Use of randomization testing to detect multiple epistatic QTLs

vqtl: An R Package for Mean-Variance QTL Mapping

We present vqtl, an R package for mean-variance QTL mapping. This QTL mapping approach tests for genetic loci that influence the mean of the phenotype, termed mean QTL, the variance of the phenotype, termed variance QTL, or some combination of the two, termed mean-variance QTL. It is unique in its ability to correct for variance heterogeneity arising not only from the QTL itself but also from nuisance factors, such as sex, batch, or housing. This package provides functions to conduct genome scans, run permutations to assess the statistical significance, and make informative plots to communicate results. Because it is inter-operable with the popular qtl package and uses many of the same data structures and input patterns, it will be straightforward for geneticists to analyze future experiments with vqtl as well as re-analyze past experiments, possibly discovering new QTL.

Consequences of Epistasis on Growth in an Erhualian × White Duroc Pig Cross

Epistasis describes an interaction between the effects of loci. We included epistasis in quantitative trait locus (QTL) mapping of growth at a series of ages in a cross of a Chinese pig breed, Erhualian, with a commercial line, White Duroc. Erhualian pigs have much lower growth rates than White Duroc. We improved a method for genomewide testing of epistasis and present a clear analysis workflow. We also suggest a new approach for interpreting epistasis results where significant additive and dominance effects of a locus in specific backgrounds are determined. In total, seventeen QTL were found and eleven showed epistasis. Loci on chromosomes 2, 3, 4 and 7 were highlighted as affecting growth at more than one age or forming an interaction network. Epistasis resulted in both the QTL on chromosomes 3 and 7 having effects in opposite directions. We believe it is the first time for the chromosome 7 locus that an allele from a Chinese breed has been found to decrease growth. The consequences of epistasis were diverse. Results were impacted by using growth rather than body weight as the phenotype and by correcting for an effect of mother. Epistasis made a considerable contribution to growth in this population and modelling epistasis was important for accurately determining QTL effects.

Genetics of Interactive Behavior in Silver Foxes (Vulpes vulpes)

Individuals involved in a social interaction exhibit different behavioral traits that, in combination, form the individual's behavioral responses. Selectively bred strains of silver foxes (Vulpes vulpes) demonstrate markedly different behaviors in their response to humans. To identify the genetic basis of these behavioral differences we constructed a large F₂ population including 537 individuals by cross-breeding tame and aggressive fox strains. 98 fox behavioral traits were recorded during social interaction with a human experimenter in a standard four-step test. Patterns of fox behaviors during the test were evaluated using principal component (PC) analysis. Genetic mapping identified eight unique significant and suggestive QTL. Mapping results for the PC phenotypes from different test steps showed little overlap suggesting that different QTL are involved in regulation of behaviors exhibited in different behavioral contexts. Many individual behavioral traits mapped to the same genomic regions as PC phenotypes. This provides additional information about specific behaviors regulated by these loci. Further, three pairs of epistatic loci were also identified for PC phenotypes suggesting more complex genetic architecture of the behavioral differences between the two strains than what has previously been observed.

MAPfastR: quantitative trait loci mapping in outbred line crosses

MAPfastR is a software package developed to analyze quantitative trait loci data from inbred and outbred line-crosses. The package includes a number of modules for fast and accurate quantitative trait loci analyses. It has been developed in the R language for fast and comprehensive analyses of large datasets. MAPfastR is freely available at: http://www.computationalgenetics.se/?page_id=7

Modelling of genetic interactions improves prediction of hybrid patterns--a case study in domestic fowl

A major challenge in complex trait genetics is to unravel how multiple loci and environmental factors together cause phenotypic diversity. Both first (F(1)) and second (F(2)) generation hybrids often display phenotypes that deviate from what is expected under intermediate inheritance. We have here studied two chicken F(2) populations generated by crossing divergent chicken lines to assess how epistatic loci, identified in earlier quantitative trait locus (QTL) studies, contribute to hybrid deviations from the mid-parent phenotype. Empirical evidence suggests that the average phenotypes of the intercross birds tend to be lower than the midpoint between the parental means in both crosses. Our results confirm that epistatic interactions, despite a relatively small contribution to the phenotypic variance, play an important role in the deviation of hybrid phenotypes from the mid-parent values (i.e. multi-locus hybrid genotypes lead to lower rather than higher body weights). To a lesser extent, dominance also appears to contribute to the mid-parent deviation, at least in one of the crosses. This observation coincides with the hypothesis that hybridization tends to break up co-adapted gene complexes, i.e. generate Bateson-Dobzhansky-Muller incompatibilities.

