Modeling extent and distribution of zygotic disequilibrium: implications for a multigenerational canine pedigree

A unified DNA sequence and non-DNA sequence mapping model of complex traits

Increasing evidence shows that quantitative inheritance is based on both DNA sequence and non-DNA sequence variants. However, how to simultaneously detect these variants from a mapping study has been unexplored, hampering our effort to illustrate the detailed genetic architecture of complex traits. We address this issue by developing a unified model of quantitative trait locus (QTL) mapping based on an open-pollinated design composed of randomly sampling maternal plants from a natural population and their half-sib seeds. This design forms a two-level hierarchical platform for a joint linkage-linkage disequilibrium analysis of population structure. The EM algorithm was implemented to estimate and test DNA sequence-based effects and non-DNA sequence-based effects of QTLs. We applied this model to analyze genetic mapping data from the OP design of a gymnosperm coniferous species, Torreya grandis, identifying 25 significant DNA sequence and non-DNA sequence QTLs for seedling height and diameter growth in different years. Results from computer simulation show that the unified model has good statistical properties and is powerful for QTL detection. Our model enables the tests of how a complex trait is affected differently by DNA-based effects and non-DNA sequence-based transgenerational effects, thus allowing a more comprehensive picture of genetic architecture to be charted and quantified.

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.

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.

Genomic Scans of Zygotic Disequilibrium and Epistatic SNPs in HapMap Phase III Populations

Previous theory indicates that zygotic linkage disequilibrium (LD) is more informative than gametic or composite digenic LD in revealing natural population history. Further, the difference between the composite digenic and maximum zygotic LDs can be used to detect epistatic selection for fitness. Here we corroborate the theory by investigating genome-wide zygotic LDs in HapMap phase III human populations. Results show that non-Africa populations have much more significant zygotic LDs than do Africa populations. Africa populations (ASW, LWK, MKK, and YRI) possess more significant zygotic LDs for the double-homozygotes (D_AABB) than any other significant zygotic LDs (D_AABb, D_AaBB, and D_AaBb), while non-Africa populations generally have more significant D_AaBb’s than any other significant zygotic LDs (D_AABB, D_AABb, and D_AaBB). Average r-squares for any significant zygotic LDs increase generally in an order of populations YRI, MKK, CEU, CHB, LWK, JPT, CHD, TSI, GIH, ASW, and MEX. Average r-squares are greater for D_AABB and D_AaBb than for D_AaBB and D_AABb in each population. YRI and MKK can be separated from LWK and ASW in terms of the pattern of average r-squares. All population divergences in zygotic LDs can be interpreted with the model of Out of Africa for modern human origins. We have also detected 19735-95921 SNP pairs exhibiting strong signals of epistatic selection in different populations. Gene-gene interactions for some epistatic SNP pairs are evident from empirical findings, but many more epistatic SNP pairs await evidence. Common epistatic SNP pairs rarely exist among all populations, but exist in distinct regions (Africa, Europe, and East Asia), which helps to understand geographical genomic medicine.

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.

Evolution of zygotic linkage disequilibrium in a finite local population

One crucial feature of zygotic linkage disequilibrium (LD) analysis is its direct use of diploid genotyping data, irrespective of the type of mating system. Previous theories from an evolutionary perspective mainly focus on gametic LD, but the equivalent development for zygotic LD is not available. Here I study the evolution of zygotic LD and the covariances between gametic and zygotic LDs or between distinct zygotic LDs in a finite local population under constant immigration from a continent population. I derive the analytical theory under genetic hitchhiking effects or in a neutral process. Results indicate that zygotic LDs (diploid level) are more informative than gametic LD (haploid level) in indicating the effects of different evolutionary forces. Zygotic LDs may be greater than or comparable to gametic LD under the epistatic selection process, but smaller than gametic LD under the non epistatic selection process. The covariances between gametic and zygotic LDs are strongly affected by the mating system, linkage distance, and genetic drift effects, but weakly affected by seed and pollen flow and natural selection. The covariances between different zygotic LDs are generally robust to the effects of gene flow, selection, and linkage distance, but sensitive to the effects of genetic drift and mating system. Consistent patterns exist for the covariances between the zygotic LDs for the two-locus genotypes with one common genotype at one locus or without any common genotype at each locus. The results highlight that zygotic LDs can be applied to detecting natural population history.

An initial assessment of linkage disequilibrium (LD) in coffee trees: LD patterns in groups of Coffea canephora Pierre using microsatellite analysis

Background

A reciprocal recurrent selection program has been under way for the Coffea canephora coffee tree for approximately thirty years in the Ivory Coast. Association genetics would help to speed up this program by more rapidly selecting zones of interest in the genome. However, prior to any such studies, the linkage disequilibrium (LD) needs to be assessed between the markers on the genome. These data are essential for guiding association studies.

