Estimating multilocus linkage disequilibria

Patterns of admixture and introgression in a mosaic Mytilus galloprovincialis and Mytilus edulis hybrid zone in SW England

The study of hybrid zones offers important insights into speciation. Earlier studies on hybrid populations of the marine mussel species Mytilus edulis and Mytilus galloprovincialis in SW England provided evidence of admixture but were constrained by the limited number of molecular markers available. We use 57 ancestry-informative SNPs, most of which have been mapped genetically, to provide evidence of distinctive differences between admixed populations in SW England and asymmetrical introgression from M. edulis to M. galloprovincialis. We combine the genetic study with analysis of phenotypic traits of potential ecological and adaptive significance. We demonstrate that hybrid individuals have brown mantle edges unlike the white or purple in the parental species, suggesting allelic or non-allelic genomic interactions. We report differences in gonad development stage between the species consistent with a prezygotic barrier between the species. By incorporating results from publications dating back to 1980, we confirm the long-term stability of the hybrid zone despite higher viability of M. galloprovincialis. This stability coincides with a dramatic change in temperature of UK coastal waters and suggests that these hybrid populations might be resisting the effects of global warming. However, a single SNP locus associated with the Notch transmembrane signalling protein shows a markedly different pattern of variation to the others and might be associated with adaptation of M. galloprovincialis to colder northern temperatures.

Recombining Your Way Out of Trouble: The Genetic Architecture of Hybrid Fitness under Environmental Stress

Hybridization between species can either promote or impede adaptation. But we know very little about the genetic basis of hybrid fitness, especially in nondomesticated organisms, and when populations are facing environmental stress. We made genetically variable F2 hybrid populations from two divergent Saccharomyces yeast species. We exposed populations to ten toxins and sequenced the most resilient hybrids on low coverage using ddRADseq to investigate four aspects of their genomes: 1) hybridity, 2) interspecific heterozygosity, 3) epistasis (positive or negative associations between nonhomologous chromosomes), and 4) ploidy. We used linear mixed-effect models and simulations to measure to which extent hybrid genome composition was contingent on the environment. Genomes grown in different environments varied in every aspect of hybridness measured, revealing strong genotype–environment interactions. We also found selection against heterozygosity or directional selection for one of the parental alleles, with larger fitness of genomes carrying more homozygous allelic combinations in an otherwise hybrid genomic background. In addition, individual chromosomes and chromosomal interactions showed significant species biases and pervasive aneuploidies. Against our expectations, we observed multiple beneficial, opposite-species chromosome associations, confirmed by epistasis- and selection-free computer simulations, which is surprising given the large divergence of parental genomes (∼15%). Together, these results suggest that successful, stress-resilient hybrid genomes can be assembled from the best features of both parents without paying high costs of negative epistasis. This illustrates the importance of measuring genetic trait architecture in an environmental context when determining the evolutionary potential of genetically diverse hybrid populations.

Variation of the adaptive substitution rate between species and within genomes

The importance of adaptive mutations in molecular evolution is extensively debated. Recent developments in population genomics allow inferring rates of adaptive mutations by fitting a distribution of fitness effects to the observed patterns of polymorphism and divergence at sites under selection and sites assumed to evolve neutrally. Here, we summarize the current state-of-the-art of these methods and review the factors that affect the molecular rate of adaptation. Several studies have reported extensive cross-species variation in the proportion of adaptive amino-acid substitutions (α) and predicted that species with larger effective population sizes undergo less genetic drift and higher rates of adaptation. Disentangling the rates of positive and negative selection, however, revealed that mutations with deleterious effects are the main driver of this population size effect and that adaptive substitution rates vary comparatively little across species. Conversely, rates of adaptive substitution have been documented to vary substantially within genomes. On a genome-wide scale, gene density, recombination and mutation rate were observed to play a role in shaping molecular rates of adaptation, as predicted under models of linked selection. At the gene level, it has been reported that the gene functional category and the macromolecular structure substantially impact the rate of adaptive mutations. Here, we deliver a comprehensive review of methods used to infer the molecular adaptive rate, the potential drivers of adaptive evolution and how positive selection shapes molecular evolution within genes, across genes within species and between species.

Unexpected mosaic distribution of two hybridizing sibling lineages in the teleplanically dispersing snail Stramonita haemastoma suggests unusual postglacial redistribution or cryptic invasion

Molecular approaches have proven efficient to identify cryptic lineages within single taxonomic entities. Sometimes these cryptic lineages maybe previously unreported or unknown invasive taxa. The genetic structure of the marine gastropod Stramonita haemastoma has been examined in the Western Mediterranean and North‐Eastern Atlantic populations with mtDNA COI sequences and three newly developed microsatellite markers. We identified two cryptic lineages, differentially fixed for alternative mtDNA COI haplogroups and significantly differentiated at microsatellite loci. The mosaic distribution of the two lineages is unusual for a warm‐temperate marine invertebrate with a teleplanic larval stage. The Atlantic lineage was unexpectedly observed as a patch enclosed in the north of the Western Mediterranean Sea between eastern Spain and the French Riviera, and the Mediterranean lineage was found in Macronesian Islands. Although cyto‐nuclear disequilibrium is globally maintained, asymmetric introgression occurs in the Spanish region where the two lineages co‐occur in a hybrid zone. A first interpretation of our results is mito‐nuclear discordance in a stable postglacial hybrid zone. Under this hypothesis, though, the location of genetic discontinuities would be unusual among planktonic dispersers. An alternative interpretation is that the Atlantic lineage, also found in Senegal and Venezuela, has been introduced by human activities in the Mediterranean area and is introgressing Mediterranean genes during its propagation, as theoretically expected. This second hypothesis would add an additional example to the growing list of cryptic marine invasions revealed by molecular studies.

