GVCBLUP: a computer package for genomic prediction and variance component estimation of additive and dominance effects

Background

Dominance effect may play an important role in genetic variation of complex traits. Full featured and easy-to-use computing tools for genomic prediction and variance component estimation of additive and dominance effects using genome-wide single nucleotide polymorphism (SNP) markers are necessary to understand dominance contribution to a complex trait and to utilize dominance for selecting individuals with favorable genetic potential.

Results

The GVCBLUP package is a shared memory parallel computing tool for genomic prediction and variance component estimation of additive and dominance effects using genome-wide SNP markers. This package currently has three main programs (GREML_CE, GREML_QM, and GCORRMX) and a graphical user interface (GUI) that integrates the three main programs with an existing program for the graphical viewing of SNP additive and dominance effects (GVCeasy). The GREML_CE and GREML_QM programs offer complementary computing advantages with identical results for genomic prediction of breeding values, dominance deviations and genotypic values, and for genomic estimation of additive and dominance variances and heritabilities using a combination of expectation-maximization (EM) algorithm and average information restricted maximum likelihood (AI-REML) algorithm. GREML_CE is designed for large numbers of SNP markers and GREML_QM for large numbers of individuals. Test results showed that GREML_CE could analyze 50,000 individuals with 400 K SNP markers and GREML_QM could analyze 100,000 individuals with 50K SNP markers. GCORRMX calculates genomic additive and dominance relationship matrices using SNP markers. GVCeasy is the GUI for GVCBLUP integrated with an existing software tool for the graphical viewing of SNP effects and a function for editing the parameter files for the three main programs.

Conclusion

The GVCBLUP package is a powerful and versatile computing tool for assessing the type and magnitude of genetic effects affecting a phenotype by estimating whole-genome additive and dominance heritabilities, for genomic prediction of breeding values, dominance deviations and genotypic values, for calculating genomic relationships, and for research and education in genomic prediction and estimation.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-270) contains supplementary material, which is available to authorized users.     

Impact of interpopulation divergence on additive and dominance variance in hybrid populations

We present a theoretical proof that the ratio of the dominance vs. the additive variance decreases with increasing genetic divergence between two populations. While the dominance variance is the major component of the variance due to specific combining ability (sigma(SCA)(2)), the additive variance is the major component of the variance due to general combining ability (sigma(GCA)(2)). Therefore, we conclude that interpopulation improvement becomes more efficient with divergent than with genetically similar heterotic groups, because performance of superior hybrids can be predicted on the basis of general combining ability effects.     

Estimation of additive, dominance and epistatic variance components using finite locus models implemented with a single-site Gibbs and a descent graph sampler

In a previous contribution, we implemented a finite locus model (FLM) for estimating additive and dominance genetic variances via a Bayesian method and a single-site Gibbs sampler. We observed a dependency of dominance variance estimates on locus number in the analysis FLM. Here, we extended the FLM to include two-locus epistasis, and implemented the analysis with two genotype samplers (Gibbs and descent graph) and three different priors for genetic effects (uniform and variable across loci, uniform and constant across loci, and normal). Phenotypic data were simulated for two pedigrees with 6300 and 12,300 individuals in closed populations, using several different, non-additive genetic models. Replications of these data were analysed with FLMs differing in the number of loci. Simulation results indicate that the dependency of non-additive genetic variance estimates on locus number persisted in all implementation strategies we investigated. However, this dependency was considerably diminished with normal priors for genetic effects as compared with uniform priors (constant or variable across loci). Descent graph sampling of genotypes modestly improved variance components estimation compared with Gibbs sampling. Moreover, a larger pedigree produced considerably better variance components estimation, suggesting this dependency might originate from data insufficiency. As the FLM represents an appealing alternative to the infinitesimal model for genetic parameter estimation and for inclusion of polygenic background variation in QTL mapping analyses, further improvements are warranted and might be achieved via improvement of the sampler or treatment of the number of loci as an unknown.     

