Joint linkage and linkage disequilibrium mapping in natural populations

Narrow genetic base shapes population structure and linkage disequilibrium in an industrial oilseed crop, Brassica carinata A. Braun

Ethiopian mustard (Brassica carinata A. Braun) is an emerging sustainable source of vegetable oil, in particular for the biofuel industry. The present study exploited genome assemblies of the Brassica diploids, Brassica nigra and Brassica oleracea, to discover over 10,000 genome-wide SNPs using genotype by sequencing of 620 B. carinata lines. The analyses revealed a SNP frequency of one every 91.7 kb, a heterozygosity level of 0.30, nucleotide diversity levels of 1.31 × 10^-05, and the first five principal components captured only 13% molecular variation, indicating low levels of genetic diversity among the B. carinata collection. Genome bias was observed, with greater SNP density found on the B subgenome. The 620 lines clustered into two distinct sub-populations (SP1 and SP2) with the majority of accessions (88%) clustered in SP1 with those from Ethiopia, the presumed centre of origin. SP2 was distinguished by a collection of breeding lines, implicating targeted selection in creating population structure. Two selective sweep regions on B3 and B8 were detected, which harbour genes involved in fatty acid and aliphatic glucosinolate biosynthesis, respectively. The assessment of genetic diversity, population structure, and LD in the global B. carinata collection provides critical information to assist future crop improvement.

Association mapping of drought tolerance-related traits in barley to complement a traditional biparental QTL mapping study

Association mapping of drought-related traits in barley was used to increase the density of existing QTL maps without recreating mapping populations. We used 109 spring barley genotypes exhibiting high or low drought tolerance to elucidate the associations between diversity array technology sequencing (DArTseq) and single nucleotide polymorphism (SNP) markers and various physiological parameters related to plant responses to drought conditions. The study was performed in controlled conditions (growth chambers), drought tolerance was phenotyped in the four-leaf seedlings. We identified 58 associations including 34 new markers (i.e., 16 DArTseq and 18 SNP markers). The results for three markers were consistent with the data obtained in an earlier traditional biparental QTL mapping study. The regions neighboring markers on linkage group 2H contained the highest number of significant marker-trait associations. Five markers related to the photosynthetic activity of photosystem II were detected on chromosome 4H. The lowest number of associations were observed for the sequences neighboring DArT markers on linkage group 6H. A chromosome 3H region related to water use efficiency and net photosynthesis rate in both biparental QTL, and association study, may be particularly valuable, as these parameters correspond to the ability of plants to remain highly productive under water deficit stress. Our findings confirm that association mapping can increase the density of existing QTL maps without recreating mapping populations.

Landscaping Crossover Interference Across a Genome

The evolutionary success of eukaryotic organisms crucially depends on the capacity to produce genetic diversity through reciprocal exchanges of each chromosome pair, or crossovers (COs), during meiosis. It has been recognized that COs arise more evenly across a given chromosome than at random. This phenomenon, termed CO interference, occurs pervasively in eukaryotes and may confer a selective advantage. We describe here a multipoint linkage analysis procedure for segregating families to quantify the strength of CO interference over the genome, and extend this procedure to illustrate the landscape of CO interference in natural populations. We further discuss the crucial role of CO interference in amplifying and maintaining genetic diversity through sex-, stress-, and age-induced differentiation.

Crop wild relative populations of Beta vulgaris allow direct mapping of agronomically important genes

Rapid identification of agronomically important genes is of pivotal interest for crop breeding. One source of such genes are crop wild relative (CWR) populations. Here we used a CWR population of <200 wild beets (B. vulgaris ssp. maritima), sampled in their natural habitat, to identify the sugar beet (Beta vulgaris ssp. vulgaris) resistance gene Rz2 with a modified version of mapping-by-sequencing (MBS). For that, we generated a draft genome sequence of the wild beet. Our results show the importance of preserving CWR in situ and demonstrate the great potential of CWR for rapid discovery of causal genes relevant for crop improvement. The candidate gene for Rz2 was identified by MBS and subsequently corroborated via RNA interference (RNAi). Rz2 encodes a CC-NB-LRR protein. Access to the DNA sequence of Rz2 opens the path to improvement of resistance towards rhizomania not only by marker-assisted breeding but also by genome editing.

Variation among wild relatives of crop plants can be used to identify genes underlying traits of agronomic importance. Here, the authors show that a modified mapping-by-sequencing approach can rapidly identify the genetic basis for viral resistance in sugar beet using wild beet populations in their natural habitat.

Multi-marker linkage disequilibrium mapping of quantitative trait loci

Single nucleotide polymorphisms (SNPs), the most common genetic markers in genome-wide association studies, are usually in linkage disequilibrium (LD) with each other within a small genomic region. Both single- and two-marker-based LD mapping methods have been developed by taking advantage of the LD structures. In this study, a more general LD mapping framework with an arbitrary number of markers has been developed to further improve LD mapping and its detection power. This method is referred as multi-marker linkage disequilibrium mapping (mmLD). For the parameter estimation, we implemented a two-phase estimation procedure: first, haplotype frequencies were estimated for known markers; then, haplotype frequencies were updated to include the unknown quantitative trait loci based on estimates from the first step. For the hypothesis testing, we proposed a novel sequential likelihood ratio test procedure, which iteratively removed haplotypes with zero frequency and subsequently determined the proper degree of freedom. To compare the proposed mmLD method with other existing mapping methods, e.g. the adjusted single-marker LD mapping and the SKAT_C, we performed extensive simulations under various scenarios. The simulation results demonstrated that the mmLD has the same or higher power than the existing methods, while maintaining the correct type I errors. We further applied the mmLD to a public data set, 'GAW17', to investigate its applicability. The result showed the good performance of mmLD. We concluded that this improved mmLD method will be useful for future genome-wide association studies and genetic association analyses.

Constructing a linkage-linkage disequilibrium map using dominant-segregating markers

The relationship between linkage disequilibrium (LD) and recombination fraction can be used to infer the pattern of genetic variation and evolutionary process in humans and other systems. We described a computational framework to construct a linkage–LD map from commonly used biallelic, single-nucleotide polymorphism (SNP) markers for outcrossing plants by which the decline of LD is visualized with genetic distance. The framework was derived from an open-pollinated (OP) design composed of plants randomly sampled from a natural population and seeds from each sampled plant, enabling simultaneous estimation of the LD in the natural population and recombination fraction due to allelic co-segregation during meiosis. We modified the framework to infer evolutionary pasts of natural populations using those marker types that are segregating in a dominant manner, given their role in creating and maintaining population genetic diversity. A sophisticated two-level EM algorithm was implemented to estimate and retrieve the missing information of segregation characterized by dominant-segregating markers such as single methylation polymorphisms. The model was applied to study the relationship between linkage and LD for a non-model outcrossing species, a gymnosperm species, Torreya grandis, naturally distributed in mountains of the southeastern China. The linkage–LD map constructed from various types of molecular markers opens a powerful gateway for studying the history of plant evolution.

