Methods of genomic value prediction are reviewed. The majority of the methods are related to mixed model methodology, either explicitly or implicitly, by treating systematic environmental effects as fixed and quantitative trait locus (QTL) effects as random. Six different methods are reviewed, including least squares (LS), ridge regression, Bayesian shrinkage, least absolute shrinkage and selection operator (Lasso), empirical Bayes and partial least squares (PLS). The LS and PLS methods are non-Bayesian because they do not require probability distributions for the data. The PLS method is introduced as a special dimension reduction scheme to handle high-density marker information. Theory and methods of cross-validation are described. The leave-one-out cross-validation approach is recommended for model validation. A working example is used to demonstrate the utility of genome selection (GS) in barley. The data set contained 150 double haploid lines and 495 DNA markers covering the entire barley genome, with an average marker interval of 2·23 cM. Eight quantitative traits were included in the analysis. GS using the empirical Bayesian method showed high predictability of the markers for all eight traits with a mean accuracy of prediction of 0·70. With traditional marker-assisted selection (MAS), the average accuracy of prediction was 0·59, giving an average gain of GS over MAS of 0·11. This study provided strong evidence that GS using marker information alone can be an efficient tool for plant breeding.

Many common human diseases and complex traits are highly heritable and influenced by multiple genetic and environmental factors. Although genome-wide association studies (GWAS) have successfully identified many disease-associated variants, these genetic variants explain only a small proportion of the heritability of most complex diseases. Genetic interactions (gene–gene and gene–environment) substantially contribute to complex traits and diseases and could be one of the main sources of the missing heritability. This paper provides an overview of the available statistical methods and related computer software for identifying genetic interactions in animal and plant experimental crosses and human genetic association studies. The main discussion falls under the three broad issues in statistical analysis of genetic interactions: the definition, detection and interpretation of genetic interactions. Recently developed methods based on modern techniques for high-dimensional data are reviewed, including penalized likelihood approaches and hierarchical models; the relationships between these methods are also discussed. I conclude this review by highlighting some areas of future research.

Whole genome data are allowing the estimation of population genetic parameters with an accuracy not imagined 50 years ago. Variation in these parameters along the genome is being found empirically where once only approximate theoretical values were available. Along with increased information, however, has come the issue of multiple testing and the realization that high values of the coefficients of variation of quantities such as relatedness measures may make it difficult to draw inferences. This review concentrates on measures of allelic association within and between individuals and within and between populations.