Gryllus bimaculatus), in which both exploratory tendency and aggression are heritable. We found that genotypes predisposed to be aggressive (due to DGEs) strongly decreased aggressiveness in opponents (due to IGEs). As a consequence, the variance in total breeding values was reduced to almost zero, implying that IGEs indeed greatly contribute to the occurrence of evolutionary stasis. IGEs were further associated with genetic variation in a non-social behaviour: explorative genotypes elicited most aggression in opponents. These key findings imply that IGEs indeed represent an important overlooked mechanism that can impact evolutionary dynamics of traits under selection.Behavioural ecology research increasingly focuses on why genetic behavioural variation can persist despite selection. Evolutionary theory predicts that directional selection leads to evolutionary change while depleting standing genetic variation. Nevertheless, evolutionary stasis may occur for traits involved in social interactions. This requires tight negative genetic correlations between direct genetic effects (DGEs) of an individual’s genes on its own phenotype and the indirect genetic effects (IGEs) it has on conspecifics, as this could diminish the amount of genetic variation available to selection to act upon. We tested this prediction using a pedigreed laboratory population of Mediterranean field crickets ( For example, frequency dependent selection1, temporal and spatial heterogeneity5, or life-history trade-offs8 have all been implied to explain the stable coexistence of different behavioural ‘types’ within populations. It is implicitly assumed that genes carried by focal individuals contribute to behavioural differences, such that directional selection should both erode variance and cause a change (over generations) in mean phenotype10. However, evolutionary theory also predicts that evolutionary stasis may occur despite directional selection in the presence of ‘indirect genetic effects’ (IGEs) generated by social interactions15. This key insight has largely been ignored in behavioural ecology theory explaining individual variation in behaviour, despite the fact that many behavioural traits are expressed as part of social interactions.Behavioural ecologists increasingly focus on studying the adaptive processes maintaining individual differences in behaviour within animal populations. Several adaptive explanations have been proposed for why selection might maintain behavioural variation rather than erode it (reviewed by15. IGEs can greatly influence evolutionary processes when they are correlated with the direct genetic effects (DGEs) of an individual’s genotype on its own phenotype. For example, in mussel cultures, individuals genetically predisposed to grow quickly in competitive situations are also genetically predisposed to reduce growth in others by depriving them of feeding opportunities16. The resulting negative genetic correlation between DGEs and IGEs can impose major evolutionary constraints, by effectively reducing the amount of variation in total breeding value of a trait within a population19. The presence of IGEs may thus lead to evolutionary stasis in the phenotype, implying that directional selection does not necessarily lead to evolutionary change. Interestingly, positive genetic correlations between DGEs and IGEs are predicted to instead speed up the response to directional selection relative to expectations from classic evolutionary theory (e.g. refs Peromyscus maniculatus) implies that this trait  can evolve very rapidly14. This is because selection for increased aggression would drive the evolution of a social environment in which aggression is more readily elicited by interacting conspecifics. Therefore, IGEs arising from social interactions can both provide a source of additional genetic variation that either facilitates rapid selection responses or serves as a source of evolutionary constraint on phenotypes20. However, to date IGEs have largely been ignored as a potential mechanism explaining evolutionary stasis in individual behaviour research24.Quantitative genetic theory implies that social interactions can have major evolutionary repercussions, particularly when an individual’s phenotype is affected by the genotypes of conspecifics: these effects are called IGEs11, i.e., traits that are expressed explicitly as part of social interactions. Interestingly, IGEs can also affect the evolution of other aspects of phenotype, including behavioural traits not expressed within a social context, provided these covary genetically with traits that do harbour IGEs25. For example, the literature on ‘behavioural syndromes’ often reports that traits expressed in social interactions  are phenotypically correlated with other risky behaviours expressed in non-social contexts, such as exploratory tendency, or anti-predator boldness . Of course, these correlations are important for evolutionary dynamics only if they are underpinned by genetic processes1027. Thus, if IGEs are