A unifying experimental design for dissecting tree genomes

Linkage mapping and association mapping are adopted as an approach of choice for dissecting complex traits, but each shows a limitation when used alone. We propose an open-pollinated (OP) family design to integrate these two approaches into an organizing framework. The design unifies the strengths of population and quantitative genetic studies for evolutionary inference and high-resolution gene mapping. It particularly suits genome dissection of forest trees given their extant populations that are mostly undomesticated.

Association and Validation of Yield-Favored Alleles in Chinese Cultivars of Common Wheat (Triticumaestivum L.)

Common wheat is one of the most important crops in China, which is the largest producer in the world. A set of 230 cultivars was used to identify yield-related loci by association mapping. This set was tested for seven yield-related traits, viz. plant height (PH), spike length (SL), spikelet number per spike (SNPS), kernel number per spike (KNPS), thousand-kernel weight (TKW), kernel weight per spike (KWPS), and sterile spikelet number (SSN) per plant in four environments. A total of 106 simple sequence repeat (SSR) markers distributed on all 21 chromosomes were used to screen the set. Twenty-one and 19 of them were associated with KNPS and TKW, respectively. Association mapping detected 73 significant associations across 50 SSRs, and the phenotypic variation explained (R²) by the associations ranged from 1.54 to 23.93%. The associated loci were distributed on all chromosomes except 4A, 7A, and 7D. Significant and potentially new alleles were present on 8 chromosomes, namely1A, 1D, 2A, 2D, 3D, 4B, 5B, and 6B. Further analysis showed that genetic effects of associated loci were greatly influenced by association panels, and the R² of crucial loci were lower in modern cultivars than in the mini core collection, probably caused by strong selection in wheat breeding. In order to confirm the results of association analysis, yield-related favorable alleles Xgwm135-1A₁₃₈, Xgwm337-1D₁₈₆, Xgwm102-2D₁₄₄, and Xgwm132-6B₁₂₈ were evaluated in a double haploid (DH) population derived from Hanxuan10 xLumai14.These favorable alleles that were validated in various populations might be valuable in breeding for high-yield.

Mapping complex traits as a dynamic system

Despite increasing emphasis on the genetic study of quantitative traits, we are still far from being able to chart a clear picture of their genetic architecture, given an inherent complexity involved in trait formation. A competing theory for studying such complex traits has emerged by viewing their phenotypic formation as a "system" in which a high-dimensional group of interconnected components act and interact across different levels of biological organization from molecules through cells to whole organisms. This system is initiated by a machinery of DNA sequences that regulate a cascade of biochemical pathways to synthesize endophenotypes and further assemble these endophenotypes toward the end-point phenotype in virtue of various developmental changes. This review focuses on a conceptual framework for genetic mapping of complex traits by which to delineate the underlying components, interactions and mechanisms that govern the system according to biological principles and understand how these components function synergistically under the control of quantitative trait loci (QTLs) to comprise a unified whole. This framework is built by a system of differential equations that quantifies how alterations of different components lead to the global change of trait development and function, and provides a quantitative and testable platform for assessing the multiscale interplay between QTLs and development. The method will enable geneticists to shed light on the genetic complexity of any biological system and predict, alter or engineer its physiological and pathological states.

Bayesian model selection for multiple QTLs mapping combining linkage disequilibrium and linkage

Linkage disequilibrium (LD) mapping is able to localize quantitative trait loci (QTL) within a rather small region (e.g. 2 cM), which is much narrower than linkage analysis (LA, usually 20 cM). The multilocus LD method utilizes haplotype information around putative mutation and takes historical recombination events into account, and thus provides a powerful method for further fine mapping. However, sometimes there are more than one QTLs in the region being studied. In this study, the Bayesian model selection implemented via the Markov chain Monte Carlo (MCMC) method is developed for fine mapping of multiple QTLs using haplotype information in a small region. The method combines LD as well as linkage information. A series of simulation experiments were conducted to investigate the behavior of the method. The results showed that this new multiple QTLs method was more efficient in separating closely linked QTLs than single-marker association studies.

A combined linkage and regional association mapping validation and fine mapping of two major pleiotropic QTLs for seed weight and silique length in rapeseed (Brassica napus L.)

BACKGROUND

Seed weight (SW) and silique length (SL) are important determinants of the yield potential in rapeseed (Brassica napus L.). However, the genetic basis of both traits is poorly understood. The main objectives of this study were to dissect the genetic basis of SW and SL in rapeseed through the preliminary mapping of quantitative trait locus (QTL) by linkage analysis and fine mapping of the target major QTL by regional association analysis.

RESULTS

Preliminary linkage mapping identified thirteen and nine consensus QTLs for SW and SL, respectively. These QTLs explained 0.7-67.1% and 2.1-54.4% of the phenotypic variance for SW and SL, respectively. Of these QTLs, three pairs of SW and SL QTLs were co-localized and integrated into three unique QTLs. In addition, the significance level and genetic effect of the three co-localized QTLs for both SW and SL showed great variation before and after the conditional analysis. Moreover, the allelic effects of the three QTLs for SW were highly consistent with those for SL. Two of the three co-localized QTLs, uq.A09-1 (mean R(2) = 20.1% and 19.0% for SW and SL, respectively) and uq.A09-3 (mean R(2) = 13.5% and 13.2% for SW and SL, respectively), were detected in all four environments and showed the opposite additive-effect direction. These QTLs were validated and fine mapped (their confidence intervals were narrowed down from 5.3 cM to 1 cM for uq.A09-1 and 13.2 cM to 2.5 cM for uq.A09-3) by regional association analysis with a panel of 576 inbred lines, which has a relatively rapid linkage disequilibrium decay (0.3 Mb) in the target QTL region.

