Heritability allows a comparison of the relative importance of genes and environment to the variation of traits within and across populations. The concept of heritability and its definition as an estimable, dimensionless population parameter was introduced by Sewall Wright and Ronald Fisher nearly a century ago. Despite continuous misunderstandings and controversies over its use and application, heritability remains key to the response to selection in evolutionary biology and agriculture, and to the prediction of disease risk in medicine. Recent reports of substantial heritability for gene expression and new estimation methods using marker data highlight the relevance of heritability in the genomics era.

Heritability in the genomics era — concepts and misconceptions

Mixed linear model (MLM) methods have proven useful in controlling for population structure and relatedness within genome-wide association studies. However, MLM-based methods can be computationally challenging for large datasets. We report a compression approach, called ‘compressed MLM’, that decreases the effective sample size of such datasets by clustering individuals into groups. We also present a complementary approach, ‘population parameters previously determined’ (P3D), that eliminates the need to re-compute variance components. We applied these two methods both independently and combined in selected genetic association datasets from human, dog and maize. The joint implementation of these two methods markedly reduced computing time and either maintained or improved statistical power. We used simulations to demonstrate the usefulness in controlling for substructure in genetic association datasets for a range of species and genetic architectures. We have made these methods available within an implementation of the software program TASSEL.

/pdf/mixed-linear-model-approach-adapted-for-genome-wide-2h7pnmzbhb.pdf

Mixed linear model approach adapted for genome-wide association studies.

Many modern genomic data analyses require implementing regressions where the number of parameters (p, e.g., the number of marker effects) exceeds sample size (n). Implementing these large-p-with-small-n regressions poses several statistical and computational challenges, some of which can be confronted using Bayesian methods. This approach allows integrating various parametric and nonparametric shrinkage and variable selection procedures in a unified and consistent manner. The BGLR R-package implements a large collection of Bayesian regression models, including parametric variable selection and shrinkage methods and semiparametric procedures (Bayesian reproducing kernel Hilbert spaces regressions, RKHS). The software was originally developed for genomic applications; however, the methods implemented are useful for many nongenomic applications as well. The response can be continuous (censored or not) or categorical (either binary or ordinal). The algorithm is based on a Gibbs sampler with scalar updates and the implementation takes advantage of efficient compiled C and Fortran routines. In this article we describe the methods implemented in BGLR, present examples of the use of the package, and discuss practical issues emerging in real-data analysis.

https://www.genetics.org/content/genetics/198/2/483.full.pdf

Genome-Wide Regression and Prediction with the BGLR Statistical Package

Representations of sensory stimuli in the cerebral cortex can undergo progressive remodelling according to the behavioural importance of the stimuli The cortex receives widespread projections from dopamine neurons in the ventral tegmental area (VTA), which are activated by new stimuli or unpredicted rewards, and are believed to provide a reinforcement signal for such learning-related cortical reorganization In the primary auditory cortex (AI) dopamine release has been observed during auditory learning that remodels the sound-frequency representations Furthermore, dopamine modulates long-term potentiation, a putative cellular mechanism underlying plasticity Here we show that stimulating the VTA together with an auditory stimulus of a particular tone increases the cortical area and selectivity of the neural responses to that sound stimulus in AI Conversely, the AI representations of nearby sound frequencies are selectively decreased Strong, sharply tuned responses to the paired tones also emerge in a second cortical area, whereas the same stimuli evoke only poor or non-selective responses in this second cortical field in naive animals In addition, we found that strong long-range coherence of neuronal discharge emerges between AI and this secondary auditory cortical area

Cortical remodelling induced by activity of ventral tegmental dopamine neurons

Variance components due to direct and maternal effects for growth traits of Australian beef cattle

Mixed Model Methodology for Farm and Ranch Beef Cattle Testing Programs

Length of Productive Life of Dairy Cows. 2. Variance Component Estimation and Sire Evaluation

Length of Productive Life of Dairy Cows. 1. Justification of a Weibull Model

Modified Equations for Sire Models with Groups

Phenotypic variances for linear and transformed weight traits were partitioned into residual, direct genetic (D) and maternal genetic (M) components using REML techniques with American Simmental Association data from calves born 1969 to 1985. Variance components were estimated separately from subclasses defined by sex (male, female) and percent Simmental (50, greater than or equal to 75). The model included fixed effects of contemporary group and age-of-dam (less than 3, 3 to 5, greater than 5 yr). Additive relationships among sires and maternal grandsires were included. Results follow for a sire-maternal grandsire model for greater than or equal to 75% Simmental untransformed data based on 143,280 male and 281,805 female weaning weights (WW) representing 4,763 and 7,406 sires, respectively. Female results are bracketed. For computational simplification, 47,650 [30,909] postweaning gain (PW) records were included in the analysis only for 114,404 [182,255] calves with birth weight (BW). Phenotypic standard deviations (kg) were: BW, 4.5 [4.1]; WW, 26.9 [23.2]; and PW, 25.9 [19.9]. Heritabilities were: BWD, .40 [.45]; WWD, .32 [.39]; PWD, .26 [.32]; BWM, .13 [.15]; WWM, .20 [.16]; and PWM, .01 [.01]. These heritabilities are higher than previously used for genetic evaluations in this breed. Moderate and positive correlations .26 to .50, existed between direct effects and were similar for both sexes. Direct and maternal effects on the same trait were correlated negatively: BW, -.45 [-.31]; and WW, -.27 [-.34]. Genetic correlation between BWM and WWM was .53 [.49]. First-cross progeny exhibited less genetic and residual variation and had lower heritabilities than Simmental calves of higher percent. Correlations between sire evaluations on the subsets were consistent with those expected given a perfect genetic correlation between traits for each sex and percent Simmental. Logarithmic transformed records were no more homogeneous than untransformed records.

/pdf/variance-heterogeneity-in-direct-and-maternal-weight-traits-3uabqk3qz4.pdf

E. J. Pollak

Papers

Mixed Model Methodology for Farm and Ranch Beef Cattle Testing Programs

Length of Productive Life of Dairy Cows. 2. Variance Component Estimation and Sire Evaluation

Length of Productive Life of Dairy Cows. 1. Justification of a Weibull Model

Modified Equations for Sire Models with Groups

Variance heterogeneity in direct and maternal weight traits by sex and percent purebred for Simmental-sired calves.