Travelling the world of gene-gene interactions

Over the last few years, main effect genetic association analysis has proven to be a successful tool to unravel genetic risk components to a variety of complex diseases. In the quest for disease susceptibility factors and the search for the 'missing heritability', supplementary and complementary efforts have been undertaken. These include the inclusion of several genetic inheritance assumptions in model development, the consideration of different sources of information, and the acknowledgement of disease underlying pathways of networks. The search for epistasis or gene-gene interaction effects on traits of interest is marked by an exponential growth, not only in terms of methodological development, but also in terms of practical applications, translation of statistical epistasis to biological epistasis and integration of omics information sources. The current popularity of the field, as well as its attraction to interdisciplinary teams, each making valuable contributions with sometimes rather unique viewpoints, renders it impossible to give an exhaustive review of to-date available approaches for epistasis screening. The purpose of this work is to give a perspective view on a selection of currently active analysis strategies and concerns in the context of epistasis detection, and to provide an eye to the future of gene-gene interaction analysis.

A general model for multilocus epistatic interactions in case-control studies

Background

Epistasis, i.e., the interaction of alleles at different loci, is thought to play a central role in the formation and progression of complex diseases. The complexity of disease expression should arise from a complex network of epistatic interactions involving multiple genes.

Methodology

We develop a general model for testing high-order epistatic interactions for a complex disease in a case-control study. We incorporate the quantitative genetic theory of high-order epistasis into the setting of cases and controls sampled from a natural population. The new model allows the identification and testing of epistasis and its various genetic components.

Conclusions

Simulation studies were used to examine the power and false positive rates of the model under different sampling strategies. The model was used to detect epistasis in a case-control study of inflammatory bowel disease, in which five SNPs at a candidate gene were typed, leading to the identification of a significant three-locus epistasis.

Chromosomal mapping of excessive physical activity in mice in response to a restricted feeding schedule

Excessive physical activity plays an important role in the progression of anorexia nervosa (AN) by accelerating weight loss during dietary restriction. To search for mechanisms underlying this trait, a panel of mouse chromosome substitution strains derived from C57BL/6J and A/J strains was exposed to a scheduled feeding paradigm and to voluntary running wheel (RW) access. Here, we showed that A/J chromosomes 4, 12 and 13 contribute to the development of a disrupted RW activity in response to daily restricted feeding. This pattern is characterized by intense RW activity during the habitual rest phase and leads to accelerated body weight loss. Regions on mouse chromosomes 4, 12 and 13 display homology with regions on human chromosomes linked with anxiety and obsessionality in AN cohorts. Therefore, our data open new roads for interspecies genetic studies of AN and for unraveling novel mechanisms and potential effective treatment strategies for these neurobehavioral traits.

Controlling false positives in the mapping of epistatic QTL

This study addresses the poorly explored issue of the control of false positive rate (FPR) in the mapping of pair-wise epistatic quantitative trait loci (QTL). A nested test framework was developed to (1) allow pre-identified QTL to be used directly to detect epistasis in one-dimensional genome scans, (2) to detect novel epistatic QTL pairs in two-dimensional genome scans and (3) to derive genome-wide thresholds through permutation and handle multiple testing. We used large-scale simulations to evaluate the performance of both the one- and two-dimensional approaches in mapping different forms and levels of epistasis and to generate profiles of FPR, power and accuracy to inform epistasis mapping studies. We showed that the nested test framework and genome-wide thresholds were essential to control FPR at the 5% level. The one-dimensional approach was generally more powerful than the two-dimensional approach in detecting QTL-associated epistasis and identified nearly all epistatic pairs detected from the two-dimensional approach. However, only the two-dimensional approach could detect epistatic QTL with weak main effects. Combining the two approaches allowed effective mapping of different forms of epistasis, whereas using the nested test framework kept the FPR under control. This approach provides a good search engine for high-throughput epistasis analyses.