present for a social behaviour such as aggression, the evolution of any trait genetically correlated either with the social behaviour or its IGEs may be affected.IGEs are expected to exist on traits such as aggression and dominanceGryllus bimaculatus) descended from wild-caught grandparents. For the data presented in this paper, we show elsewhere that exploratory behaviour and aggressiveness are both repeatable and heritable (subject to DGEs) but not genetically correlated . Here we expand upon these analyses by quantifying (i) whether IGEs also contributed to genetic variance in aggressiveness, (ii) whether, for aggressiveness, DGEs (tendency to act aggressively) and IGEs (tendency to elicit aggressiveness) were correlated, and (iii) whether IGEs on aggression were also correlated with DGEs for exploration, a trait not directly involved in social interactions. Our approach thus implies that drawing evolutionary predictions while ignoring IGEs not only on the focal trait, but also on other seemingly independent traits, can be greatly misleading.Here, we investigated whether IGEs contribute to the genetic architecture of behavioural variation expressed in social and non-social contexts. We repeatedly measured two behavioural traits  in a pedigreed laboratory population of Mediterranean field crickets (r = 0.45) and heritable (h2 = 0.28) . Aggressiveness was also significantly repeatable (rf = 0.17) and heritable (h2 = 0.05), while it additionally harboured a significant opponent identity effect (ro = 0.11)     was considerably smaller  than what ‘traditional’ estimates of heritability based on DGEs would (inappropriately) conclude  (Table G). However, the genetic correlation between DGEs on exploration and DGEs on aggression was close to zero and non-significant    using AIC  genetic architecture of behaviour that should be considered when making predictions on the evolution of traits studied in ‘personality’ research. Our results generally imply that IGEs can have consequences for the evolutionary trajectories of a wide range of traits, including those not expressed as part of social interactions .This study investigated a largely overlooked mechanism, indirect genetic effects, which may contribute to the observed behavioural variation in social traits under selection and impact their evolutionary dynamics. Our study on male Mediterranean field crickets confirmed that the phenotypic expression of aggression and exploration was repeatable, and showed that the former depended on opponent, as well as focal identity. Both behaviours harboured additive genetic variance, but—importantly—heritable variation in focal aggressiveness arose jointly from the genotypes of the focals (DGEs) and opponents (IGEs) Table . As aggr14 . An important consequence of the strong negative covariance between direct and indirect genetic effects is that the total heritable variation for aggressiveness is reduced18. This is highlighted in our results by the discrepancies between the (direct) heritability estimates (h2 aggression = 0.051), and the total heritable variation for aggression including IGEs and their covariance with DGEs . While indirect effects (genetic and non-genetic component) clearly contribute to variance in focal aggressiveness, the negative correlation between IGEs and DGEs means that the potential for evolution of the phenotypic mean in response to directional selection is even lower than suggested by the (direct) heritability30.The estimated magnitude of IGEs on aggression in this study was similar to that documented in other species (e.g. refs 14) direct-indirect (genetic) covariance will be positive. Conversely, negative correlations arise when aggression is asymmetric, being directed by more competitive (or dominant) individuals towards subordinate social partners. This is because, in a dyadic contest, a genotype predisposing to contest winning by the focal will necessarily predispose to losing when encountered in an opponent202832. Thus, the negative genetic correlation found here actually suggests that, at least within the context of the behavioural trials conducted, aggression is being used to assert social dominance in this species. The importance of such correlations applies to any species displaying aggressive interactions, regardless of whether aggression is part of stereotyped escalated context or linked to dominance.The sign of this correlation can also be interpreted in terms of behavioural feedback processes and the functional role of aggression. For example, in species (or contexts) where individuals escalate agonistic behaviour through positive feedbacks , leading to the suggestion of an integrated ‘aggression-boldness syndrome’  merits for exploration and aggression elicited in conspecifics  . However, it does not follow that the IGEs constraining evolution of mean aggression will necessarily constrain the evolution of exploration behaviour too. In general, IGEs arising from competition related processes are expected to impose constraints on traits