Many studies have provided evidence of the existence of genetic heterogeneity of environmental variance, suggesting that it could be exploited to improve robustness and uniformity of livestock by selection. However, little is known about the perspectives of such a selection strategy in beef cattle.A two-step approach was applied to study the genetic heterogeneity of residual variance of weight gain from birth to weaning and long-yearling weight in a Nellore beef cattle population. First, an animal model was fitted to the data and second, the influence of additive and environmental effects on the residual variance of these traits was investigated with different models, in which the log squared estimated residuals for each phenotypic record were analyzed using the restricted maximum likelihood method. Monte Carlo simulation was performed to assess the reliability of variance component estimates from the second step and the accuracy of estimated breeding values for residual variation.The results suggest that both genetic and environmental factors have an effect on the residual variance of weight gain from birth to weaning and long-yearling in Nellore beef cattle and that uniformity of these traits could be improved by selecting for lower residual variance, when considering a large amount of information to predict genetic merit for this criterion. Simulations suggested that using the two-step approach would lead to biased estimates of variance components, such that more adequate methods are needed to study the genetic heterogeneity of residual variance in beef cattle. Although uniformity is an important issue in beef production, few studies have explored the advantages of introducing this as a selection criterion in beef cattle breeding programs. A primary concern of beef producers is to improve uniformity of production traits such as carcass weight, fat deposition and carcass composition because the price paid to producers is based on these criteria. Another interesting issue would be to increase the proportion of animals within a desired range for growth-related traits such as birth weight and mature weight.Genetic heterogeneity of residual variance has been investigated using structural models that can estimate genetic effects on the mean and the residual variance in a single step -3. A freRowe et al.  employedGiven the standard structure of beef cattle data with a relatively large number of progeny per sire and a few sibs per dam, analysis of the log squared estimated residuals should be suitable to investigate the influence of environmental and additive effects on residual variance in large populations of beef cattle. Neves et al.  used thiAs suggested by Gutierrez et al. , this apThus, the objectives of this study were: (1) to investigate the influence of additive and environmental effects on residual variance of two traits related to body weight in a large Nellore beef cattle population using a two-step approach and (2) to apply a Monte Carlo simulation of the second step, to assess the reliability of variance component estimation and the accuracy of estimated breeding values for residual variation.We used data from the Aliança Nelore database, comprising records from 382 Nellore herds raised with pasture systems in Brazil and Paraguay, collected from 1996 to 2009. Weight gain from birth to weaning  and long-yearling weight  were chosen as traits for this study. Homogeneity in GBW is an important criterion because animals with too low weights at weaning are not desired and animals with very large weights tend to have poorer performances in the subsequent period of food restriction (dry season). Likewise, more uniformity in YW would be valuable to avoid the penalties that are applied for carcass weights outside the optimum range.Mulder et al.  investigFor both traits, contemporary groups (CG) were defined based on concatenations of herd, year, and season of birth, sex, date of measurement, and management group. Genetic connectedness among CG was verified using the AMC software . BrieflyTo reduce the impact of outliers on the estimates of variance components, only records within the range of the trait mean ± 3.5 SD were considered. In all analyses, only records for animals reared in CG with a minimum of 25 animals and sired by bulls with at least 50 progenies were considered in both steps (described in the next sections).Information on the number of levels of fixed effects (CG), number of sires, number of dams and average progeny size of sires after data editing is presented in Table Univariate animal models were fitted using the ASREML-R package , in ordeIn matrix notation, the model used to analyze GBW can be represented as:y = vector of observations; b = vector of fixed effects; a = vector of direct additive genetic effects; m = vector of maternal additive genetic effects; c = vector of maternal permanent environmental effects; e = vector of residual random errors associated with observations. X, Z1, Z2 and W are incidence matrices that associate b, a, m and c to y, respectively. The assumptions of this model are:in which: G = matrix of genetic covariances between direct and maternal effects, A = numerator relationship matrix, σ²c = maternal permanent environmental variance, Id = identity matrix of order equal to the number of dams, In = identity matrix of order equal to the number of observations, R = residual (co) variance matrix. It was assumed that σ²a = variance of direct additive genetic effects, σ²m = variance of maternal additive genetic effects, and σam = covariance between maternal and direct additive genetic effects. Since only a few dams had more than one offspring of each sex with information on GBW, the maternal permanent environmental effect was not included when the information of each sex was considered separately because the data structure would not allow adequate estimation of this parameter. Also due to the data structure, σam was set to zero in all analyses .where: R of equation 1 is a diagonal matrix, in which the elements are either equal to σ²e (model HOM) or equal to σ²ej (model HET), where σ²ej is the residual variance specific to the progeny of the jth sire.In order to estimate the effect of allowing for heterogeneous residual variances in the first step, a first set of analyses was carried out by assuming a homoscedastic model (HOM). Then, an equivalent set of analyses was carried out, allowing for different residual variances for each sire family (model HET). Therefore, matrix The model used to analyze the YW trait included only direct additive effects and residuals as random effects. This model was chosen because including both types of maternal effects described in equation (1) did not improve model fitting  and the Bayesian Information Criterion (BIC)).Thus, variance components for GBW and YW were estimated by considering different sources of data  and different assumptions on residual variance in the first step (i.e. HOM or HET model). In addition, 10-fold cross-validation was performed to investigate the predictive ability of the HOM and HET models for each analyzed dataset. In this case, each dataset was randomly partitioned into 10 disjoint subsets, each with approximately one tenth of the records. In each case, nine of the subsets were used for model fitting (training set), after which the observations in the remaining subset were predicted (testing set) and the mean squared error (MSE) of prediction was calculated. At the end of this process, the average of the MSE was calculated, with the estimates of MSE obtained separately for each testing set.Solutions obtained in the first step were used to estimate the residual (ê) for each observation. For each trait, log squared estimated residuals, ln(ê²), were used as a measure of the residual variance, as discussed previously.In order to investigate the influence of fixed effects (CG) and additive genetic effects on the residual variance of GBW and YW, different models were fitted to the log squared estimated residuals in ASREML-R. The full model of the second step can be represented by:ln(ê²) = vector of individual log squared estimated residuals for the trait analyzed; b* = vector of fixed effects; a* = vector of direct additive genetic effects; m* = vector of maternal additive genetic effects, and ϵ = vector of residual random errors associated with the log squared estimated residuals. Assumptions of model (2) were:where G* = matrix of genetic covariances, A = numerator relationship matrix, In = identity matrix of order equal to the number of observations, R* = residual variance (σ²ϵ).where: σ²Av,exp is the variance due to direct additive genetic effects and σ²m,exp is the variance due to maternal additive genetic effects on the log squared estimated residuals. As in the first step, maternal effects only improved model fitting for GBW (according to AIC and BIC) and thus were not considered in the case of YW.It was assumed that Results from model (2) and reduced models were compared to evaluate the importance of including direct additive genetic effects and maternal additive effects in the analyses of the log squared estimated residuals. A likelihood-ratio test was applied to assess the significance of considering additive genetic effects at the level of residual variance. The statistics BIC and AIC were also calculated, in order to penalize models with a larger number of parameters.v) were calculated in order to measure the strength of genetic variation on residual variance and also to compare our results with those of previous studies. Because the additive variance estimates  from the second step were expressed on an exponential scale, they were transformed as proposed by [σ²AV), which were used to compute Ev.Two parameters, namely evolvability of residual variance (Ev) and heritability of residual variance (h²posed by  into estσAV/ σ²ê). Parameter σ²ê is an estimate of the residual variance and was equal to the REML estimate of residual variance for the HOM model and the average of residual variance among sire families for the HET model.Evolvability was proposed by Houle  to quantv) was derived by [Av) on squared phenotypes and it has been used as a central parameter in calculation of the accuracy of predicted breeding values for residual variance . Here, h²v was calculated as reported in [v.The heritability of residual variance  of sires for the mean and for log squared estimated residuals was calculated to provide a rough indication of the genetic association between these criteria, since direct estimation of this parameter is not feasible with the two-step approach. Because this estimate is dependent on the accuracy of EBV, only sires with more than 50 progeny were used, in order to reduce this source of bias.The data structure of the population described previously was used to simulate trait Y. Twenty replicates were simulated for each scenario described below. We considered animals of both sexes with information on YW Table .For individuals with records, trait Y, expressed in kg, was simulated as follows:bmi is the fixed effect simulated for the ith CG, amij is the breeding value of animal j for the mean of Y and the last term replicates random residual effects according to the exponential model described by SanCristóbal-Gaudy et al. [th CG (bvi), the breeding value of jth animal (avij) and ϵij is independent and identically distributed as N .where y et al. . At the m were drawn from a uniform distribution defined by U and values for bv were drawn from a uniform distribution U.With the aim of mimicking the real effects of CG on the mean and the residual variance of Y, CG effects bam and av were simulated from a MVN, in which ²a = 200 and σ²Av,exp equal to 0.01, 0.09 or 0.25. The covariance between direct additive genetic effects on the mean and the residual variance (σmv) was simulated such that three scenarios for the additive genetic correlation between the mean and the residual variance of Y could be investigated .For the founder animals, For subsequent generations, breeding values of non-founder animals were simulated as the average of the breeding values of the sire and dam plus a random Mendelian sampling term.e) is equal to exp(bv)*exp. Thus, Y was simulated to resemble a trait with heritability around 0.40, a mean equal