Genetic analysis of an F(2) intercross between two chicken lines divergently selected for body-weight

BACKGROUND

We have performed Quantitative Trait Loci (QTL) analysis of an F(2) intercross between two chicken lines divergently selected for juvenile body-weight. In a previous study 13 identified loci with effects on body-weight, only explained a small proportion of the large variation in the F(2) population. Epistatic interaction analysis however, indicated that a network of interacting loci with large effect contributed to the difference in body-weight of the parental lines. This previous analysis was, however, based on a sparse microsatellite linkage map and the limited coverage could have affected the main conclusions. Here we present a revised QTL analysis based on a high-density linkage map that provided a more complete coverage of the chicken genome. Furthermore, we utilized genotype data from ~13,000 SNPs to search the genome for potential selective sweeps that have occurred in the selected lines.

RESULTS

We constructed a linkage map comprising 434 genetic markers, covering 31 chromosomes but leaving seven microchromosomes uncovered. The analysis showed that seven regions harbor QTL that influence growth. The pair-wise interaction analysis identified 15 unique QTL pairs and notable is that nine of those involved interactions with a locus on chromosome 7, forming a network of interacting loci. The analysis of ~13,000 SNPs showed that a substantial proportion of the genetic variation present in the founder population has been lost in either of the two selected lines since ~60% of the SNPs polymorphic among lines showed fixation in one of the lines. With the current marker coverage and QTL map resolution we did not observe clear signs of selective sweeps within QTL intervals.

CONCLUSION

The results from the QTL analysis using the new improved linkage map are to a large extent in concordance with our previous analysis of this pedigree. The difference in body-weight between the parental chicken lines is caused by many QTL each with a small individual effect. Although the increased chromosomal marker coverage did not lead to the identification of additional QTL, we were able to refine the localization of QTL. The importance of epistatic interaction as a mechanism contributing significantly to the remarkable selection response was further strengthened because additional pairs of interacting loci were detected with the improved map.

Genetic architecture of tameness in a rat model of animal domestication

A common feature of domestic animals is tameness-i.e., they tolerate and are unafraid of human presence and handling. To gain insight into the genetic basis of tameness and aggression, we studied an intercross between two lines of rats (Rattus norvegicus) selected over >60 generations for increased tameness and increased aggression against humans, respectively. We measured 45 traits, including tameness and aggression, anxiety-related traits, organ weights, and levels of serum components in >700 rats from an intercross population. Using 201 genetic markers, we identified two significant quantitative trait loci (QTL) for tameness. These loci overlap with QTL for adrenal gland weight and for anxiety-related traits and are part of a five-locus epistatic network influencing tameness. An additional QTL influences the occurrence of white coat spots, but shows no significant effect on tameness. The loci described here are important starting points for finding the genes that cause tameness in these rats and potentially in domestic animals in general.

Dissection of the genetic architecture of body weight in chicken reveals the impact of epistasis on domestication traits

In this contribution, we study the genetic mechanisms leading to differences in the observed growth patterns of domesticated White Leghorn chickens and their wild ancestor the red jungle fowl. An epistatic QTL analysis for several body-weight measures from hatch to adulthood confirms earlier findings that polymorphisms at >15 loci contribute to body-weight determination in an F(2) intercross between these populations and that many loci are involved in complex genetic interactions. Here, we use a new genetic model to decompose the genetic effects of this multilocus epistatic genetic network. The results show how the functional modeling of genetic effects provides new insights into how genetic interactions in a large set of loci jointly contribute to phenotypic expression. By exploring the functional effects of QTL alleles, we show that some alleles can display temporal shifts in the expression of genetic effects due to their dependencies on the genetic background. Our results demonstrate that the effects of many genes are dependent on genetic interactions with other loci and how their involvement in the domestication process relies on these interactions.

