Estimation of multilocus linkage disequilibria in diploid populations with dominant markers

Recombination disequilibrium in ideal and natural populations

Following Hardy-Weinberg disequilibrium (HWD) occurring at a single locus and linkage disequilibrium (LD) between two loci in generations, we here proposed the third genetic disequilibrium in a population: recombination disequilibrium (RD). RD is a measurement of crossover interference among multiple loci in a random mating population. In natural populations besides recombination interference, RD may also be due to selection, mutation, gene conversion, drift and/or migration. Therefore, similarly to LD, RD will also reflect the history of natural selection and mutation. In breeding populations, RD purely results from recombination interference and hence can be used to build or evaluate and correct a linkage map. Practical examples from F₂, testcross and human populations indeed demonstrate that RD is useful for measuring recombination interference between two short intervals and evaluating linkage maps. As with LD, RD will be important for studying genetic mapping, association of haplotypes with disease, plant breading and population history.

Potential of Genomic Selection in Mass Selection Breeding of an Allogamous Crop: An Empirical Study to Increase Yield of Common Buckwheat

To evaluate the potential of genomic selection (GS), a selection experiment with GS and phenotypic selection (PS) was performed in an allogamous crop, common buckwheat (Fagopyrum esculentum Moench). To indirectly select for seed yield per unit area, which cannot be measured on a single-plant basis, a selection index was constructed from seven agro-morphological traits measurable on a single plant basis. Over 3 years, we performed two GS and one PS cycles per year for improvement in the selection index. In GS, a prediction model was updated every year on the basis of genotypes of 14,598-50,000 markers and phenotypes. Plants grown from seeds derived from a series of generations of GS and PS populations were evaluated for the traits in the selection index and other yield-related traits. GS resulted in a 20.9% increase and PS in a 15.0% increase in the selection index in comparison with the initial population. Although the level of linkage disequilibrium in the breeding population was low, the target trait was improved with GS. Traits with higher weights in the selection index were improved more than those with lower weights, especially when prediction accuracy was high. No trait changed in an unintended direction in either GS or PS. The accuracy of genomic prediction models built in the first cycle decreased in the later cycles because the genetic bottleneck through the selection cycles changed linkage disequilibrium patterns in the breeding population. The present study emphasizes the importance of updating models in GS and demonstrates the potential of GS in mass selection of allogamous crop species, and provided a pilot example of successful application of GS to plant breeding.

Genetic diversity, linkage disequilibrium, and association mapping analyses of Gossypium barbadense L. germplasm

Limited polymorphism and narrow genetic base, due to genetic bottleneck through historic domestication, highlight a need for comprehensive characterization and utilization of existing genetic diversity in cotton germplasm collections. In this study, 288 worldwide Gossypium barbadense L. cotton germplasm accessions were evaluated in two diverse environments (Uzbekistan and USA). These accessions were assessed for genetic diversity, population structure, linkage disequilibrium (LD), and LD-based association mapping (AM) of fiber quality traits using 108 genome-wide simple sequence repeat (SSR) markers. Analyses revealed structured population characteristics and a high level of intra-variability (67.2%) and moderate interpopulation differentiation (32.8%). Eight percent and 4.3% of markers revealed LD in the genome of the G. barbadense at critical values of r2 ≥ 0.1 and r2 ≥ 0.2, respectively. The LD decay was on average 24.8 cM at the threshold of r2 ≥ 0.05. LD retained on average distance of 3.36 cM at the threshold of r2 ≥ 0.1. Based on the phenotypic evaluations in the two diverse environments, 100 marker loci revealed a strong association with major fiber quality traits using mixed linear model (MLM) based association mapping approach. Fourteen marker loci were found to be consistent with previously identified quantitative trait loci (QTLs), and 86 were found to be new unreported marker loci. Our results provide insights into the breeding history and genetic relationship of G. barbadense germplasm and should be helpful for the improvement of cotton cultivars using molecular breeding and omics-based technologies.

Next generation breeding

The genomic revolution of the past decade has greatly improved our understanding of the genetic make-up of living organisms. The sequencing of crop genomes has completely changed our vision and interpretation of genome organization and evolution. Re-sequencing allows the identification of an unlimited number of markers as well as the analysis of germplasm allelic diversity based on allele mining approaches. High throughput marker technologies coupled with advanced phenotyping platforms provide new opportunities for discovering marker-trait associations which can sustain genomic-assisted breeding. The availability of genome sequencing information is enabling genome editing (site-specific mutagenesis), to obtain gene sequences desired by breeders. This review illustrates how next generation sequencing-derived information can be used to tailor genomic tools for different breeders' needs to revolutionize crop improvement.

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.

