A comprehensive understanding of the genetic basis of phenotypic adaptation in nature requires the identification of the functional allelic variation underlying adaptive phenotypes. The manner in which organisms respond to temperature extremes is an adaptation in many species. In the current study, we investigate the role of molecular variation in senescence marker protein-30 (Smp-30) on natural phenotypic variation in cold tolerance in Drosophila melanogaster. Smp-30 encodes a product that is thought to be involved in the regulation of Ca2+ ion homeostasis and has been shown previously to be differentially expressed in response to cold stress. Thus, we sought to assess whether molecular variation in Smp-30 was associated with natural phenotypic variation in cold tolerance in a panel of naturally derived inbred lines from a population in Raleigh, North Carolina. We identified four non-coding polymorphisms that were strongly associated with natural phenotypic variation in cold tolerance. Interestingly, two polymorphisms that were in close proximity to one another (2 bp apart) exhibited opposite phenotypic effects. Consistent with the maintenance of a pair of antagonistically acting polymorphisms, tests of molecular evolution identified a significant excess of maintained variation in this region, suggesting balancing selection is acting to maintain this variation. These results suggest that multiple mutations in non-coding regions can have significant effects on phenotypic variation in adaptive traits within natural populations, and that balancing selection can maintain polymorphisms with opposite effects on phenotypic variation.

A challenge when predicting total genetic values for complex quantitative traits is that an unknown number of quantitative trait loci may affect phenotypes via cryptic interactions. If markers are available, assuming that their effects on phenotypes are additive may lead to poor predictive ability. Non-parametric radial basis function (RBF) regression, which does not assume a particular form of the genotype–phenotype relationship, was investigated here by simulation and analysis of body weight and food conversion rate data in broilers. The simulation included a toy example in which an arbitrary non-linear genotype–phenotype relationship was assumed, and five different scenarios representing different broad sense heritability levels (0·1, 0·25, 0·5, 0·75 and 0·9) were created. In addition, a whole genome simulation was carried out, in which three different gene action modes (pure additive, additive+dominance and pure epistasis) were considered. In all analyses, a training set was used to fit the model and a testing set was used to evaluate predictive performance. The latter was measured by correlation and predictive mean-squared error (PMSE) on the testing data. For comparison, a linear additive model known as Bayes A was used as benchmark. Two RBF models with single nucleotide polymorphism (SNP)-specific (RBF I) and common (RBF II) weights were examined. Results indicated that, in the presence of complex genotype–phenotype relationships (i.e. non-linearity and non-additivity), RBF outperformed Bayes A in predicting total genetic values using SNP markers. Extension of Bayes A to include all additive, dominance and epistatic effects could improve its prediction accuracy. RBF I was generally better than RBF II, and was able to identify relevant SNPs in the toy example.

Prediction of genetic values is a central problem in quantitative genetics. Over many decades, such predictions have been successfully accomplished using information on phenotypic records and family structure usually represented with a pedigree. Dense molecular markers are now available in the genome of humans, plants and animals, and this information can be used to enhance the prediction of genetic values. However, the incorporation of dense molecular marker data into models poses many statistical and computational challenges, such as how models can cope with the genetic complexity of multi-factorial traits and with the curse of dimensionality that arises when the number of markers exceeds the number of data points. Reproducing kernel Hilbert spaces regressions can be used to address some of these challenges. The methodology allows regressions on almost any type of prediction sets (covariates, graphs, strings, images, etc.) and has important computational advantages relative to many parametric approaches. Moreover, some parametric models appear as special cases. This article provides an overview of the methodology, a discussion of the problem of kernel choice with a focus on genetic applications, algorithms for kernel selection and an assessment of the proposed methods using a collection of 599 wheat lines evaluated for grain yield in four mega environments.