that are consequent, rather than causal to, contest outcomes (and thus resource acquisition35), a scenario that is not clearly the case here. We fully acknowledge that our study is not directly informative for the causal pathways linking aggression to exploration, but several possibilities can be hypothesised. For example, the positive association could arise if exploration in a novel environment increases the likelihood of encountering rivals (and thereby provoking more attacks from conspecifics). Exploration could also be favoured in individuals eliciting aggression as a result of competition for territories in the population. Alternatively, exploratory tendency may be  correlated with other traits that directly mediate agonistic behaviour in competitive interactions .A question not previously considered is whether IGE on aggression  will also have evolutionary implications for non-social aspects of ‘animal personality’36. In this latter framework, an interaction effect coefficient ψ (‘psi’), captures the effect of a measured conspecific trait (or traits) on focal phenotype. ψ represents a standardized reaction norm slope, hence the level of phenotypic plasticity to a social environmental gradient11. In the context of our study, ψ is captured by the correlation between DGEs and IGEs: individuals responded to the aggressiveness and explorative tendency expressed by social partners (because IGEs on aggression are correlated to DGEs of both behaviours), implying that ψ is multivariate in nature. A hot question in quantitative genetics revolves around the issue of whether genotypes differ in their responsiveness to phenotypes of conspecifics, which would imply heritable variation in ψ38. An interesting follow-up question is thus whether responsiveness to other individuals (ψ) varies according to behavioural ‘types’, as has recently been suggested in the personality literature39. Importantly, a genetic architecture that includes genetic variation in ψ and its covariance with other DGEs and IGEs would likely reveal further interesting repercussions for evolutionary processes of behavioural traits.We also note that the variance partitioning approach used to model IGEs in this paper is mathematically equivalent to the alternative (but complementary) ‘trait based’ approach advocated by others40. Doing so allows us to address outstanding questions about the evolution of behaviour. Importantly, this heuristic framework may be broadly applied to any trait associated with traits involved in social interactions. Indeed, traits such as coloration, ornaments, badge of status, are often correlated with aggression or dominance30. More generally, our study also demonstrates the importance of viewing the phenotype (or genotype) from a multivariate perspective. That is, predictions of how ‘personality’ traits respond to selection can be profoundly misleading if effects of social interactions mediated by IGEs are not considered.In conclusion, a crucial consequence of social interactions is that they generate IGEs that not only contribute to the observed variance but also impact evolutionary dynamics of traits under selection. In this case, constraints on the phenotypic evolution of mean aggression arise from the negative correlation of direct and indirect genetic effects. More generally, we note that the role of IGEs has received little attention in ‘animal personality’ research, despite their potential implications for generating (and possibly maintaining) among-individual behavioural differences. The merit of our approach is that by including IGEs into behavioural ecology’s existing ecological frameworks to study ‘personality’, we may finally start fully integrating distinct areas of evolutionary biology such as quantitative genetics and behavioural ecology2 near Capalbio, Italy (42°42′46.7′ N 11°33′99.3′ E) in July 2013. We collected a total of 100 individuals: 34 adult males, 33 adult females, 12 near-final instar males, and 21 near-final instar females. Following capture, crickets were transported to a climate controlled chamber at the Ludwig Maximilians University of Munich , where they were housed at 26 °C ( ± 0.5) and 65% ( ± 0.5) humidity, under a 14:10 light:dark photoperiod (h) that wild crickets experienced at the time of capture.The parental generation of crickets was collected from a tomato field of approximately 2500 m41 for the F1 and F2 generations by having each male fertilize the clutches of two females. We used a total of 35 males and 70 females from the F1 generation, and 15 males and 30 females from the F2 generation. This resulted in 47 F2 and 21 F3 viable full-sib families. Details on the breeding and rearing protocol are provided in the Supplementary Material.Sexually mature wild-caught individuals from the parental generation were randomly paired 4 days after arrival in the laboratory. A total of 35 males and 35 females produced a total of 34 clutches from which offspring hatched. We raised 40 offspring (F1) per parental pair , from which we randomly