CONCLUSIONS

A few QTLs with major effects and several QTLs with moderate effects might contribute to the natural variation of SW and SL in rapeseed. The meta-, conditional and allelic effect analyses suggested that pleiotropy, rather than tight linkage, was the genetic basis of the three pairs of co-localized of SW and SL QTLs. Regional association analysis was an effective and highly efficient strategy for the direct fine mapping of target major QTL identified by preliminary linkage mapping.

Genome-wide two-marker linkage disequilibrium mapping of quantitative trait loci

BACKGROUND

In a natural population, the alleles of multiple tightly linked loci on the same chromosome co-segregate and are passed non-randomly from generation to generation. Capitalizing on this phenomenon, a group of mapping methods, commonly referred to as the linkage disequilibrium-based mapping (LD mapping), have been developed recently for detecting genetic associations. However, most current LD mapping methods mainly employed single-marker analysis, overlooking the rich information contained within adjacent linked loci.

RESULTS

We extend the single-marker LD mapping to include two linked loci and explicitly incorporate their LD information into genetic mapping models (tmLD). We establish the theoretical foundations for the tmLD mapping method and also provide a thorough examination of its statistical properties. Our simulation studies demonstrate that the tmLD mapping method significantly improves the detection power of association compared to the single-marker based and also haplotype based mapping methods. The practical usage and properties of the tmLD mapping method were further elucidated through the analysis of a large-scale dental caries GWAS data set. It shows that the tmLD mapping method can identify significant SNPs that are missed by the traditional single-marker association analysis and haplotype based mapping method. An R package for our proposed method has been developed and is freely available.

CONCLUSIONS

The proposed tmLD mapping method is more powerful than single marker mapping generally used in GWAS data analysis. We recommend the usage of this improved method over the traditional single marker association analysis.

Genetic diversity and population structure in the US Upland cotton (Gossypium hirsutum L.)

Genetic diversity and population structure in the US Upland cotton was established and core sets of allelic richness were identified for developing association mapping populations in cotton. Elite plant breeding programs could likely benefit from the unexploited standing genetic variation of obsolete cultivars without the yield drag typically associated with wild accessions. A set of 381 accessions comprising 378 Upland (Gossypium hirsutum L.) and 3 G. barbadense L. accessions of the United States cotton belt were genotyped using 120 genome-wide SSR markers to establish the genetic diversity and population structure in tetraploid cotton. These accessions represent more than 100 years of Upland cotton breeding in the United States. Genetic diversity analysis identified a total of 546 alleles across 141 marker loci. Twenty-two percent of the alleles in Upland accessions were unique, specific to a single accession. Population structure analysis revealed extensive admixture and identified five subgroups corresponding to Southeastern, Midsouth, Southwest, and Western zones of cotton growing areas in the United States, with the three accessions of G. barbadense forming a separate cluster. Phylogenetic analysis supported the subgroups identified by STRUCTURE. Average genetic distance between G. hirsutum accessions was 0.195 indicating low levels of genetic diversity in Upland cotton germplasm pool. The results from both population structure and phylogenetic analysis were in agreement with pedigree information, although there were a few exceptions. Further, core sets of different sizes representing different levels of allelic richness in Upland cotton were identified. Establishment of genetic diversity, population structure, and identification of core sets from this study could be useful for genetic and genomic analysis and systematic utilization of the standing genetic variation in Upland cotton.

Statistical analysis of genomic data

In this chapter we describe methods for statistical analysis of GWAS data with the goal of quantifying evidence for genomic effects associated with trait variation, while avoiding spurious associations due to evidence not being well quantified or due to population structure.Single marker analysis and imputation are discussed in Sect. 1, and a Bayesian multi-locus analysis using the BayesQTLBIC R package (1, 2) is described in Sect. 2. The multi-locus analysis, applied in a genomic window, enables local inference of the QTL genetic architecture and is an alternative to imputation. Multi-locus analysis with BayesQTLBIC, including calculation of posterior probabilities for alternative models, posterior probabilities for number of QTL, marginal probabilities for markers, and Bayes factors for individual chromosomes, is demonstrated for simulated QTL data. Methods for correcting the population structure and the possible effects of population structure on power are discussed in Sect. 3. Section 4 considers analysis combining information from linkage and linkage disequilibrium when sampling from a pedigree. Section 5 considers combining information from two different studies-showing that data from an existing QTL mapping family can be profitably used in combination with an association study-prior odds are higher for candidate genes mapping into a QTL region in the QTL mapping family, and, optionally, the number of markers genotyped in an association study can be reduced. Examples using R and the R packages BayesQTLBIC, ncdf are given.

Systems mapping of HIV-1 infection

Mathematical models of viral dynamics in vivo provide incredible insights into the mechanisms for the nonlinear interaction between virus and host cell populations, the dynamics of viral drug resistance, and the way to eliminate virus infection from individual patients by drug treatment. The integration of these mathematical models with high-throughput genetic and genomic data within a statistical framework will raise a hope for effective treatment of infections with HIV virus through developing potent antiviral drugs based on individual patients’ genetic makeup. In this opinion article, we will show a conceptual model for mapping and dictating a comprehensive picture of genetic control mechanisms for viral dynamics through incorporating a group of differential equations that quantify the emergent properties of a system.

Model and algorithm for linkage disequilibrium analysis in a non-equilibrium population

The multilocus analysis of polymorphisms has emerged as a vital ingredient of population genetics and evolutionary biology. A fundamental assumption used for existing multilocus analysis approaches is Hardy-Weinberg equilibrium at which maternally- and paternally-derived gametes unite randomly during fertilization. Given the fact that natural populations are rarely panmictic, these approaches will have a significant limitation for practical use. We present a robust model for multilocus linkage disequilibrium analysis which does not rely on the assumption of random mating. This new disequilibrium model capitalizes on Weir's definition of zygotic disequilibria and is based on an open-pollinated design in which multiple maternal individuals and their half-sib families are sampled from a natural population. This design captures two levels of associations: one is at the upper level that describes the pattern of cosegregation between different loci in the parental population and the other is at the lower level that specifies the extent of co-transmission of non-alleles at different loci from parents to their offspring. An MCMC method was implemented to estimate genetic parameters that define these associations. Simulation studies were used to validate the statistical behavior of the new model.

Mapping QTL for agronomic traits in breeding populations

Detection of quantitative trait loci (QTL) in breeding populations offers the advantage that these QTL are of direct relevance for the improvement of crops via knowledge-based breeding. As phenotypic data are routinely generated in breeding programs and the costs for genotyping are constantly decreasing, it is tempting to exploit this information to unravel the genetic architecture underlying important agronomic traits in crops. This review characterizes the germplasm from breeding populations available for QTL detection, provides a classification of the different QTL mapping approaches that are available, and highlights important considerations concerning study design and biometrical models suitable for QTL analysis.