As an emerging powerful approach for mapping quantitative trait loci (QTLs) responsible for dynamic traits, functional mapping models the time-dependent mean vector with biologically meaningful equations and are likely to generate biologically relevant and interpretable results. Given the autocorrelation nature of a dynamic trait, functional mapping needs the implementation of the models for the structure of the covariance matrix. In this article, we have provided a comprehensive set of approaches for modelling the covariance structure and incorporated each of these approaches into the framework of functional mapping. The Bayesian information criterion (BIC) values are used as a model selection criterion to choose the optimal combination of the submodels for the mean vector and covariance structure. In an example for leaf age growth from a rice molecular genetic project, the best submodel combination was found between the Gaussian model for the correlation structure, power equation of order 1 for the variance and the power curve for the mean vector. Under this combination, several significant QTLs for leaf age growth trajectories were detected on different chromosomes. Our model can be well used to study the genetic architecture of dynamic traits of agricultural values.

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.

The objective of this study was to investigate, both empirically and deterministically, the ability to explain genetic variation resulting from a copy number polymorphism (CNP) by including the CNP, either by its genotype or by a continuous derivation thereof, alone or together with a nearby single nucleotide polymorphism (SNP) in the model. This continuous measure of a CNP genotype could be a raw hybridization measurement, or a predicted CNP genotype. Results from simulations showed that the linkage disequilibrium (LD) between an SNP and CNP was lower than LD between two SNPs, due to the higher mutation rate at the CNP loci. The model R2 values from analysing the simulated data were very similar to the R2 values predicted with the deterministic formulae. Under the assumption that x copies at a CNP locus lead to the effect of x times the effect of 1 copy, including a continuous measure of a CNP locus in the model together with the genotype of a nearby SNP increased power to explain variation at the CNP locus, even when the continuous measure explained only 15% of the variation at the CNP locus.

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.

Epistasis underlying fertility plays an important role in crop breeding. Although a new female sterile mutant in wheat, XND126, has been identified and a major quantitative trait locus (QTL), taf1, for the female sterility has been mapped, the genetic architecture of the female sterility needs to be further addressed. To identify the interaction involving the gene(s) controlling the female sterility, an investigation was carried out for the seed setting ratio in an F2 population derived from the cross between XND126 and Gaocheng 8901. Among 1250 simple sequence repeat (SSR) primer pairs in the whole genome, a total of 21 markers, obtained by recessive class approach, along with other ten tightly linked markers on reference maps in wheat, were used to survey 243 F2 individuals. As a result, 28 markers were mapped into five genetic linkage groups. The performance for female sterility for each F2 individual was evaluated simultaneously at the Urumqi and Huai'an experimental stations in 2006–2007. The two phenotypic datasets along with marker information were jointly analysed in the detection of QTL using penalized maximum likelihood approach. A total of six QTLs, including two main-effect QTLs, three epistatic QTLs and one environmental interaction and accounting for 0·67–24·55% of the total phenotypic variance, were identified. All estimated effects accounted for 53·26% of the total phenotypic variation. The taf1 detected in previous study was also located on the same marker interval on chromosome 2DS. These results enrich our understanding of the genetic basis of the female sterility.

Analysis of the temporal variation in allele frequencies is useful for studying microevolutionary processes. However, many statistical methods routinely used to test temporal changes in allele frequencies fail to establish a proper hypothesis or have theoretical or practical limitations. Here, a Bayesian statistical test is proposed in which the distribution of the distances among sampling frequencies is approached with computer simulations, and hypergeometric sampling is considered instead of binomial sampling. To validate the test and compare its performance with other tests, agent-based model simulations were run for a variety of scenarios, and two real molecular databases were analysed. The results showed that the simulation test (ST) maintained the significance value used (α=0·05) for a vast combination of parameter values, whereas other tests were sensitive to the effect of genetic drift or binomial sampling. The differences between binomial and hypergeometric sampling were more complex than expected, and a novel effect was described. This study suggests that the ST is especially useful for studies with small populations and many alleles, as in microsatellite or sequencing molecular data.

