Maternal,paternal, additive,and dominance components of variance in Gerbera

Summary Estimates of additive, dominance, maternal, and paternal components of variance were obtained for a sample of 18 traits, including measurements of yield, scapes, flowers, disk, ray and trans florets, leaves, and branching in the Davis population of Gerbera hybrida. The results, based on the covariance of reciprocals, indicate that although heritability averaged 0.52, extranuclear maternal or paternal effects are not important sources of variability. Therefore, reciprocal differences do not seriously affect estimates of additive variance or heritability in this population.     

Prediction of additive and dominance effects in selected or unselected populations with inbreeding

Summary A genetic model with either 64 or 1,600 unlinked biallelic loci and complete dominance was used to study prediction of additive and dominance effects in selected or unselected populations with inbreeding. For each locus the initial frequency of the favourable allele was 0.2, 0.5, or 0.8 in different alternatives, while the initial narrow-sense heritability was fixed at 0.30. A population of size 40 (20 males and 20 females) was simulated 1,000 times for five generations. In each generation 5 males and 10 or 20 females were mated, with each mating producing four or two offspring, respectively. Breeding individuals were selected randomly, on own phenotypic performance or such yielding increased inbreeding levels in subsequent generations. A statistical model containing individual additive and dominance effects but ignoring changes in mean and genetic covariances associated with dominance due to inbreeding resulted in significantly biased predictions of both effects in generations with inbreeding. Bias, assessed as the average difference between predicted and simulated genetic effects in each generation, increased almost linearly with the inbreeding coefficient. In a second statistical model the average effect of inbreeding on the mean was accounted for by a regression of phenotypic value on the inbreeding coefficient. The total dominance effect of an individual in that case was the sum of the average effect of inbreeding and an individual effect of dominance. Despite a high mean inbreeding coefficient (up to 0.35), predictions of additive and dominance effects obtained with this model were empirically unbiased for each initial frequency in the absence of selection and 64 unlinked loci. With phenotypic selection of 5 males and only 10 females in each generation and 64 loci, however, predictions of additive and dominance effects were significantly biased. Observed biases disappeared with 1,600 loci for allelic frequencies at 0.2 and 0.5. Bias was due to a considerable change in allelic frequency with phenotypic selection. Ignoring both the covariance between additive and dominance effects with inbreeding and the change in dominance variance due to inbreeding did not significantly bias prediction of additive and dominance effects in selected or unselected populations with inbreeding.     

Estimation of additive genetic variance in commercial layer poultry and simulated populations under selection

Changes in genetic parameters over generations for a selected commercial population and simulated populations of poultry with different sizes were studied. The traits analyzed from the commercial population were rate of lay, age at first egg, egg weight, deformation, and body weight. In the simulated population, a trait measured on both sexes and a sex-limited trait, measured only on one sex, each with a heritability of 0.1 and 0.5, were analyzed. In the commercial and simulated populations, males and females were selected on the basis of family selection indexes and data was available only after many generations of selection. Parameters for each generation were estimated by fitting an animal model using derivative free maximum likelihood (DFREML) with different data structures. In structure 1, data included the given (base) generation for which the parameters were to be estimated, and all subsequent generations. In structure 2, only data on birds in the given generation and their progeny were included. In both structures, parents of base-generation birds were assumed unrelated and pedigrees traced back to these parents. With commercial data using structure 1, estimates of _a ² and h² decreased by 14 to 37% across five generations. With structure 2, no trends were observed, though estimates were lower than for structure 1. For simulated data, with a heritability of 0.1, both structures yielded apparently unbiased estimates of the observed additive genetic variances in the (selected) base generation, no matter how many generations of data were utilized, for both sex-limited and normal traits. However, with a heritability of 0.5 the estimated additive genetic variance for both types of trait decreased with a decrease in the number of generations used in the estimation. Estimates based on the first two generations underestimated, while estimates based on five generations of data overestimated, the observed genetic variances in the defined base. The combinations of conditions that lead to varying degrees of bias remain undefined.     

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.     

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 nonrandom mating on genetic variance and gene flow in populations with mass selection

The mechanisms by which nonrandom mating affects selected populations are not completely understood and remain a subject of scientific debate in the development of tractable predictors of population characteristics. The main objective of this study was to provide a predictive model for the genetic variance and covariance among mates for traits subjected to directional selection in populations with nonrandom mating based on the pedigree. Stochastic simulations were used to check the validity of this model. Our predictions indicate that the positive covariance among mates that is expected to result with preferential mating of relatives can be severely overpredicted from neutral expectations. The covariance expected from neutral theory is offset by an opposing covariance between the genetic mean of an individual's family and the Mendelian sampling term of its mate. This mechanism was able to predict the reduction in covariance among mates that we observed in the simulated populations and, in consequence, the equilibrium genetic variance and expected long-term genetic contributions. Additionally, this study provided confirmatory evidence on the postulated relationships of long-term genetic contributions with both the rate of genetic gain and the rate of inbreeding (deltaF) with nonrandom mating. The coefficient of variation of the expected gene flow among individuals and deltaF was sensitive to nonrandom mating when heritability was low, but less so as heritability increased, and the theory developed in the study was sufficient to explain this phenomenon.     