Single Marker and Haplotype-Based Association Analysis of Semolina and Pasta Colour in Elite Durum Wheat Breeding Lines Using a High-Density Consensus Map

Association mapping is usually performed by testing the correlation between a single marker and phenotypes. However, because patterns of variation within genomes are inherited as blocks, clustering markers into haplotypes for genome-wide scans could be a worthwhile approach to improve statistical power to detect associations. The availability of high-density molecular data allows the possibility to assess the potential of both approaches to identify marker-trait associations in durum wheat. In the present study, we used single marker- and haplotype-based approaches to identify loci associated with semolina and pasta colour in durum wheat, the main objective being to evaluate the potential benefits of haplotype-based analysis for identifying quantitative trait loci. One hundred sixty-nine durum lines were genotyped using the Illumina 90K Infinium iSelect assay, and 12,234 polymorphic single nucleotide polymorphism (SNP) markers were generated and used to assess the population structure and the linkage disequilibrium (LD) patterns. A total of 8,581 SNPs previously localized to a high-density consensus map were clustered into 406 haplotype blocks based on the average LD distance of 5.3 cM. Combining multiple SNPs into haplotype blocks increased the average polymorphism information content (PIC) from 0.27 per SNP to 0.50 per haplotype. The haplotype-based analysis identified 12 loci associated with grain pigment colour traits, including the five loci identified by the single marker-based analysis. Furthermore, the haplotype-based analysis resulted in an increase of the phenotypic variance explained (50.4% on average) and the allelic effect (33.7% on average) when compared to single marker analysis. The presence of multiple allelic combinations within each haplotype locus offers potential for screening the most favorable haplotype series and may facilitate marker-assisted selection of grain pigment colour in durum wheat. These results suggest a benefit of haplotype-based analysis over single marker analysis to detect loci associated with colour traits in durum wheat.

What, if anything, are hybrids: enduring truths and challenges associated with population structure and gene flow

Hybridization is a potent evolutionary process that can affect the origin, maintenance, and loss of biodiversity. Because of its ecological and evolutionary consequences, an understanding of hybridization is important for basic and applied sciences, including conservation biology and agriculture. Herein, we review and discuss ideas that are relevant to the recognition of hybrids and hybridization. We supplement this discussion with simulations. The ideas we present have a long history, particularly in botany, and clarifying them should have practical consequences for managing hybridization and gene flow in plants. One of our primary goals is to illustrate what we can and cannot infer about hybrids and hybridization from molecular data; in other words, we ask when genetic analyses commonly used to study hybridization might mislead us about the history or nature of gene flow and selection. We focus on patterns of variation when hybridization is recent and populations are polymorphic, which are particularly informative for applied issues, such as contemporary hybridization following recent ecological change. We show that hybridization is not a singular process, but instead a collection of related processes with variable outcomes and consequences. Thus, it will often be inappropriate to generalize about the threats or benefits of hybridization from individual studies, and at minimum, it will be important to avoid categorical thinking about what hybridization and hybrids are. We recommend potential sampling and analytical approaches that should help us confront these complexities of hybridization.

Genomic selection in maritime pine

A two-generation maritime pine (Pinus pinaster Ait.) breeding population (n=661) was genotyped using 2500 SNP markers. The extent of linkage disequilibrium and utility of genomic selection for growth and stem straightness improvement were investigated. The overall intra-chromosomal linkage disequilibrium was r(2)=0.01. Linkage disequilibrium corrected for genomic relationships derived from markers was smaller (rV(2)=0.006). Genomic BLUP, Bayesian ridge regression and Bayesian LASSO regression statistical models were used to obtain genomic estimated breeding values. Two validation methods (random sampling 50% of the population and 10% of the progeny generation as validation sets) were used with 100 replications. The average predictive ability across statistical models and validation methods was about 0.49 for stem sweep, and 0.47 and 0.43 for total height and tree diameter, respectively. The sensitivity analysis suggested that prior densities (variance explained by markers) had little or no discernible effect on posterior means (residual variance) in Bayesian prediction models. Sampling from the progeny generation for model validation increased the predictive ability of markers for tree diameter and stem sweep but not for total height. The results are promising despite low linkage disequilibrium and low marker coverage of the genome (∼1.39 markers/cM).

Estimation of the dispersal of a major pest of maize by cline analysis of a temporary contact zone between two invasive outbreaks

Dispersal is a key factor in invasion and in the persistence and evolution of species. Despite the importance of estimates of dispersal distance, dispersal measurement remains a real methodological challenge. In this study, we characterized dispersal by exploiting a specific case of biological invasion, in which multiple introductions in disconnected areas lead to secondary contact between two differentiated expanding outbreaks. By applying cline theory to this ecological setting, we estimated σ, the standard deviation of the parent-offspring distance distribution, of the western corn rootworm, Diabrotica virgifera virgifera, one of the most destructive pests of maize. This species is currently invading Europe, and the two largest invasive outbreaks, in northern Italy and Central Europe, have recently formed a secondary contact zone in northern Italy. We identified vanishing clines at 12 microsatellite loci throughout the contact zone. By analysing both the rate of change of cline slope and the spatial variation of linkage disequilibrium at these markers, we obtained two σ estimates of about 20 km/generation(1/2). Simulations indicated that these estimates were robust to changes in dispersal kernels and differences in population density between the two outbreaks, despite a systematic weak bias. These estimates are consistent with the results of direct methods for measuring dispersal applied to the same species. We conclude that secondary contact resulting from multiple introductions is very useful for the inference of dispersal parameters and should be more widely used in other species.

Contribution of an additive locus to genetic variance when inheritance is multi-factorial with implications on interpretation of GWAS

Although the effects of linkage disequilibrium (LD) on partition of genetic variance have received attention in quantitative genetics, there has been little discussion on how this phenomenon affects attribution of variance to a given locus. This paper reinforces the point that standard metrics used for assessing the contribution of a locus to variance can be misleading when there is linkage LD and that factors such as distribution of effects and of allelic frequencies over loci, or existence of frequency-dependent effects, play a role as well. An apparently new metric is proposed for measuring how much of the variability is contributed by a locus when LD exists. Effects of intervening factors, such as type and extent of LD, number of loci, distribution of effects, and of allelic frequencies over loci, as well as a model for generating frequency-dependent effects, are illustrated via hypothetical simulation scenarios. Implications on the interpretation of genome-wide association studies (GWAS), as typically carried out in human genetics, where single marker regression and the assumption of a sole quantitative trait locus (QTL) are common, are discussed. It is concluded that the standard attributions to variance contributed by a single QTL from a GWAS analysis may be misleading, conceptually and statistically, when a trait is complex and affected by sets of many genes in linkage disequilibrium. Yet another factor to consider in the "missing heritability" saga?.