Expression profiles reveal parallel evolution of epistatic interactions involving the CRP regulon in Escherichia coli

The extent and nature of epistatic interactions between mutations are issues of fundamental importance in evolutionary biology. However, they are difficult to study and their influence on adaptation remains poorly understood. Here, we use a systems-level approach to examine epistatic interactions that arose during the evolution of Escherichia coli in a defined environment. We used expression arrays to compare the effect on global patterns of gene expression of deleting a central regulatory gene, crp. Effects were measured in two lineages that had independently evolved for 20,000 generations and in their common ancestor. We found that deleting crp had a much more dramatic effect on the expression profile of the two evolved lines than on the ancestor. Because the sequence of the crp gene was unchanged during evolution, these differences indicate epistatic interactions between crp and mutations at other loci that accumulated during evolution. Moreover, a striking degree of parallelism was observed between the two independently evolved lines; 115 genes that were not crp-dependent in the ancestor became dependent on crp in both evolved lines. An analysis of changes in crp dependence of well-characterized regulons identified a number of regulatory genes as candidates for harboring beneficial mutations that could account for these parallel expression changes. Mutations within three of these genes have previously been found and shown to contribute to fitness. Overall, these findings indicate that epistasis has been important in the adaptive evolution of these lines, and they provide new insight into the types of genetic changes through which epistasis can evolve. More generally, we demonstrate that expression profiles can be profitably used to investigate epistatic interactions.

The effect of a genetic mutation can depend on the genotype of the organism in which it occurs. For example, a mutation that is beneficial in one genetic background might be neutral or even deleterious in another. The interactions between genes that cause this dependence—known as epistasis—play an important role in many evolutionary theories. However, they are difficult to study and remain poorly understood. We used a novel approach to examine the evolution of interactions arising between a key regulatory gene, crp, and mutations that occurred during the adaptation of a bacterium, Escherichia coli, to a laboratory environment. To do this, we measured the effect of deleting crp on the expression of all genes in the organism, providing a sensitive measure to identify new interactions involving this gene. We found that deleting crp had a dramatic and parallel effect on gene expression in two independently evolved populations, but much less effect in their ancestor. An analysis of these changes identified a number of regulatory genes as candidates for harboring beneficial mutations that could account for the parallel changes. These findings indicate that epistasis has played an important role in the evolution of these populations, and they provide insight into the types of genetic changes through which epistasis can evolve.

Locating multiple interacting quantitative trait Loci using rank-based model selection

In previous work, a modified version of the Bayesian information criterion (mBIC) was proposed to locate multiple interacting quantitative trait loci (QTL). Simulation studies and real data analysis demonstrate good properties of the mBIC in situations where the error distribution is approximately normal. However, as with other standard techniques of QTL mapping, the performance of the mBIC strongly deteriorates when the trait distribution is heavy tailed or when the data contain a significant proportion of outliers. In the present article, we propose a suitable robust version of the mBIC that is based on ranks. We investigate the properties of the resulting method on the basis of theoretical calculations, computer simulations, and a real data analysis. Our simulation results show that for the sample sizes typically used in QTL mapping, the methods based on ranks are almost as efficient as standard techniques when the data are normal and are much better when the data come from some heavy-tailed distribution or include a proportion of outliers.