to 350 kg and a phenotypic variance of about 480 kg² . According to formulas in [σ²Av,exp  .Accordingly, the expected value of the environmental variance  were employed, except that maternal additive effects were not included. Estimates of In order to investigate the adequacy of the methods proposed here with a more balanced dataset, the same simulation parameters as described in the previous section were used to simulate five generations of an artificial population with 25 000 records. The base population consisted in 5 000 dams and 100 sires. At each generation, sires (dams) had 50 (1) offspring and records were distributed across 100 CG, such that each CG included the progeny of five sires, each with 10 sons. The simulation process considered a 20% replacement rate for both sexes per generation, assuming random mating and no selection. Data were analyzed and results were compared in the same way as described in the previous section.Summary statistics of data for GBW and YW are presented in Table Although the estimates of variance components were very similar for models HOM and HET for both GBW and YW, model HET had a better fit according to AIC, while model HOM provided a better fit according to BIC Table . As a geWhen each sex was analyzed separately, estimates of direct heritability (h²) were higher for males than for females  for both models HOM and HET. Higher estimates of average residual variance and genetic additive  variance were also obtained for males than for females, possibly because of scale effects. When the data on males and females were considered jointly, the estimates of h² (s.e.) were similar for models HOM and HET, i.e. about 0.12 (0.02) and 0.41 (0.03) for GBW and YW, respectively.If the residuals from the first step are normally distributed, their squares will follow a χ² distribution . For botEstimates of variance components and related parameters obtained from the second step are presented in Table Conversely, the influence of additive genetic effects on residual variance was weaker when model HOM was fitted in the first step. Information criteria did not favor the model with additive effects on residual variance for YW, regardless of the source of information , while these criteria only favored the model with additive genetic effects on the residual variation of GBW when records of both males and females were analyzed jointly . For all traits, regardless of the animal’s sex, a 95% confidence interval for σ²,expAv did not include zero when the first step accounted for differences between sire families in residual variance.For both traits, estimates of additive variance for the log squared estimated residuals from model HET were at least 12-fold larger than comparable estimates from model HOM Table . In addiIn the case of GBW, taking into account both direct and maternal additive effects improved the model fitting in the second step. When model HOM was fitted in the first step, estimates of the maternal additive effect for ln(ê²) were between 40% and 80% larger than those obtained when model HET was fitted in the first step.σ²,expAv estimates were at least two-fold higher in males than in females. For a same trait, the σ²,expAv estimated for females was close to that obtained when records of both sexes were analyzed jointly  were always less than 0.5% under model HOM, while they ranged from 3 to 6% when model HET was fitted. Again, h²v estimates were higher in males than in females, for both GBW and YW. The approximated standard error of h²v was small when model HET was fitted in the first step (data not shown), such that the 95% confidence interval did not include zero.Values of the heritability of residual variance . The only exception was for YW in males, for which the estimated correlation was very close to zero Table .For both sets of simulations (using observed or simulated pedigrees), the estimated variance components for the mean of the simulated trait were in reasonable agreement with the simulated (true) values, such that the absolute values of the relative bias for estimates of additive variance and residual variance were at most 3.7% and 1.7%, respectively (data not shown). Also, there was no evidence that fitting model HET instead of model HOM in the first step resulted in estimates of residual variance closer to the simulated values, for all scenarios of additive variance, residual variance and correlation between mean and residual variance.σ²,expAv were biased downwards   Table  and if mσ²,expAv was equal to 0.01. In this case, σ²,expAv was underestimated in the simulation using the observed pedigree, while it was overestimated in the simulation using the simulated pedigree.With a more balanced design (simulated pedigree), the amount of bias in estimates from the second step was similar to that obtained in the simulations using the observed pedigree Table . The onlσ²,expAv, the lower the amount of relative bias, which was not observed for model HOM , this parameter was overestimated almost 20-fold (30-fold) under model HET compared to the true value in the case of simulations using the observed (simulated) pedigree. Similarly, the higher the values simulated for σ²,expAv, the closer the agreement between the true additive genetic correlation between mean and residual variance and the estimates based on Pearson’s correlation between estimated breeding values for these criteria (rˆmv), regardless of the assumptions about residual variance in the first step.For both sets of simulations, when heterogeneous residual variances among sire families were accounted for in the first step, the higher the simulated values for OM Table . It shouv). In general, meaningful values (above 0.50) were observed only for accuracies averaged across all sires when σ²,expAv was greater than 0.09  for sires (between 8% and 20% higher) Table .Parameters associated with additive genetic effects on GBW and YW means obtained after the first step of this study are consistent with results of previous studies reporting low to moderate estimates of heritability for direct and maternal effects on pre-weaning growth traits ,19, and When analyses were carried out separately for each sex, heritability estimates were higher in males, for both GBW and YW (notably in the case of YW). Conversely, heritability estimates were higher in females for yearling weight gain in Holstein cattle , body weResults from the second step showed stronger evidence for genetic heterogeneity of residual variance if heterogeneous residual variances were allowed for in the first step, although more extensive comparisons could not be made based on restricted likelihood, e.g. comparison of models that assume different combinations of fixed effects on residual variance.Similar to results reported by , it is nGenetic parameters for residual variance in this same population were estimated in an exploratory study , in whicDespite this, results of both studies suggest that genetic additive effects act on the residual variance, while there is reasonable evidence of both genetic and environmental heterogeneity of residual variance for traits related to body weight in other livestock species, such as broilers ,11,23, rThe estimated Ev under model HET were more consistent with previous estimates for body weight in other species ,6, whileNevertheless, given the magnitude of the estimated Ev for weight gain from birth to weaning and long-yearling weight, when model HET was fitted in the first step, a meaningful response to selection on EBV for residual variance of these traits would be expected in the case of large sire families.Results from other studies also indicate that selection on EBV for residual variance can improve uniformity. In broilers,  predicteConsiderable differences between males and females were observed in genetic parameters for residual variation. Similar results were also reported by , which sAlthough this question deserves further investigation, using a well-designed dataset, implementing sex-specific analyses is not possible in situations in which the number of progeny of each sex is small and the data structure does not permit adequate estimation of effects at the level of residual variance. For instance, due to the restrictions imposed on the size of contemporary groups and progeny groups, a substantial amount of data could not be considered in sex-specific analyses .mv). Since direct estimation of rmv was not feasible under the current approach, the correlation between sire EBV for mean and residual variance (rˆmv) was used as an indicator of the direction of this association, as also applied by [mv depended on the magnitude of the genetic variance of residual variance.An important issue in selection for residual variance is the genetic association between mean and residual variance . Thus, it is expected that true values for genetic variance of residual variance of GBW and YW are somewhat intermediate between those obtained under models HOM and HET.Although the amount of bias was higher when model HET rather than model HOM was fitted in the first step, the accuracies of prediction were also higher for model HET. These findings must be interpreted with caution since the environmental noise simulated at the level of the residual variance was only due to a fixed effect (CG), which is probably a situation more favorable to prediction of breeding values for residual variance than in the case of real data.An important issue when analyzing field data in a study on genetic heterogeneity of residual variance is that, if the data is not carefully collected for this purpose, it can lead to severe confounding between environmental and genetic effects, which are much more difficult to disentangle than when the focus is on analysis of the mean of a trait ,6.We hypothesized that this type of confounding could be more marked in the case of GBW, because this trait is more influenced by maternal effects. Although more sophisticated procedures are probably needed to provide stronger support for the existence of genetic variance of residual variance of beef cattle traits, we found Ev estimates of comparable magnitude for both traits studied.mv, are dependent of the scale on which the data are analyzed under a structural model. However, it is not clear to which extent scale effects influence inferences under the two-step approach. Also, Yang et al. [Yang et al.  verifiedg et al.  highlighg et al. . Thus, eAs pointed out in Wilson and Hilferty , it is emv and an extension of heteroscedastic models to multi-trait analyses could be the subject of future research in order to optimize selection for both average performance and increased uniformity in beef cattle.The two-step approach provided some evidence of useful genetic variability on the residual variance of GBW and YW, but important drawbacks were identified. Thus it would be interesting to apply more sophisticated procedures in order to obtain more precise estimates of variance components of residual variance in beef cattle. In this context, structural models implemented in a Bayesian framework are especially appealing, while REML approaches ,27 are eResults suggest that both genetic and environmental effects influence residual variance of weight gain from birth to weaning and long-yearling in Nellore beef cattle and that uniformity of these traits could be improved by selecting for lower residual variance, when considering a large amount of information to predict genetic merit for this criterion. Stronger statistical support for the action of genetic effects on residual variances was obtained when the model for the mean of each trait accounted for heterogeneous residual variances among sire families. More adequate methods are needed to study the genetic heterogeneity of residual variance in beef cattle.The authors declare they have no competing interests.HHRN participated in the design of the study, carried out data preparation, simulations and variance component estimation, participated in the analysis of results and drafted the manuscript. RC participated in the design of the study, data preparation and analysis of results and drafted the manuscript. SAQ participated in the design of the study and analysis of results and drafted the manuscript. All authors read and approved the final manuscript.