Estimation of dominance components in noninbred populations by using additive animal model residuals

In the case of noninbred and unselected populations with linkage equilibrium, the additive and dominance genetic effects are uncorrelated and the variance-covariance matrix of the second component is simply a product of its variance by a matrix that can be computed from the numerator relationship matrix A. The aim of this study is to present a new approach to estimate the dominance part with a reduced set of equations and hence a lower computing cost. The method proposed is based on the processing of the residual terms resulting from the BLUP methodology applied to an additive animal model. Best linear unbiased prediction of the dominance component d is almost identical to the one given by the full mixed model equations. Based on this approach, an algorithm for restricted maximum likelihood (REML) estimation of the variance components is also presented. By way of illustration, two numerical examples are given and a comparison between the parameters estimated with the expectation maximization (EM) algorithm and those obtained by the proposed algorithm is made. The proposed algorithm is iterative and yields estimates that are close to those obtained by EM, which is also iterative.     

Prediction of effects of genetic drift on variance components under a general model of epistasis

For a model of diallelic loci with arbitrary epistasis, Barton and Turelli [2004. Effects of genetic drift on variance components under a general model of epistasis. Evolution 58, 2111-2132] gave results for variances among and within replicate lines obtained by inbreeding without selection. Here, we discuss the relation between their population genetic methods and classical quantitative genetic arguments. In particular, we consider the case of no dominance using classical identity by descent arguments, which generalizes their results from two alleles to multiple alleles. To clarify the connections between the alternative methods, we obtain the same results using an intermediate method, which explicitly identifies the statistical effects of sets of loci. We also discuss the effects of population bottlenecks on covariances among relatives.     

Partitioning additive genetic variance into genomic and remaining polygenic components for complex traits in dairy cattle

ABSTRACT: BACKGROUND: Low cost genotyping of individuals using high density genomic markers were recently introduced as genomic selection in genetic improvement programs in dairy cattle. Most implementations of genomic selection only use marker information, in the models used for prediction of genetic merit. However, in other species it has been shown that only a fraction of the total genetic variance can be explained by markers. Using 5217 bulls in the Nordic Holstein population that were genotyped and had genetic evaluations based on progeny, we partitioned the total additive genetic variance into a genomic component explained by markers and a remaining component explained by familial relationships. The traits analyzed were production and fitness related traits in dairy cattle. Furthermore, we estimated the genomic variance that can be attributed to individual chromosomes and we illustrate methods that can predict the amount of additive genetic variance that can be explained by sets of markers with different density. RESULTS: The amount of additive genetic variance that can be explained by markers was estimated by an analysis of the matrix of genomic relationships. For the traits in the analysis, most of the additive genetic variance can be explained by 44 K informative SNP markers. The same amount of variance can be attributed to individual chromosomes but surprisingly the relation between chromosomal variance and chromosome length was weak. In models including both genomic (marker) and familial (pedigree) effects most (on average 77.2%) of total additive genetic variance was explained by genomic effects while the remaining was explained by familial relationships. CONCLUSIONS: Most of the additive genetic variance for the traits in the Nordic Holstein population can be explained using 44 K informative SNP markers. By analyzing the genomic relationship matrix it is possible to predict the amount of additive genetic variance that can be explained by a reduced (or increased) set of markers. For the population analyzed the improvement of genomic prediction by increasing marker density beyond 44 K is limited.     

The effect of genetic drift on the variance/covariance components generated by multilocus additive x additive epistatic systems

The effect of population bottlenecks on the components of the genetic variance/covariance generated by n neutral independent additive x additive loci has been studied theoretically. In its simplest version, this situation can be modelled by specifying the allele frequencies and homozygous effects at each locus, and an additional factor measuring the strength of the n-th order epistatic interaction. The variance/covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t bottlenecks of size N (derived components). Formulae were obtained giving the derived components (and the between-line variance) as functions of the ancestral ones (alternatively, in terms of allele frequencies and effects) and the corresponding inbreeding coefficient F(t). The n-th order derived component of the genetic variance/covariance is continuously eroded by inbreeding, but the remaining components may increase initially until a critical F(t) value is attained, which is inversely related to the order of the pertinent component, and subsequently decline to zero. These changes can be assigned to the between-line variances/covariances of gene substitution and epistatic effects induced by drift. Numerical examples indicate that: (1) the derived additive variance/covariance component will generally exceed its ancestral value unless epistasis is weak; (2) the derived epistatic variance/covariance components will generally exceed their ancestral values unless allele frequencies are extreme; (3) for systems showing equal ancestral additive and total non-additive variance/covariance components, those including a smaller number of epistatic loci may generate a larger excess in additive variance/covariance after bottlenecks than others involving a larger number of loci, provided that F(t) is low. Our results indicate that it is unlikely that the rate of evolution may be significantly accelerated after population bottlenecks, in spite of occasional increments of the derived additive variance over its ancestral value.     