Effects of natural selection on interpopulation divergence at polymorphic sites in human protein-coding Loci

To develop new strategies for searching for genetic associations with complex human diseases, we analyzed 2784 single-nucleotide polymorphisms (SNPs) in 396 protein-coding genes involved in biological processes relevant to cancer and other complex diseases, with respect to gene diversity within samples of individuals representing the three major historic human populations (African, European, and Asian) and with respect to interpopulation genetic distance. Reduced levels of both intrapopulation gene diversity and interpopulation genetic distance were seen in the case of SNPs located within the 5'-UTR and at nonsynonymous SNPs, causing radical changes to protein structure. Reduction of gene diversity at SNP loci in these categories was evidence of purifying selection acting at these sites, which in turn causes a reduction in interpopulation divergence. By contrast, a small number of SNP sites in these categories revealed unusually high genetic distances between the two most diverged populations (African and Asian); these loci may have historically been subject to divergent selection pressures.     

Neutral additive genetic variance in a metapopulation

For neutral, additive quantitative characters, the amount of additive genetic variance within and among populations is predictable from Wright's FST, the effective population size and the mutational variance. The structure of quantitative genetic variance in a subdivided metapopulation can be predicted from results from coalescent theory, thereby allowing single-locus results to predict quantitative genetic processes. The expected total amount of additive genetic variance in a metapopulation of diploid individual is given by 2Ne sigma m2 (1 + FST), where FST is Wright's among-population fixation index, Ne is the eigenvalue effective size of the metapopulation, and sigma m2 is the mutational variance. The expected additive genetic variance within populations is given by 2Ne sigma e2(1-FST), and the variance among demes is given by 4FSTNe sigma m2. These results are general with respect to the types of population structure involved. Furthermore, the dimensionless measure of the quantitative genetic variance among populations, QST, is shown to be generally equal to FST for the neutral additive model. Thus, for all population structures, a value of QST greater than FST for neutral loci is evidence for spatially divergent evolution by natural selection.     

Phenotypic divergence along lines of genetic variance

Natural populations inhabiting the same environment often independently evolve the same phenotype. Is this replicated evolution a result of genetic constraints imposed by patterns of genetic covariation? We looked for associations between directions of morphological divergence and the orientation of the genetic variance-covariance matrix (G) by using an experimental system of morphological evolution in two allopatric nonsister species of rainbow fish. Replicate populations of both Melanotaenia eachamensis and Melanotaenia duboulayi have independently adapted to lake versus stream hydrodynamic environments. The major axis of divergence (z) among all eight study populations was closely associated with the direction of greatest genetic variance (gmax), suggesting directional genetic constraint on evolution. However, the direction of hydrodynamic adaptation was strongly associated with vectors of G describing relatively small proportions of the total genetic variance, and was only weakly associated with gmax. In contrast, divergence between replicate populations within each habitat was approximately proportional to the level of genetic variance, a result consistent with theoretical predictions for neutral phenotypic divergence. Divergence between the two species was also primarily along major eigenvectors of G. Our results therefore suggest that hydrodynamic adaptation in rainbow fish was not directionally constrained by the dominant eigenvector of G. Without partitioning divergence as a consequence of the adaptation of interest (here, hydrodynamic adaptation) from divergence due to other processes, empirical studies are likely to overestimate the potential for the major eigenvectors of G to directionally constrain adaptive evolution.     

Impact of developmental variance on behavior of models for insect populations I. Models for populations with unrestricted growth

The concept of developmental variance is discussed with reference to its use in models for insect populations. When included in a model, developmental variance is typically used to describe the variation of developmental periods among individuals. However, its presence in a model can also have indirect impact on survival and fertility schedules. This impact can lead to significant changes in population growth rates and generation times. These relationships between developmental variance and population growth in models are quantified and discussed.     

Molecular divergence and hybrid performance in rice

This study was undertaken to determine the relationship between genetic distance of the parents based on molecular markers and F₁ performance in a set of diallel crosses involving eight commonly used parental lines in hybrid rice production. The F₁s and their parents were measured for five traits including heading date, plant height, straw weight, grain yield and biomass. The parental lines were assayed for DNA polymorphisms using two classes of markers: 140 probes for restriction fragment length polymorphisms (RFLPs) and 12 simple sequence repeats (SSRs), resulting in a total of 105 polymorphic markers well spaced along the 12 rice chromosomes. SSRs detected more polymorphism than RFLPs among the eight lines. A cluster analysis based on marker genotypes separated these eight lines into three groups which agree essentially with the available pedigree information. Correlations were mostly low between general heterozygosity based on all the markers and F₁ performance and heterosis. In contrast, very high correlations were detected between midparent heterosis and specific heterozygosity based on the markers that detected significant effects for all the five traits; these correlations may have practical utility in predicting heterosis. The analyses also suggest the existence of two likely heterotic groups in the rice germplasm represented by these eight lines.     

