Estimates of genetic variance in an F2 maize population

Maize (Zea mays L.) breeders have used several genetic-statistical models to study the inheritance of quantitative traits. These models provide information on the importance of additive, dominance, and epistatic genetic variance for a quantitative trait. Estimates of genetic variances are useful in understanding heterosis and determining the response to selection. The objectives of this study were to estimate additive and dominance genetic variances and the average level of dominance for an F2 population derived from the B73 x Mo17 hybrid and use weighted least squares to determine the importance of digenic epistatic variances relative to additive and dominance variances. Genetic variances were estimated using Design III and weighted least squares analyses. Both analyses determined that dominance variance was more important than additive variance for grain yield. For other traits, additive genetic variance was more important than dominance variance. The average level of dominance suggests either overdominant gene effects were present for grain yield or pseudo-overdominance because of linkage disequilibrium in the F2 population. Epistatic variances generally were not significantly different from zero and therefore were relatively less important than additive and dominance variances. For several traits estimates of additive by additive epistatic variance decreased estimates of additive genetic variance, but generally the decrease in additive genetic variance was not significant.     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

Non-additive genetic effects for fertility traits in Canadian Holstein cattle (Open Access publication )

The effects of additive, dominance, additive by dominance, additive by additive and dominance by dominance genetic effects on age at first service, non-return rates and interval from calving to first service were estimated. Practical considerations of computing additive and dominance relationships using the genomic relationship matrix are discussed. The final strategy utilized several groups of 1000 animals (heifers or cows) in which all animals had a non-zero dominance relationship with at least one other animal in the group. Direct inversion of relationship matrices was possible within the 1000 animal subsets. Estimates of variances were obtained using Bayesian methodology via Gibbs sampling. Estimated non-additive genetic variances were generally as large as or larger than the additive genetic variance in most cases, except for non-return rates and interval from calving to first service for cows. Non-additive genetic effects appear to be of sizeable magnitude for fertility traits and should be included in models intended for estimating additive genetic merit. However, computing additive and dominance relationships for all possible pairs of individuals is very time consuming in populations of more than 200 000 animals.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER. Xviii. Clinal and Uniform Genetic Variation over Populations

It has been reported in the previous papers of this series that in the eastern United States and Japan there is a north-to-south cline of additive genetic variance of viability and that the amount of the additive genetic variance in the northern population can be explained by mutation-selection balance. To determine whether or not the difference in the genetic variation in northern and southern populations can be explained by the differences in mutation rate and/or effective population size, numerical calculations were made using population genetic parameters. In addition, the average heterozygosities of the northern and southern populations at ten of 19 polymorphic structural loci surveyed were estimated in relation to the cline of additive genetic variance of viability, and the following findings were obtained. (1) The changes in mutation rate and population size cannot simultaneously explain the difference in additive genetic variance and inbreeding decline between the northern and southern populations. Thus, the operation of some kind of balancing selection, most likely diversifying selection, was suggested to explain the observed excess of additive genetic variance. (2) Estimates of the average heterozygosities of the southern population were not significantly different from those of the northern population. Thus, it was strongly suggested that the excess of additive genetic variance in the southern population cannot be caused by structural loci, but by factors outside the structural loci, and that protein polymorphisms are selectively neutral or nearly neutral.     

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.     

A symmetric two locus model with viability and fertility selection

A two locus deterministic population genetic model is analysed. One locus is under viability selection, the other under fertility selection with both forms of selection completely symmetric. It is shown that linkage equilibrium may occur at two different equilibrium points. For a two-locus polymorphism to be stable, it is necessary that the viability locus be overdominant but not necessary that the fertility locus, considered separately, be able to support a stable polymorphism. The overlaps in stability are not as complex as under two locus symmetric fertilities, but considerably more complex than with symmetric viabilities. Extensions of the analysis for the central linkage equilibrium point with multiple viability and fertility loci are indicated.Research supported in part by NIH grants GM 28106 and GM 10452     

The effect of non-additive genetic interactions on selection in multi-locus genetic models

Additive genetic variance might usually be expected to decrease in a finite population because of genetic drift. However, both theoretical and empirical studies have shown that the additive genetic variance of a population could, in some cases, actually increase owing to the action of genetic drift in presence of non-additive effects. We used Monte-Carlo simulations to address a less-well-studied issue: the effects of directional truncation selection on a trait affected by non-additive genetic variation. We investigated the effects on genetic variance and the response to selection. We compared two different genetic models, representing various numbers of loci. We found that the additive genetic variance could also increase in the case of truncation selection, when dominance and epistasis was present. Additive-by-additive epistatic effects generally gave a higher increase in additive variance compared to dominance. However, the magnitude of the increase differed depending on the particular model and on the number of loci.     