Most quantitative traits are controlled by multiple quantitative trait loci (QTL). The contribution of each locus may be negligible but the collective contribution of all loci is usually significant. Genome selection that uses markers of the entire genome to predict the genomic values of individual plants or animals can be more efficient than selection on phenotypic values and pedigree information alone for genetic improvement. When a quantitative trait is contributed by epistatic effects, using all markers (main effects) and marker pairs (epistatic effects) to predict the genomic values of plants can achieve the maximum efficiency for genetic improvement.In this study, we created 126 recombinant inbred lines of soybean and genotyped 80 makers across the genome. We applied the genome selection technique to predict the genomic value of somatic embryo number (a quantitative trait) for each line. Cross validation analysis showed that the squared correlation coefficient between the observed and predicted embryo numbers was 0.33 when only main (additive) effects were used for prediction. When the interaction (epistatic) effects were also included in the model, the squared correlation coefficient reached 0.78.This study provided an excellent example for the application of genome selection to plant breeding. Genome selection refers to a method for genomic value prediction using markers of the entire genome ,2. It isThe importance of epistasis in genetic determination may vary across different species. In agricultural crops, most quantitative traits in barley do not have a strong basis of epistatic effects . HoweverThe number of somatic embryos is an important trait for consideration in soybean breeding program because it is directly related to the plant regeneration system that is essential for effective gene transfer. The capacity of plant regeneration through immature embryo culture of soybean is genetically determined, reflected by significant variation across different lines (from 0% to 100% of regeneration). The genetic knowledge of the regeneration trait based on immature embryo culture and the discovery of molecular markers associated with regeneration will offer a great opportunity to develop efficient elite inbred lines with increased regeneration capacity. However, studies on the genetic basis of embryogenesis are lacking. There is no information available about the role of epistasis. In this study, we used advanced statistical methods to investigate not only the main effects but also pair-wise interaction (epistatic) effects for soybean somatic embryogenesis.Statistical methods for QTL mapping are available but mainly for individual marker (main effect) analysis and individual marker pair (epistatic effect) analysis -12. The The numerical codes (marker IDs) and names of the 80 markers are given in Table We now examine the result of cross validation. All the 80 markers were ordered from the largest to the smallest according to the LOD scores. We then used the cross validation analysis to calculate the squared correlation coefficient between the observed phenotypic values and the predicted genomic values. For the prediction, we examined the change of the r-square with the number of markers included in the model for prediction. The result is plotted in Figure The epistatic effect model included 3240 (80 main + 3160 epistatic) effects. The LOD scores of the 3160 epistatic effects are given in Figure The 66 effects were selected from the leave-one-out cross validation analysis. Figure Figure The conclusion from the epistatic model analysis was that selecting the top 66 effects for prediction, the accuracy (r-square) can reach 78%. If all effects are included, the accuracy decreased slightly to 0.73. Therefore, genome selection using the epistatic model can be very effective in soybean breeding for the embryogenesis trait.R2 value in multiple regression analysis. The r-square here is the squared correlation between the observed phenotypes and the estimated genetic values in which the individual lines predicted contribute to the parameter estimation. The r-square of our epistatic effect model was very high (0.78). In the cross validation generated correlation, the lines predicted do not contribute to the parameter estimation, and thus the squared correlation is a good indication of the predictability. If a new line occurs from the same population but has no phenotypic value, using the marker effects estimated from the existing lines to predict the genetic value of the new line will be as accurate as 0.78. This can save tremendous resources for plant breeding because we can use marker information alone to select plants in several cycles without field evaluation of the phenotypes.We evaluated two models of genome selection for soybean embryogenesis, the main effect model and the epistatic effect model. The main effect model is already very efficient with a 0.33 r-square between the observed phenotypes and the predicted genomic values. With the epistatic effect model, the squared correlation was 0.78, more than twice the efficiency of the main effect model. This discovery provides surprisingly good news to soybean breeders. The squared correlation coefficient between the observed phenotypes and the predicted genomic values is different from the Cross validation analysis showed that the main effect model found 27 important markers, but none of the 27 markers appeared as main effects in the epistatic effect model. This means that epistasis plays a more important role in determining the variation of soybean embryogenesis. These 27 markers did not disappear completely; parts of their effects have been absorbed by the epistatic effects due to correlation of variables in the design matrix. The epistatic model provides better prediction of the genomic values, but it does not disqualify the main effect model. When epistatic effects are excluded from the model, parts of their effects have been absorbed by the main effects due to complicated correlation among the design matrices of the effects. If a breeder decides to use the additive effect model alone for genome selection, he/she still has an accuracy of 0.33.We used the cross validation analysis to select markers and marker pairs for genome selection. We progressively increased the number of effects in the model to monitor the change in the accuracy of prediction. The optimal number of effects included is the one that maximizes the accuracy of prediction or minimizes the prediction error. The pattern of the change depends on the models used and the traits analyzed. For the main effect model, including more effects than necessary is detrimental to genome selection. For the epistatic effect model, the decrease of the prediction accuracy does not seem to be significant after the optimal number of effects is reached. The reason for the difference in the two models (additive and epistatic) is due to the fact that the large number of effects in the epistatic model caused strong shrinkage of the estimated regression coefficients. Once the prediction accuracy reached the peak value, additional effects included all have extremely small values . Including these zero effects does not cause much damage to the prediction. These patterns of the correlation profiles cannot be generalized to other situations. Therefore, cross validation must be performed for different traits in different experiments.Unfortunately, the marker density in this experiment was very low in the experiment, which prevented us from using the interval mapping and composite interval mapping approaches for fine mapping. The average interval for the 77 mapped markers was 40 cM. For such a low marker density, we were more concerned about not detecting any QTL. To our surprise, we found more QTL than we originally anticipated. Our cross validation analysis confirmed 27 main effects and 66 epistatic effects. Therefore, we conclude that the soybean embryogenesis is a polygenic trait. The current analysis provides a guideline for further study in fine mapping of QTL for embryogenesis of soybean. The next step is to develop more markers to saturate the entire genome. With a high density marker map, more efficient genome selection can be conducted.The number of somatic embryos is a discrete trait, which can be modeled by the Poisson distribution. In this particular experiment, each original data point was the average of 10 plants. Therefore, treating the average value as a continuous trait is more reasonable than fitting the Poisson model. For curiosity, we did analyze the data using the Poisson distribution. We also performed a data transformation using the square root of the data . The resThe main purpose of this study was not to develop new statistical methods for genome selection; rather, we used an existing method  to invesIn plant breeding, it is common to select superior cultivars from a random pool of existing accessions. The empirical Bayesian method used in this study works equally well for such randomly selected populations. It is also common to select superior RILs from an RIL crossing experiment derived from two inbred lines . The resThis study demonstrates the importance of epistasis in determination of the embryogenesis of soybean. This finding is clearly in contrast to what Xu and Jia  discoverAlthough there were hundreds of studies in the past decades claiming discovery of major QTL in plants, only a few of them have successfully cloned QTL . QTL maphttp://www.statgen.ucr.edu).The entire data analysis was conducted using the QTL procedure in SAS, called PROC QTL . This pr5:6 recombinant inbred lines (RILs) that were advanced by single seed descent from the cross of Peking (higher primary and secondary embryogenesis) and Keburi (lower primary and secondary embryogenesis) parents. This population was evaluated for primary embryogenesis capacity from immature embryo cultures by measuring the somatic embryo number per explant. A total of 80 simple sequence repeat markers were available and used for the QTL study. Among the 80 markers, 77 of them were mapped to 19 linkage groups [n = 3 × 126 = 378. Detailed information about this experiment can be found from Song et al. [The mapping population consisted of 126 Fe groups . The marg et al. . To remoA1A1 and A2A2, respectively. The genotype of each marker locus was numerically coded and represented by a variable Zjk for the jth data point for j = 1, ..., n and the kth marker for k = 1, ..., m, where n = 378 is the number of data points collected from the 126 recombinant inbred lines and m = 80 is the number of markers. The numerical coding for Zjk is shown below,Genotypes of the Peking cultivar (high embryogenesis) and the Keburi cultivar (low embryogenesis) are denoted by The linear model for the plot-mean-adjusted phenotypic value isβ is the population mean, γk is the effect of the kth marker and εj ~ N is the residual error. The marker effect k γis equivalent to the classical definition of the additive effect a defined in Falconer and Mackay [where d Mackay . Model /2 = 3240, including m = 80 main effects and m(m - 1)/2 = 3160 epistatic effects.where k γor kk'γ, was assigned a normal prior distributionBoth the main effect model and the epistatic effect model were analyzed using the empirical Bayesian method  implemenwhere the variance τ, ω) were chosen using the leave-one-out cross validation approach [τ, ω) =  generated the best result for this data in terms of generating the maximum correlation between the predicted and observed trait values and the minimum prediction error. This set of hyper priors is equivalent to the uniform prior for p, jk Z*is the corresponding design matrix for the kth effect and m* is the number of effects included in the model for prediction. The effects were ordered from the highest to the lowest based on their LOD scores. For example, if m* = 15, the model only includes the best 15 effects in the model for prediction. The squared correlation coefficient between the observed and predicted trait values m* for m* = 1, ..., 80 (the main effect model) and for m* for m* = 1, ..., 3240 (the epistatic effect model). The optimal m* is the one that maximizes the squared correlation coefficient where is the squared correlation coefficient. Note that this statistic is not the Pearson correlation; rather, it represents the proportion of the phenotypic variance explained by the markers.ZQ wrote the computer program and performed data analyses. YL, XS and YH provided the experimental material, carried out the molecular genetic studies and participated in the field investigation. XC improved the computer program and helped drafting the manuscript. SX participated in the design of this project, developed the statistical method and drafted the manuscript. WL conceived the project, designed the experiment, supervised students and postdocs involved in the project and revised the manuscript. All authors have read and approved the final manuscript.