Identification of recent hybridization between gray wolves and domesticated dogs by SNP genotyping

The ability to detect recent hybridization between dogs and wolves is important for conservation and legal actions, which often require accurate and rapid resolution of ancestry. The availability of a genetic test for dog-wolf hybrids would greatly support federal and legal enforcement efforts, particularly when the individual in question lacks prior ancestry information. We have developed a panel of 100 unlinked ancestry-informative SNP markers that can detect mixed ancestry within up to four generations of dog-wolf hybridization based on simulations of seven genealogical classes constructed following the rules of Mendelian inheritance. We establish 95 % confidence regions around the spatial clustering of each genealogical class using a tertiary plot of allele dosage and heterozygosity. The first- and second-backcrossed-generation hybrids were the most distinct from parental populations, with >90 % correctly assigned to genealogical class. In this article we provide a tool kit with population-level statistical quantification that can detect recent dog-wolf hybridization using a panel of dog-wolf ancestry-informative SNPs with divergent allele frequency distributions.

Strong selection against hybrids maintains a narrow contact zone between morphologically cryptic lineages in a rainforest lizard

Phenotypically cryptic lineages comprise an important yet understudied part of biodiversity; in particular, we have much to learn about how these lineages are formed and maintained. To better understand the evolutionary significance of such lineages, we studied a hybrid zone between two morphologically cryptic phylogeographic lineages in the rainforest lizard, Lampropholis coggeri. Analyzing a multilocus genetic dataset through cline inference, individual-based methods and population measures of disequilibrium and using simulations to explore our genetic results in context of theoretical expectations, we inferred the processes maintaining this hybrid zone. We find that these lineages meet in a hybrid zone that is narrow (≈400 m) relative to inferred dispersal rate. Further, the hybrid zone exhibits substantial genetic disequilibrium and sharply coincident and largely concordant clines. Based on our knowledge about the region's biogeography, the species' natural history, and our simulation results, we suggest that strong selection against hybrids structures this system. As all clines show a relatively narrow range of introgression, we posit that this hybrid zone might not yet be in equilibrium. Nonetheless, our results clearly show that phylogeographic lineages can evolve substantial reproductive isolation without concomitant morphological diversification, suggesting that such lineages can constitute a significant component of evolutionary diversity.

Widespread introgression does not leak into allotopy in a broad sympatric zone

Species that overlap over a large part of their range and habitat requirements are challenging for the study of speciation and hybridization. In this respect, the study of broadscale introgressive hybridization has raised recent interest. Here we studied hybridization between two closely related amphibians Lissotriton helveticus and Lissotriton vulgaris that reproduce over a wide sympatric zone. We used mitochondrial and microsatellite markers on 1272 individuals in 37 sites over Europe to detect hybrids at the individual-level and to analyse Hardy-Weinberg and linkage disequilibria at the population-level. Morphological traits showed a strong bimodal distribution. Consistently, hybrid frequency was low (1.7%). We found asymmetric introgression with five times more hybrids in L. vulgaris than in L. helveticus, a pattern probably explained by an unequal effective population size in a study part wherein L. helveticus numerically predominates. Strikingly, significant levels of introgression were detected in 73% of sites shared by both species. Our study showed that introgression is widespread but remains confined to the sites where the two species reproduce at the same time. This pattern may explain why these species remain genetically distinct over a broad sympatric zone.

A variable-sized sliding-window approach for genetic association studies via principal component analysis

Recently with the rapid improvements in high-throughout genotyping techniques, researchers are facing the very challenging task of analysing large-scale genetic associations, especially at the whole-genome level, without an optimal solution. In this study, we propose a new approach for genetic association analysis that is based on a variable-sized sliding-window framework and employs principal component analysis to find the optimum window size. With the help of the bisection algorithm in window-size searching, our method is more computationally efficient than available approaches. We evaluate the performance of the proposed method by comparing it with two other methods-a single-marker method and a variable-length Markov chain method. We demonstrate that, in most cases, the proposed method out-performs the other two methods. Furthermore, since the proposed method is based on genotype data, it does not require any computationally intensive phasing program to account for uncertain haplotype phase.

Genetic hitchhiking in a subdivided population of Mytilus edulis

BACKGROUND

Few models of genetic hitchhiking in subdivided populations have been developed and the rarity of empirical examples is even more striking. We here provide evidences of genetic hitchhiking in a subdivided population of the marine mussel Mytilus edulis. In the Bay of Biscay (France), a patch of M. edulis populations happens to be separated from its North Sea conspecifics by a wide region occupied only by the sister species M. galloprovincialis. Although genetic differentiation between the two M. edulis regions is largely non-significant at ten marker loci (average FST~0.007), a strong genetic differentiation is observed at a single locus (FST = 0.25). We validated the outlier status of this locus, and analysed DNA sequence polymorphism in order to identify the nature of the selection responsible for the unusual differentiation.

RESULTS

We first showed that introgression of M. galloprovincialis alleles was very weak in both populations and did not significantly affect their differentiation. Secondly, we observed the genetic signature of a selective sweep within both M. edulis populations in the form of a star-shaped clade of alleles. This clade was nearly fixed in the North Sea and was segregating at a moderate frequency in the Bay of Biscay, explaining their genetic differentiation. Incomplete fixation reveals that selection was not direct on the locus but that the studied sequence recombined with a positively selected allele at a linked locus while it was on its way to fixation. Finally, using a deterministic model we showed that the wave of advance of a favourable allele at a linked locus, when crossing a strong enough barrier to gene flow, generates a step in neutral allele frequencies comparable to the step observed between the two M. edulis populations at the outlier locus. In our case, the position of the barrier is now materialised by a large patch of heterospecific M. galloprovincialis populations.

CONCLUSION

High FST outlier loci are usually interpreted as being the consequence of ongoing divergent local adaptation. Combining models and data we show that among-population differentiation can also dramatically increase following a selective sweep in a structured population. Our study illustrates how a striking geographical pattern of neutral diversity can emerge from past indirect hitchhiking selection in a structured population. NOTE: Nucleotide sequences reported in this paper are available in the GenBanktrade mark database under the accession numbers EU684165 - EU684228.