Selection on outlier loci and their association with adaptive phenotypes in Littorina saxatilis contact zones

A fundamental issue in speciation research is to evaluate phenotypic variation and the genomics driving the evolution of reproductive isolation between sister taxa. Above all, hybrid zones are excellent study systems for researchers to examine the association of genetic differentiation, phenotypic variation and the strength of selection. We investigated two contact zones in the marine gastropod Littorina saxatilis and utilized landmark-based geometric morphometric analysis together with amplified fragment length polymorphism (AFLP) markers to assess phenotypic and genomic divergence between ecotypes under divergent selection. From genetic markers, we calculated the cline width, linkage disequilibrium and the average effective selection on a locus. Additionally, we conducted an association analysis linking the outlier loci and phenotypic variation between ecotypes and show that a proportion of outlier loci are associated with key adaptive phenotypic traits.

Development of SSR Markers in Hickory (Carya cathayensis Sarg.) and Their Transferability to Other Species of Carya

Hickory (Carya cathayensis Sarg.), an important nut-producing species in Southeastern China, has high economic value, but so far there has been no cultivar bred under species although it is mostly propagated by seeding and some elite individuals have been found. It has been found recently that this species has a certain rate of apomixis and poor knowledge of its genetic background has influenced development of a feasible breeding strategy. Here in this paper we first release SSR (Simple sequence repeat) markers developed in this species and their transferability to other three species of the same genus, Carya. A total of 311 pairs of SSR primers in hickory were developed based on sequenced cDNAs of a fruit development-associated cDNA library and RNA-seq data of developing female floral buds and could be used to distinguish hickory, C. hunanensis Cheng et R. H. Chang ex R. H. Chang et Lu, C. illinoensis K. Koch (pecan) and C. dabieshanensis M. C. Liu et Z. J. Li, but they were monomorphic in both hickory and C. hunanensis although multi-alleles have been identified in all the four species. There is a transferability rate of 63.02% observed between hickory and pecan and the markers can be applied to study genetic diversity of accessions in pecan. When used in C. dabieshanensis, it was revealed that C. dabieshanensis had the number of alleles per locus ranging from 2 to 4, observed heterozygosity from 0 to 0.6667 and expected heterozygosity from 0.333 to 0.8667, respectively, which supports the existence of C. dabieshanensis as a separate species different from hickory and indicates that there is potential for selection and breeding in this species.

Will genomic selection be a practical method for plant breeding?

BACKGROUND

Genomic selection or genome-wide selection (GS) has been highlighted as a new approach for marker-assisted selection (MAS) in recent years. GS is a form of MAS that selects favourable individuals based on genomic estimated breeding values. Previous studies have suggested the utility of GS, especially for capturing small-effect quantitative trait loci, but GS has not become a popular methodology in the field of plant breeding, possibly because there is insufficient information available on GS for practical use.

SCOPE

In this review, GS is discussed from a practical breeding viewpoint. Statistical approaches employed in GS are briefly described, before the recent progress in GS studies is surveyed. GS practices in plant breeding are then reviewed before future prospects are discussed.

CONCLUSIONS

Statistical concepts used in GS are discussed with genetic models and variance decomposition, heritability, breeding value and linear model. Recent progress in GS studies is reviewed with a focus on empirical studies. For the practice of GS in plant breeding, several specific points are discussed including linkage disequilibrium, feature of populations and genotyped markers and breeding scheme. Currently, GS is not perfect, but it is a potent, attractive and valuable approach for plant breeding. This method will be integrated into many practical breeding programmes in the near future with further advances and the maturing of its theory.

A genome scan and linkage disequilibrium analysis among chromosomal races of the Australian grasshopper Vandiemenella viatica

In the past decade the interest surrounding the role of recombination in speciation has been re-kindled by a new generation of chromosomal speciation models that invoke the recombination-suppression properties of some types of chromosomal rearrangement. A common prediction of recombination-suppression models is that gene exchange between diverging populations will be more restricted in regions of the genome that experience low recombination. We carried out a genome scan of three chromosomal races of the grasshopper Vandiemenella viatica (Orthoptera: Morabinae), occurring on Kangaroo Island, South Australia, using 1517 AFLP loci, with a view to elucidating the roles that selection and chromosomal variation have played in the formation of these taxa. An analysis of molecular variance demonstrated that chromosomal race accounted for a significant proportion of the genetic variance in the total dataset, which concurred with the findings of an earlier study. Sampling across one previously-identified hybrid zone, and the identification of outlier loci between parental races allowed us to establish that, in admixed populations, outlier loci which potentially pre-date the isolation of populations of races on Kangaroo Island exhibit higher levels of linkage disequilibrium with each other than putatively neutral loci. In turn this suggests that they might reside within genomic regions of low recombination, or be closely linked with each other.

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.