Fusarium graminearum sensu stricto (s.s.) is an ubiquitous pathogen of cereals. The economic impact of Fusarium head blight (FHB) is characterized by crop losses and mycotoxin contamination. Our objective was to associate SNP diversity within candidate genes with phenotypic traits. A total of 77 F. graminearum s.s. isolates was tested for severity of fungal infection (= aggressiveness) and deoxynivalenol (DON) production in an inoculated field experiment at two locations in each of two years. For seven genes known to control fungal growth  or DON production  single nucleotides polymorphic sites (SNPs) were determined and evaluated for the extent of linkage disequilibrium (LD). Associations of SNPs with both phenotypic traits were tested using linear mixed models.MetAP1 and one SNP in Erf2 were significantly (P < 0.05) associated with aggressiveness explaining proportions of genotypic variance (Gp) of 25.6%, 0.5%, and 13.1%, respectively. One SNP in TRI1 was significantly associated with DON production (G p= 4.4).Decay of LD was in most instances fast. Two neighboring SNPs in Fusarium graminearum as a template to amplify comparative sequence parts of candidate genes is an effective method to detect quantitative trait loci. Our findings underline the potential of candidate gene association mapping approaches to identify functional SNPs underlying aggressiveness and DON production for F. graminearum s.s populations.We argue that using the published sequence information of  Fusarium graminearum (teleomorph Gibberella zeae) is considered to be the main causal agent of this disease in addition to other species such as F. culmorum [F. graminearum complex has been subdivided into several cryptic species [F. graminearum sensu stricto (s.s.) [-1 [Fusarium head blight (FHB) is a destructive disease to cereals including wheat and barley. culmorum . F. gram species , the maio (s.s.) . FHB diso (s.s.)  with cono (s.s.) . DON is .s.) [-1 .F. graminearum are still unclear. To date, only one QTL (quantitative trait locus) study from a single cross was reported detecting at least two QTL for aggressiveness [F. graminearum s.s. using SSR (simple sequence repeat) markers. Comparing 12 individual field populations each consisting of 30 isolates, Talas et al. [F. graminearum is a haploid, homothallic fungus and propagates asexually by conidia and sexually by ascospores allowing both selfing and outcrossing [F. graminearum [TRI1, TRI5, TRI6, TRI10, TRI14) [Fusarium spp.  [F. graminearum estimated by different types of genetic makers such as VNTR, AFLP, RFLP [The quantitative ability of an isolate to cause disease on a susceptible host plant in a non-race specific pathosystem is defined as aggressiveness . Aggresssiveness . It was crossing . With thminearum , it is nminearum . The can, TRI14) ,16 or ar1, Erf2) ,18. Cand1, Erf2) . The res1, Erf2) . Low LD LP, RFLP ,11,21, bErf2 and MetAP1 for testing whether they affect the quantitative variation for aggressiveness, and (iv) evaluate associations of SNPs in TRI1 and other four genes of the TRI5 cluster with variation in DON production.The specific objectives of our study were to: (i) investigate the nucleotide diversity on gene level, (ii) investigate the extent of LD between single nucleotide polymorphic sites (SNPs) within and among candidate genes, (iii) identify SNPs of candidate genes F. graminearum s.s. isolates produced symptoms of FHB disease in all environments. Briefly, genotypic proportion of phenotypic variance of the isolates was significant (P < 0.01) for both traits: Aggressiveness measured as FHB rating on scale from 0 to 100 and DON production measured as DON concentration in wheat kernels in mg kg-1. Isolate × environment interaction variance was significant (P < 0.01) only for mean FHB rating but not for DON production. Entry-mean heritability was moderate for mean FHB rating (0.55) and DON production (0.62).Phenotypic data were analyzed in detail in a companion study . All 77 -1 ranging from 3.5 to 21.6 mg kg-1. One isolate (WET24) produced a very low concentration of DON (0.3 mg kg-1) and was found to be a nivalenol producer by chemotype-specific primers.Histograms based on best linear unbiased estimators (BLUEs) followed a normal distribution for both traits Figure . The meaPrincipal coordinate analysis (PCoA) based on modified Rogers' distances between all isolates did not show a distinct separation of the isolates sampled from different locations Figure . ExplainTRI10b to 8.8% (65/734) on MetAP1 indicating a high nucleotide diversity in most tested genes  is low (2 r< 0.1). Interestingly, 48%, 19%, and 45% of the SNP pairs between the genes TRI10/MetAP1, MetAP1/TRI5 and MetAP1/Erf2, respectively, have higher values of 2 rthan 0.1, although they are located on different chromosomes. Low 2 rvalues (< 0.1) were observed for SNPs of gene pairs TRI10/Erf2 and TRI5/Erf2, whereas 2 rvalues of 0.2 were detected between SNP pairs of TRI10b and TRI5, followed by a rapid decay of LD.Percentage of polymorphic sites per total sequenced region of each gene (without singletons) varied from 0.9% 5/513) on 3 on TRI1.8% 65/73 on MetAPMetAP1 were significantly associated (P < 0.05 using Bonferroni-Holm correction) [G p= 25.6 and 0.5, respectively   with mealy Table . Additio1% Table . A singlon Table . All detF. graminearum. This is a totally different approach than using knock-out mutants [Association mapping based on candidate genes is a promising tool for high-resolution mapping of genes contributing to quantitative traits . Neverth mutants , becauseTRI5 cluster), TRI1 gene belong to a second smaller cluster that has a different chromosomal localization [TRI1, TRI5, TRI14 have a direct effect on the production of DON or acetylated DON, TRI6 and TRI10 are regulating this pathway. TRI14 export the deoxynivalenol outside the mycelia in addition to its major role in aggressiveness [The genes for deoxynivalenol (DON) biosynthesis reside primarily in a 25 kb cluster  especially in the region that includes the TRI5 gene cluster [2 rand physical distance in addition to the large proportion of unlinked SNP with significant LD, such as SNPs between gene pairs TRI5/MetAP1, TRI10/MetAP1, or MetAP1/Erf2 , and fungal biomass and DON content  were reported among 50 F. graminearum isolates [F. graminearum population sample.Two SNPs in isolates . NeverthTRI1 was associated with DON production in F. graminearum. TRI1 encodes a cytochrome P450 monooxygenase that catalyzes hydroxylation of C-8 position during trichothecene biosynthesis [A single SNP detected in ynthesis . This coF. graminearum s.s. The described associations should be validated using a larger number of isolates and different environments. The validated genes are an important starting point for further functional analyses.This is the first candidate gene association mapping study provided insights on some genes involved in aggressiveness and DON concentration of Triticum aestivum L.) showing symptoms of FHB were sampled from three commercial fields in Germany to establish a fungal population of F. graminearum s.s.: Stuttgart-Hohenheim in southwest Germany in 2008, Wetze and Schickelsheim in Lower Saxony in 2006 and 2007, respectively. From each infected head, one isolate was recovered, transferred onto a fresh SNA plate and placed under permanent UV light for induction of sporulation as described recently [F. graminearum s.s. (former lineage 7) were inoculated on the moderately resistant German spring wheat cultivar Taifun  for analyzing aggressiveness and DON production in the field.Ears of winter wheat  and Oberer Lindenhof , resulting in four environments (location × year combinations). Mean annual temperatures at HOH and OLI were 10.1°C and 9.0°C, respectively, mean annual precipitations were 644 mm and 723 mm, respectively, across 2009 and 2010. Plants were grown in two-rowed micro-plots of 1 m length and 0.42 m width. Plots were arranged in a chessboard-like design, i.e., each plot with a wheat entry was bordered by four plots of similar size that were planted with a long-strawed spring triticale cultivar Nilex  to reduce inter-plot interference caused by drifting of inoculum during spraying or secondary distribution of spores. The experiment was arranged in a split-plot design with two replications. The main plot factor was the 5 spores ml-1 onto the wheat heads of each plot. Inoculation was performed at full flowering time of the wheat cultivar to ensure maximum susceptibility of wheat to F. graminearum. Fusarium head blight (FHB) aggressiveness was rated visually four times as the percentage of infected spikelets per plot (0-100%). This rating included both the number of infected spikes per plot and the number of infected spikelets per spike. To compare FHB reactions, the arithmetic means of four ratings were used and assigned as mean FHB rating throughout the paper. All plots were harvested by hand, threshed, and the grain analyzed to quantify the amount of DON by a commercially available immunotest  as previously described in detail [-1 DON concentration. Prediction of NIV chemotype was done using the primers N11, 15D11, 3D11, and 11R in a multiplex polymerase chain reaction (PCR) as designed by Zhang et al. [Inoculum was sprayed with a concentration of 2 × 10n detail . This ten detail . In eachg et al. .In order to analyze the population structure, all isolates were fingerprinted with 19 simple sequence repeat (SSR) markers dispersed throughout the whole genome following standard protocols .TRI1, TRI5, TRI6, TRI10, and TRI14). Two other, yet uncharacterized candidate genes in Fusarium spp.  were tested for a possible association with aggressiveness. Nucleotide sequences of these genes were imported from Fusarium graminearum database FGDB [TRI1 (FGSG_00071), TRI5 (FGSG_03538), TRI6 (FGSG_16251), TRI10 (FGSG_03538), TRI14 (FGSG_03543), MetAP1 (FGSG_01397), and Erf2 (FGSG_08531). Specific primers were designed . The sequence was performed once for each isolate, hence the alignment was mostly identical . Expected sizes of PCR products were obtained for all tested genes. All sequences of TRI6 and TRI14 were located in the coding region of the genes  were stretched over two exons. Sequences of genes were obtained from right to left sides of PCR products, just genes MetAP1 and Erf2 were obtained from left to right side. Sequence of TRI1 was located over four exons according to the reference sequence. Number of identified SNPs was high over all sequenced regions of candidate genes (Table