Mapping QTL for agronomic traits in breeding populations

Detection of quantitative trait loci (QTL) in breeding populations offers the advantage that these QTL are of direct relevance for the improvement of crops via knowledge-based breeding. As phenotypic data are routinely generated in breeding programs and the costs for genotyping are constantly decreasing, it is tempting to exploit this information to unravel the genetic architecture underlying important agronomic traits in crops. This review characterizes the germplasm from breeding populations available for QTL detection, provides a classification of the different QTL mapping approaches that are available, and highlights important considerations concerning study design and biometrical models suitable for QTL analysis.

Inheritance of long staple fiber quality traits of Gossypium barbadense in G. hirsutum background using CSILs

Gossypium hirsutum is a high yield cotton species that exhibits only moderate performance in fiber qualities. A promising but challenging approach to improving its phenotypes is interspecific introgression, the transfer of valuable traits or genes from the germplasm of another species such as G. barbadense, an important cultivated extra long staple cotton species. One set of chromosome segment introgression lines (CSILs) was developed, where TM-1, the genetic standard in G. hirsutum, was used as the recipient parent and the long staple cotton G. barbadense Hai7124 was used as the donor parent by molecular marker-assisted selection (MAS) in BC(5)S(1–4) and BC(4)S(1–3) generations. After four rounds of MAS, the CSIL population was comprised of 174 lines containing 298 introgressed segments, of which 86 (49.4%) lines had single introgressed segments. The total introgressed segment length covered 2,948.7 cM with an average length of 16.7 cM and represented 83.3% of tetraploid cotton genome. The CSILs were highly varied in major fiber qualities. By integrated analysis of data collected in four environments, a total of 43 additive quantitative trait loci (QTL) and six epistatic QTL associated with fiber qualities were detected by QTL IciMapping 3.0 and multi-QTL joint analysis. Six stable QTL were detected in various environments. The CSILs developed and the analyses presented here will enhance the understanding of the genetics of fiber qualities in long staple G. barbadense and facilitate further molecular breeding to improve fiber quality in Upland cotton.

Joint linkage-linkage disequilibrium mapping is a powerful approach to detecting quantitative trait loci underlying drought tolerance in maize

This paper describes two joint linkage-linkage disequilibrium (LD) mapping approaches: parallel mapping (independent linkage and LD analysis) and integrated mapping (datasets analyzed in combination). These approaches were achieved using 2,052 single nucleotide polymorphism (SNP) markers, including 659 SNPs developed from drought-response candidate genes, screened across three recombinant inbred line (RIL) populations and 305 diverse inbred lines, with anthesis-silking interval (ASI), an important trait for maize drought tolerance, as the target trait. Mapping efficiency was improved significantly due to increased population size and allele diversity and balanced allele frequencies. Integrated mapping identified 18 additional quantitative trait loci (QTL) not detected by parallel mapping. The use of haplotypes improved mapping efficiency, with the sum of phenotypic variation explained (PVE) increasing from 5.4% to 23.3% for single SNP-based analysis. Integrated mapping with haplotype further improved the mapping efficiency, and the most significant QTL had a PVE of up to 34.7%. Normal allele frequencies for 113 of 277 (40.8%) SNPs with minor allele frequency (<5%) in 305 lines were recovered in three RIL populations, three of which were significantly associated with ASI. The candidate genes identified by two significant haplotype loci included one for a SET domain protein involved in the control of flowering time and the other encoding aldo/keto reductase associated with detoxification pathways that contribute to cellular damage due to environmental stress. Joint linkage-LD mapping is a powerful approach for detecting QTL underlying complex traits, including drought tolerance.

Sex-specific population structure, natural selection, and linkage disequilibrium in a wild bird population as revealed by genome-wide microsatellite analyses

Background

Sexual dimorphism in ecologically important traits is widespread, yet the differences in the genomic architecture between the two sexes are largely unexplored. We employed a genome-wide multilocus approach to examine the sexual differences in population subdivision, natural selection and linkage disequilibrium (LD) in a wild Siberian jay (Perisoreus infaustus) population, using genotypes at a total of 107 autosomal and Z-chromosomal microsatellites.

Results

Mean observed heterozygosity was significantly higher in females (H_O = 0.567) than in males (H_O = 0.532), and autosomal markers (H_O = 0.561) were more variable than Z-chromosomal markers (H_O = 0.512). Genetic differentiation (F_ST = 0.002, P < 0.05) between the two sexes was low but significant and males were on average significantly more genetically related to each other than females. Genomescan analyses revealed that 3 out of 101 (3%) autosomal loci were under directional selection, while 4 out of 6 (67%) Z-chromosomal markers were indicated to be under balancing selection. This suggests a significantly greater but contrasting selection force on the Z-chromosome in comparison to autosomes, which is consistent with an overall significantly (P < 0.05) lower F_STvalue for Z-chromosomal (-0.014, 95% CI: -0.025 - -0.011) than for the autosomal loci (0.003, 95% CI: 0.001 - 0.004). Analysis of syntenic marker pairs revealed high levels of LD in both sexes but significantly (P < 0.05) lower levels of LD in the females both on autosomes and Z-chromosome, probably due to the higher rate of dispersal and the higher recombination rates on autosomes, as well as the pseudoautosomal markers. In both sexes LD decayed rapidly with genetic distance in a similar fashion on autosomes, while a more rapid decay of LD in Z-chromosome was detected in females than in males.

Conclusion

We conclude that there are many clear differences in genomic architecture between the sexes studied here which can be at least partly understood in the light of higher dispersal rate of females as compared to males and the unusual structure of the Z-chromosome of the species.