THE EVOLUTIONARY GENETICS OF MALE LIFE-HISTORY CHARACTERS IN DROSOPHILA MELANOGASTER

Alternative models of the maintenance of genetic variability, theories of life-history evolution, and theories of sexual selection and mate choice can be tested by measuring additive and nonadditive genetic variances of components of fitness. A quantitative genetic breeding design was used to produce estimates of genetic variances for male life-history traits in Drosophila melanogaster. Additive genetic covariances and correlations between traits were also estimated. Flies from a large, outbred, laboratory population were assayed for age-specific competitive mating ability, age-specific survivorship, body mass, and fertility. Variance-component analysis then allowed the decomposition of phenotypic variation into components associated with additive genetic, nonadditive genetic, and environmental variability. A comparison of dominance and additive components of genetic variation provides little support for an important role for balancing selection in maintaining genetic variance in this suite of traits. The results provide support for the mutation-accumulation theory, but not the antagonistic-pleiotropy theory of senescence. No evidence is found for the positive genetic correlations between mating success and offspring quality or quantity that are predicted by “good genes” models of sexual selection. Additive genetic coefficients of variation for life-history characters are larger than those for body weight. Finally, this set of male life-history characters exhibits a very low correspondence between estimates of genetic and phenotypic correlations.     

DIFFERENTIAL DOMINANCE OF PLEIOTROPIC LOCI FOR MOUSE SKELETAL TRAITS

The term "differential dominance" describes the situation in which the dominance effects at a pleiotropic locus vary between traits. Directional selection on the phenotype can lead to balancing selection on differentially dominant pleiotropic loci. Even without any individual overdominant traits, some linear combination of traits will display overdominance at a locus displaying differential dominance. Multivariate overdominance may be responsible, in part, for high levels of heterozygosity found in natural populations. We examine differential dominance of 70 mouse skeletal traits at 92 quantitative trait loci (QTL). Our results indicate moderate to strong additive and dominance effects at pleiotropic loci, low levels of individual-trait overdominance, and universal multivariate overdominance. Multivariate overdominance affects a range of 6% to 81% of morphospace, with a mean of 32%. Multivariate overdominance tends to affect a larger percentage of morphospace at pleiotropic loci with antagonistic effects on multiple traits (42%). We conclude that multivariate overdominance is common and should be considered in models and in empirical studies of the role of genetic variation in evolvability.     

Genomic selection of purebred animals for crossbred performance in the presence of dominant gene action

Background

Genomic selection is an appealing method to select purebreds for crossbred performance. In the case of crossbred records, single nucleotide polymorphism (SNP) effects can be estimated using an additive model or a breed-specific allele model. In most studies, additive gene action is assumed. However, dominance is the likely genetic basis of heterosis. Advantages of incorporating dominance in genomic selection were investigated in a two-way crossbreeding program for a trait with different magnitudes of dominance. Training was carried out only once in the simulation.

Results

When the dominance variance and heterosis were large and overdominance was present, a dominance model including both additive and dominance SNP effects gave substantially greater cumulative response to selection than the additive model. Extra response was the result of an increase in heterosis but at a cost of reduced purebred performance. When the dominance variance and heterosis were realistic but with overdominance, the advantage of the dominance model decreased but was still significant. When overdominance was absent, the dominance model was slightly favored over the additive model, but the difference in response between the models increased as the number of quantitative trait loci increased. This reveals the importance of exploiting dominance even in the absence of overdominance. When there was no dominance, response to selection for the dominance model was as high as for the additive model, indicating robustness of the dominance model. The breed-specific allele model was inferior to the dominance model in all cases and to the additive model except when the dominance variance and heterosis were large and with overdominance. However, the advantage of the dominance model over the breed-specific allele model may decrease as differences in linkage disequilibrium between the breeds increase. Retraining is expected to reduce the advantage of the dominance model over the alternatives, because in general, the advantage becomes important only after five or six generations post-training.

Conclusion

Under dominance and without retraining, genomic selection based on the dominance model is superior to the additive model and the breed-specific allele model to maximize crossbred performance through purebred selection.     