Evidence for evolutionary change associated with the recent range expansion of the British butterfly, Aricia agestis, in response to climate change

Poleward range expansions are widespread responses to recent climate change and are crucial for the future persistence of many species. However, evolutionary change in traits such as colonization history and habitat preference may also be necessary to track environmental change across a fragmented landscape. Understanding the likelihood and speed of such adaptive change is important in determining the rate of species extinction with ongoing climate change. We conducted an amplified fragment length polymorphism (AFLP)-based genome scan across the recently expanded UK range of the Brown Argus butterfly, Aricia agestis, and used outlier-based (DFDIST and BayeScan) and association-based (Isolation-By-Adaptation) statistical approaches to identify signatures of evolutionary change associated with range expansion and habitat use. We present evidence for (i) limited effects of range expansion on population genetic structure and (ii) strong signatures of selection at approximately 5% AFLP loci associated with both the poleward range expansion of A. agestis and differences in habitat use across long-established and recently colonized sites. Patterns of allele frequency variation at these candidate loci suggest that adaptation to new habitats at the range margin has involved selection on genetic variation in habitat use found across the long-established part of the range. Our results suggest that evolutionary change is likely to affect species' responses to climate change and that genetic variation in ecological traits across species' distributions should be maximized to facilitate range shifts across a fragmented landscape, particularly in species that show strong associations with particular habitats.

A first insight into population structure and linkage disequilibrium in the US peanut minicore collection

Knowledge of genetic diversity, population structure, and degree of linkage disequilibrium (LD) in target association mapping populations is of great importance and is a prerequisite for LD-based mapping. In the present study, 96 genotypes comprising 92 accessions of the US peanut minicore collection, a component line of the tetraploid variety Florunner, diploid progenitors A. duranensis (AA) and A. ipaënsis (BB), and synthetic amphidiploid accession TxAG-6 were investigated with 392 simple sequence repeat (SSR) marker bands amplified using 32 highly-polymorphic SSR primer pairs. Both distance- and model-based (Bayesian) cluster analysis revealed the presence of structured diversity. In general, the wild-species accessions and the synthetic amphidiploid grouped separately from most minicore accessions except for COC155, and were eliminated from most subsequent analyses. UPGMA analysis divided the population into four subgroups, two major subgroups representing subspecies fastigiata and hypogaea, a third group containing individuals from each subspecies or possibly of mixed ancestry, and a fourth group, either consisting of COC155 alone if wild species were excluded, or of COC155, the diploid species, and the synthetic amphidiploid. Model-based clustering identified four subgroups- one each for fastigiata and hypogaea subspecies, a third consisting of individuals of both subspecies or of mixed ancestry predominantly from Africa or Asia, and a fourth group, consisting of individuals predominantly of var fastigiata, peruviana, and aequatoriana accessions from South America, including COC155. Analysis of molecular variance (AMOVA) revealed statistically-significant (P < 0.0001) genetic variance of 16.87% among subgroups. A total of 4.85% of SSR marker pairs revealed significant LD (at r(2) ≥ 0.1). Of the syntenic marker pairs separated by distances < 10 cM, 11-20 cM, 21-50 cM, and > 50 cM, 19.33, 5.19, 6.25 and 5.29% of marker pairs were found in strong LD (P ≤ 0.01), in accord with LD extending to great distances in self pollinated crops. A threshold value of r(2) > 0.035 was found to distinguish mean r(2) values of linkage distance groups statistically from the mean r(2) values of unlinked markers; LD was found to extend to 10 cM over the entire minicore collection by this criterion. However, there were large differences in r(2) values among marker pairs even among tightly-linked markers. The implications of these findings with regard to the possibility of using association mapping for detection of genome-wide SSR marker-phenotype association are discussed.

Application of association mapping to understanding the genetic diversity of plant germplasm resources

Compared to the conventional linkage mapping, linkage disequilibrium (LD)-mapping, using the nonrandom associations of loci in haplotypes, is a powerful high-resolution mapping tool for complex quantitative traits. The recent advances in the development of unbiased association mapping approaches for plant population with their successful applications in dissecting a number of simple to complex traits in many crop species demonstrate a flourish of the approach as a “powerful gene tagging” tool for crops in the plant genomics era of 21st century. The goal of this review is to provide nonexpert readers of crop breeding community with (1) the basic concept, merits, and simple description of existing methodologies for an association mapping with the recent improvements for plant populations, and (2) the details of some of pioneer and recent studies on association mapping in various crop species to demonstrate the feasibility, success, problems, and future perspectives of the efforts in plants. This should be helpful for interested readers of international plant research community as a guideline for the basic understanding, choosing the appropriate methods, and its application.

