Doubled haploids for estimating genetic variances and a scheme for population improvement in self-pollinating crops

Summary An analysis is derived for a diallel experiment in which each cross is represented by a number of homozygous Unes developed by the doubled haploid method. Both additive and additive x additive genetic variances can be estimated with this analysis. A population-improvement scheme involving the doubled haploid or single seed descent methods is also proposed.     

Analytical results concerning linkage disequilibrium in models with genetic transformation and conjugation

Expressions are obtained for the expected levels of linkage disequilibrium under three different equilibrium neutral models that make different assumptions about how recombination takes place. A transformation model is considered in which exchange events involve only one locus at a time. Two conjugation models are considered one with a linear genome and one with a circular genome. In the conjugation models large blocks of genes can be transferred with each conjugation. Consistent with published simulation results, it is found that if the transformation rate per locus is more than twenty times the mutation rate per locus, then the levels of linkage disequilibrium are quite low. If the number of loci being sampled is greater than 10, conjugation with a circular genome can be considerably more effective than transformation in reducing linkage disequilibrium. When recombination rates are high, expected linkage disequilibrium is shown to be proportional to the inverse of the transformation rate (or conjugation rate.)     

Score tests of genetic association in the presence of linkage based on the additive genetic gamma frailty model

Nuclear families with multiple affected sibs are often collected for genetic linkage analysis of complex diseases. Once linkage evidence is established, dense markers are often typed in the linked region for genetic association analysis based on linkage disequilibrium (LD). Detection of association in the presence of linkage localizes disease genes more accurately than the methods that rely on linkage alone. However, test of association due to LD in the linked region needs to account for dependency of the allele transmissions to different sibs within a family. In this paper, we define a joint model for genetic linkage and association and derive the corresponding joint survival function of age of onset for the sibs within a sibship. The joint survival function is a function of both the inheritance vector and the genotypes at the candidate marker locus. Based on this joint survival function, we derive score tests for genetic association. The proposed methods utilize the phenotype data of all the sibs and have the advantages of family-based designs which can avoid the potential spurious association caused by population admixture. In addition, the methods can account for variable age of onset or age at censoring and possible covariate effects, and therefore provide important tools for modelling disease heterogeneity. Simulation studies and application to the data sets from the 12th Genetic Analysis Workshop indicate that the proposed methods have correct type 1 error rates and increased power over other existing methods for testing allelic association.     

Software for genetic linkage analysis

Recent developments in human genetic linkage analysis have included the appearance of new software and collections of data and program resources, accessible by means of the Internet. Many of these new programs and collections are described, including their availability, literature background, and specific technical information.     

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

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

A FORTRAN program for the calculation and analysis of two-locus linkage disequilibrium coefficients

Summary A FORTRAN program was written that calculates composite linkage disequilibrium coefficients from genotypic data. Chi-square tests determine whether coefficients calculated for allele and locus pairs are significantly greater than zero. A subroutine is provided that partitions the variance in linkage disequilibrium into within- and between-subpopulation components. Output obtained from analysis of allozyme data collected from natural subpopulations of the house fly (Musca domestica L.) are included to illustrate features of the program.Journal Paper No. J-11345 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2411     

Expectations of means and genetic variances in backcross populations

Summary The genetic variance among F₂-derived lines of backcrosses (BC_gF₂-derived lines) depends on the backcross generation (g), the number of F₁ plants crossed and selfed in generations 1 through g, and the number of BC_gF₂-derived lines evaluated. Additive genetic variance decreases linearly with backcrossing when one BCF₁ plant per generation is crossed and selfed. The relationship is curvilinear if more than one BCF₁ plant is used; as the number of BCF₁ plants increases, additive genetic variance among BC₁F₂-derived lines approaches that among BC₀F₂-derived lines. The effect of population size on genetic variance is due both to fixation of alleles in previous generations and to sampling of genotypes in the population being evaluated. Dominance and repulsion linkage can cause small increases in genetic variance from BC₀ to BC₁.Joint contribution of USDA-ARS and Journal Paper No. J-11095 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2471     

SHEsis, a powerful software platform for analyses of linkage disequilibrium, haplotype construction, and genetic association at polymorphism loci

In multiloci-based genetic association studies of complex diseases, a powerful and high efficient tool for analyses of linkage disequilibrium (LD) between markers, haplotype distributions and many chi-square/p values with a large number of samples has been sought for long. In order to achieve the goal of obtaining meaningful results directly from raw data,we developed a robust and user-friendly software platform with a series of tools for analysis in association study with high efficiency. The platform has been well evaluated by several sets of real data.     