Polymerase chain reaction (PCR) was performed using the designed primers related to each gene separately following standard protocols, however, with a different annealing temperature for each gene Table . Purificijn y= μ+iIso+jEnv+(Iso × Env)ij +nRep+ijne, where μ is the population mean, i Isothe genetic effect of the ith isolate, j Envthe effect of the jth environment, Iso × Env the isolate times environment interaction effect, n Repthe effect of the nth replication, and ijn ethe residual error. Variance components were determined by the restricted maximum likelihood (REML) method using the software ASReml 2.0 . Significance for variance component estimates was tested by model comparison with likelihood ratio tests where the halfed P values were used as an approximation [2h) on an entry-mean basis was estimated as the ratio of genotypic to phenotypic variance according to Melchinger et al. [The following linear mixed model was used to estimate variance components: ximation . Heritabr et al. . Further2 r[Genetic relatedness among the 77 isolates was determined by applying principal coordinate analysis (PCoA)  based onr2  and signr2 . LD and r2 .ijn y= μ+pa+iIso+jEnv+ijpe, where p ais the effect of allele p. The allele effect p awas modeled as fixed effect whereas i Isoand j Envwere regarded as random effects. We assumed that the variance of the random genetic effect was Var(g) = 2Kσ2g, where σ2g refers to the genetic variance estimated by REML and K was a 77 × 77 matrix of kinship coefficients that define the degree of genetic covariance between all pairs of entries. We followed the suggestion of Bernardo [ij between isolates i and j on the basis of the SSR marker data as ij K= 1+(ijS-1)/(1-ijT), where Sij is the proportion of marker loci with shared variants between isolates i and j, and Tij is the average probability that a variant from one isolate i and a variant from one isolate j are alike in state, given that they are not identical by descent. The coefficient Tij was estimated separately for each gene and trait using a REML method setting negative kinship values between isolates to zero. SNPs with allele frequencies < 0.1 were not considered in the association analysis or LD estimation. The obtained optimum T values were for DON content: TRI1 (0.025), TRI5 (0.575), TRI10 (0.375), MetAP1 (0.300), and Erf2 (0.400). For mean FHB rating: TRI1 (0.600), TRI5 (0.150), TRI10 (0.200), MetAP1 (0.075), and Erf2 (0.275). For the detection of main effects of the candidate gene SNPs, these were fitted as fixed effects in the mixed model and their significance was tested by a Wald F test. Based on the Wald F statistic, we performed tests for the presence of marker-phenotype associations with a significant (P < 0.05) effect on DON content and mean FHB rating applying the Bonferroni-Holm procedure [A two-step association approach was applied in this study and the BLUEs per environment were used as input for the association analysis. The linear mixed model for the association approach was: Bernardo  and calcrocedure  to correGp) explained by the detected SNP was calculated by fitting each SNP in a linear model to obtain 2adjR. The ratio G p= 2adjR/2 hyielded the proportion of genotypic variance [MetAP1, where two SNPs were detected for mean FHB rating, both were simultaneously fitted in the linear model in the order of their P values to correct for collinearity. Haplotype analyses were performed with the same procedure to test the association with both phenotypic traits (Additional file The proportion of genotypic variance (variance . In the The authors declare that they have no competing interests.FT carried out the phenotypic and molecular analyses, performed parts of the statistical analyses and drafted the manuscript. TW performed parts of the statistical analyses and helped to draft the manuscript, JCR edited the manuscript, HKP† participated in the design of the study and supported the technical realization. TM participated in the design of the field study and helped to draft the manuscript. All authors read and approved the final manuscript.Genomic organizations of the seven candidate genes with exons in black color. The sequenced region is shown as a green bar above each gene.Click here for fileTable S1. Haplotype analysis of the genes MetAP1 and TRI1.Click here for file


Purpose. Twin studies provide evidence that genetic influences contribute strongly to individual differences in exercise behavior. We hypothesize that part of this heritability is explained by genetic variation in the dopaminergic reward system. Eight single nucleotide polymorphisms  and three variable number of tandem repeats  were investigated for an association with regular leisure time exercise behavior. Materials and Methods. Data on exercise activities and at least one SNP/VNTR were available for 8,768 individuals aged 7 to 50 years old that were part of the Netherlands Twin Register. Exercise behavior was quantified as weekly metabolic equivalents of task (MET) spent on exercise activities. Mixed models were fitted in SPSS with genetic relatedness as a random effect. Results. None of the genetic variants were associated with exercise behavior (P > .02), despite sufficient power to detect small effects. Discussion and Conclusions. We did not confirm that allelic variants involved in dopaminergic function play a role in creating individual differences in exercise behavior. A plea is made for large genome-wide association studies to unravel the genetic pathways that affect this health-enhancing behavior. We selected four SNPs and two VNTRs that affect the dopamine receptors for this study: rs265981 is located within the DRD1 gene and has two possible alleles, A (minor) and G (major). The A allele has been associated with a decrease of DRD1 expression levels and thus worse dopamine transmission compared to the G allele [ rs6275  is a synonymous SNP located within the DRD2 gene. The G allele has been associated with increased DRD2 expression levels [ DRD2 gene [ rs6280 lies within the DRD3 gene and is translated to one of two amino acids in the D3 receptor protein: glycine  or serine , with glycine having a higher affinity for dopamine compared to serine [ rs1800955  is located in close proximity to the DRD4 gene and has been shown to influence promoter activity, with the C allele potentially enhancing activity compared to the T allele [ DRD4 gene was investigated consisting of 48 base pairs with varying repeats ranging from 2 to 11. The 7-repeat allele has been shown to have a lower affinity for dopamine compared to the other repeats [ DRD5 transcription start site consists of a dinucleotide polymorphism with alleles ranging from 130 to 166 base pairs and has been hypothesized to be in strong linkage disequilibrium with one or more functional variants in the DRD5 gene. The 148 allele has been associated with decreased DRD5 expression levels [G allele . rs6275 n levels . The rs1RD2 gene , 29 and RD2 gene . rs6280 o serine  and thusT allele , 33. A V repeats , thus in repeats . A VNTR n levels .β-hydroxylaseDopamine  (DBH) converts dopamine to norepinephrine and is encoded by the DBH gene. rs1611115  is located in the promoter region of the DBH gene. This polymorphism has been shown to account for 30–50% of the variance in DBH activity. More specifically, the C allele has been associated with higher plasma levels of DBH and thus lower dopamine levels [ rs2519152 polymorphism  is situated within the DBH gene and the T allele has been associated with lower DBH activity and thus higher dopamine levels compared to the C allele [e levels , 38. TheC allele . DAT1 (=SLC6A3) gene and the COMT gene, respectively. The dopamine active transporter is encoded by the DAT1 gene and clears dopamine from the synapse by depositing it back into the cells. A VNTR in the 3′ untranslated region of the DAT1 gene was investigated that consists of a 40-base pair repeat with three alleles: 440, 480, and 520. We investigated the effect of the 480 allele in the present study as it has been associated with higher expression of the transporter, resulting in higher dopamine reuptake and thus lower levels of dopamine [ Catechol-O-methyltransferase is encoded by the COMT gene and degrades dopamine. The SNP rs4680  lies within the COMT gene and is either translated to methionine (Met) or valine , depending on the allelic variant that an individual has . The COMT-Met enzyme degrades dopamine slower than the COMT-Val enzyme does and therefore results in higher dopamine levels [Finally, two genes were selected based on their association with dopamine reuptake and dopamine degradation: thedopamine . Catechoe levels , therebye levels .The aim of the present study was to specifically test candidate alleles with a known function in the dopaminergic reward system for their association with regular leisure time exercise behavior, assuming that higher dopamine levels and stronger dopamine transmission are associated with higher reward sensitivity and thus more exercise behavior. The specific hypotheses are summarized in Data originated from twins and their family members that agreed to participate in longitudinal research of the Netherlands Twin Register (NTR) which has been set up to investigate individual differences in human behavior. The data collection protocol was approved by the Medical Research Ethics Committee of the VU University Medical Centre. The final sample consisted of 8,768 individuals , of which 38% were males and 62% were females, with a mean age of 32.5 years .Twins and their families are involved in research projects: for 7-, 10-, and 12-year-olds, both mothers and fathers are invited to fill in surveys on their twins' health, lifestyle, and behavior. From 13 years onwards, the twins and their siblings are invited to complete self-report surveys. When reaching adulthood (18 years), the twins are asked to fill in surveys every 2-3 years and additional family members are invited to take part in research projects . Characteristics and recruitment of participants are described in van Beijsterveldt et al.  and Will leisure time exercise behavior since we were interested in voluntary (leisure time) physical activity that might be affected by individual differences in reward sensitivity. Participants  were asked to indicate (1) which exercise activities they participated in and (if any) (2) for how many years, (3) how many months a year, (4) how many times a week, and (5) how many minutes each time they participated in the respective