Sample size needed to detect gene-gene interactions using linkage analysis

Gene-gene interactions have received much attention recently because most human traits may be under the control of several genetic factors, as well as environmental factors, and these factors likely interact among each other to influence these traits. Gauderman (2002) and Wang & Zhao (2003) have reported systematic studies on the statistical power to detect gene-gene interactions through association studies. In this article we investigated the power of the affected sib pair (ASP) design to detect gene-gene interaction at two disease loci. Different definitions of gene-gene interaction were considered and different disease models (including both logistic models considered in previous studies and several two-locus models with fixed penetrances) were examined. Our results indicate that comparisons between power to detect gene-gene interaction using ASP designs and association designs heavily depend on the definition of gene-gene interaction. Under the definition of gene-gene interaction with departure from independence between two marginal IBD sharings, the association design is much more powerful than the ASP design, and the additive model is more powerful than dominant and recessive models for rare diseases, while for common diseases for example with a population prevalence of 10%, the recessive model is more powerful than the additive and dominant models. Under the definitions of departure from a multiplicative model, additive model, and heterogeneity model (Risch, 1990), the ASP design is as powerful as, or more powerful than, both family-based and population-based association designs for rare disease,, but less powerful for more common diseases. Under the definition of correlation between two marginal IBD sharings, the association design is much more powerful than the ASP design.

Bayesian multiple quantitative trait loci mapping for complex traits using markers of the entire genome

A Bayesian methodology has been developed for multiple quantitative trait loci (QTL) mapping of complex binary traits that follow liability threshold models. Unlike most QTL mapping methods where only one or a few markers are used at a time, the proposed method utilizes all markers across the genome simultaneously. The outperformance of our Bayesian method over the traditional single-marker analysis and interval mapping has been illustrated via simulations and real data analysis to identify candidate loci associated with colorectal cancer.

Statistical epistasis is a generic feature of gene regulatory networks

Functional dependencies between genes are a defining characteristic of gene networks underlying quantitative traits. However, recent studies show that the proportion of the genetic variation that can be attributed to statistical epistasis varies from almost zero to very high. It is thus of fundamental as well as instrumental importance to better understand whether different functional dependency patterns among polymorphic genes give rise to distinct statistical interaction patterns or not. Here we address this issue by combining a quantitative genetic model approach with genotype-phenotype models capable of translating allelic variation and regulatory principles into phenotypic variation at the level of gene expression. We show that gene regulatory networks with and without feedback motifs can exhibit a wide range of possible statistical genetic architectures with regard to both type of effect explaining phenotypic variance and number of apparent loci underlying the observed phenotypic effect. Although all motifs are capable of harboring significant interactions, positive feedback gives rise to higher amounts and more types of statistical epistasis. The results also suggest that the inclusion of statistical interaction terms in genetic models will increase the chance to detect additional QTL as well as functional dependencies between genetic loci over a broad range of regulatory regimes. This article illustrates how statistical genetic methods can fruitfully be combined with nonlinear systems dynamics to elucidate biological issues beyond reach of each methodology in isolation.

Mapping quantitative trait loci by an extension of the Haley-Knott regression method using estimating equations

The Haley-Knott (HK) regression method continues to be a popular approximation to standard interval mapping (IM) of quantitative trait loci (QTL) in experimental crosses. The HK method is favored for its dramatic reduction in computation time compared to the IM method, something that is particularly important in simultaneous searches for multiple interacting QTL. While the HK method often approximates the IM method well in estimating QTL effects and in power to detect QTL, it may perform poorly if, for example, there is strong epistasis between QTL or if QTL are linked. Also, it is well known that the estimation of the residual variance by the HK method is biased. Here, we present an extension of the HK method that uses estimating equations based on both means and variances. For normally distributed phenotypes this estimating equation (EE) method is more efficient than the HK method. Furthermore, computer simulations show that the EE method performs well for very different genetic models and data set structures, including nonnormal phenotype distributions, nonrandom missing data patterns, varying degrees of epistasis, and varying degrees of linkage between QTL. The EE method retains key qualities of the HK method such as computational speed and robustness against nonnormal phenotype distributions, while approximating the IM method better in terms of accuracy and precision of parameter estimates and power to detect QTL.

On locating multiple interacting quantitative trait loci in intercross designs

A modified version (mBIC) of the Bayesian Information Criterion (BIC) has been previously proposed for backcross designs to locate multiple interacting quantitative trait loci. In this article, we extend the method to intercross designs. We also propose two modifications of the mBIC. First we investigate a two-stage procedure in the spirit of empirical Bayes methods involving an adaptive (i.e., data-based) choice of the penalty. The purpose of the second modification is to increase the power of detecting epistasis effects at loci where main effects have already been detected. We investigate the proposed methods by computer simulations under a wide range of realistic genetic models, with nonequidistant marker spacings and missing data. In the case of large intermarker distances we use imputations according to Haley and Knott regression to reduce the distance between searched positions to not more than 10 cM. Haley and Knott regression is also used to handle missing data. The simulation study as well as real data analyses demonstrates good properties of the proposed method of QTL detection.