Dominance Genetic Variance for Traits Under Directional Selection in Drosophila serrata

In contrast to our growing understanding of patterns of additive genetic variance in single- and multi-trait combinations, the relative contribution of nonadditive genetic variance, particularly dominance variance, to multivariate phenotypes is largely unknown. While mechanisms for the evolution of dominance genetic variance have been, and to some degree remain, subject to debate, the pervasiveness of dominance is widely recognized and may play a key role in several evolutionary processes. Theoretical and empirical evidence suggests that the contribution of dominance variance to phenotypic variance may increase with the correlation between a trait and fitness; however, direct tests of this hypothesis are few. Using a multigenerational breeding design in an unmanipulated population of Drosophila serrata, we estimated additive and dominance genetic covariance matrices for multivariate wing-shape phenotypes, together with a comprehensive measure of fitness, to determine whether there is an association between directional selection and dominance variance. Fitness, a trait unequivocally under directional selection, had no detectable additive genetic variance, but significant dominance genetic variance contributing 32% of the phenotypic variance. For single and multivariate morphological traits, however, no relationship was observed between trait–fitness correlations and dominance variance. A similar proportion of additive and dominance variance was found to contribute to phenotypic variance for single traits, and double the amount of additive compared to dominance variance was found for the multivariate trait combination under directional selection. These data suggest that for many fitness components a positive association between directional selection and dominance genetic variance may not be expected.     

Genetic variation maintained in multilocus models of additive quantitative traits under stabilizing selection.

Stabilizing selection for an intermediate optimum is generally considered to deplete genetic variation in quantitative traits. However, conflicting results from various types of models have been obtained. While classical analyses assuming a large number of independent additive loci with individually small effects indicated that no genetic variation is preserved under stabilizing selection, several analyses of two-locus models showed the contrary. We perform a complete analysis of a generalization of Wright's two-locus quadratic-optimum model and investigate numerically the ability of quadratic stabilizing selection to maintain genetic variation in additive quantitative traits controlled by up to five loci. A statistical approach is employed by choosing randomly 4000 parameter sets (allelic effects, recombination rates, and strength of selection) for a given number of loci. For each parameter set we iterate the recursion equations that describe the dynamics of gamete frequencies starting from 20 randomly chosen initial conditions until an equilibrium is reached, record the quantities of interest, and calculate their corresponding mean values. As the number of loci increases from two to five, the fraction of the genome expected to be polymorphic declines surprisingly rapidly, and the loci that are polymorphic increasingly are those with small effects on the trait. As a result, the genetic variance expected to be maintained under stabilizing selection decreases very rapidly with increased number of loci. The equilibrium structure expected under stabilizing selection on an additive trait differs markedly from that expected under selection with no constraints on genotypic fitness values. The expected genetic variance, the expected polymorphic fraction of the genome, as well as other quantities of interest, are only weakly dependent on the selection intensity and the level of recombination.     

Genetics of tassel branch number in maize and its implications for a selection program for small tassel size

Summary Tassel branch numbers of six crosses of maize (Zea mays L.) were analyzed to determine inheritance of this trait. Generation mean analyses were used to estimate genetic effects, and additive and nonadditive components of variance were calculated and evaluated for bias due to linkage. Both narrow-sense and broad-sense heritabilities were estimated. Additive genetic variance estimates were significant in five of the six crosses, whereas estimates of variance due to nonadditive components were significant in only three crosses. Additionally, estimates of additive variance components usually were larger than corresponding nonadditive components. There was no evidence for linkage bias in these estimates. Estimates of additive genetic effects were significant in four of six crosses, but significant dominance, additive × additive and additive × dominance effects also were detected. Additive, dominance, and epistatic gene action, therefore, all influenced the inheritance of tassel branch number, but additive gene action was most important. Both narrow-sense and broadsense heritability estimates were larger than those reported for other physiological traits of maize and corroborated conclusions concerning the importance of additive gene action inferred from analyses of genetic effects and variances. We concluded that selection for smalltasseled inbreds could be accomplished most easily through a mass-selection and/or pedigree-selection system. Production of a small-tasseled hybrid would require crossing of two small-tasseled inbreds. We proposed two genetic models to explain unexpected results obtained for two crosses. One model involved five interacting loci and the other employed two loci displaying only additive and additive × additive gene action.Journal Paper No. J-9231 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa 50011. Project No. 2152     

Relative roles of mutation and selection in the maintenance of genetic variability