selected breeders once reaching adulthood. We adopted a full-sib/half-sib breeding designAdult males of the F2 and F3 generation were subjected to repeated behavioural assays. The study focused on males only because aggression through escalated stereotyped fights is largely male-limited, thus more difficult to measure in females. The number of available adult offspring (of both sexes) per female was n = 622 for the F2 and n = 281 for the F3 . Of these, a total of 455 males were selected and screened for behavioural phenotypes (335 from the F2 and 120 from the F3).24; the same individual was assayed for each behaviour 6 times, with measurements taken approximately one week apart (range 7–9 days). Because individual identification is required for the aggression test (detailed below), subjects were marked with coloured tape on the pronotum  the day before a focal trial . The two tests were always done sequentially and in the same order; carry-over effects could therefore not be modelled. We chose this set-up because it ensured that all individuals were given the exact same treatment since this greatly facilitates comparison between individuals43.Behavioural trials were conducted between January and June 2014. Each individual was repeatedly assayed for each of 2 behaviours on the same day  following24). All individuals within a group were tested on the same day , randomized for time of the day and test location. Dyads of males paired for the aggression tests were randomly assigned amongst the non-related individuals within the same group to produce social environments that were homogenous with respect to relatedness.The 455 males were divided into 7 groups of 40 individuals (F2), one group of 55 individuals (F2), and 3 groups of 40 individuals (F3). 15 individuals of the F2 were only tested twice, because they were subsequently used for other purposes. Individuals were divided into groups according to their estimated age (days post-moulting) to avoid any possible age-related effects on aggression  and 3 of 608 (F3) for exploration trials (respectively 1.64% and 0.49%), and 27 of 944 (F2) and 5 of 304 (F3) for aggression trials (respectively 2.86% and 1.64%) due to technical problems with data recording or video-tracking. Note that the total number of aggression trials is approximately half of that of other trials since two individuals are involved in each aggression test. The final sample size  was therefore 2462 for exploration  and 1195 for aggression  tests.24 . Briefly, at the onset of the exploration test, each individual was moved (inside its own shelter) from its home container to the exploration arena. Exploration activity was then recorded automatically for 30 minutes. Following the exploration test, the shelters were removed and the individuals given a further 10 minutes to acclimatize. The divider between two arenas was then lifted, after which we filmed each dyad engaging in social interactions for a period of 10 minutes. We then returned the crickets to their home containers in the allotted housing slots within the climate room.Exploration and aggression behaviour were assayed following the protocol in44). For the aggression test, we calculated the total time each individual spent moving towards the opponent (‘relative movement’ for simplicity), by summing up only the consecutive samples (frames) where the relative distance between subjects decreased . We set a maximum interaction distance between the two subjects of 8 cm based on pilot trials to define a range in which the directional movement towards the other cricket would be meaningful. We validated the choice of the variable ‘relative movement’ for aggression both for a related cricket species and for a subset of the current dataset. Relative movement was highly correlated with the variable ‘approach’ towards the opponent that we scored manually, and is commonly used in aggression tests44. The choice and validation of relative movement as a measure for aggression is detailed in the Supplementary Material.Exploration and aggression videos were analysed using Ethovision version 11.0 . This software package enables tracking of isolated individuals and extracts the spatial coordinates for each video frame. We summed up all distances to calculate the total distance moved in the novel environment (exploration test), viewed as proxy for ‘exploration behaviour’ (followingP) for each measured trait  into its underlying components: residual within-individual variance (VR) and among-individual variance (VI(f)) for the focal individual. The latter component represents the statistical signature of “personality” variation45 and so was tested in its own right before we further partitioned it in another model into direct (additive) genetic (VDGE) and permanent environmental (VPE(f)) effects. For aggression, we also estimated the variance explained by the opponent identity (VI(o)), which was, in turn, also split into its environmental (VPE(o)) and genetic (VIGE) components. Partitioning of genetic from non-genetic