Fine mapping quantitative trait loci under selective phenotyping strategies based on linkage and linkage disequilibrium criteria

In fine mapping of a large-scale experimental population where collection of phenotypes are very expensive, difficult to record or time-demanding, selective phenotyping could be used to phenotype the most informative individuals. Linkage analyses based sampling criteria (LAC) and linkage disequilibrium-based sampling criteria (LDC) for selecting individuals to phenotype are compared to random phenotyping in a quantitative trait loci (QTL) verification experiment using stochastic simulation. Several strategies based on LAC and LDC for selecting the most informative 30%, 40% or 50% of individuals for phenotyping to extract maximum power and precision in a QTL fine mapping experiment were developed and assessed. Linkage analyses for the mapping was performed for individuals sampled on LAC within families and combined linkage disequilibrium and linkage analyses was performed for individuals sampled across the whole population based on LDC. The results showed that selecting individuals with similar haplotypes to the paternal haplotypes (minimum recombination criterion) using LAC compared to random phenotyping gave at least the same power to detect a QTL but decreased the accuracy of the QTL position. However, in order to estimate unbiased QTL parameters based on LAC in a large half-sib family, prior information on QTL position was required. The LDC improved the accuracy to estimate the QTL position but not significantly compared to random phenotyping with the same sample size. When applying LDC (all phenotyping levels), the estimated QTL effect were closer to the true value in comparison to LAC. The results showed that the LDC were better than the LAC to select individuals for phenotyping and contributed to detection of the QTL.

Extensive linkage disequilibrium in a wild bird population

Knowledge about the extent and patterns of linkage disequilibrium (LD) can provide important insights into demographic processes and strategies to identify the genetic basis of complex phenotypes in wild populations. However, data on the extent and patterns of LD from non-model vertebrate species from the wild are still scarce. We conducted so far the most extensive and detailed examination of LD in a pedigreed wild bird population using genotypes from 97 autosomal and 6 gonosomal microsatellites and a recently established linkage map of Siberian jays (Perisoreus infaustus). Analysis of syntenic marker pairs showed high levels of LD that extended over tens of centimorgans or several megabases and generally decayed as an increasing function of intermarker distance. In addition, significant LD was also very common between nonsyntenic markers. Patterns of LD varied across different linkage groups possibly because of the differences in chromosomal structure (macro-, micro-, and Z-chromosome). In particular, the level of LD was significantly lower on the Z-chromosome than on the autosomes at comparable genetic distances. In general, the high levels and extent of LD in this population are likely owing to its relatively small size, significant intrapopulation genetic structure, and occurrence of inbreeding. Whatever the cause, the long-range LD between syntenic loci suggests that LD mapping of phenotypic traits in this population using low-density markers maps is feasible. However, the frequent occurrence of LD between nonsyntenic markers suggests that the combined use of linkage and LD methods is needed to reduce the likelihood of false-positive associations between marker loci and traits of ecological and evolutionary interest.

Association mapping: critical considerations shift from genotyping to experimental design

The goal of many plant scientists' research is to explain natural phenotypic variation in terms of simple changes in DNA sequence. Traditionally, linkage mapping has been the most commonly employed method to reach this goal: experimental crosses are made to generate a family with known relatedness, and attempts are made to identify cosegregation of genetic markers and phenotypes within this family. In vertebrate systems, association mapping (also known as linkage disequilibrium mapping) is increasingly being adopted as the mapping method of choice. Association mapping involves searching for genotype-phenotype correlations in unrelated individuals and often is more rapid and cost-effective than traditional linkage mapping. We emphasize here that linkage and association mapping are complementary approaches and are more similar than is often assumed. Unlike in vertebrates, where controlled crosses can be expensive or impossible (e.g., in humans), the plant scientific community can exploit the advantages of both controlled crosses and association mapping to increase statistical power and mapping resolution. While the time and money required for the collection of genotype data were critical considerations in the past, the increasing availability of inexpensive DNA sequencing and genotyping methods should prompt researchers to shift their attention to experimental design. This review provides thoughts on finding the optimal experimental mix of association mapping using unrelated individuals and controlled crosses to identify the genes underlying phenotypic variation.

Multilocus genomics of outcrossing plant populations

The structure and organization of natural plant populations can be understood by estimating the genetic parameters related to mating behavior, recombination frequency, and gene associations with DNA-based markers typed throughout the genome. We developed a statistical and computational model for estimating and testing these parameters from multilocus data collected in a natural population. This model, constructed by a maximum likelihood approach and implemented within the EM algorithm, is shown to be robust for simultaneously estimating the outcrossing rate, recombination frequencies and linkage disequilibria. The algorithm built with three or more markers allows the characterization of crossover interference in meiosis and high-order disequilibria among different genes, thus providing a powerful tool for illustrating a detailed picture of genetic diversity and organization in natural populations. Computer simulations demonstrate the statistical properties of the proposed model. This multilocus model will be useful for studying the pattern and amount of genetic variation within and among populations to further infer the evolutionary history of a plant species.

An algorithmic model for constructing a linkage and linkage disequilibrium map in outcrossing plant populations

A linkage-linkage disequilibrium map that describes the pattern and extent of linkage dis-equilibrium (LD) decay with genomic distance has now emerged as a viable tool to unravel the genetic structure of population differentiation and fine-map genes for complex traits. The prerequisite for constructing such a map is the simultaneous estimation of the linkage and LD between different loci. Here, we develop a computational algorithm for simultaneously estimating the recombination fraction and LD in a natural outcrossing population with multilocus marker data, which are often estimated separately in most molecular genetic studies. The algorithm is founded on a commonly used progeny test with open-pollinated offspring sampled from a natural population. The information about LD is reflected in the co-segregation of alleles at different loci among parents in the population. Open mating of parents will reveal the genetic linkage of alleles during meiosis. The algorithm was constructed within the polynomial-based mixture framework and implemented with the Expectation-Maximization (EM) algorithm. The by-product of the derivation of this algorithm is the estimation of outcrossing rate, a parameter useful to explore the genetic diversity of the population. We performed computer simulation to investigate the influences of different sampling strategies and different values of parameters on parameter estimation. By providing a number of testable hypotheses about population genetic parameters, this algorithmic model will open a broad gateway to understand the genetic structure and dynamics of an outcrossing population under natural selection.

Genetic design and statistical power of nested association mapping in maize

We investigated the genetic and statistical properties of the nested association mapping (NAM) design currently being implemented in maize (26 diverse founders and 5000 distinct immortal genotypes) to dissect the genetic basis of complex quantitative traits. The NAM design simultaneously exploits the advantages of both linkage analysis and association mapping. We demonstrated the power of NAM for high-power cost-effective genome scans through computer simulations based on empirical marker data and simulated traits with different complexities. With common-parent-specific (CPS) markers genotyped for the founders and the progenies, the inheritance of chromosome segments nested within two adjacent CPS markers was inferred through linkage. Genotyping the founders with additional high-density markers enabled the projection of genetic information, capturing linkage disequilibrium information, from founders to progenies. With 5000 genotypes, 30-79% of the simulated quantitative trait loci (QTL) were precisely identified. By integrating genetic design, natural diversity, and genomics technologies, this new complex trait dissection strategy should greatly facilitate endeavors to link molecular variation with phenotypic variation for various complex traits.