Results

This article describes the first results of an LD assessment in a coffee tree species. Guinean and Congolese breeding populations of C. canephora have been used for this work, with the goal of identifying ways of using these populations in association genetics. We identified changes in the LD along the genome within the different C. canephora diversity groups. In the different diversity groups studied, the LD was variable. Some diversity groups displayed disequilibria over long distances (up to 25 cM), whereas others had disequilibria not exceeding 1 cM. We also discovered a fine structure within the Guinean group.

Conclusions

Given these results, association studies can be used within the species C. canephora. The coffee recurrent selection scheme being implemented in the Ivory Coast can thus be optimized. Lastly, our results could be used to improve C. arabica because one of its parents is closely related to C. canephora.

Genome-wide analysis of zygotic linkage disequilibrium and its components in crossbred cattle

Background

Linkage disequilibrium (LD) between genes at linked or independent loci can occur at gametic and zygotic levels known asgametic LD and zygotic LD, respectively. Gametic LD is well known for its roles in fine-scale mapping of quantitative trait loci, genomic selection and evolutionary inference. The less-well studied is the zygotic LD and its components that can be also estimated directly from the unphased SNPs.

Results

This study was set up to investigate the genome-wide extent and patterns of zygotic LD and its components in a crossbred cattle population using the genomic data from the Illumina BovineSNP50 beadchip. The animal population arose from repeated crossbreeding of multiple breeds and selection for growth and cow reproduction. The study showed that similar genomic structures in gametic and zygotic LD were observed, with zygotic LD decaying faster than gametic LD over marker distance. The trigenic and quadrigenic disequilibria were generally two- to three-fold smaller than the usual digenic disequilibria (gametic or composite LD). There was less power of testing for these high-order genic disequilibria than for the digenic disequilibria. The power estimates decreased with the marker distance between markers though the decay trend is more obvious for the digenic disequilibria than for high-order disequilibria.

Conclusions

This study is the first major genome-wide survey of all non-allelic associations between pairs of SNPs in a cattle population. Such analysis allows us to assess the relative importance of gametic LD vs. all other non-allelic genic LDs regardless of whether or not the population is in HWE. The observed predominance of digenic LD (gametic or composite LD) coupled with insignificant high-order trigenic and quadrigenic disequilibria supports the current intensive focus on the use of high-density SNP markers for genome-wide association studies and genomic selection activities in the cattle population.

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.

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.

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.

Estimation of multilocus linkage disequilibria in diploid populations with dominant markers

Analysis of population structure and organization with DNA-based markers can provide important information regarding the history and evolution of a species. Linkage disequilibrium (LD) analysis based on allelic associations between different loci is emerging as a viable tool to unravel the genetic basis of population differentiation. In this article, we derive the EM algorithm to obtain the maximum-likelihood estimates of the linkage disequilibria between dominant markers, to study the patterns of genetic diversity for a diploid species. The algorithm was expanded to estimate and test linkage disequilibria of different orders among three dominant markers and can be technically extended to manipulate an arbitrary number of dominant markers. The feasibility of the proposed algorithm is validated by an example of population genetic studies of hickory trees, native to southeastern China, using dominant random amplified polymorphic DNA markers. Extensive simulation studies were performed to investigate the statistical properties of this algorithm. The precision of the estimates of linkage disequilibrium between dominant markers was compared with that between codominant markers. Results from simulation studies suggest that three-locus LD analysis displays increased power of LD detection relative to two-locus LD analysis. This algorithm is useful for studying the pattern and amount of genetic variation within and among populations.

A random model for mapping imprinted quantitative trait loci in a structured pedigree: an implication for mapping canine hip dysplasia

Genetic imprinting may have played a more notable role in shaping embryonic development of plants, animals, and humans than previously appreciated. Quantitative trait loci that are imprinted (iQTL) exert monoallelic effects, depending on the parent of origin, which is an exception to the laws of Mendelian genetics. In this article, we present a modified random effect-based mapping model to use in a genome-wide scan for the distribution of iQTL that contribute to genetic variance for a complex trait in a structured pedigree. This model, implemented with the maximum likelihood method, capitalizes on a network of relatedness for maternally and paternally derived alleles through identical-by-descent sharing, thus allowing for the discrimination of the genetic variances due to alleles derived from maternal and paternal parents. The model was employed to map iQTL responsible for canine hip dysplasia in a multihierarchical canine pedigree, founded with seven greyhounds and six Labrador retrievers. Of eight significant QTL detected, three, located on CFA1, CFA8, and CF28, were found to trigger significant parent-of-origin effects on the age of femoral capital ossification measured at the left and right hips of a canine. The detected iQTL provide important candidate regions for fine-mapping of imprinted genes and for studying their structure and function in the control of complex traits.