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Abstract With an increase in the number of animals genotyped there has been a shift from using pedigree relationship matrices (A) to genomic ones. As the use of genomic relationship matrices (G) has increased, new methods to build or approximate G have developed. We investigated whether the way variance components are estimated should reflect these changes. We estimated variance components for maternal sow traits by solving with restricted maximum likelihood, with four methods of calculating the inverse of the relationship matrix. These methods included using just the inverse of A (A−1), combining A−1 and the direct inverse of G (HDIRECT−1), including metafounders (HMETA−1), or combining A−1 with an approximated inverse of G using the algorithm for proven and young animals (HAPY−1). There was a tendency for higher additive genetic variances and lower permanent environmental variances estimated with A−1 compared with the three H−1 methods, which supports that G−1 is better than A−1 at separating genetic and permanent environmental components, due to a better definition of the actual relationships between animals. There were limited or no differences in variance estimates between HDIRECT−1, HMETA−1, and HAPY−1. Importantly, there was limited differences in variance components, repeatability or heritability estimates between methods. Heritabilities ranged between <0.01 to 0.04 for stayability after second cycle, and farrowing rate, between 0.08 and 0.15 for litter weight variation, maximum cycle number, total number born, total number still born, and prolonged interval between weaning and first insemination, and between 0.39 and 0.44 for litter birth weight and gestation length. The limited differences in heritabilities suggest that there would be very limited changes to estimated breeding values or ranking of animals across models using the different sets of variance components. It is suggested that variance estimates continue to be made using A−1, however including G−1 is possibly more appropriate if refining the model, for traits that fit a permanent environmental effect.

We propose leave-out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An approximation algorithm is provided that enables accurate computation of the estimator in very large data sets. We study the large sample properties of our estimator allowing the number of regressors to grow in proportion to the number of observations. Consistency is established in a variety of settings where plug-in methods and estimators predicated on homoscedasticity exhibit first-order biases. For quadratic forms of increasing rank, the limiting distribution can be represented by a linear combination of normal and non-central χ² random variables, with normality ensuing under strong identification. Standard error estimators are proposed that enable tests of linear restrictions and the construction of uniformly valid confidence intervals for quadratic forms of interest. We find in Italian social security records that leave-out estimates of a variance decomposition in a two-way fixed effects model of wage determination yield substantially different conclusions regarding the relative contribution of workers, firms, and worker-firm sorting to wage inequality than conventional methods. Monte Carlo exercises corroborate the accuracy of our asymptotic approximations, with clear evidence of non-normality emerging when worker mobility between blocks of firms is limited.

The software Selegen-REML/BLUP uses mixed models, and was developed to optimize the routine of plant breeding programs. It addresses the following plants categories: allogamous, automagous, of mixed mating system, and of clonal propagation. It considers several experimental designs, mating designs, genotype x environment interaction, experiments repeated over sites, repeated measures, progenies belonging to several populations, among other factors. The software adjusts effects, estimates variance components, genetic additive, dominance and genotypic values of individuals, genetic gain with selection, effective population size, and other parameters of interest to plant breeding. It allows testing the significance of the effects by means of likelihood ratio test (LRT) and analysis of deviance. It addresses continuous variables (linear models) and categorical variables (generalized linear models). Selegen-REML/ BLUP is friendly, easy to use and interpret, and allows dealing efficiently with most of the situations in plant breeding. It is free and available at http://www.det.ufv.br/ppestbio/corpo_docente.php under the author’s name.

Genomic prediction methods based on multiple markers have potential to include nonadditive effects in prediction and analysis of complex traits. However, most developments assume a Hardy–Weinberg equilibrium (HWE). Statistical approaches for genomic selection that account for dominance and epistasis in a general context, without assuming HWE (e.g., crosses or homozygous lines), are therefore needed. Our method expands the natural and orthogonal interactions (NOIA) approach, which builds incidence matrices based on genotypic (not allelic) frequencies, to include genome-wide epistasis for an arbitrary number of interacting loci in a genomic evaluation context. This results in an orthogonal partition of the variances, which is not warranted otherwise. We also present the partition of variance as a function of genotypic values and frequencies following Cockerham’s orthogonal contrast approach. Then we prove for the first time that, even not in HWE, the multiple-loci NOIA method is equivalent to construct epistatic genomic relationship matrices for higher-order interactions using Hadamard products of additive and dominant genomic orthogonal relationships. A standardization based on the trace of the relationship matrices is, however, needed. We illustrate these results with two simulated F1 (not in HWE) populations, either in linkage equilibrium (LE), or in linkage disequilibrium (LD) and divergent selection, and pure biological dominant pairwise epistasis. In the LE case, correct and orthogonal estimates of variances were obtained using NOIA genomic relationships but not if relationships were constructed assuming HWE. For the LD simulation, differences were smaller, due to the smaller deviation of the F1 from HWE. Wrongly assuming HWE to build genomic relationships and estimate variance components yields biased estimates, inflates the total genetic variance, and the estimates are not empirically orthogonal. The NOIA method to build genomic relationships, coupled with the use of Hadamard products for epistatic terms, allows the obtaining of correct estimates in populations either in HWE or not in HWE, and extends to any order of epistatic interactions.