Molecular and morphological patterns of introgression between two large white-headed gull species in a zone of recent secondary contact

Incomplete reproductive isolation promotes gene flow between diverging taxa. However, any gene encoding for traits involved in the reproductive barriers will be less prone to introgression than neutral markers. Comparing introgression rates among loci is thus informative of the number and functions of loci involved in the reproductive barriers. This study aimed at identifying possible mechanisms of restriction to gene flow across a zone of recent secondary contact between Larus argentatus and Larus cachinnans by comparing introgression patterns for nine microsatellite loci, a fragment of mitochondrial DNA and a set of phenotypic traits. The low linkage disequilibrium between neutral nuclear markers indicated introgression without any barrier to gene flow. However, asymmetric introgression of mitochondrial DNA suggested that interspecific crosses may be more successful in one direction. The introgression rate for phenotypic traits was variable and low compared to neutral molecular markers. This was particularly evident in colouration of bare parts: individuals with intermediate colouration were scarcer in sympatry than expected if the genomes recombined freely. We hypothesized that one of these variables, the orbital ring colour, may play a role in mate choice, acting as an incomplete premating barrier through assortative mating. This study emphasizes that multilocus approaches are useful to discriminate among possible mechanisms responsible for the maintenance of hybrid zones.

Natural hybridization between a clonally propagated crop, cassava (Manihot esculenta Crantz) and a wild relative in French Guiana

Because domestication rarely leads to speciation, domesticated populations often hybridize with wild relatives when they occur in close proximity. Little work has focused on this question in clonally propagated crops. If selection on the capacity for sexual reproduction has been relaxed, these crops would not be expected to hybridize with their wild relatives as frequently as seed-propagated crops. Cassava is one of the most important clonally propagated plants in tropical agriculture. Gene flow between cassava and wild relatives has often been postulated, but never demonstrated in nature. We studied a population of a wild Manihot sp. in French Guiana, which was recently in contact with domesticated cassava, and characterized phenotypes (10 morphological traits) and genotypes (six microsatellite loci) of individuals in a transect parallel to the direction of hypothesized gene flow. Wild and domesticated populations were strongly differentiated at microsatellite loci. We identified many hybrids forming a continuum between these two populations, and phenotypic variation was strongly correlated with the degree of hybridization as determined by molecular markers. Analysis of linkage disequilibrium and of the diversity of hybrid pedigrees showed that hybridization has gone on for at least three generations and that no strong barrier prevents admixture of the populations. Hybrids were more heterozygous than either wild or domesticated individuals, and phenotypic comparisons suggested heterosis in vegetative traits. Our results also suggest that this situation is not uncommon, at least in French Guiana, and demonstrate the need for integrated management of wild and domesticated populations even in clonally propagated crops.

Association mapping via regularized regression analysis of single-nucleotide-polymorphism haplotypes in variable-sized sliding windows

Large-scale haplotype association analysis, especially at the whole-genome level, is still a very challenging task without an optimal solution. In this study, we propose a new approach for haplotype association analysis that is based on a variable-sized sliding-window framework and employs regularized regression analysis to tackle the problem of multiple degrees of freedom in the haplotype test. Our method can handle a large number of haplotypes in association analyses more efficiently and effectively than do currently available approaches. We implement a procedure in which the maximum size of a sliding window is determined by local haplotype diversity and sample size, an attractive feature for large-scale haplotype analyses, such as a whole-genome scan, in which linkage disequilibrium patterns are expected to vary widely. We compare the performance of our method with that of three other methods--a test based on a single-nucleotide polymorphism, a cladistic analysis of haplotypes, and variable-length Markov chains--with use of both simulated and experimental data. By analyzing data sets simulated under different disease models, we demonstrate that our method consistently outperforms the other three methods, especially when the region under study has high haplotype diversity. Built on the regression analysis framework, our method can incorporate other risk-factor information into haplotype-based association analysis, which is becoming an increasingly necessary step for studying common disorders to which both genetic and environmental risk factors contribute.

Morphological and genetic divergence of intralacustrine stickleback morphs in Iceland: a case for selective differentiation?

The evolutionary processes involved in population divergence and local adaptation are poorly understood. Theory predicts that divergence of adjacent populations is possible but depends on several factors including gene flow, divergent selection, population size and the number of genes involved in divergence and their distribution on the genome. We analyse variation in neutral markers, markers linked to putative quantitative trait loci and morphological traits in a recent (<10000 years) zone of primary divergence between stickleback morphs in Lake Thingvallavatn, Iceland. Environmental factors, especially predation, are clearly implicated in reducing gene flow between morphs. There is continuous morphological and genetic variation between habitats with a zone centre similar to secondary contact zones. Individual microsatellite loci are implicated as being linked to adaptive variation by direct tests as well as by differences in cline shape. Patterns of linkage disequilibria indicate that the morphs have diverged at several loci. This divergence shows parallels and differences with the well-studied limnetic-benthic stickleback morphs, both in phenotypic divergence and at the genomic level.

Quantifying the amount of missing information in genetic association studies

Many genetic analyses are done with incomplete information; for example, unknown phase in haplotype-based association studies. Measures of the amount of available information can be used for efficient planning of studies and/or analyses. In particular, the linkage disequilibrium (LD) between two sets of markers can be interpreted as the amount of information one set of markers contains for testing allele frequency differences in the second set, and measuring LD can be viewed as quantifying information in a missing data problem. We introduce a framework for measuring the association between two sets of variables; for example, genotype data for two distinct groups of markers, or haplotype and genotype data for a given set of polymorphisms. The goal is to quantify how much information is in one data set, e.g. genotype data for a set of SNPs, for estimating parameters that are functions of frequencies in the second data set, e.g. haplotype frequencies, relative to the ideal case of actually observing the complete data, e.g. haplotypes. In the case of genotype data on two mutually exclusive sets of markers, the measure determines the amount of multi-locus LD, and is equal to the classical measure r(2), if the sets consist each of one bi-allelic marker. In general, the measures are interpreted as the asymptotic ratio of sample sizes necessary to achieve the same power in case-control testing. The focus of this paper is on case-control allele/haplotype tests, but the framework can be extended easily to other settings like regressing quantitative traits on allele/haplotype counts, or tests on genotypes or diplotypes. We highlight applications of the approach, including tools for navigating the HapMap database [The International HapMap Consortium, 2003], and genotyping strategies for positional cloning studies.