Competitive divergence in non-random mating populations

A haploid model of frequency-dependent selection and assortative mating is introduced and analyzed for the case of a single multiallelic autosomal locus. Frequency-dependent selection is due to intraspecific competition mediated by a quantitative character under stabilizing or directional selection. Assortment is induced by the same trait. We analyze the equilibrium structure and the local stability properties of all possible equilibria. In the limit of weak selection we obtain global stability properties by finding a Lyapunov function. We provide necessary and sufficient conditions for the maintenance of polymorphism in terms of the strength of stabilizing selection, intraspecific competition and assortment. Our results also include criteria for the ability of extreme types to invade the population. Furthermore, we study the occurrence of disruptive selection and provide necessary and sufficient conditions for intraspecific divergence to occur.     

Impact of developmental variance on behavior of models for insect populations II. Models for populations with density dependent restrictions on growth

The impact of variation in developmental times on behavior of models for insect populations is investigated with special reference to models which include various types of intraspecific competition. At low densities, increases in developmental variation led to decreases in reproductive rate. At high densities, increases in developmental variation led to increases in reproductive rate. There was little change in the relationship between developmental variance and generation time as density increased.     

Factors affecting cork oak growth under dry conditions: local adaptation and contrasting additive genetic variance within populations

Increased drought severity is expected in the Mediterranean Basin over the twenty-first century, but our understanding of the potential of most forest tree species to cope with it remains uncertain. In this study, (1) we examined the potential effects of long-term selection and the capacity to respond to future changes in selective pressures in three populations of cork oak (Quercus suber L.). For this purpose, we evaluated the response to dry conditions of 45 open-pollinated trees originating from populations in Morocco, Portugal, and Spain. Growth, leaf size, specific leaf area (SLA), carbon isotope discrimination (Δ¹³C), leaf nitrogen content (N_mass), and total chlorophyll content (Chl_mass) were measured in 9-year-old plants. (2) We also investigated the relationships between functional traits and aboveground growth by regression models. Plants presenting larger and more sclerophyllous leaves (low SLA and high leaf thickness) exhibited higher growths, with results suggesting that these traits are subjected to divergent selection in this species. Heritability estimates were moderately high for Δ¹³C (0.43 ± 0.25–0.83 ± 0.31) and stem diameter (0.40 ± 0.15–0.71 ± 0.28) for the tree populations. For the rest of the traits (except for annual growth), heritability values varied among populations, particularly for height, leaf size, leaf thickness, and N_mass. Our results suggest that natural selection has led to local adaptations and has also affected the genetic variance intrapopulation in these cork oak populations, although studies with a higher number of populations should be carried out across different years. Additionally, the absence of significant genetic correlations and the fact that correlated traits did not undergo opposing selection provided little evidence for constraints on evolution caused by genetic correlations.     

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.     

Genetic divergence and hybrid performance in mung bean

Summary Genetic divergence in 35 populations (10 parents and 25 F₁'s) of mung bean was studied by D² and canonical analyses. The ten parents formed as many as eight separate clusters, suggesting that the genetic divergence between them was quite substantial. The parent BR-2 was highly divergent from all the other entries. It was found that flowering time, maturity, seed density and seed size (100-seed weight) contributed substantially to the divergence. Canonical analysis supported the divergence pattern obtained by D² analysis and the contribution of different characters to genetic divergence. The relationship between genetic divergence (D²) and heterosis was evaluated. In general, there was fair agreement between the extent of heterosis and the genetic divergence between the parents.     

Impact of depth of pedigree and inclusion of historical data on the estimation of additive variance and breeding values in a sugarcane breeding program

Sugarcane breeders in Australia combine data across four selection programs to obtain estimates of breeding value for parents. When these data are combined with full pedigree information back to founding parents, computing limitations mean it is not possible to obtain information on all parents. Family data from one sugarcane selection program were analysed using two different genetic models to investigate how different depths of pedigree and amount of data affect the reliability of estimating breeding value of sugarcane parents. These were the parental and animal models. Additive variance components and breeding values estimated from different amounts of information were compared for both models. The accuracy of estimating additive variance components and breeding values improved as more pedigree information and historical data were included in analyses. However, adding years of data had a much larger effect on the estimation of variance components of the population, and breeding values of the parents. To accurately estimate breeding values of all sugarcane parents, a minimum of three generations of pedigree and 5 years of historical data were required, while more information (four generations of pedigree and 7 years of historical data) was required when identifying top parents to be selected for future cross pollination.