Genome-enabled hitchhiking mapping identifies QTLs for stress resistance in natural Drosophila

Identification of genes underlying complex traits is an important problem. Quantitative trait loci (QTL) are mapped using marker-trait co-segregation in large panels of recombinant genotypes. Most frequently, recombinant inbred lines derived from two isogenic parents are used. Segregation patterns are also studied in pedigrees from multiple families. Great advances have been made through creative use of these techniques, but narrow sampling and inadequate power represent strong limitations. Here, we propose an approach combining the strengths of both techniques. We established a mapping population from a sample of natural genotypes, and applied artificial selection for a complex character. Selection changed the frequencies of alleles in QTLs contributing to the selection response. We infer QTLs with dense genotyping microarrays by identifying blocks of linked markers undergoing selective changes in allele frequency. We demonstrated this approach with an experimental population composed from 20 isogenic strains. Selection for starvation survival was executed in three replicated populations with three control non-selected populations. Three individuals per population were genotyped using Affymetrix GeneChips. Two regions of the genome, one each on the left arms of the second and third chromosomes, showed significant divergence between control and selected populations. For the former region, we inferred allele frequencies in selected and control populations by pyrosequencing. We conclude that the allele frequency difference, averaging approximately 40% between selected and control lines, contributed to selection response. Our approach can contribute to the fine scale decomposition of the genetics of direct and indirect selection responses, and genotype by environment interactions.

Functional mapping - how to map and study the genetic architecture of dynamic complex traits

The development of any organism is a complex dynamic process that is controlled by a network of genes as well as by environmental factors. Traditional mapping approaches for analysing phenotypic data measured at a single time point are too simple to reveal the genetic control of developmental processes. A general statistical mapping framework, called functional mapping, has been proposed to characterize, in a single step, the quantitative trait loci (QTLs) or nucleotides (QTNs) that underlie a complex dynamic trait. Functional mapping estimates mathematical parameters that describe the developmental mechanisms of trait formation and expression for each QTL or QTN. The approach provides a useful quantitative and testable framework for assessing the interplay between gene actions or interactions and developmental changes.

Bayesian analyses of admixture in wild and domestic cats (Felis silvestris) using linked microsatellite loci

Methods recently developed to infer population structure and admixture mostly use individual genotypes described by unlinked neutral markers. However, Hardy-Weinberg and linkage disequilibria among independent markers decline rapidly with admixture time, and the admixture signals could be lost in a few generations. In this study, we aimed to describe genetic admixture in 182 European wild and domestic cats (Felis silvestris), which hybridize sporadically in Italy and extensively in Hungary. Cats were genotyped at 27 microsatellites, including 21 linked loci mapping on five distinct feline linkage groups. Genotypes were analysed with structure 2.1, a Bayesian procedure designed to model admixture linkage disequilibrium, which promises to assess efficiently older admixture events using tightly linked markers. Results showed that domestic and wild cats sampled in Italy were split into two distinct clusters with average proportions of membership Q > 0.90, congruent with prior morphological identifications. In contrast, free-living cats sampled in Hungary were assigned partly to the domestic and the wild cat clusters, with Q < 0.50. Admixture analyses of individual genotypes identified, respectively, 5/61 (8%), and 16-20/65 (25-31%) hybrids among the Italian wildcats and Hungarian free-living cats. Similar results were obtained in the past using unlinked loci, although the new linked markers identified additional admixed wildcats in Italy. Linkage analyses confirm that hybridization is limited in Italian, but widespread in Hungarian wildcats, a population that is threatened by cross-breeding with free-ranging domestic cats. The total panel of 27 loci performed better than the linked loci alone in the identification of domestic and known hybrid cats, suggesting that a large number of linked plus unlinked markers can improve the results of admixture analyses. Inferred recombination events led to identify the population of origin of chromosomal segments, suggesting that admixture mapping experiments can be designed also in wild populations.

Linkage disequilibrium and association studies in higher plants: present status and future prospects

During the last two decades, DNA-based molecular markers have been extensively utilized for a variety of studies in both plant and animal systems. One of the major uses of these markers is the construction of genome-wide molecular maps and the genetic analysis of simple and complex traits. However, these studies are generally based on linkage analysis in mapping populations, thus placing serious limitations in using molecular markers for genetic analysis in a variety of plant systems. Therefore, alternative approaches have been suggested, and one of these approaches makes use of linkage disequilibrium (LD)-based association analysis. Although this approach of association analysis has already been used for studies on genetics of complex traits (including different diseases) in humans, its use in plants has just started. In the present review, we first define and distinguish between LD and association mapping, and then briefly describe various measures of LD and the two methods of its depiction. We then give a list of different factors that affect LD without discussing them, and also discuss the current issues of LD research in plants. Later, we also describe the various uses of LD in plant genomics research and summarize the present status of LD research in different plant genomes. In the end, we discuss briefly the future prospects of LD research in plants, and give a list of softwares that are useful in LD research, which is available as electronic supplementary material (ESM).

Sex-linked Markers Facilitate Genetic Parentage Analyses in Knobbed Whelk Broods

To explore the potential of sex-linked polymorphisms for genetic parentage analyses in natural populations, we have employed a recently discovered "X-linked" microsatellite marker (in conjunction with polymorphic autosomal loci) to deduce biological paternity and maternity for large numbers of encapsulated embryos within individual broods of the knobbed whelk (Busycon carica). Empirical findings illustrate how such sex-linked genetic tags can in special instances find at least three novel utilities in genetic dissections of large-clutch species: clarification of paternity assignments that had remained ambiguous from di-locus autosomal data alone; elucidation of linkage relationships among pairs of autosomal loci; and illumination of maternity (and thereby paternity also) in broods for which neither biological parent was known from independent evidence.

Simultaneous detection of linkage disequilibrium and genetic differentiation of subdivided populations

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

Hybrid zones as a tool for identifying adaptive genetic variation in outbreeding forest trees: lessons from wild annual sunflowers (Helianthus spp.)