Fitness landscapes support the dominance theory of post-zygotic isolation in the mussels Mytilus edulis and M. galloprovincialis

We studied the genetic basis of post-zygotic isolation in the marine mussels Mytilus edulis and Mytilus galloprovincialis. Evidence was obtained for a high number of recessive Dobzhansky-Muller substitutions in the genome of these two mussel taxa. We analysed the segregation of unlinked diagnostic markers in the progeny of two backcrosses and an F2 cross, 36 h and 200 days after fertilization. Directional selection favouring M. galloprovincialis genotypes was observed in both kinds of cross. In the F2, epistatic interactions between each pair of chromosome fragments mapped by the markers were identified in addition. Our results imply that homozygous-homozygous interactions are required for breakdown of coadaptation, in accordance with the dominance theory of post-zygotic isolation. Endogenous post-zygotic selection distributed over many loci throughout the genome provides the missing factor explaining the astonishing persistence and strength of barriers to neutral introgression in such a dispersive taxon as Mytilus.

The use of genetic clines to estimate dispersal distances of marine larvae

Many unresolved issues in the ecology and evolution of marine populations center on how far planktonic larvae disperse away from their parents. Genetic tools provide a promising way to define the spatial spread of larvae, yet their accurate interpretation depends on the extent to which genetic loci are under selection. Genetic clines, geographic zones in which genetically differentiated populations interbreed, provide opportunities to explicitly and simultaneously quantify the relative roles of selection and dispersal. Here, we review the theory and analysis of genetic clines and apply these techniques to published studies of multilocus clines in the sea. The geographic width of a stable genetic cline is determined by a balance between the homogenizing effects of dispersal and the diversifying effects of selection. For marine researchers, the power of genetic clines is that, if selection and clinal width are quantified, then the average geographic distances that larvae move can be inferred. Measuring selection or dispersal through laboratory or field-based experimentation is possible, though logistically difficult, for pelagically dispersed organisms. Instead, dispersal may be more robustly quantified from the degree of linkage disequilibrium between two or more loci, because linkage disequilibrium integrates selection across multiple life stages and generations. It is also relatively insensitive to whether exogenous or endogenous selection operates. Even without quantifying linkage disequilibrium, the theory of genetic clines indicates that the average dispersal distance of larvae is a fraction (i.e., generally <35%) of the clinal width. Because cline theory is based on several underlying assumptions, including near-equilibrium between selection and migration, the dispersal distances inferred from empirical data should be of the correct order but may not be precise. Even so, such estimates of larval dispersal are valuable, as they can be utilized to design appropriate scales for future investigations and provide some guidance to conservation efforts.

The use of genetic clines to estimate dispersal distances of marine larvae

Many unresolved issues in the ecology and evolution of marine populations center on how far planktonic larvae disperse away from their parents. Genetic tools provide a promising way to define the spatial spread of larvae, yet their accurate interpretation depends on the extent to which genetic loci are under selection. Genetic clines, geographic zones in which genetically differentiated populations interbreed, provide opportunities to explicitly and simultaneously quantify the relative roles of selection and dispersal. Here, we review the theory and analysis of genetic clines and apply these techniques to published studies of multilocus clines in the sea. The geographic width of a stable genetic cline is determined by a balance between the homogenizing effects of dispersal and the diversifying effects of selection. For marine researchers, the power of genetic clines is that, if selection and clinal width are quantified, then the average geographic distances that larvae move can be inferred. Measuring selection or dispersal through laboratory or field-based experimentation is possible, though logistically difficult, for pelagically dispersed organisms. Instead, dispersal may be more robustly quantified from the degree of linkage disequilibrium between two or more loci, because linkage disequilibrium integrates selection across multiple life stages and generations. It is also relatively insensitive to whether exogenous or endogenous selection operates. Even without quantifying linkage disequilibrium, the theory of genetic clines indicates that the average dispersal distance of larvae is a fraction (i.e., generally <35%) of the clinal width. Because cline theory is based on several underlying assumptions, including near-equilibrium between selection and migration, the dispersal distances inferred from empirical data should be of the correct order but may not be precise. Even so, such estimates of larval dispersal are valuable, as they can be utilized to design appropriate scales for future investigations and provide some guidance to conservation efforts.

THE USE OF GENETIC CLINES TO ESTIMATE DISPERSAL DISTANCES OF MARINE LARVAE

Many unresolved issues in the ecology and evolution of marine populations center on how far planktonic larvae disperse away from their parents. Genetic tools provide a promising way to define the spatial spread of larvae, yet their accurate interpretation depends on the extent to which genetic loci are under selection. Genetic clines, geographic zones in which genetically differentiated populations interbreed, provide opportunities to explicitly and simultaneously quantify the relative roles of selection and dispersal. Here, we review the theory and analysis of genetic clines and apply these techniques to published studies of multilocus clines in the sea. The geographic width of a stable genetic cline is determined by a balance between the homogenizing effects of dispersal and the diversifying effects of selection. For marine researchers, the power of genetic clines is that, if selection and clinal width are quantified, then the average geographic distances that larvae move can be inferred. Measuring selection or dispersal through laboratory or field-based experimentation is possible, though logistically difficult, for pelagically dispersed organisms. Instead, dispersal may be more robustly quantified from the degree of linkage disequilibrium between two or more loci, because linkage disequilibrium integrates selection across multiple life stages and generations. It is also relatively insensitive to whether exogenous or endogenous selection operates. Even without quantifying linkage disequilibrium, the theory of genetic clines indicates that the average dispersal distance of larvae is a fraction (i.e., generally <35%) of the clinal width. Because cline theory is based on several underlying assumptions, including near-equilibrium between selection and migration, the dispersal distances inferred from empirical data should be of the correct order but may not be precise. Even so, such estimates of larval dispersal are valuable, as they can be utilized to design appropriate scales for future investigations and provide some guidance to conservation efforts.