From genetical genomics to systems genetics: potential applications in quantitative genomics and animal breeding

This article reviews methods of integration of transcriptomics (and equally proteomics and metabolomics), genetics, and genomics in the form of systems genetics into existing genome analyses and their potential use in animal breeding and quantitative genomic modeling of complex traits. Genetical genomics or the expression quantitative trait loci (eQTL) mapping method and key findings in this research are reviewed. Various procedures and potential uses of eQTL mapping, global linkage clustering, and systems genetics are illustrated using actual analysis on recombinant inbred lines of mice with data on gene expression (for diabetes- and obesity-related genes), pathway, and single nucleotide polymorphism (SNP) linkage maps. Experimental and bioinformatics difficulties and possible solutions are discussed. The main uses of this systems genetics approach in quantitative genomics were shown to be in refinement of the identified QTL, candidate gene and SNP discovery, understanding gene-environment and gene-gene interactions, detection of candidate regulator genes/eQTL, discriminating multiple QTL/eQTL, and detection of pleiotropic QTL/eQTL, in addition to its use in reconstructing regulatory networks. The potential uses in animal breeding are direct selection on heritable gene expression measures, termed “expression assisted selection,” and genetical genomic selection of both QTL and eQTL based on breeding values of the respective genes, termed “expression-assisted evaluation.”

Epistatic regulation of behavioural and morphological traits in the zebrafish (Danio rerio)

There is currently a lack of studies examining epistasis in general, and specifically for behavioural traits of evolutionary significance. The advent of more efficient analytical methods for exploring epistasis in QTL studies removes the computational restraint on this type of analysis and suggests that performing further analyses of existing datasets may reveal a more complete picture of the genetic architecture of the traits. Here we report the results from an epistatic QTL analysis of an F2 cross between a wild population and a standard laboratory strain of zebrafish. This further analysis was performed using a simultaneous search to identify epistatically interacting QTL affecting behavioural and morphological traits and uncovered several novel epistatic interactions that reached either genome-wide or suggestive significance levels as determined by a randomisation testing approach. These results provide novel insight into the genetic architecture of the regulation of behavioural as well as morphological phenotypes and call for more studies of epistasis for this group of traits.

GAIA: an easy-to-use web-based application for interaction analysis of case-control data

Background

The advent of cheap, large scale genotyping has led to widespread adoption of genetic association mapping as the tool of choice in the search for loci underlying susceptibility to common complex disease. Whilst simple single locus analysis is relatively trivial to conduct, this is not true of more complex analysis such as those involving interactions between loci. The importance of testing for interactions between loci in association analysis has been highlighted in a number of recent high profile publications.

Results

Genetic Association Interaction Analysis (GAIA) is a web-based application for testing for statistical interactions between loci. It is based upon the widely used case-control study design for genetic association analysis and is designed so that non-specialists may routinely apply tests for interaction. GAIA allows simple testing of both additive and additive plus dominance interaction models and includes permutation testing to appropriately correct for multiple testing. The application will find use both in candidate gene based studies and in genome-wide association studies. For large scale studies GAIA includes a screening approach which prioritizes loci (based on the significance of main effects at one or both loci) for further interaction analysis.