The extent and pattern of protein and DNA polymorphisms are discussed with emphasis on the mechanism of maintenance of the polymorphisms. Statistical studies suggest that a large proportion of genetic variability at the molecular level is maintained by a mutation-drift balance. At some loci, such as those for histocompatibility in mammals, however, a form of overdominant selection seems to be involved. In the presence of overdominant selection, polymorphic alleles may be maintained for tens of millions of years, so that the number of nucleotide differences between alleles is often very large, as in the case of self-incompatibility alleles in plants. There are also an increasing number of examples in which an adaptive change of a morphological or physiological character is caused by a single nucleotide substitution. Nevertheless, these mutations seem to be a small proportion of the total nucleotide changes that contribute to genetic variability and evolution. Although there are many examples of frequency-dependent selection, this form of selection is apparently unimportant for the maintenance of genetic variability except in some special cases. Observations on the evolutionary change of DNA suggest that the driving force of evolution is mutation rather than selection.     

Including Dominance Effects in the Genomic BLUP Method for Genomic Evaluation

We evaluated the performance of GBLUP including dominance genetic effect (GBLUP-D) by estimating variances and predicting genetic merits in a computer simulation and 2 actual traits (T4 and T5) in pigs. In simulation data, GBLUP-D explained more than 50% of dominance genetic variance. Moreover, GBLUP-D yielded estimated total genetic effects over 1.2% more accurate than those yielded by GBLUP. In particular, when the dominance genetic variance was large, the accuracy could be substantially improved by increasing the number of markers. The dominance genetic variances in T4 and T5 accounted for 9.6% and 6.3% of the phenotypic variances, respectively. Estimates of such small dominance genetic variances contributed little to the improvement of the accuracies of estimated total genetic effects. In both simulation and pig data, there were nearly no differences in the estimates of additive genetic effects or their variance between GBLUP-D and GBLUP. Therefore, we conclude GBLUP-D is a feasible approach to improve genetic performance in crossbred populations with large dominance genetic variation and identify mating systems with good combining ability.     

Improvement of Prediction Ability for Genomic Selection of Dairy Cattle by Including Dominance Effects

Dominance may be an important source of non-additive genetic variance for many traits of dairy cattle. However, nearly all prediction models for dairy cattle have included only additive effects because of the limited number of cows with both genotypes and phenotypes. The role of dominance in the Holstein and Jersey breeds was investigated for eight traits: milk, fat, and protein yields; productive life; daughter pregnancy rate; somatic cell score; fat percent and protein percent. Additive and dominance variance components were estimated and then used to estimate additive and dominance effects of single nucleotide polymorphisms (SNPs). The predictive abilities of three models with both additive and dominance effects and a model with additive effects only were assessed using ten-fold cross-validation. One procedure estimated dominance values, and another estimated dominance deviations; calculation of the dominance relationship matrix was different for the two methods. The third approach enlarged the dataset by including cows with genotype probabilities derived using genotyped ancestors. For yield traits, dominance variance accounted for 5 and 7% of total variance for Holsteins and Jerseys, respectively; using dominance deviations resulted in smaller dominance and larger additive variance estimates. For non-yield traits, dominance variances were very small for both breeds. For yield traits, including additive and dominance effects fit the data better than including only additive effects; average correlations between estimated genetic effects and phenotypes showed that prediction accuracy increased when both effects rather than just additive effects were included. No corresponding gains in prediction ability were found for non-yield traits. Including cows with derived genotype probabilities from genotyped ancestors did not improve prediction accuracy. The largest additive effects were located on chromosome 14 near DGAT1 for yield traits for both breeds; those SNPs also showed the largest dominance effects for fat yield (both breeds) as well as for Holstein milk yield.     

Mutation Rate and Dominance of Genes Affecting Viability in DROSOPHILA MELANOGASTER

Spontaneous mutations were allowed to accumulate in a second chromosome that was transmitted only through heterozygous males for 40 generations. At 10-generation intervals the chromosomes were assayed for homozygous effects of the accumulated mutants. From the regression of homozygous viability on the number of generations of mutant accumulation and from the increase in genetic variance between replicate chromosomes it is possible to estimate the mutation rate and average effect of the individual mutants. Lethal mutations arose at a rate of 0.0060 per chromosome per generation. The mutants having small effects on viability are estimated to arise with a frequency at least 10 times as high as lethals, more likely 20 times as high, and possibly many more times as high if there is a large class of very nearly neutral mutations.-The dominance of such mutants was measured for chromosomes extracted from a natural population. This was determined from the regression of heterozygous viability on that of the sum of the two constituent homozygotes. The average dominance for minor viability genes in an equilibrium population was estimated to be 0.21. This is lower than the value for new mutants, as expected since those with the greatest heterozygous effect are most quickly eliminated from the population. That these mutants have a disproportionately large heterozygous effect on total fitness (as well as on the viability component thereof) is shown by the low ratio of the genetic load in equilibrium homozygotes to that of new mutant homozygotes.     