Endemic North African Quercus afares Pomel originates from hybridisation between two genetically very distant oak species (Q. suber L. and Q. canariensis Willd.): evidence from nuclear and cytoplasmic markers

Hybridisation is a potent force in plant evolution, although there are few reported examples of stabilised species that have been created through homoploid hybridisation. We focus here on Quercus afares, an endemic North African species that combines morphological, physiological and ecological traits of both Q. suber and Q. canariensis, two phylogenetically distant species. These two species are sympatric with Q. afares over most of its distribution. We studied two Q. afares populations (one from Algeria and one from Tunisia), as well as several populations of both Q. suber and Q. canariensis sampled both within and outside areas where these species overlap with Q. afares. A genetic analysis was conducted using both nuclear (allozymes) and chloroplastic markers, which shows that Q. afares originates from a Q. suber x Q. canariensis hybridisation. At most loci, Q. afares predominantly possesses alleles from Q. suber, suggesting that the initial cross between Q. suber and Q. canariensis was followed by backcrossing with Q. suber. Other hypotheses that can account for this result, including genetic drift, gene silencing, gene conversion and selection, are discussed. A single Q. suber chlorotype was detected, and all Q. afares individuals displayed this chlorotype, indicating that Q. suber was the maternal parent. Q. afares is genetically, morphologically and ecologically differentiated from its parental species, and can therefore be considered as a stabilised hybrid species.

Evolution of Sexual Isolation during Secondary Contact: Genotypic versus Phenotypic Changes in Laboratory Populations

We monitored the phenotypic and genotypic changes that occur when two behavioral races come into contact in laboratory populations. Drosophila melanogaster from Zimbabwe and nearby regions (Z type) show strong but asymmetric sexual isolation from their cosmopolitan counterparts (M type). Crosses of Z females and M males do not take place readily when other choices are available. At least 15 loci are known to control Z-type mating preferences and performance. By thoroughly mixing the genomes of the two types in laboratory populations, we artificially created maximum secondary contact. Despite the strength of sexual selection favoring Z-type male characters, Z-type behavior is eliminated or greatly diminished in all 12 hybrid populations after only 60 generations. This trend is consistent with the spread of the M-type behavior throughout the world as well as a detailed analysis of fitness components. Surprisingly, in contrast with the phenotypic convergence toward the M-type, genotypic samples broadly covering the genomic regions of mapped behavioral loci show no such trend. The genome appears to be "fine grained," with adjacent loci having different evolutionary dynamics and genealogical histories.

INVITED REVIEW: Local adaptation and species segregation in two mussel (Mytilus edulis × Mytilus trossulus) hybrid zones

Few marine hybrid zones have been studied extensively, the major exception being the hybrid zone between the mussels Mytilus edulis and Mytilus galloprovincialis in southwestern Europe. Here, we focus on two less studied hybrid zones that also involve Mytilus spp.; Mytilus edulis and Mytilus trossulus are sympatric and hybridize on both western and eastern coasts of the Atlantic Ocean. We review the dynamics of hybridization in these two hybrid zones and evaluate the role of local adaptation for maintaining species boundaries. In Scandinavia, hybridization and gene introgression is so extensive that no individuals with pure M. trossulus genotypes have been found. However, M. trossulus alleles are maintained at high frequencies in the extremely low salinity Baltic Sea for some allozyme genes. A synthesis of reciprocal transplantation experiments between different salinity regimes shows that unlinked Gpi and Pgm alleles change frequency following transplantation, such that post-transplantation allelic composition resembles native populations found in the same salinity. These experiments provide strong evidence for salinity adaptation at Gpi and Pgm (or genes linked to them). In the Canadian Maritimes, pure M. edulis and M. trossulus individuals are abundant, and limited data suggest that M. edulis predominates in low salinity and sheltered conditions, whereas M. trossulus are more abundant on the wave-exposed open coasts. We suggest that these conflicting patterns of species segregation are, in part, caused by local adaptation of Scandinavian M. trossulus to the extremely low salinity Baltic Sea environment.

Mating patterns in a hybrid zone of fire-bellied toads (Bombina): inferences from adult and full-sib genotypes

We present two novel methods to infer mating patterns from genetic data. They differ from existing statistical methods of parentage inference in that they apply to populations that deviate from Hardy-Weinberg and linkage equilibrium, and so are suited for the study of assortative mating in hybrid zones. The core data set consists of genotypes at several loci for a number of full-sib clutches of unknown parentage. Our inference is based throughout on estimates of allelic associations within and across loci, such as heterozygote deficit and pairwise linkage disequilibrium. In the first method, the most likely parents of a given clutch are determined from the genotypic distribution of the associated adult population, given an explicit model of nonrandom mating. This leads to estimates of the strength of assortment. The second approach is based solely on the offspring genotypes and relies on the fact that a linear relation exists between associations among the offspring and those in the population of breeding pairs. We apply both methods to a sample from the hybrid zone between the fire-bellied toads Bombina bombina and B. variegata (Anura: Disco glossidae) in Croatia. Consistently, both approaches provide no evidence for a departure from random mating, despite adequate statistical power. Instead, B. variegata-like individuals among the adults contributed disproportionately to the offspring cohort, consistent with their preference for the type of breeding habitat in which this study was conducted.

Environment-dependent admixture dynamics in a tiger salamander hybrid zone

After an estimated five million years of independent evolution, the barred tiger salamander (Ambystoma tigrinum mavortium) was introduced by bait dealers into the native range of the California tiger salamander (A. californiense). Hybridization and backcrossing have been occurring in central California for 50-60 years, or an estimated 15-30 generations. We studied genetic and ecological factors influencing admixture of these two divergent gene pools by analyzing frequencies of hybrid genotypes in three kinds of breeding habitats: natural vernal pools, ephemeral man-made cattle ponds, and perennial man-made ponds. Perennial ponds tended to have higher frequencies of nonnative alleles than either type of seasonal pond, even in cases where perennial and seasonal ponds are within a few hundred meters. Thus, the hybrid zone has a mosaic structure that depends on pond hydrology or ecology. The presence of some broadly acting constraints on admixture is suggested by linkage disequilibria between physically unlinked molecular markers within ponds. In addition, we found several marker-specific deviations from Hardy-Weinberg equilibrium. One marker showed a consistent deficit of heterozygotes across pond types. Another showed heterozygote deficits only in vernal pools. A third was more likely to have heterozygote excess in ephemeral cattle ponds. These patterns indicate that admixture is influenced by complex genotype-by-environment interactions.