activity. Test-retest reliability of this questionnaire was high (>0.82) in previous studies [ regular leisure time exercise behavior, explicitly excluding irregular activities such as sailing camps or ski holidays , non-leisure activities such as transportation , gardening, house cleaning, and–for younger participants–compulsory physical education classes. Each activity was recoded into its metabolic equivalent of task (MET), reflecting energy expenditure during a specific activity as a multiple of energy expended at rest . For individuals younger than 18 years old, Ridley et al's. [N = 31 of the final sample), the score was truncated at 120 MET hours.For this study, we focused on regular studies , 47 and  studies . Our focet al's.  compendiet al's. . The proN = 7,349), adolescents' data (N = 997), and children's data (N = 422).Exercise data of several longitudinal assessments were combined into one score. First, exercise data of individuals that were >50 years old were changed to missing and exercise data (of the respective assessment only) were removed when participants were injured at the time of survey completion. Subsequently, the data were combined by creating a new “weekly MET hours”-variable based on the most recent questionnaire of adults. Missing values were then replaced with older data of those individuals–preferentially, with data at an adult age and, if unavailable, with data of adolescents and children . The association analysis was thus run on the joint exercise-variable that was composed of adults' data  were selected for this candidate gene study based on their known function in the dopaminergic reward system. For some individuals, genotype data were available from fingerprint sets that included 30–38 SNPs and 5–7 VNTRs in candidate genes  and three VNTRs (a 48-bp VNTR in exon III ofnes (see ). For otIn the fingerprint set, samples were excluded based on low sample call rate, sex errors, inconsistencies between duplicate samples, Mendelian errors, and erroneous IBS/IBD relationships. In the imputed dataset, samples were filtered on the same criteria, as well as on excessive heterozygosity. If samples were present in both the fingerprint and the imputed dataset, they were included only if they survived quality control (QC) in both sets.P value >.00001, minor allele frequencies (MAF) >.01, Mendelian error rate <.02, SNP call rate >.95, SNP concordance rate >.99, and allele frequency difference with the reference set <.20. Haplotype phasing and imputation of missing genotyped SNPs was done in MACH 1.0 and subsequent imputation of the missing SNPs was done with Minimach using 1000G as a reference set . After imputation, SNPs were tested for HWE, Mendelian error rate, allele frequency difference with the reference set, and imputation quality (R²). For two SNPs (rs1611115 and rs1800955), we decided to use the fingerprint data only, since they showed a low R² and/or a high rate of Mendelian errors in the imputed set as well as a low concordance between the fingerprint set and the imputed set (<95%). MAF and HWE for the final data set are depicted in In the fingerprint set, SNPs and VNTRs were tested for Hardy-Weinberg Equilibrium (HWE), Mendelian error rate, SNP/VNTR call rate, concordance rate for duplicate samples, and allele frequency difference with a reference set (HapMap CEU). In the genome-wide SNP dataset, SNPs were filtered on the following criteria before imputation: HWE In individuals with genome-wide SNP data, information on ancestry was based on Principal Component Analysis . For theThe SNPs were coded based on the presence of one or two of each of the two alleles in the called genotype . For the SNPs, the exact combination of alleles corresponding to 0, 1, and 2 can be found in As a first step, the analyses were performed for each genetic variant separately. Mixed models were run in SPSS for Windows  and were based on maximum likelihood estimation. The dependent variable was weekly MET hours. The following variables were included as fixed effects: sex , age (z-score), sex x age interaction, and the respective SNP/VNTR. We tested whether correction for a number of possible confounders had a significant effect on the results, namely, ancestry differences within the Dutch population , ancestry differences based on the 1000 Genomes project , differences due to batch effects , and a dummy variable to correct for differences between genotyping platforms.As the next steps, (1) multiple variants were included into a single mixed model to test their effects simultaneously and (2) mixed models were run with a polygenic risk score computed as the sum of the alleles that are hypothesized to increase dopamine level  across multiple variants. As data were derived from family members , we added genetic relatedness as a random effect to the models. The chosen alpha level was .05/11 .R code available upon request). Due to differences in sample sizes and family structures between the “fingerprint data only” and the “ imputed data”, the power was calculated for four genetic variants: (1) the SNP with the smallest sample size , (2) the SNP with the largest sample size within the five variants that we had fingerprint data for only , (3) the SNP with the smallest sample size within the six variants that included imputed data , and (4) the SNP with the largest sample size . Thus, we approximated the upper and lower bounds of power within (a) five variants that were derived from the fingerprint set and (b) six variants that were derived from the imputed/combined set. The power calculations were based on 1000 replications and the chosen alpha level was .05/11. For the smaller data set, the power ranged from .36  to .58 (.55–.61) to detect an effect explaining 0.5% of the phenotypic variance. The power to detect an effect explaining 1% of the variance ranged from .78  to .91 (.89–.92). For the larger data set, the power ranged from .69  to .75 (.72–.77) to detect an effect explaining 0.25% of the variance. The power to detect an effect explaining 0.5% of the variance ranged from .96 (.94–.97) to .97 (.96–.98). These estimates are conservative as age and sex were not taken into account.To get an indication of the power to detect genetic effects, simulated data was used, as this allows us to accommodate the large variation in family composition and the truncation of the phenotype distribution . The sample size is lower for those variants that were collected with the fingerprint chip only  compared to the remaining variants that were derived from the fingerprint chip and complemented with imputed data, or derived from the imputed data only. Also, the fingerprint data were derived from relatively young participants. The P values in the table are based on the model that included sex, age, sex × age interaction, and the respective variant as fixed effects and familial relatedness as a random effect. Main effects of sex and age were significant (P < .001) with males and younger participants showing higher levels of exercise behavior and so was the sex x age interaction (P < .004). Importantly, none of the SNPs or VNTRs had a significant effect on exercise behavior (P > .02). First, all variants were included, reducing the sample size to 1,954 individuals with full genotypic and phenotypic data. Second, only SNPs were included that we had imputed data for , resulting in 7,734 individuals with full genotypic and phenotypic data. In both cases, the joint effect of the variants was non-significant .In additional analyses, we (1) added possible confounders  to the model and (2) reran the analyses on dosage scores (in which the uncertainty of imputation is taken into account). The effect of each SNP and VNTR remained nonsignificant. Next, multiple variants were included into a single mixed model to investigate their joint effect. As the VNTRs and two SNPs  were derived from the fingerprint chip only, the number of individuals dropped to less than 2,000 individuals when including only individuals that had been genotyped on all variants. Therefore, a potential overall effect was tested in two steps.P > .15). Mixed models on the sum of the effect alleles across multiple variants were again run in two steps. First, the complete set of variants was included and, second, only the variants we had the larger sample size for were included.Finally, the analyses on the polygenic risk scores also failed to show a significant association  with a known function in the dopaminergic reward system were investigated. None of them was significantly associated with exercise behavior.This study aimed to investigate the genetic basis of regular leisure time exercise behavior. Eight SNPs  and three VNTRs . In children, genetic effects have been shown to explain slightly more than 20% of the variance in exercise behavior [ which genes contribute to individual differences in exercise behavior.It is well established from twin studies that exercise behavior is a heritable trait . Twin stbehavior . This hebehavior  and stabbehavior . HoweverA priori, genetic variation in the dopaminergic signaling pathway provided a promising source for the biological basis of this phenotype. Dopaminergic neurotransmission is implicated in the experience of reward which in turn is likely to be a crucial agent in the take-up and maintenance of exercise behavior . EngaginOur study was founded on the solid expectation that we would find an association between known functional allelic variations in the dopaminergic signaling pathway and the narrow, but well-defined, trait of regular leisure time exercise behavior. This expectation was clearly not borne out by the results. Do our findings rule out a role for the dopaminergic system in individual differences in regular leisure time exercise behavior? There are a number of reasons why this conclusion would be premature.First, the selected SNPs and VNTRs might not have covered all genetic variation within the dopaminergic genes examined, specifically in the case of low linkage disequilibrium between variants within a gene. We opted to choose alleles with known functional effects and/or previously reported effects on relevant phenotypes instead of examining the larger set of SNPs tagging the major haplotypes within dopaminergic genes . Also, bSecond, one might argue that the effect sizes of the genetic variants measured here may have been too low to detect even with the substantial sample sizes available to us. Exercise behavior is a very complex phenotype and is likely to be affected by a lot