Genetic control of in vitro shoot regeneration from leaf explants inSolanum chacoense Bitt.

Although the heritable nature of plant tissue culture responses is now well documented in many species, only a few studies have been conducted to elucidate complete inheritance patterns. Genetic control of in vitro shoot regeneration from leaf explants was investigated inSolanum chacoense using parental, F₁ and F₂ generations. Broad-sense heritability estimates were high for frequency (percentage) of responsive leaf explants (61–83%) and number of shoots regenerated per responsive explant (53–75%). Consistent with high heritability estimates, a hypothesis involving three genes could be formulated to explain the variability in the response observed in this study. This model implies that homozygous recessive alleles at any two (out of three) loci are required for the highest response, i.e., more than two shoots per explant in more than 40% of the explants. The presence of homozygous recessive alleles at any one of the three loci produces an intermediate response, i.e., fewer than 40% of the explants regenerating fewer than two shoots per explant, and a dominant allele at all the three loci results in non-responsiveness. Additional minor modifier genes, each with a small effect, would also be required to account for the variable intensity of regeneration within groups. Such a relatively simple genetic control of in vitro regenerability suggests that incorporation of this trait should be easy in potato improvement programmes.     

Maternal dominance, maternal condition, and offspring sex ratio in ungulate mammals

Trivers and Willard's suggestion that natural selection favors maternal control of offspring sex ratio in relation to maternal condition has been much debated. The theoretical plausibility of the idea, under some conditions, is firmly established, and there is strong empirical support for conditional sex allocation in some taxa. However, the extent to which this hypothesis can be applied to mammals, particularly ungulates, has been more controversial. We used meta-analysis to review published studies of the Trivers-Willard hypothesis within ungulates and to assess the overall level of empirical support for the hypothesis. Overall, data from 37 studies of 18 species suggested a weak but significant positive correlation between maternal condition and sex ratio (r=+0.09). However, average effect size differed markedly between different categories of studies. Studies using measures of maternal condition that were taken preconception and on the basis of behavioral dominance provided strong evidence for a relationship between maternal condition and the sex ratio (r=+0.17-0.25). In contrast, studies that used morphological or physiological measures of condition that were measured postconception provided little or no evidence for a relationship between maternal condition and sex ratio (r=+0.05-0.06). There are several reasons to suggest that data collected postconception and relying on morphological measures of condition are less likely to capture variables that cause selection for biased sex allocation. In addition, we found that the relationship between sex ratio and maternal condition depended on life-history characteristics; relationships were stronger when sexual size dimorphism was more male biased and when gestation periods were longer. Overall, our analyses suggest that data from ungulates are consistent with the Trivers-Willard hypothesis but only when appropriate measures are used.     

Maternal and paternal origin of extra chromosome in trisomy 21

Summary Fluorescence markers were studied in 40 patients with Down's syndrome and their parents. In 11 cases maternal and in 5 cases paternal non-disjunction could be shown. The disjunctional event occurred in the first meiotic division in 5 maternal and in 2 paternal cases. A second division failure was found in 4 maternal and 2 paternal cases. In 3 cases the failure could either be of first or second meiotic division origin.     

Theory for modelling means and covariances in a two-breed population with dominance inheritance

This paper presents theory and methods to compute genotypic means and covariances in a two breed population under dominance inheritance, assuming multiple unlinked loci. It is shown that the genotypic mean is a linear function of five location parameters and that the genotypic covariance between relatives is a linear function of 25 dispersion parameters. Recursive procedures are given to compute the necessary identity coefficients. In the absence of inbreeding, the number of parameters for the mean is reduced from five to three and the number for the covariance is reduced from 25 to 12. In a two-breed population, for traits exhibiting dominance, the theory presented here can be used to obtain genetic evaluations by best linear unbiased prediction and to estimate genetic parameters by maximum likelihood.Supported in part by the Illinois Agricultural Experiment Station, Hatch Projects 35-0345 (R.L.F.) and 35-0367 (M.G.). A computer program implementing the methods described here is available upon request to R.L.F.     