Change in Genetic Variance under Selection in a Self-Fertilizing Population

In this study we show how the genetic variance of a quantitative trait changes in a self-fertilizing population under repeated cycles of truncation selection, with the analysis based on the infinitesimal model in which it is assumed that the trait is determined by an infinite number of unlinked loci without epistasis. The genetic variance is reduced not as a consequence of the genotypic frequency change but due to the build-up of linkage disequilibrium under truncation selection in this model. We assume that the order of the genotypic contribution from each locus is n(-1/2), where n is the number of loci involved, and investigate the change in linkage disequilibrium resulting from selection and self-fertilization using genotypic frequency dynamics in order to analyze the change in the genetic variance. Our analysis gives recurrence relations of genetic variance among the succeeding generations for the three cases of gene action, i.e., purely additive action, pure dominance without additive effect and the presence of both additive effect and dominance, respectively. Numerical examples are also given as a check on the recurrence formulas.     

Interval Mapping of Viability Loci Causing Heterosis in Arabidopsis

The genetic basis of heterosis has implications for many problems in genetics and evolution. Heterosis and inbreeding depression affect human genetic diseases, maintenance of genetic variation, evolution of breeding systems, agricultural productivity, and conservation biology. Despite decades of theoretical and empirical studies, the genetic basis of heterosis has remained unclear. I mapped viability loci contributing to heterosis in Arabidopsis. An overdominant factor with large effects on viability mapped to a short interval on chromosome I. Homozygotes had 50% lower viability than heterozygotes in this chromosomal region. Statistical analysis of viability data in this cross indicates that observed viability heterosis is better explained by functional overdominance than by pseudo-overdominance. Overdominance sometimes may be an important cause of hybrid vigor, especially in habitually inbreeding species. Finally, I developed a maximum likelihood interval mapping procedure that can be used to examine chromosomal regions showing segregation distortion or viability selection.     

Genomic analysis of dominance effects on milk production and conformation traits in Fleckvieh cattle

Background

Estimates of dominance variance in dairy cattle based on pedigree data vary considerably across traits and amount to up to 50% of the total genetic variance for conformation traits and up to 43% for milk production traits. Using bovine SNP (single nucleotide polymorphism) genotypes, dominance variance can be estimated both at the marker level and at the animal level using genomic dominance effect relationship matrices. Yield deviations of high-density genotyped Fleckvieh cows were used to assess cross-validation accuracy of genomic predictions with additive and dominance models. The potential use of dominance variance in planned matings was also investigated.

Results

Variance components of nine milk production and conformation traits were estimated with additive and dominance models using yield deviations of 1996 Fleckvieh cows and ranged from 3.3% to 50.5% of the total genetic variance. REML and Gibbs sampling estimates showed good concordance. Although standard errors of estimates of dominance variance were rather large, estimates of dominance variance for milk, fat and protein yields, somatic cell score and milkability were significantly different from 0. Cross-validation accuracy of predicted breeding values was higher with genomic models than with the pedigree model. Inclusion of dominance effects did not increase the accuracy of the predicted breeding and total genetic values. Additive and dominance SNP effects for milk yield and protein yield were estimated with a BLUP (best linear unbiased prediction) model and used to calculate expectations of breeding values and total genetic values for putative offspring. Selection on total genetic value instead of breeding value would result in a larger expected total genetic superiority in progeny, i.e. 14.8% for milk yield and 27.8% for protein yield and reduce the expected additive genetic gain only by 4.5% for milk yield and 2.6% for protein yield.

Conclusions

Estimated dominance variance was substantial for most of the analyzed traits. Due to small dominance effect relationships between cows, predictions of individual dominance deviations were very inaccurate and including dominance in the model did not improve prediction accuracy in the cross-validation study. Exploitation of dominance variance in assortative matings was promising and did not appear to severely compromise additive genetic gain.