both systems are about the same; however, the normalized variance in linkage disequilibrium sigma 2d of the cytonuclear system is about twice as large as that for the corresponding nuclear system. For the migration process, two sets of steady state solutions are provided, one for the variables before migration and the other for the variables after migration. Diffusion approximations for both the principal rate of decay and steady state solutions in both systems are found to be satisfactory. A more accurate backward diffusion equation for a two-locus nuclear system is provided when the recombination fraction R is large.