Abstract Genetic analysis in autopolyploids is a very complicated subject due to the enormous number of genotypes at a locus that needs to be considered. For instance, the number of... In developing countries, the sweetpotato, Ipomoea batatas (L.) Lam. (2n=6x=90), is an important autopolyploid species, both socially and economically. However, quantitative trait loci (QTL) mapping has remained limited due to its genetic complexity. Current fixed-effect models can fit only a single QTL and are generally hard to interpret. Here, we report the use of a random-effect model approach to map multiple QTL based on score statistics in a sweetpotato biparental population (‘Beauregard’ × ‘Tanzania’) with 315 full-sibs. Phenotypic data were collected for eight yield component traits in six environments in Peru, and jointly adjusted means were obtained using mixed-effect models. An integrated linkage map consisting of 30,684 markers distributed along 15 linkage groups (LGs) was used to obtain the genotype conditional probabilities of putative QTL at every centiMorgan position. Multiple interval mapping was performed using our R package QTLpoly and detected a total of 13 QTL, ranging from none to four QTL per trait, which explained up to 55% of the total variance. Some regions, such as those on LGs 3 and 15, were consistently detected among root number and yield traits, and provided a basis for candidate gene search. In addition, some QTL were found to affect commercial and noncommercial root traits distinctly. Further best linear unbiased predictions were decomposed into additive allele effects and were used to compute multiple QTL-based breeding values for selection. Together with quantitative genotyping and its appropriate usage in linkage analyses, this QTL mapping methodology will facilitate the use of genomic tools in sweetpotato breeding as well as in other autopolyploids.

In this paper, a multivariate heterogeneous variance components model was developed which allows for determination of location specific variance components in the analysis of multiple related traits. In addition to spatial heterogeneity, genetic similarities are also considered by assigning genetic variance components. The performance of the developed model was evaluated through an extensive simulation study and comparison of models was conducted by heritability estimations. The simulation study reveals that the developed method can control the locational heterogeneity well and the heritability estimations are close to desired proportions for the developed model. A real plant breeding data set was used for illustration.

ABSTRACT Maize is an important cereal that is grown and consumed all over the world. Among the selection methods that contribute to increasing the frequency of favorable alleles in native maize populations, selection between and within and stratified mass selection in half-sibling families has proven efficient. This study aimed to conduct an individual selection between and within and stratified mass selection in ten half-sibling families of native maize and to estimate the variance components, genetic parameters, and selection gains for them. Ten half-brother families of families were evaluated. The experimental design was DBC, with two replications totaling 20 experimental units, evaluating four plants per plot. The spacing used was 0.8 by 0.3 m. The following were evaluated: stalk diameter (SD), ear length (EL), ear diameter (ED), number of rows (NF), number of grains per row (NGR), ear mass (EM), and total grain mass (TGM) were evaluated. Individual analyses were carried out for all the traits evaluated, selected to increase the original means with a selection intensity of 50% between/50% within. Stratified mass selection yielded higher selection gains than selection between and within families. The selection of the character’s ear mass and total grain mass showed the highest estimates of genetic gain, 54.45 and 48.37%, respectively.

The question of what drives corporate social performance (CSP) has become a vital concern for many managers and researchers of large corporations. This study addresses this question by adopting a multilevel, multistakeholder, and multimethod approach to theorize and estimate the relative influence of macro (national business system and country), meso (industry), and micro (firm-level) factors on CSP. Applying three different methods of variance decomposition analysis to an international sample of 2060 large public companies over a time span of 5 years, our results show that firm-level factors explain the largest proportion of variance in aggregate CSP as well as CSP oriented toward communities, the natural environment, and employees. These results support our hypotheses according to which CSP is not primarily driven by macrolevel or mesolevel factors, except for shareholder-oriented CSP, which is relatively more influenced by country-level factors. As a whole, our findings also point to the value of subdividing CSP into its stakeholder-specific components as this disaggregation allows for a more careful examination of distinct drivers of distinct aspects of CSP.

The limits of agreement (LoA) method proposed by Bland and Altman has become a standard for assessing agreement between different methods measuring the same quantity. Virtually, all method comparison studies have reported only point estimates of LoA due largely to the lack of simple confidence interval procedures. In this article, we address confidence interval estimation for LoA when multiple measurements per individual are available. Separate procedures are proposed for situations when the underlying true value of the measured quantity is assumed changing and when it is perceived as stable. A fixed number of replicates per individual is not needed for the procedures to work. As shown by the worked examples, the construction of these confidence intervals requires only quantiles from the standard normal and chi-square distributions. Simulation results show the proposed procedures perform well. A SAS macro implementing the methods is available on the publisher's website.