focal (direct) and, for aggressiveness, opponent (indirect) variances was done using a univariate mixed-effects “animal” model46 that utilised the (additive) relatedness matrix determined from the pedigree. Covariance between direct and indirect effects was modelled in both genetic and permanent environment parts of the model. Behavioural data was available for both partners in every dyadic aggression trial, meaning the designations of focal and opponent within a dyad are arbitrary. Thus, for a two individuals in a dyad , we model the indirect effect of j on i’s phenotype and vice versa . We note that a possible issue arises since residuals are likely to be correlated between the two observations per dyad, but since the correlation is likely negative where aggression reflects dominance, this is not readily accounted for by modelling a random effect of dyad. We therefore blocked the data file into two “realizations” of focal versus opponent designation, each block containing focal records on one individual within each dyad. The two data blocks were then analysed simultaneously within a single mixed model formulation, with no cross-block covariance terms fitted, but under an imposed constraint that within-block (co)variance components to be estimated are equal in the two data blocks. More detail and ASReml code to implement this modelling strategy is provided in the Supplementary material.We conducted two sets of statistical analyses. First, using univariate mixed-effects models we partitioned the total phenotypic variance (V47). All models were fitted using restricted maximum likelihood; dependent variables were mean-centred and variance standardized to facilitate comparison of variance components across traits. Throughout, we assumed a Gaussian error distribution, which was confirmed for all response variables after visual inspection of model residuals.To statistically control for sources of variation in behaviours not directly relevant to our hypotheses, we included the following fixed effects: test sequence , generation (F2 or F3) and clutch number (first or second)  = VPE(f) + VDGE). For aggression, we estimated both focal and opponent repeatabilities. Direct heritability (h2), indirect genetic effects (IGEs), and the proportional contribution of VPE(f) (pe(f)2) and VPE(o) (pe(o)2) relative to the total phenotypic variance were estimated as each variance component divided by total phenotypic variance not attributable to fixed effects. From this latter model, we further calculated the variance in total breeding value (VTBV) for aggression. VTBV allows estimating the total heritable variation for this trait available to selection, taking into account DGEs, IGEs, and their genetic covariance. VTBV was calculated following28  as VTBV = VDGE + VIGE + 2COVDGE,IGE. We calculated the total heritable variation for aggression as τ2 = VTBV/VTOT28.Adjusted individual repeatabilityI) level, further partitioned into the permanent environmental and genetic levels by respectively estimating the PE and G matrices. This allowed us to estimate the correlation between the opponent identity effect on aggressiveness and the focal identity effect on exploration (I matrix), and to partition it into its genetic and environmental components. We fitted exploration and aggression as response variables and included only fixed effects that explained significant variation in univariate analyses (detailed above).As a next step, we used a multivariate extension of the framework described above to estimate patterns of between-trait  covariance at the among-individual . We started with a phenotypic model that contained only fixed effects and residual variation (Model 1). We then tested for differences among individuals in the focals (Model 2) and the opponents (Model 3) by sequentially fitting individual and opponent identities respectively. Model 4 tested for the phenotypic correlation between the two. We repeated the same structure when testing for genetic variation and added DGEs (Model 5), IGEs (model 6), and their correlation (model 7). We assumed a χ2-distribution for the test statistic which is calculated as twice the difference in log-likelihood between a model where a target random effect was fitted versus not fitted52. Variances are bound to be positive, therefore in testing them we applied the LRT assuming (for testing a single variance component) an equal mixture of χ20 and χ21 55.We tested model fixed effects using conditional F-tests with denominator degrees of freedom (df) estimated from the algebraic algorithm in ASReml 4.121) as described above. This led to 5 alternative multivariate models, differing in the correlation structure . This provides an overall (i.e. matrix level) test for nonzero covariance structure. We further tested the significance of each covariance separately by applying a LRT (assuming χSupplementary Information