of genes, each of which has only a small effect. These small effects might not be detectable in a sample of less than ten thousands of individuals. For six of the eleven variants, data of around 8,000 individuals were available and for the remaining five variants, data of around 2,500 individuals were available. A power analysis revealed that—for the larger samples—the power to detect an effect explaining 0.5% of the phenotypic variance was very good, and the power to detect an effect explaining 0.25% of the variance was acceptable, taking into account multiple testing, family structures, and the phenotypic distribution. For the smaller samples, power was more modest, but still the power to detect an effect explaining 1% of the phenotypic variance ranged between .78 and .91. Apart from increasing sample size, power could be increased by using intermediate phenotypes . For insThird, we should bear in mind that dopaminergic neurotransmission may mediate the effect of entirely different genetic variants on exercise behavior, in the absence of a direct effect of dopaminergic genes. For instance, there might be genetic variants that increase exercise ability, thereby triggering increased dopaminergic neurotransmission during exercise activities as it is rewarding to perform an activity that one is good at. In this case, genetic variants within the dopaminergic pathway may not be directly involved, but dopaminergic neurotransmission may still indirectly convey genetic effects on exercise behavior.We did not confirm our hypothesis that allelic variants involved in dopaminergic function create individual differences in exercise behavior. This leads us to plea for a large scale GWAS on leisure time exercise behavior involving more research groups as the success of GWAS efforts clearly scales with the number of participants. Currently, leisure time exercise behavior is less frequently assessed than general physical activity, in spite of the potentially less favorable psychometric properties of the latter. We believe that a GWAS effort on leisure time exercise behavior is worth pursuing. In order to pick up effects, assessing intermediate phenotypes such as exercise motivation should be considered. An inactive lifestyle is one of the major public health burdens nowadays and interventions that aim to tackle the problem are mostly unsuccessful. Given the substantial heritability of leisure time exercise behavior, it is of outmost importance to better understand its biological basis in order to improve intervention on this health-enhancing lifestyle.


Motivation: Association tests based on next-generation sequencing data are often under-powered due to the presence of rare variants and large amount of neutral or protective variants. A successful strategy is to aggregate genetic information within meaningful single-nucleotide polymorphism (SNP) sets, e.g. genes or pathways, and test association on SNP sets. Many existing methods for group-wise tests require specific assumptions about the direction of individual SNP effects and/or perform poorly in the presence of interactions.Results: We propose a joint association test strategy based on two key components: a nonlinear supervised dimension reduction approach for effective SNP information aggregation and a novel kernel specially designed for qualitative genotype data. The new test demonstrates superior performance in identifying causal genes over existing methods across a large variety of disease models simulated from sequence data of real genes. In general, the proposed method provides an association test strategy that can (i) detect both rare and common causal variants, (ii) deal with both additive and interaction effect, (iii) handle both quantitative traits and disease dichotomies and (iv) incorporate non-genetic covariates. In addition, the new kernel can potentially boost the power of the entire family of kernel-based methods for genetic data analysis.Availability: The method is implemented in MATLAB. Source code is available upon request.Contact:hongjie.zhu@duke.edu Availability of rare variant information presents unique opportunities to evaluate the ‘common disease rare variants’ hypothesis. This hypothesis states that a complex disease can be attributed to multiple rare variants with relatively high risks, and it has attracted much attention in recent studies. Attesting to this hypothesis, a number of deleterious or protective rare variants have been identified for low plasma levels of high-density lipoprotein cholesterol (Genome-wide association studies (GWASs) based on single-nucleotide polymorphism (SNP) chips have enjoyed varying degrees of success in identifying genes associated with complex diseases or traits . It has P-values by permutations within each group. Both methods consider rare variants with MAF falling below a pre-specified threshold and exclude common variants from analysis. This separate treatment seems counterproductive because in reality both common and rare variants can be informative. The pooling strategy of Identifying disease associated rare variants, however, is challenging, because a particular rare disease predisposing allele may be present in only a handful of patients. Henceforth, traditional single marker tests that capture only marginal effects are doomed to have low power. A useful strategy to address this challenge is to effectively merge information in SNP variants by some meaningful SNP sets, for instance, genes or pathways, and then to identify disease-associated genes or pathways rather than disease variants. Following this idea, several aggregation-based association test approaches have been developed. The field of statistical dimension reduction (DR) offers a useful and appealing means for genotype aggregation. It is based on the belief that high-dimensional data can be effectively summarized in a low-dimensional space, and the subsequent modeling can concentrate on the reduced space. The most commonly used dimension reduction approach is principal components analysis (PCA). In this article, we develop a powerful association mapping approach based on next-generation sequencing data. Two key ingredients of the proposed method are a statistical DR that achieves supervised and nonlinear reduction, and a new kernel that is based on Markov chain theory and particularly suitable for qualitative SNP data. Our contributions are mainly 2-folds. First, the proposed association mapping approach simultaneously takes into account (i) both rare and common variants, (ii) both additive and interaction effect, (iii) quantitative traits as well as disease dichotomies and (iv) non-genetic covariates. Second, the commonly used kernels, such as Gaussian, polynomial and spline, work successfully with continuous attributes, but may perform poorly for discrete genetic data. The proposed new kernel is specially designed for discrete attributes and can effectively capture the similarity between individual genotypes. Moreover, the new kernel is novelly derived from powerful Markov chain theory and can benefit many kernel-based learning methods in general. We compare our proposal with some state-of-the-art aggregation and mapping solutions and find that our method clearly achieves superior power in a variety of different genetic model scenarios.The remainder of the article is organized as follows. n study individuals are genotyped at a SNP set (e.g. a gene) that is composed of p SNPs denoted by X1,...,pX, and the trait Y can be either binary (case–control study) or quantitative. Potential non-genetic covariates, such as sex, age smoke, and are denoted by C1,...,tC. There can be multiple SNP sets, and we treat ‘one set at a time’. The goal is to test the association of the trait and all markers in the SNP-set ‘jointly’, after adjusting for non-genetic covariates. In sequence studies, the number of markers p is potentially large and can outnumber the number of subjects n. Our proposed group-wise association test consists of two key elements: a nonlinear supervised DR method that aggregates markers and produces summary features and a novel kernel that encodes genomic similarity. The nonlinear DR method was first proposed in Suppose p SNPs, PCA seeks linear combinations of SNPs that have maximal variances. It is solved by an eigen decomposition of SNP covariance matrix. Then, the eigenvectors with leading eigenvalues give the coefficients of linear combinations being sought. The linear transformed SNPs form the eigen-SNPs used in the subsequent analysis. Despite its widespread applications, however, PCA conducts DR without utilization of the phenotypic trait information, and thus there is no guarantee that the top extracted principle components are relevant to the traits. Consider a simple illustrative example. Suppose two SNPs X1 and X2 are in linkage disequilibrium (LD). Then, the variance of the linear combination X1 + X2 is larger than that of X1 − X2 and thus the eigen-gene found by PCA will be closer to the direction X1 + X2 than to X1 − X2. If in truth these two SNPs have opposite effects—one deleterious the other protective—then the trait depends on the SNPs through X1 − X2 and the eigen-gene would contain no signal for association.We begin with a brief review of PCA, which has been an extremely popular tool in analysis of genetic and genomic data. For instance, PCA has been used to adjust for population stratification  the ‘linear sufficient predictors’, which will serve as the induced summary features in subsequent analysis. There have been many methods proposed for SDR, many of which can be formulated as a generalized eigen decomposition problem. Specifically, a reduction estimate can be obtained by the first d eigenvectors jηs that correspond to the nonzero eigenvalues jλs in a descending order from the decomposition: xηjΩ = jΣxηj, jλ = 1,...,d, where xΣ = Cov(X) and xΩ is a method-specific p×p semi-positive definite matrix (xΩ = Cov{E(X|Y)−E(X)}. This family of DR methods differ from PCA in that the response information is used in the DR phase. It is also interesting to note that all those SDR methods impose no parametric assumption on Y|X. Instead, they require the marginal distribution of X to be elliptically symmetric. This is often viewed as a mild condition, since it holds approximately when p goes to infinity. We assume the condition holds since we are dealing with a very large p.Intuitively, it is natural to incorporate the trait information during the phase of DR, and this leads us to the family of ‘supervised’ sufficient dimensional reduction (SDR) approaches. For a regression of a response e matrix . For inse matrix  is a widX. This could have some limitations. Consider an illustrative example, where X =  and Y = X1 + X2X3 + X42 + X5X6 + ε, with an independent error ε. In this case, no linear reduction is possible. Another potential limitation is that one needs to invert a p×p covariance matrix xΣ, whereas its sample estimator is not invertible when p exceeds the sample size n. These observations motivate us to consider a ‘nonlinear’ DR strategy.The above SDR methods yield ‘linear’ DR, because the reduction admits the form of linear combinations of ϕ(·), with an associated kernel matrix K, to map X to ϕ(X). One then performs a linear DR in the space of ϕ(X), which in effect results in a nonlinear DR in the original predictor space ϕ(X), which is high or even infinite, to a dual problem that only depends on the sample size. Consequently, the method works for n < p. Specifically, in analogy to linear reduction in η1TdX,...,ηTX) are replaced by the inner products Y depends on X only through those inner products. We refer them as the ‘nonlinear sufficient predictors’ and assume the number n,p). In terms of estimation, conceptually, one can estimate jβs in a way analogous to linear reduction, i.e. through the eigen decomposition: ϕ= Cov{ϕ(X)} and Ωϕ is defined similarly as Ωx except we replace X with ϕ(X). Given {,...,}, estimation of βjs is obtained by substituting in the corresponding sample counterparts: ϕ(X) can be very high, sometimes even infinite. As such, a direct decomposition is not feasible computationally.The basic idea is to use a function j,ϕβ(X)〉, rather than jβ themselves. Then, given a pre-specified kernel function k, these inner products can be obtained by solving a dual problem: J is a method-specific n×n matrix. J matrix for different SDR methods, including the one for kernel SIR that will be used in the numerical studies of this article. Then, for a new observation j,ϕβ(x)〈 can be obtained from the kernel k and jαs. It is noted that the proposed nonlinear DR approach only involves decomposition of an n×n matrix, so it can handle n < p. Its flexible reduction form beyond the linear combination is also expected to facilitate DR. For the illustrative example considered above, if one uses a quadratic kernel, then only one linear combination in the mapped feature space is needed to summarize all regression information, and thus substantial reduction is achieved.The problem can be solved by noting that the target of nonlinear DR estimation are the inner products 〈xi and xj coded by numbers of minor alleles assf is the MAF of the variant, up-weighting the importance of rare variants.Critical to success of any kernel-based methods for genotype data analysis is the design of kernels that can effectively capture genomic similarity ,b. The mIBS and weighted IBS kernels can be regarded as sums of simple similarities evaluated at each individual SNP, which, however, may result in loss of power when complex interactions dominate the genetic effect of the SNP set. This motivates us to propose new kernels for genotype data.k is a possibly asymmetric kernel and K is the corresponding kernel matrix with all eigenvalues positive, thenK +TK)/2 is symmetric and positive definite; kernels. Suppose Fact 1 follows from an inequality due to Fan , which can be efficiently estimated from genotypes of all individuals (π (itx) = (itx + tα)/N +|α| and |α| = ∑t=1pαt. k is an irreversible Markov transition kernel and its stationary distribution is not known explicitly but can be well approximated by a Dirichlet-multinomial distribution with parameter α. It is well known that k has positive eigenvalues iλ = (2p)i][/(2p)i = 2p(2p−1)···(2p−i+1)/(2p)i for i = 0,...,2p−1 . COL6A3 encodes one component of Type-VI collagen; mutations in this gene have been found related to Bethlem myopathy and Ullrich congenital muscular dystrophy (http://ghr.nlm.nih.gov/gene/COL6A3). In the dataset, TG contains 146 SNPs, among which 10 are common variants (MAF>10%) and 113 are rare variants (MAF<1%); COL6A3 contains 187 SNPs, among which 10 are common variants and 143 are rare variants. In the two genes, only a few pairs of SNPs have high LD  by the Genetic Analysis Workshop 17 (GAW17). We investigate the empirical power and Type-I error of our method on the basis of the LD structure of two genes,  high LD . Figure Q0 = ∈, where ∈ is a standard normal noise. The top 50% of the distribution of Q0 are then declared affected, by which we define a binary disease status. It is easy to see that, under the null model, the quantitative trait and disease status do not depend on genotypes.In order to make a comprehensive performance comparison between the proposed methods and existing ones, a variety of true genetic effects are examined in different simulation studies . For eacXj}{'s are SNPs in descending order according to their MAFs and f is the true genetic effect model, which differs among simulation scenarios. A binary disease status based on Q1 is defined in a similar way as Q0. For reference purpose, if in f = ∑j=1p βjXj}{ is a linear additive model, then conditional on the fact that this is an half-affected-half-control sample and assuming that existence of causal SNPs in the gene does not heavily influence the general cutoff to Q1 (which is the case for most of our simulation studies shown below), there is an approximate correspondence between coefficient jβ and odds ratio of the SNP Xj}{: odds ratio ≈ )/Φ, where Φ represents cumulative normal distribution function with mean μ and standard deviation σ. Therefore, a coefficient β from 0.2 to 1 corresponds to an odds ratio from 1.4 to 5.3. On the contrary, a coefficient β from −0.2 to −1 reduces odds ratio to 0.7–0.2.Then, under the alternative model, a quantitative trait is generated according toP-values over 1000 replications are less than a nominal significance level of α = 0.05 under the alternative model using the designated causal SNPs. An empirical Type-I error was evaluated in a similar fashion except that the trait was generated under the null model. As mentioned above, we designed various scenarios to evaluate methods. Results are summarized in We compared our method of DR followed by LR model  with kernel-based adaptive cluster (KBAC) method of The last two rows of Simulations 1–4 represent main effect models. In Simulations 1 and 2, informative SNPs are all common variants, whose MAFs all fall into the range of 0.32–0.43. When all SNPs are deleterious (Simulation 1), VT outperforms KBAC, linear and nonlinear DR methods. However, when two of the informative alleles are protective (Simulation 2), the performance of VT drops dramatically, while the performance of the other methods does not. In this case, WF works the best and IBS is the second. In Simulation 3 and 4, informative SNPs are all rare variants, whose MAFs are between 0.005 and 0.0086. Note that few people have totally more than one minor alleles over these 10 SNPs. No matter there are protective rare variants or not, WF and IBS have the best and second best performance, respectively. VT has a comparable performance when there are only deleterious effect (Simulation 3), but the existence of protective variants destroys its performance again (Simulation 4). Note that under these linear genetic models, the WF and IBS kSIR's still work better than the LR and linear SIR, while the Gaussian kSIR does not. This reflects the superiority of these kernels for sequence data.Simulation 5 represents a model with both main and epistasis effects. For each gene, both of the two informative SNPs are common variants with very low LD. In this case, WF works better than IBS, which then outperforms KBAC, VT and other DR-based methods. Simulations 6 and 7 are pure epistasis models among three common SNPs with low LD between each other, while Simulations 8 and 9 represent epistasis between common and rare variants. It is clear that nonlinear DR methods with WF or IBS kernel outperform linear dimension reduction methods as well as KBAC and VT. KBAC loses most of its power in detecting common and rare variant interactions. VT performs poorly when there are protective effects.Weighted IBS kernel using weights TG. For Model (3), SNR is defined as the ratio of the variance of the signal f and the error variance. A number of SNR values were simulated by multiplying f with different coefficients. We further evaluated the performance of kSIR with WF kernel at different signal-to-noise ratios (SNRs) using gene In conclusion, VT is extremely vulnerable to protective variants and less sensitive to epistasis effects. KBAC does not capture interactions between rare and common variants. Even if the true genetic model is additive, linear DR-based methods do not outperform nonlinear DR methods with kernels specifically designed for genotype data. Among the different kernel methods, the proposed WF kernel always outperforms IBS kernel, which then works better than Gaussian kernel.Ideally, an association test should be able to handle: (i) high dimensionality of genomic dataset, which typically far exceeds the sample size; (ii) both rare and common variants; (iii) additive, recessive and dominant models of gene action; (iv) both quantitative traits and disease dichotomies and (v) non-genetic covariates. Most of existing solutions could not deliver across the board judged by all those criteria. To bridge the gap, we have proposed a strategy based on nonlinear supervised DR and a new kernel to effectively aggregate genotype information. Such an aggregation increases the likelihood of detecting multiple causal variants, whereas nonlinear reduction permits complex interactive relationship among genetic variants. Moreover, the GLM framework based on the aggregated features can naturally handle both quantitative and categorical traits, and incorporate non-genetic predictors and/or environmental variables. Finally, the proposed WF kernel based on Markov chain theory for genotype data has been proven useful compared with some existing kernels and can potentially benefit a wide range of kernel methods, such as kernel PCA, support vector machines and nonparametric and semiparametric regressions.There are a number of possible avenues for future extensions. First, a number of Markov chain kernels in addition to the WF kernel can be explored, for instance, Ehrenfest kernels, hypergeometric kernels and Dirichlet-Multinomial kernels . Second,