The effects of linkage and gene flow on local adaptation: a two-locus continent-island model

Population subdivision and migration are generally considered to be important causes of linkage disequilibrium (LD). We explore the combined effects of recombination and gene flow on the amount of LD, the maintenance of polymorphism, and the degree of local adaptation in a subdivided population by analyzing a diploid, deterministic continent–island model with genic selection on two linked loci (i.e., no dominance or epistasis). For this simple model, we characterize explicitly all possible equilibrium configurations. Simple and intuitive approximations for many quantities of interest are obtained in limiting cases, such as weak migration, weak selection, weak or strong recombination. For instance, we derive explicit expressions for the measures and r² (the squared correlation in allelic state) of LD. They depend in qualitatively different ways on the migration rate. Remarkably high values of r² are maintained between weakly linked loci, especially if gene flow is low. We determine how the maximum amount of gene flow that admits preservation of the locally adapted haplotype, hence of polymorphism at both loci, depends on recombination rate and selection coefficients. We also investigate the evolution of differentiation by examining the invasion of beneficial mutants of small effect that are linked to an already present, locally adapted allele. Mutants of much smaller effect can invade successfully than predicted by naive single-locus theory provided they are at least weakly linked. Finally, the influence of linkage on the degree of local adaptation, the migration load, and the effective migration rate at a neutral locus is explored. We discuss possible consequences for the evolution of genetic architecture, in particular, for the emergence of clusters of tightly linked, slightly beneficial mutations and the evolution of recombination and chromosome inversions.     

Gene mapping by linkage and association analysis

Genetic analysis is used to map genes, including disease loci, to positions within the human genome. Linkage analysis depends on the co-segregation of a gene (locus) and a phenotype through a pedigree, while association analysis, or linkage disequilibrium mapping, depends on measuring deviation from the random occurrence of alleles in a haplotype in unrelated individuals or nuclear families. Complex computer programs may be used in both forms of analysis. In recent years most interest has focused on identifying genes involved in common, multifactorial diseases. Here I review some current and developing techniques of genetic analysis and give references to where further information can be obtained.     

Combining dependent tests for linkage or association across multiple phenotypic traits

A robust statistical method to detect linkage or association between a genetic marker and a set of distinct phenotypic traits is to combine univariate trait-specific test statistics for a more powerful overall test. This procedure does not need complex modeling assumptions, can easily handle the problem with partially missing trait values, and is applicable to the case with a mixture of qualitative and quantitative traits. In this note, we propose a simple test procedure along this line, and show its advantages over the standard combination tests for linkage or association in the literature through a data set from Genetic Analysis Workshop 12 (GAW12) and an extensive simulation study.     

Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

Optimal structure of protocol designs for building genetic linkage maps in livestock

We investigated protocol designs for gene mapping in livestock. The optimization of the population structure was based on the empirical variance of the recombination rate estimator. We concluded that a mixture of half-sib and full-sib families is preferred to half-sib families; a knowledge of parental phases does not improve the quality of the estimation for typical livestock families with five offspring or more; and measurements of the genotype of the mates in half-sib families are not useful. Graphs and algebraic approximations for the practical choice of family size and structure are given.     

Evolution of linkage disequilibrium of the founders in exponentially growing populations

Evolution of linkage disequilibrium of the founders in exponentially growing populations was studied using a time-inhomogeneous It? process model. The model is an extension of the diffusion approximation of the Wright-Fisher model. As a measure of linkage disequilibrium, the squared standard linkage deviation, which is defined by a ratio of the moments, was considered. A system of ordinary differential equations that these moments obey was obtained. This system can be solved numerically. By simulations, it was shown that the squared standard linkage deviation gives a good approximation of the expectation of the squared correlation coefficient of gamete frequencies. In addition, a perturbative solution was obtained when the growth rate is not large. By using the perturbation, an asymptotic formula for the squared standard linkage deviation after a large number of generations was obtained. According to the formula, the squared standard linkage deviation tends to be 1/(4Nc), where N is the current size of the population and c is the recombination fraction between two loci. It is dependent on neither the initial effective size, the growth rate, nor the mutation rate. In exponentially growing populations, linkage disequilibrium will be asymptotically the same as that in a constant size population, the effective size of which is the current effective size.     

Evaluation of genetic behavior of some Egyption Cotton genotypes for tolerance to water stress conditions