The L2-Boosting algorithm is one of the most promising machine-learning techniques that has appeared in recent decades. It may be applied to high-dimensional problems such as whole-genome studies, and it is relatively simple from a computational point of view. In this study, we used this algorithm in a genomic selection context to make predictions of yet to be observed outcomes. Two data sets were used: (1) productive lifetime predicted transmitting abilities from 4702 Holstein sires genotyped for 32 611 single nucleotide polymorphisms (SNPs) derived from the Illumina® BovineSNP50 BeadChip, and (2) progeny averages of food conversion rate, pre-corrected by environmental and mate effects, in 394 broilers genotyped for 3481 SNPs. Each of these data sets was split into training and testing sets, the latter comprising dairy or broiler sires whose ancestors were in the training set. Two weak learners, ordinary least squares (OLS) and non-parametric (NP) regression were used for the L2-Boosting algorithm, to provide a stringent evaluation of the procedure. This algorithm was compared with BL [Bayesian LASSO (least absolute shrinkage and selection operator)] and BayesA regression. Learning tasks were carried out in the training set, whereas validation of the models was performed in the testing set. Pearson correlations between predicted and observed responses in the dairy cattle (broiler) data set were 0·65 (0·33), 0·53 (0·37), 0·66 (0·26) and 0·63 (0·27) for OLS-Boosting, NP-Boosting, BL and BayesA, respectively. The smallest bias and mean-squared errors (MSEs) were obtained with OLS-Boosting in both the dairy cattle (0·08 and 1·08, respectively) and broiler (−0·011 and 0·006) data sets, respectively. In the dairy cattle data set, the BL was more accurate (bias=0·10 and MSE=1·10) than BayesA (bias=1·26 and MSE=2·81), whereas no differences between these two methods were found in the broiler data set. L2-Boosting with a suitable learner was found to be a competitive alternative for genomic selection applications, providing high accuracy and low bias in genomic-assisted evaluations with a relatively short computational time.

Quantitative trait loci (QTLs) mapping often results in data on a number of traits that have well-established causal relationships. Many multi-trait QTL mapping methods that account for correlation among the multiple traits have been developed to improve the statistical power and the precision of QTL parameter estimation. However, none of these methods are capable of incorporating the causal structure among the traits. Consequently, genetic functions of the QTL may not be fully understood. In this paper, we developed a Bayesian multiple QTL mapping method for causally related traits using a mixture structural equation model (SEM), which allows researchers to decompose QTL effects into direct, indirect and total effects. Parameters are estimated based on their marginal posterior distribution. The posterior distributions of parameters are estimated using Markov Chain Monte Carlo methods such as the Gibbs sampler and the Metropolis–Hasting algorithm. The number of QTLs affecting traits is determined by the Bayes factor. The performance of the proposed method is evaluated by simulation study and applied to data from a wheat experiment. Compared with single trait Bayesian analysis, our proposed method not only improved the statistical power of QTL detection, accuracy and precision of parameter estimates but also provided important insight into how genes regulate traits directly and indirectly by fitting a more biologically sensible model.

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.

The incorporation of genetic information such as quantitative trait loci (QTL) data into breeding schemes has become feasible as DNA technologies have advanced. Such strategies allow the frequency of desirable QTL to be controlled over a predefined time frame, allowing the allele trajectory for QTL to be manipulated. A continuous approximation to changes in allele frequency was developed to approximate the selection procedure as a continuous rather than a discrete process, and analytical solutions were obtained, which shed light on how allele trajectories behave under different objective functions. Three different objectives were considered: (1) minimizing the total selection intensity, (2) minimizing the sum of squared selection intensities and (3) equalizing the selection intensity applied over time. Simulations and genetic algorithms were performed to test the accuracy and robustness of the continuous approximation. Theory shows firstly that the total selection intensity required for moving an allele from a starting frequency to another frequency point can be predicted independent of its trajectory, and secondly that objectives (2) and (3) are equivalent as the number of selection opportunities (T) becomes large. The prediction of total selection intensity provides a good fit for these two objectives, with the accuracy of prediction improving as T increases. However, for (1) the continuous approximation does not fit due to the existence of a discontinuous solution in which the continuous approximation is applied before the frequency of the selected allele reaches 0·5 followed by rapid fixation.

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.