Conclusion

GAIA is available at

Identification of Trait Loci Affecting White Meat Percentage and Other Growth and Carcass Traits in Commercial Broiler Chickens

White meat is the most economically valuable part of a broiler chicken. Increasing white meat relative to overall body size (white meat percentage, WM%) makes a broiler, gram for gram, a more valuable animal. However, accurately measuring WM% requires removing the bird from the breeding flock. Identification of markers for genomic regions associated with WM% would allow direct genetic selection on breeders. The objective of the current study was to identify genomic regions affecting WM% and other growth and carcass traits in an F2 cross between 2 commercial broiler lines that differed in WM%. Two commercial lines were crossed to generate 5 F1 half-sib families of each reciprocal cross type. One male from each family was crossed with 3 females from each of the other families within each reciprocal cross type. Seven F2 half-sib families, totaling 430 F2 individuals, were analyzed. Microsatellite markers (n = 73) on the 11 largest chromosomes were analyzed for associations with various growth and carcass traits by least squares interval mapping using line-cross, half-sib, combined, and parent of origin models. Sixty-eight QTL were identified at the 5% chromosome-wise level, including 6 QTL affecting WM%. Ten QTL reached 5% genome-wise significance, including 1 WM% QTL on Gga 2. The current study identified genomic regions harboring QTL affecting WM% and other carcass and growth traits, which may be useful for direct genetic selection, and also identified putative imprinted QTL in the chicken. The advantage of using multiple statistical models was evident because QTL were identified with the combined and parent of origin models that were not identified with the line-cross or half-sib models.

QTL analysis of body composition and metabolic traits in an intercross between chicken lines divergently selected for growth

The high- and low-growth lines of chickens have been developed from a single founder population by divergent selection for body weight at 56 days of age for more than 40 generations. The two lines show a ninefold difference in body weight at selection age and several interesting correlated selection responses such as altered body composition and metabolic differences. We have generated a reciprocal intercross comprising >800 F2 birds. In a previous study, we reported the detection of 13 quantitative trait loci (QTLs) affecting growth. Here we report QTLs for body composition (fat deposition, muscle development), weight of internal organs, and metabolic traits (plasma concentrations of glucose, insulin, cholesterol, glucagon, triglycerides, and IGF-I). Most of the QTLs with convincing statistical support mapped in the vicinity of growth QTLs. One of the most interesting observations was that the type of reciprocal cross had highly significant effects on body weight at hatch and on plasma concentrations of glucose, cholesterol, insulin, and IGF-I, but it had no significant effect on body weight at 56 days of age. The reciprocal cross explained between 15 and 35% of the phenotypic variance for weight at hatch and for plasma concentrations of glucose and insulin. The observed pattern indicated that these effects were caused by maternal effects or by genetic differences in mitochondrial DNA.

Regression-based quantitative trait loci mapping: robust, efficient and effective

Regression has always been an important tool for quantitative geneticists. The use of maximum likelihood (ML) has been advocated for the detection of quantitative trait loci (QTL) through linkage with molecular markers, and this approach can be very effective. However, linear regression models have also been proposed which perform similarly to ML, while retaining the many beneficial features of regression and, hence, can be more tractable and versatile than ML in some circumstances. Here, the use of linear regression to detect QTL in structured outbred populations is reviewed and its perceived shortfalls are revisited. It is argued that the approach is valuable now and will remain so in the future.

A computational method to detect epistatic effects contributing to a quantitative trait

We develop a new computational method to detect epistatic effects that contribute to a complex quantitative trait. Rather than looking for epistatic effects that show statistical significance when considered in isolation, we search for a close approximation to the quantitative trait by a sum of epistatic effects. Our search algorithm consists of a sequence of random walks around the space of sums of epistatic effects. An important feature of our approach is that there is learning between random walks, i.e. the control mechanism that chooses steps in our random walks adapts to the experiences of earlier random walks. We test the effectiveness of our algorithms by applying them to synthetic datasets where the phenotype is a sum of epistatic effects plus normally distributed noise. Our test statistic is the rate of success that our methods achieve in identifying the underlying epistatic effects. We report on the effectiveness of our methods as we vary parameters that are intrinsic to the computation (length of random walks and degree of learning) as well as parameters that are extrinsic to the computation (number of markers, number of individuals, noise level, architecture of the epistatic effects).