The identification and study of adaptively important genes in forest trees represents a formidable challenge because of their long generation spans. In annual or perennial herbs, formal genetic studies can be employed to identify the quantitative trait loci (QTLs) and/or candidate genes that underlie important traits, and the segregating populations can be transplanted into natural populations to measure the strength and direction of selection. However, the application of these methods to forest trees is difficult, because the creation of appropriate genetic material is extremely time-consuming in long-lived, woody plants, and lifetime fitness estimates are difficult or impossible to obtain. Although QTL mapping should in principle be feasible in wild intraspecific populations (as an alternative to artificial crosses), this approach is less likely to be successful in trees because LD (linkage disequilibrium) will decay quickly in large outbreeding plant populations. Within the present paper, we discuss a modified approach based on natural hybrid zones. We describe the use of wild annual sunflowers (Helianthus spp.) as a model for exploring the hybrid zone approach. Transplanted experimental hybrids allowed us to assess the adaptive value of individual chromosomal blocks in nature, and data on natural Helianthus hybrids suggest that similar approaches are possible in natural hybrid zones. Our results allowed us to test the role of hybridization in the origin of ecological divergence in wild sunflowers. In addition, they have practical implications for identifying adaptively important genes or QTLs in trees. This is exemplified by three temperate forest taxa, Populus (poplars, aspens, cottonwoods), Fraxinus (ash), and Quercus (oak). All three are diploid and important genomic tools are under development. Moreover, all three offer extensive hybrid zones whose likely age can be inferred from fossil data. Age data enables estimates of the size and frequency of chromosomal blocks in hybrids, thereby providing guidance in designing marker-based experiments. We predict that natural hybrid zones will be valuable tools for identifying the QTLs and/or candidate genes responsible for adaptive traits in forest trees.

The extent and distribution of linkage disequilibrium in a multi-hierarchic outbred canine pedigree

A canine integrated linkage-radiation map has been recently constructed by using microsatellite markers. This map, with a good coverage of the canine genome, allows for a genome-wide search for the extent and distribution of linkage disequilibrium derived from linkage and evolutionary forces. In this study, we genotyped an outbred pedigree between Labrador retriever and Greyhound breeds with a set of microsatellite markers (240) from the canine linkage map. Linkage disequilibrium was measured between all syntenic and nonsyntenic marker pairs. Analysis of syntenic pairs revealed a significant correlation (-0.229, P < 0.001) between linkage disequilibrium and genetic distance (log transformed). Significant linkage disequilibria were observed more frequently between syntenic pairs spaced <40 cM than those paced >40 cM. There is a clear trend for linkage disequilibrium to decline with marker distance. From our results, a genome-wide screen with markers at low to moderate density (1-2 per 10 cM) should take full advantage of linkage disequilibrium for quantitative trait locus mapping in dogs. This study supports the appropriateness of linkage disequilibrium analysis to detect and map quantitative trait loci underlying complex traits in dogs.

Genetic variability of the marine mussel Mytilus galloprovincialis assessed using two-dimensional electrophoresis

Two-dimensional electrophoresis (2-DE) has been used to measure the degree of genetic variability of the marine mussel Mytilus galloprovincialis. Genetic polymorphisms were detected in 33 of a total of 86 polypeptides scored among the most abundant proteins from foot samples in 38 individuals. Estimates of average heterozygosity were 0.101+/-0.018 and 0.114+/-0.021 in a natural and a cultured population, respectively, from the NW of the Iberian Peninsula. These are the highest estimates of average heterozygosity reported by 2-DE in an animal species to date. We consider that these data throw open the question of the level of genetic variability detectable by two-dimensional electrophoresis. Multilocus genotype data were used to infer haplotypic frequencies by means of the EM algorithm in order to detect linkage disequilibrium between loci coding abundant proteins. Significant associations were found in 22.7% of the 406 two-locus pairs analysed. Also, clusters of loci in which all pairwise combinations exhibit statistically significant associations were detected and physical linkage between some of these loci is postulated from the linkage disequilibrium data.

Fine mapping of complex trait genes combining pedigree and linkage disequilibrium information: a Bayesian unified framework

We present a Bayesian method that combines linkage and linkage disequilibrium (LDL) information for quantitative trait locus (QTL) mapping. This method uses jointly all marker information (haplotypes) and all available pedigree information; i.e., it is not restricted to any specific experimental design and it is not required that phases are known. Infinitesimal genetic effects or environmental noise ("fixed") effects can equally be fitted. A diallelic QTL is assumed and both additive and dominant effects can be estimated. We have implemented a combined Gibbs/Metropolis-Hastings sampling to obtain the marginal posterior distributions of the parameters of interest. We have also implemented a Bayesian variant of usual disequilibrium measures like D' and r(2) between QTL and markers. We illustrate the method with simulated data in "simple" (two-generation full-sib families) and "complex" (four-generation) pedigrees. We compared the estimates with and without using linkage disequilibrium information. In general, using LDL resulted in estimates of QTL position that were much better than linkage-only estimates when there was complete disequilibrium between the mutant QTL allele and the marker. This advantage, however, decreased when the association was only partial. In all cases, additive and dominant effects were estimated accurately either with or without disequilibrium information.

A haplotype-based algorithm for multilocus linkage disequilibrium mapping of quantitative trait loci with epistasis

For tightly linked loci, cosegregation may lead to nonrandom associations between alleles in a population. Because of its evolutionary relationship with linkage, this phenomenon is called linkage disequilibrium. Today, linkage disequilibrium-based mapping has become a major focus of recent genome research into mapping complex traits. In this article, we present a new statistical method for mapping quantitative trait loci (QTL) of additive, dominant, and epistatic effects in equilibrium natural populations. Our method is based on haplotype analysis of multilocus linkage disequilibrium and exhibits two significant advantages over current disequilibrium mapping methods. First, we have derived closed-form solutions for estimating the marker-QTL haplotype frequencies within the maximum-likelihood framework implemented by the EM algorithm. The allele frequencies of putative QTL and their linkage disequilibria with the markers are estimated by solving a system of regular equations. This procedure has significantly improved the computational efficiency and the precision of parameter estimation. Second, our method can detect marker-QTL disequilibria of different orders and QTL epistatic interactions of various kinds on the basis of a multilocus analysis. This can not only enhance the precision of parameter estimation, but also make it possible to perform whole-genome association studies. We carried out extensive simulation studies to examine the robustness and statistical performance of our method. The application of the new method was validated using a case study from humans, in which we successfully detected significant QTL affecting human body heights. Finally, we discuss the implications of our method for genome projects and its extension to a broader circumstance. The computer program for the method proposed in this article is available at the webpage http://www.ifasstat.ufl.edu/genome/~LD.

