Over the past 30 years, the characteristics that have made the nematode Caenorhabditis elegans one of the premier animal model systems have also allowed it to emerge as a powerful model system for determining the genetic basis of quantitative traits, particularly for the identification of naturally segregating and/or lab-adapted alleles with large phenotypic effects. To better understand the genetic underpinnings of natural variation in other complex phenotypes, C. elegans is uniquely poised in the emerging field of quantitative systems biology because of the extensive knowledge of cellular and neural bases to such traits. However, perturbations in standing genetic variation and patterns of linkage disequilibrium among loci are likely to limit our ability to tie understanding of molecular function to a broader evolutionary context. Coupling the experimental strengths of the C. elegans system with the ecological advantages of closely related nematodes should provide a powerful means of understanding both the molecular and evolutionary genetics of quantitative traits.

The expression of behaviours is influenced by many segregating genes. Behaviours are, therefore, complex traits. They have, however, unique characteristics that set them apart from physiological and morphological quantitative traits. First, behaviours are the ultimate expression of the nervous system. This means that understanding the genetic underpinnings of behaviours requires a neurobiological context, i.e. an understanding of the genes–brain–behaviour axis. In other words, how do ensembles of genes empower specific neural circuits to drive behaviours? Second, behaviours represent the interface between an organism and its environment. Thus, environmental effects are likely to make substantial contributions to determining behavioural outputs and genotype-by-environment interactions are expected to be prominent. It is important to differentiate between genes that contribute to the manifestation of the behavioural phenotype and genes that contribute to phenotypic variation in behaviour. The former are identified by classical mutagenesis experiments, whereas the latter can be detected through quantitative genetic approaches. Genes that contribute to phenotypic variation in behaviour harbour polymorphisms that provide the substrates for evolution. This review focuses on olfactory behaviour in Drosophila with the goal to illustrate how fundamental insights derived from studies on chemosensation can be applied to a wide range of behavioural phenotypes.

Human gene expression profiles have emerged as an effective model system for the dissection of quantitative genetic traits. Peripheral blood and transformed lymphoblasts are particularly attractive for their ready availability and repeatability, respectively, and the advent of relatively inexpensive genotyping and microarray analysis technologies has facilitated genome-wide association for transcript abundance in numerous settings. Thousands of genes have been shown to harbour regulatory polymorphisms that have large local effects on transcription, explaining 20% or more of the variance in many cases, but the focus on such results obscures the reality that the vast majority of the genetic component of transcriptional variance remains to be ascertained. This mini-review surveys the inferences derived from genome-wide association studies (GWAS) for gene expression to date, and discusses some of the issues we face in finding the remainder of the heritability and understanding how environmental and genetic regulatory factors orchestrate the highly structured architecture of transcriptional variation.

Height has been studied in human genetics since the late 1800s. We review what we have learned about the genetic architecture of this trait from the resemblance between relatives and from genetic marker data. All empirical evidence points towards height being highly polygenic, with many loci contributing to variation in the population and most effect sizes appear to be small. Nevertheless, combining new genetic and genomic technologies with phenotypic measures on height on large samples facilitates new answers to old questions, including the basis of assortative mating in humans, estimation of non-additive genetic variation and partitioning between-cohort phenotypic differences into genetic and non-genetic underlying causes.

Environmental variation (VE) in a quantitative trait – variation in phenotype that cannot be explained by genetic variation or identifiable genetic differences – can be regarded as being under some degree of genetic control. Such variation may be either between repeated expressions of the same trait within individuals (e.g. for bilateral traits), in the phenotype of different individuals, where variation within families may differ, or in both components. We consider alternative models for defining the distribution of phenotypes to include a component due to heterogeneity of VE. We review evidence for the presence of genetic variation in VE and estimates of its magnitude. Typically the heritability of VE is under 10%, but its genetic coefficient of variation is typically 20% or more. We consider experimental designs appropriate for estimating genetic variance in VE and review alternative methods of estimation. We consider the effects of stabilizing and directional selection on VE and review both the forces that might be maintaining levels of VE and heritability found in populations. We also evaluate the opportunities for reducing VE in breeding programmes. Although empirical and theoretical studies have increased our understanding of genetic control of environmental variance, many issues remain unresolved.

Population genomics is the study of the amount and causes of genome-wide variability in natural populations, a topic that has been under discussion since Darwin. This paper first briefly reviews the early development of molecular approaches to the subject: the pioneering unbiased surveys of genetic variability at multiple loci by means of gel electrophoresis and restriction enzyme mapping. The results of surveys of levels of genome-wide variability using DNA resequencing studies are then discussed. Studies of the extent to which variability for different classes of variants (non-synonymous, synonymous and non-coding) are affected by natural selection, or other directional forces such as biased gene conversion, are also described. Finally, the effects of deleterious mutations on population fitness and the possible role of Hill–Robertson interference in shaping patterns of sequence variability are discussed.

Most traits of economic importance in livestock are either quantitative or complex. Despite considerable efforts, there has been only limited success in identifying the polymorphisms that cause variation in these traits. Nevertheless, selection based on estimated breeding values (BVs), calculated from data on phenotypic performance and pedigree has been very successful. Genomic tools, such as single nucleotide polymorphism (SNP) chips, have led to a new method of selection called ‘genomic selection’ in which dense SNP genotypes covering the genome are used to predict the BV. In this review we consider the statistical methodology for estimating BVs from SNP data, factors affecting the accuracy, the long-term response to genomic selection and the design of breeding programmes including the management of inbreeding.

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.