WHEN VICARS MEET: A NARROW CONTACT ZONE BETWEEN MORPHOLOGICALLY CRYPTIC PHYLOGEOGRAPHIC LINEAGES OF THE RAINFOREST SKINK, CARLIA RUBRIGULARIS

Phylogeographic analyses of the fauna of the Australian wet tropics rainforest have provided strong evidence for long-term isolation of populations among allopatric refugia, yet typically there is no corresponding divergence in morphology. This system provides an opportunity to examine the consequences of geographic isolation, independent of morphological divergence, and thus to assess the broader significance of historical subdivisions revealed through mitochondrial DNA phylogeography. We have located and characterized a zone of secondary contact between two long isolated (mtDNA divergence > 15%) lineages of the skink Carlia rubrigularis using one mitochondrial and eight nuclear (two intron, six microsatellite) markers. This revealed a remarkably narrow (width < 3 km) hybrid zone with substantial linkage disequilibrium and strong deficits of heterozygotes at two of three nuclear loci with diagnostic alleles. Cline centers were coincident across loci. Using a novel form of likelihood analysis, we were unable to distinguish between sigmoidal and stepped cline shapes except at one nuclear locus for which the latter was inferred. Given estimated dispersal rates of 90-133 m x gen(-1/2) and assuming equilibrium, the observed cline widths suggest effective selection against heterozygotes of at least 22-49% and possibly as high as 70%. These observations reveal substantial postmating isolation, although the absence of consistent deviations from Hardy-Weinberg equilibrium at diagnostic loci suggests that there is little accompanying premating isolation. The tight geographic correspondence between transitions in mtDNA and those for nuclear genes and corresponding evidence for selection against hybrids indicates that these morphologically cryptic phylogroups could be considered as incipient species. Nonetheless, we caution against the use of mtDNA phylogeography as a sole criterion for defining species boundaries.

The genomic rate of adaptive amino acid substitution in Drosophila

The proportion of amino acid substitutions driven by adaptive evolution can potentially be estimated from polymorphism and divergence data by an extension of the McDonald-Kreitman test. We have developed a maximum-likelihood method to do this and have applied our method to several data sets from three Drosophila species: D. melanogaster, D. simulans, and D. yakuba. The estimated number of adaptive substitutions per codon is not uniformly distributed among genes, but follows a leptokurtic distribution. However, the proportion of amino acid substitutions fixed by adaptive evolution seems to be remarkably constant across the genome (i.e., the proportion of amino acid substitutions that are adaptive appears to be the same in fast-evolving and slow-evolving genes; fast-evolving genes have higher numbers of both adaptive and neutral substitutions). Our estimates do not seem to be significantly biased by selection on synonymous codon use or by the assumption of independence among sites. Nevertheless, an accurate estimate is hampered by the existence of slightly deleterious mutations and variations in effective population size. The analysis of several Drosophila data sets suggests that approximately 25% +/- 20% of amino acid substitutions were driven by positive selection in the divergence between D. simulans and D. yakuba.

The maintenance of reproductive isolation in a mosaic hybrid zone between the fire-bellied toads Bombina bombina and B. variegata

Mosaic hybrid zones arise when ecologically differentiated taxa hybridize across a network of habitat patches. Frequent interbreeding across a small-scale patchwork can erode species differences that might have been preserved in a clinal hybrid zone. In particular, the rapid breakdown of neutral divergence sets an upper limit to the time for which differences at marker loci can persist. We present here a case study of a mosaic hybrid zone between the fire-bellied toads Bombina bombina and B. variegata (Anura: Discoglossidae) near Apahida in Romania. In our 20 x 20 km study area, we detected no evidence of a clinal transition but found a strong association between aquatic habitat and mean allele frequencies at four molecular markers. In particular, pure populations of B. bombina in ponds appear to cause massive introgression into the surrounding B. variegata gene pool found in temporary aquatic sites. Nevertheless, the genetic structure of these hybrid populations was remarkably similar to those of a previously studied transect near Pescenica (Croatia), which had both clinal and mosaic features: estimates of heterozygote deficit and linkage disequilibrium in each country are similar. In Apahida, the observed strong linkage disequilibria should stem from an imperfect habitat preference that guides most (but not all) adults into the habitats to which they are adapted. In the absence of a clinal structure, the inferred migration rate between habitats implies that associations between selected loci and neutral markers should break down rapidly. Although plausible selection strengths can maintain differentiation at those loci adapting the toads to either permanent or temporary breeding sites, the divergence at neutral markers must be transient. The hybrid zone may be approaching a state in which the gene pools are homogenized at all but the selected loci, not dissimilar from an early stage of sympatric divergence.

Direct selection on allozymes is not required to explain heterogeneity among marker loci across a Mytilus hybrid zone

Unequal differentiation between two types of loci (allozyme and DNA markers) across a Mytilus hybrid zone has recently been claimed as evidence for direct selection on some allozyme loci. We provide here a counter-example: a noncoding DNA locus that exhibits as much differentiation as the incriminated allozymes do. The levels of genetic differentiation varied widely among both allozymes and noncoding DNA markers and no clear difference emerged between the two types of markers. This suggests that the strong interlocus variance in genetic differentiation has been confounded with a discrepancy between marker types as a result of an insufficient and unbalanced locus sampling. Heterogeneity in differentiation among neutral loci can be created by stochastic variance during the allopatric divergence preceding a secondary contact. In hybrid zones, a further source of variance is differential introgression among chromosomal regions after the secondary contact owing to the local influence of selected genes on more or less distant markers. However, the degree of differentiation alone gives no way to distinguish indirect pseudo-selection (a regular and ubiquitous feature of hybrid zones) from direct selection. More generally, we suggest that comparative neutrality tests based on discrepancies among marker types have to be applied with caution when the presence of semi-permeable genetic barriers to gene exchange is suspected.