Model selection in binary trait locus mapping

Quantitative trait locus (QTL) mapping methodology for continuous normally distributed traits is the subject of much attention in the literature. Binary trait locus (BTL) mapping in experimental populations has received much less attention. A binary trait by definition has only two possible values, and the penetrance parameter is restricted to values between zero and one. Due to this restriction, the infinitesimal model appears to come into play even when only a few loci are involved, making selection of an appropriate genetic model in BTL mapping challenging. We present a probability model for an arbitrary number of BTL and demonstrate that, given adequate sample sizes, the power for detecting loci is high under a wide range of genetic models, including most epistatic models. A novel model selection strategy based upon the underlying genetic map is employed for choosing the genetic model. We propose selecting the "best" marker from each linkage group, regardless of significance. This reduces the model space so that an efficient search for epistatic loci can be conducted without invoking stepwise model selection. This procedure can identify unlinked epistatic BTL, demonstrated by our simulations and the reanalysis of Oncorhynchus mykiss experimental data.

Simultaneous mapping of epistatic QTL in DU6i × DBA/2 mice

We have mapped epistatic quantitative trait loci (QTL) in an F2 cross between DU6i x DBA/2 mice. By including these epistatic QTL and their interaction parameters in the genetic model, we were able to increase the genetic variance explained substantially (8.8%-128.3%) for several growth and body composition traits. We used an analysis method based on a simultaneous search for epistatic QTL pairs without assuming that the QTL had any effect individually. We were able to detect several QTL that could not be detected in a search for marginal QTL effects because the epistasis cancelled out the individual effects of the QTL. In total, 23 genomic regions were found to contain QTL affecting one or several of the traits and eight of these QTL did not have significant individual effects. We identified 44 QTL pairs with significant effects on the traits, and, for 28 of the pairs, an epistatic QTL model fit the data significantly better than a model without interactions. The epistatic pairs were classified by the significance of the epistatic parameters in the genetic model, and visual inspection of the two-locus genotype means identified six types of related genotype-phenotype patterns among the pairs. Five of these patterns resembled previously published patterns of QTL interactions.

Quantitative trait locus analyses and the study of evolutionary process

The past decade has seen a proliferation of studies that employ quantitative trait locus (QTL) approaches to diagnose the genetic basis of trait evolution. Advances in molecular techniques and analytical methods have suggested that an exact genetic description of the number and distribution of genes affecting a trait can be obtained. Although this possibility has met with some success in model systems such as Drosophila and Arabidopsis, the pursuit of an exact description of QTL effects, i.e. individual gene effect, in most cases has proven problematic. We discuss why QTL methods will have difficulty in identifying individual genes contributing to trait variation, and distinguish between the identification of QTL (or marker intervals) and the identification of individual genes or nucleotide differences within genes (QTN). This review focuses on what ecologists and evolutionary biologists working with natural populations can realistically expect to learn from QTL studies. We highlight representative issues in ecology and evolutionary biology and discuss the range of questions that can be addressed satisfactorily using QTL approaches. We specifically address developing approaches to QTL analysis in outbred populations, and discuss practical considerations of experimental (cross) design and application of different marker types. Throughout this review we attempt to provide a balanced description of the benefits of QTL methodology to studies in ecology and evolution as well as the inherent assumptions and limitations that may constrain its application.

A global search reveals epistatic interaction between QTL for early growth in the chicken

We have identified quantitative trait loci (QTL) explaining a large proportion of the variation in body weights at different ages and growth between chronological ages in an F(2) intercross between red junglefowl and White Leghorn chickens. QTL were mapped using forward selection for loci with significant marginal genetic effects and with a simultaneous search for epistatic QTL pairs. We found 22 significant loci contributing to these traits, nine of these were only found by the simultaneous two-dimensional search, which demonstrates the power of this approach for detecting loci affecting complex traits. We have also estimated the relative contribution of additive, dominance, and epistasis effects to growth and the contribution of epistasis was more pronounced prior to 46 days of age, whereas additive genetic effects explained the major portion of the genetic variance later in life. Several of the detected loci affected either early or late growth but not both. Very few loci affected the entire growth process, which points out that early and late growth, at least to some extent, have different genetic regulation.