Immunological responses of swine to porcine reproductive and respiratory syndrome virus infection

The immunology of porcine reproductive and respiratory syndrome virus (PRRS) begins with an initial encounter of PRRSV with the pig. Regardless of the route of entry of PRRSV--via inhalation, intramuscular vaccination, insemination, or other routes--productive infection occurs predominately in alveolar macrophages of the lung. Thus, innate responses of the lung and the alveolar macrophage comprise the initial defense against PRRSV. The virus appears not to elicit innate interferon and cytokine responses characteristic of other strongly immunogenic viral pathogens, and its effects are consistent with induction of a weak adaptive immune response. Humoral and cell-mediated immunity is induced in due course, and results in clearance of virus from the circulation but not from lymphoid tissues, where the infection becomes persistent. Subsequent reexposure to PRRSV elicits an anamnestic response that is partially to completely protective. Within this unconventional picture of anti-PRRSV immunity lie a variety of unresolved issues, including the nature of protective immunity within individual pigs and among pigs in commercial populations, the efficacy of protective immunity against genetically different PRRSV isolates, the effects of developmental age, sex, genetics, and other host factors on the immune response to PRRSV, and the possible suppression of host immunity to other pathogens.

Finding genes influencing susceptibility to complex diseases in the post-genome era

During the last decade, hundreds of genes that harbor mutations causing simple Mendelian disorders have been identified using a combination of linkage analysis and positional cloning techniques. Traditional approaches to gene mapping have been largely unsuccessful in mapping genes influencing so-called 'complex' genetic diseases, however, because of low power and other factors. Complex genetic diseases do not display simple Mendelian patterns of inheritance, although genes do have an influence and close relatives of probands consequently have an increased risk. These disorders are thought to be due to the combined effects of variation at multiple interacting genes and the environment. Complex diseases have a significant impact on human health because of their high population incidence (unlike simple Mendelian disorders, which tend to be rare). New techniques are being developed aimed specifically at mapping genes conferring susceptibility to complex diseases. A project aimed at mapping genes influencing susceptibility to a complex disease may be undertaken in several stages: establishing a genetic basis for the disease in one or more populations; measuring the distribution of gene effects; studying statistical power using models; carrying out marker-based mapping studies using linkage or association. Quantitative genetic models can be used to estimate the heritability of a complex (polygenic) disease, as well as to predict the distribution of gene effects and to test whether one or more quantitative trait loci (QTLs) exist. Such models can be used to predict the power of different mapping approaches, but are often unrealistic and therefore provide only approximate predictions. Linkage analyses, association studies and family-based association tests are all hindered by low power and other specific problems. Association studies tend to be more powerful but can generate spurious associations due to population admixture. Alternative strategies for association mapping include the use of recent founder populations or unique isolated populations that are genetically homogeneous, and the use of unlinked markers (so-called genomic controls) to assign different regions of the genome of an admixed individual to particular source populations. Linkage disequilibrium observed in a sample of unrelated affected and normal individuals can also be used to fine-map a disease susceptibility locus in a candidate region. New Bayesian strategies make use of an annotated human genome sequence to further refine the position of a candidate disease susceptibility locus.

Simultaneous maximum likelihood estimation of linkage and linkage phases in outcrossing species

With the advent of new molecular marker technologies, it is now feasible to initiate genome projects for outcrossing plant species, which have not received much attention in genetic research, despite their great agricultural and environmental value. Because outcrossing species typically have heterogeneous genomes, data structure for molecular markers representing an entire genome is complex: some markers may have more alleles than others, some markers are codominant whereas others are dominant, and some markers are heterozygous in one parent but fixed in the other parent whereas the opposite can be true for other markers. A major difficulty in analyzing these different types of marker at the same time arises from uncertainty about parental linkage phases over markers. In this paper, we present a general maximum-likelihood-based algorithm for simultaneously estimating linkage and linkage phases for a mixed set of different marker types containing fully informative markers (segregating 1:1:1:1) and partially informative markers (or missing markers, segregating 1:2:1, 3:1, and 1:1) in a full-sib family derived from two outbred parent plants. The characterization of linkage phases is based on the posterior probability distribution of the assignment of alternative alleles at given markers to two homologous chromosomes of each parent, conditional on the observed phenotypes of the markers. Two- and multi-point analyses are performed to estimate the recombination fraction and determine the most likely linkage phase between different types of markers. A numerical example is presented to demonstrate the statistical properties of the model for characterizing the linkage phase between markers.

Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations

Linkage analysis and allelic association (also referred to as linkage disequilibrium) studies are two major approaches for mapping genes that control simple or complex traits in plants, animals, and humans. But these two approaches have limited utility when used alone, because they use only part of the information that is available for a mapping population. More recently, a new mapping strategy has been designed to integrate the advantages of linkage analysis and linkage disequilibrium analysis for genome mapping in outcrossing populations. The new strategy makes use of a random sample from a panmictic population and the open-pollinated progeny of the sample. In this article, we extend the new strategy to map quantitative trait loci (QTL), using molecular markers within the EM-implemented maximum-likelihood framework. The most significant advantage of this extension is that both linkage and linkage disequilibrium between a marker and QTL can be estimated simultaneously, thus increasing the efficiency and effectiveness of genome mapping for recalcitrant outcrossing species. Simulation studies are performed to test the statistical properties of the MLEs of genetic and genomic parameters including QTL allele frequency, QTL effects, QTL position, and the linkage disequilibrium of the QTL and a marker. The potential utility of our mapping strategy is discussed.

The genetic architecture of quantitative traits

Phenotypic variation for quantitative traits results from the segregation of alleles at multiple quantitative trait loci (QTL) with effects that are sensitive to the genetic, sexual, and external environments. Major challenges for biology in the post-genome era are to map the molecular polymorphisms responsible for variation in medically, agriculturally, and evolutionarily important complex traits; and to determine their gene frequencies and their homozygous, heterozygous, epistatic, and pleiotropic effects in multiple environments. The ease with which QTL can be mapped to genomic intervals bounded by molecular markers belies the difficulty in matching the QTL to a genetic locus. The latter requires high-resolution recombination or linkage disequilibrium mapping to nominate putative candidate genes, followed by genetic and/or functional complementation and gene expression analyses. Complete genome sequences and improved technologies for polymorphism detection will greatly advance the genetic dissection of quantitative traits in model organisms, which will open avenues for exploration of homologous QTL in related taxa.