Habitat preference and the marine-speciation paradox

Marine organisms challenge the classical theories of local adaptation and speciation because their planktonic larvae have the potential to maintain high gene flow. The marine-speciation paradox is illustrated by contact zones between incipient species that are so large that allopatric divergence seems unlikely. For this reason any mechanism preventing sympatric larvae of two incipient species from coexisting in the same habitats can be a powerful promoter of speciation. The contact zone between two hybridizing taxa of mussel, Mytilus edulis and M. galloprovincialis, in Europe provides an excellent example. Although the zone itself extends over thousands of kilometres, the opportunities for interbreeding are considerably reduced by the small-scale mosaic structure of the zone, where local patches of each taxon alternate at scales of kilometres or less, in response to locally variable ecological factors. Habitat choice by settling larvae would be a less costly mechanism than post-settlement selection to maintain such a mosaic structure. Unfortunately the role of selective settlement has remained hypothetical because larvae could not be scored by classical genetic markers. PCR markers allowed us to study larvae and settlement in ecologically contrasting sites within the zone. We show that only a subset of the genotypes present in the plankton settle in some sites, and that the adults on these sites show the same genetic bias. Genetically based variation in pre-settlement processes therefore accounts for the ecological segregation observed, though it is not the only factor involved in limiting successful interbreeding. The present dataset also supports previous reports of partial spawning asynchrony.

A new approach to detecting mixed families

There are several analyses in evolutionary ecology which assume that a family of offspring has come from only two parents. Here, we present a simple test for detecting when a batch involves two or more subfamilies. It is based on the fact that the mixing of families generates associations amongst unlinked marker loci. We also present simulations illustrating the power of our method for varying numbers of loci, alleles per locus and genotyped individuals.

Introgression patterns in the mosaic hybrid zone between Mytilus edulis and M. galloprovincialis

Hybrid zones are fascinating systems to investigate the structure of genetic barriers. Marine hybrid zones deserve more investigation because of the generally high dispersion potential of planktonic larvae which allows migration on scales unrivalled by terrestrial species. Here we analyse the genetic structure of the mosaic hybrid zone between the marine mussels Mytilus edulis and M. galloprovincialis, using three length-polymorphic PCR loci as neutral and diagnostic markers on 32 samples along the Atlantic coast of Europe. Instead of a single genetic gradient from M. galloprovincialis on the Iberian Peninsula to M. edulis populations in the North Sea, three successive transitions were observed in France. From South to North, the frequency of alleles typical of M. galloprovincialis first decreases in the southern Bay of Biscay, remains low in Charente, then increases in South Brittany, remains high in most of Brittany, and finally decreases again in South Normandy. The two enclosed patches observed in the midst of the mosaic hybrid zone in Charente and Brittany, although predominantly M. edulis-like and M. galloprovincialis-like, respectively, are genetically original in two respects. First, considering only the various alleles typical of one species, the patches show differentiated frequencies compared to the reference external populations. Second, each patch is partly introgressed by alleles of the other species. When introgression is taken into account, linkage disequilibria appear close to their maximum possible values, indicating a strong genetic barrier within all transition zones. Some pre- or postzygotic isolation mechanisms (habitat specialization, spawning asynchrony, assortative fertilization and hybrid depression) have been documented in previous studies, although their relative importance remains to be evaluated. We also provided evidence for a recent migratory 'short-cut' connecting M. edulis-like populations of the Charente patch to an external M. edulis population in Normandy and thought to reflect artificial transfer of spat for aquaculture.

Associations between cytoplasmic and nuclear Loci in hybridizing populations

We extend current multilocus models to describe the effects of migration, recombination, selection, and nonrandom mating on sets of genes in diploids with varied modes of inheritance, allowing us to consider the patterns of nuclear and cytonuclear associations (disequilibria) under various models of migration. We show the relationship between the multilocus notation recently presented by Kirkpatrick, Johnson, and Barton (developed from previous work by Barton and Turelli) and the cytonuclear parameterization of Asmussen, Arnold, and Avise and extend this notation to describe associations between cytoplasmic elements and multiple nuclear genes. Under models with sexual symmetry, both nuclear-nuclear and cytonuclear disequilibria are equivalent. They differ, however, in cases involving some type of sexual asymmetry, which is then reflected in the asymmetric inheritance of cytoplasmic markers. An example given is the case of different migration rates in males and females; simulations using 2, 3, 4, or 5 unlinked autosomal markers with a maternally inherited cytoplasmic marker illustrate how nuclear-nuclear and cytonuclear associations can be used to separately estimate female and male migration rates. The general framework developed here allows us to investigate conditions where associations between loci with different modes of inheritance are not equivalent and to use this nonequivalence to test for deviations from simple models of admixture.

General models of multilocus evolution

In 1991, Barton and Turelli developed recursions to describe the evolution of multilocus systems under arbitrary forms of selection. This article generalizes their approach to allow for arbitrary modes of inheritance, including diploidy, polyploidy, sex linkage, cytoplasmic inheritance, and genomic imprinting. The framework is also extended to allow for other deterministic evolutionary forces, including migration and mutation. Exact recursions that fully describe the state of the population are presented; these are implemented in a computer algebra package (available on the Web at http://helios.bto.ed.ac.uk/evolgen). Despite the generality of our framework, it can describe evolutionary dynamics exactly by just two equations. These recursions can be further simplified using a "quasi-linkage equilibrium" (QLE) approximation. We illustrate the methods by finding the effect of natural selection, sexual selection, mutation, and migration on the genetic composition of a population.

Analysis of multilocus zygotic associations

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

A model-based method for identifying species hybrids using multilocus genetic data

We present a statistical method for identifying species hybrids using data on multiple, unlinked markers. The method does not require that allele frequencies be known in the parental species nor that separate, pure samples of the parental species be available. The method is suitable for both markers with fixed allelic differences between the species and markers without fixed differences. The probability model used is one in which parentals and various classes of hybrids (F(1)'s, F(2)'s, and various backcrosses) form a mixture from which the sample is drawn. Using the framework of Bayesian model-based clustering allows us to compute, by Markov chain Monte Carlo, the posterior probability that each individual belongs to each of the distinct hybrid classes. We demonstrate the method on allozyme data from two species of hybridizing trout, as well as on two simulated data sets.

Joint linkage and linkage disequilibrium mapping in natural populations

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