Water stress is a critical abiotic stress for plant reduction in arid and semiarid zones and, has been discovered to be detrimental to the development of seedlings as well as the growth and physiological characteristics of many crops such as cotton. The objectives of our study were to determine the combining ability and genetic components for five quantitative traits [(leaf area (LA), leaf dry weight (LDW), plant height (PH), fiber length (2.5 percent SL), and lint cotton yield/plant (LCY/P)] under water shortage stress, a half diallel cross between six cotton genotypes representing a wide range of cotton characteristics was evaluated in RCBD with four replications. The genotype mean squares were significant for all traits studied, demonstrating significant variation among genotypes for all characters under water shortage stress. LCY/P had the highest phenotypic and genotypic correlation co-efficient with PH, LDW, and LA shortage. The highest direct effect on lint cotton yield was exhibited by leaf area (3.905), and the highest indirect effects of all traits were through LA, with the exception of 2.5 percent SL, which was through LDW. The highest dissimilarity (Euclidean Distance) between parental genotypes was between G.87 and G.94, followed by G.87 and Menoufi. G.94 was also a well-adapted genotype, and the combinations G.87 x G.94 and G.87 x Menoufi may outperform their parents. The combining ability analysis revealed highly significant differences between parental GCA effects and F1 crosses SCA effects. The variation of GCA and SCA demonstrated the assurance of additive and non- additive gene action in the inheritance of all traits studied. In terms of general combining ability (GCA) effects, parental genotype G.94 demonstrated the highest significant and positive GCA effects for all traits studied, with the exception of 2.5 percent SL, where G.87 revealed the highest significant and positive GCA effects. The effects of specific combining ability (SCA) revealed that the cross (G.87 x2G.94) revealed stable, positive, and significant SCA for all of the studied traits.     

Linkage and association studies of QTL for nuclear families by mixed models

The transmission disequilibrium test (TDT) has been utilized to test the linkage and association between a genetic trait locus and a marker. Spielman et al. (1993) introduced TDT to test linkage between a qualitative trait and a marker in the presence of association. In the presence of linkage, TDT can be applied to test for association for fine mapping (Martin et al., 1997; Spielman and Ewens, 1996). In recent years, extensive research has been carried out on the TDT between a quantitative trait and a marker locus (Allison, 1997; Fan et al., 2002; George et al., 1999; Rabinowitz, 1997; Xiong et al., 1998; Zhu and Elston, 2000, 2001). The original TDT for both qualitative and quantitative traits requires unrelated offspring of heterozygous parents for analysis, and much research has been carried out to extend it to fit for different settings. For nuclear families with multiple offspring, one approach is to treat each child independently for analysis. Obviously, this may not be a valid method since offspring of one family are related to each other. Another approach is to select one offspring randomly from each family for analysis. However, with this method much information may be lost. Martin et al. (1997, 2000) constructed useful statistical tests to analyse the data for qualitative traits. In this paper, we propose to use mixed models to analyse sample data of nuclear families with multiple offspring for quantitative traits according to the models in Amos (1994). The method uses data of all offspring by taking into account their trait mean and variance-covariance structures, which contain all the effects of major gene locus, polygenic loci and environment. A test statistic based on mixed models is shown to be more powerful than the test statistic proposed by George et al. (1999) under moderate disequilibrium for nuclear families. Moreover, it has higher power than the TDT statistic which is constructed by randomly choosing a single offspring from each nuclear family.     

Validation of whole genome linkage‐linkage disequilibrium and association results,and identification of markers to predict genetic merit for twinning

A previous genome‐wide search with a moderate density 10K marker set identified many marker associations with twinning rate, either through single‐marker analysis or combined linkage‐linkage disequilibrium (LLD; haplotype) analysis. The objective of the current study was to validate putative marker associations using an independent set of phenotypic data. Holstein bulls (n = 921) from 100 paternal half‐sib families were genotyped. Twinning rate predicted transmitting abilities were calculated using calving records from 1994 to 1998 (Data I) and 1999 to 2006 (Data II), and the underlying liability scores from threshold model analysis were used as the trait in marker association analyses. The previous analysis used 201 bulls with daughter records in Data I. In the current analysis, this was increased to 434, providing a revised estimate of effect and significance. Bulls with daughter records in Data II totaled 851, and analysis of this data provided the validation of results from analysis of Data I. Single nucleotide polymorphisms (SNPs) were selected to validate previously significant single‐marker associations and LLD results. Bulls were genotyped for a total of 306 markers. Nine of 13 LLD regions located on chromosomes 1, 2, 3, 6, 9, 22, 23(2) and 26 were validated, showing significant results for both Data I and II. Association analysis revealed 55 of 174 markers validated, equating to a single‐marker validation rate of 31%. Stepwise backward elimination and cross‐validation analyses identified 18 SNPs for use in a final reduced marker panel explaining 34% of the genetic variation, and to allow prediction of genetic merit for twinning rate.     

Evolutionary conservation of the linkage between the structural loci for serum albumin and vitamin D binding protein (Gc) in cattle

Summary. Evidence is presented for close genetic linkage between the structural loci for serum albumin and the vitamin D binding protein (Gc) in Belgian Blue and White cattle. Five recombinants were observed in a total of 342 informative offspring. The recombination frequency between the two loci was estimated as 1.5%± 0.9. The observed distribution of the haplotypes deviated from the expected one in the population, probably due to selection and significant linkage disequilibrium.