Linkage disequilibrium based association mapping of fiber quality traits in G. hirsutum L. variety germplasm

Cotton is the world's leading cash crop, but it lags behind other major crops for marker-assisted breeding due to limited polymorphisms and a genetic bottleneck through historic domestication. This underlies a need for characterization, tagging, and utilization of existing natural polymorphisms in cotton germplasm collections. Here we report genetic diversity, population characteristics, the extent of linkage disequilibrium (LD), and association mapping of fiber quality traits using 202 microsatellite marker primer pairs in 335 G. hirsutum germplasm grown in two diverse environments, Uzbekistan and Mexico. At the significance threshold (r (2) >or= 0.1), a genome-wide average of LD extended up to genetic distance of 25 cM in assayed cotton variety accessions. Genome wide LD at r (2) >or= 0.2 was reduced to approximately 5-6 cM, providing evidence of the potential for association mapping of agronomically important traits in cotton. Results suggest linkage, selection, inbreeding, population stratification, and genetic drift as the potential LD-generating factors in cotton. In two environments, an average of ~20 SSR markers was associated with each main fiber quality traits using a unified mixed liner model (MLM) incorporating population structure and kinship. These MLM-derived significant associations were confirmed in general linear model and structured association test, accounting for population structure and permutation-based multiple testing. Several common markers, showing the significant associations in both Uzbekistan and Mexican environments, were determined. Between 7 and 43% of the MLM-derived significant associations were supported by a minimum Bayes factor at 'moderate to strong' and 'strong to very strong' evidence levels, suggesting their usefulness for marker-assisted breeding programs and overall effectiveness of association mapping using cotton germplasm resources.

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.

Evidence of genetic recombination in wheat yellow rust populations of a Chinese oversummering area

Wheat yellow rust (Puccinia striiformis f.sp. tritici) (PST) has been described as a strongly clonal species in both European and Australian populations, with very limited molecular diversity but rapidly evolving virulences. Contrastingly, marked genetic diversity has been reported in Chinese PST populations. To test whether such variability could originate from oversummering areas, we assessed the diversity of virulence and molecular markers (AFLP and SSR) using 412 PST isolates from the highlands of Tianshui county in Gansu province. Very marked phenotypic and genotypic diversity (38% and 89%, respectively) was found. No genetic structure dependent on the sites sampled (Fst=0.004) or altitude distribution (Fst=0.0098) was detected, indicating important gene flow at the county scale. This study also revealed genetic recombination between molecular markers and thus strongly suggests the existence of a sexual or parasexual cycle in PST in Tianshui county. The observations of higher rates of sexual spore production in genotypes originating from Tianshui are the very first elements suggestive of the existence of a sexual cycle in this species.

Molecular diversity and association mapping of fiber quality traits in exotic G. hirsutum L. germplasm

The narrow genetic base of cultivated cotton germplasm is hindering the cotton productivity worldwide. Although potential genetic diversity exists in Gossypium genus, it is largely 'underutilized' due to photoperiodism and the lack of innovative tools to overcome such challenges. The application of linkage disequilibrium (LD)-based association mapping is an alternative powerful molecular tool to dissect and exploit the natural genetic diversity conserved within cotton germplasm collections, greatly accelerating still 'lagging' cotton marker-assisted selection (MAS) programs. However, the extent of genome-wide linkage disequilibrium (LD) has not been determined in cotton. We report the extent of genome-wide LD and association mapping of fiber quality traits by using a 95 core set of microsatellite markers in a total of 285 exotic Gossypium hirsutum accessions, comprising of 208 landrace stocks and 77 photoperiodic variety accessions. We demonstrated the existence of useful genetic diversity within exotic cotton germplasm. In this germplasm set, 11-12% of SSR loci pairs revealed a significant LD. At the significance threshold (r(2)>/=0.1), a genome-wide average of LD declines within the genetic distance at <10 cM in the landrace stocks germplasm and >30 cM in variety germplasm. Genome wide LD at r(2)>/=0.2 was reduced on average to approximately 1-2 cM in the landrace stock germplasm and 6-8 cM in variety germplasm, providing evidence of the potential for association mapping of agronomically important traits in cotton. We observed significant population structure and relatedness in assayed germplasm. Consequently, the application of the mixed liner model (MLM), considering both kinship (K) and population structure (Q) detected between 6% and 13% of SSR markers associated with the main fiber quality traits in cotton. Our results highlight for the first time the feasibility and potential of association mapping, with consideration of the population structure and stratification existing in cotton germplasm resources. The number of SSR markers associated with fiber quality traits in diverse cotton germplasm, which broadly covered many historical meiotic events, should be useful to effectively exploit potentially new genetic variation by using MAS programs.

Development of 16 polymorphic simple sequence repeat markers for Lycoris longituba from expressed sequence tags

Lycoris longituba is a tulip-like ornamental plant in China. We report on the data mining of L. longituba expressed sequence tags (ESTs) to generate simple sequence repeat (SSRs) markers. Eighteen EST-SSRs were isolated and validated for 32 individuals. These markers will be valuable for studying the genetic structure and diversity of populations for L. longituba.