Quantitative analysis of correlations among flower traits in Gerbera hybrida, Compositae. III. Genetic variability and structure of principal component traits

 A sample of 36 flower traits consisting of six morphological categories in the Davis population of gerbera was restructured into phenotypic and genetic principal component traits. The first 5 phenotypic principal component traits accounted for 62% of the total phenotypic variance of the 36 traits and have moderate to high heritablities. The first 5 genetic principal component traits account for 97% of total genetic variance and all have high heritability. Morphological structure of these component traits suggest an underlying process identified by the first genetic principal component involving largely trans and disk floret traits. The results of this study indicate that the quantitative genetic structure of the gerbera flower is controlled by a few independent components and that principal component analysis is a useful tool to reveal variation in this structure. These composite traits are heritable and are expected to respond to selection. Received: 20 September 1997 / Accepted: 19 January 1998     

Maternal and paternal periods in the development of infant Callimico goeldii

The paternal-maternal-infant interactions of contact and nursing are reported from extensive longitudinal observations on two successive Callimico births in one family. For the first two weeks, the maternal period, the infant clings exclusively to the female. In the third week the infant shifts abruptly to the male. Subsequently, during the paternal period most of the maternal-infant contact involves nursing. The infant Callimico remains almost totally dependent until week 6, but even in week 11 it spends less than 50% of the time off a parent.     

Genetic and environmental contributions to the variance of body height in a sample of first and second degree relatives.

Height was measured in a health screening of the population in Nord-Trøndelag, Norway. Correlations were computed for 24,281 pairs of spouses, 43,613 pairs of parents and offspring, 19,168 pairs of siblings, 1,318 pairs of grandparents and grandchildren, 1,218 cognate avuncular pairs, 849 noncognate avuncular pairs, 175 pairs of same-sexed twins, and smaller groups of other types of relatives. Fitting of structural equation models showed proportions of additive genetic variance of approximately 0.8 for both sexes and small sex-specific effects that probably reflect genetic dominance or environmental sibling effects. The correlations between parents and offspring were significantly lower in old than young cohorts, seeming to imply some kind of interaction effect between genes and environment. © 1992 Wiley-Liss, Inc.     

Relative family performance and variance structure of open-pollinated Douglas-fir seedlings grown in three competitive environments

Summary Open-pollinated Douglas-fir (Pseudotsuga menziesii var menziesii (Mirb.) Franco) families were tested in three contrasting competitive environments to test the hypothesis that relative performance as measured by total seedling dry weight is dependent upon distance or genotype of neighbors. The three competitive environmnts included (1) a mixture of individuals from all families planted at close spacing, (2) single (pure) family blocks planted at close spacing, and (3) individuals from all families planted at a wide, non-competitive spacing. Despite occasional large changes in rank between competitive environments and only moderate correlations of family means between competitive environments, the family x competitive environment interaction was non-significant. Furthermore, families did not differ significantly in competitive ability or density tolerance. The competitive environment in which seedlings were grown, however, had a large effect on estimates of variance components, which in turn led to large differences in estimates of heritability and genetic gain. Evaluation of families in mixture resulted in the largest estimates of heritability, while evaluation in pure family blocks resulted in the lowest. Analysis of correlated response to selection indicated that testing and selection in mixture result in the largest estimated gain, even if progeny of selected individuals are subsequently grown in a pure or non-competitive environment.Paper No. 2659 of the Forest Research Laboratory, Oregon State University     

Heritability and components of phenotypic expression in skin reflectance of Mestizos from the Peruvian Lowlands

Skin reflectance was measured on the inner upper arm and forehead of a sample of 209 Mestizos ranging in age from 2 to 64 years living in the town of Lamas in the Eastern Peruvian Lowlands. The sample consisted of 43 father-son, 42 father-daughter, 62 mother-son, and 70 mother-daughter pairs. The sample also consisted of 57 brother-brother, 60 sister-sister and 139 brother-sister pairs. The reflectance measurements were made with a Photovolt Reflection Meter, model 670. Stepwise polynomial regression techniques were used to derive standardized residual values. Then using these residual values parent-offspring, sibling intraclass correlations and components of the phenotypic expression of skin reflectance were calculated. The study indicates that 1) the parent-offspring and sibling correlation coefficients conformed with the theoretical correlations expected assuming polygenic inheritance; 2) the husband-wife correlations indicate a high degree of assortative mating for skin color, but despite this effect the parent-offspring and sibling correlation coefficients are lower than the values expected under the influence of autosomal genes; 3) estimates of heritability and components of phenotypic expression indicate that about 55% of the total variability in skin reflectance could be attributed to the influence of additive genetic factors; and 4) there is no evidence of X-linkage in the inheritance of skin color.