Drosophila Genetic Reference Panel (DGRP).Obesity-related diseases are major contributors to morbidity and mortality in the developed world. Molecular diagnostics and targets of therapies to combat nutritional imbalance are urgently needed in the clinic. Invertebrate animals have been a cornerstone of basic research efforts to dissect the genetics of metabolism and nutrient response. We set out to use fruit flies reared on restricted and nutrient-rich diets to identify genes associated with starvation resistance, body mass and composition, in a survey of genetic variation across the CG43921 (which we rename heavyweight), and previously unknown functions for the diacylglycerol kinase rdgA, the huntingtin homolog htt, and the ceramide synthase schlank in nutrient-dependent body mass, starvation resistance, and lifespan.We measured starvation resistance, body weight and composition in DGRP lines on each of two diets and used several association mapping strategies to harness this panel of phenotypes for molecular insights. We tested DNA sequence variants for a relationship with single metabolic traits and with multiple traits at once, using a scheme for cross-phenotype association mapping; we focused our association tests on homologs of human disease genes and common polymorphisms; and we tested for gene-by-diet interactions. The results revealed gene and gene-by-diet associations between 17 variants and body mass, whole-body triglyceride and glucose content, or starvation resistance. Focused molecular experiments validated the role in body mass of an uncharacterized gene, htt, rdgA, hwt and schlank.Our findings implicate a wealth of gene candidates in fly metabolism and nutrient response, and ascribe novel functions to The online version of this article (doi:10.1186/s12864-016-3137-9) contains supplementary material, which is available to authorized users. Obesity is a worldwide epidemic and among the leading causes of morbidity and mortality in the US, increasing susceptibility to chronic pathologies that impact many body systems . AgainstDrosophila Genetic Reference Panel (DGRP) enables the mapping of natural phenotypic variation to DNA sequence in flies with an association paradigm [The advent of the paradigm , 17. Genparadigm , 18–22.A potential strategy to boost power in GWAS is the use of cross-phenotype association tests, to search for cases in which a genetic variant associates with multiple traits at once . The recad libitum, AL, 5 % yeast; dietary restriction, DR, 0.5 % yeast), using non-virgin females to avoid effects of mating status on diet–responsive phenotypes [R2 = 0.53-0.69; Additional file We surveyed natural genetic variation across genetically distinct fly lines in metabolic behaviors and their dependence on dietary yeast restriction. Dietary yeast levels are known to modulate fly body composition, stress resistance, and lifespan in laboratory strains –30. We renotypes . In eachenotypes –36, on animb3, to measurements of resistance of acute starvation, and another locus, 14-3-3 epsilon, to whole-body triglyceride content , which have roles in the development of neural processes and axonal defasciculation [Notch (association p = 0.006), among whose many biological roles is that of axon guidance [beat-Ib, beat-IIIb, and beat-Va , which are involved in motor neuron defasciculation [As an additional strategy to improve mapping power in the DGRP, we developed a scheme for analysis of polymorphisms at which the minor allele was very common. We expected that common variants mapped to a given trait might only represent a fraction of its full genetic architecture, but we considered this restriction a justifiable trade-off in light of the expected high power in association tests of common variants where the number of observations among individuals bearing the minor allele is maximized. For a first evaluation of this strategy, we applied our linear model association test framework for a given trait, including genotype and gene-by-diet interaction effects, to the 734,670 markers in the DGRP with minor allele frequency ≥25 %. This genome-scale scan uncovered significant, diet-independent association between genotype at culation , 53. Alsguidance , and “beculation . These rculation .CG43921, in which an intronic polymorphism associated with body mass across DGRP lines in a diet-independent manner .For a validation of a top-scoring locus from our association tests of common variants, we focused on the uncharacterized gene er Table . To verials Fig. . We did CG43462, a suspected determinant of fly lifespan [rdgA  and two phosphatidylinositol phosphatases , highlighting the potential for variants throughout phospholipid pathways that could perturb metabolism in the DGRP.Paralleling our analyses of low-frequency variants, we used the set of common variants in the DGRP as input into tests for cross-phenotype associations, analyzing each pair of our phenotypes on each diet. Two significant single-locus mapping results emerged from analysis of flies reared on DR. Genotype at lifespan , was assgA Table , whose mrdgA for an additional validation case study, on the strength of previous evidence that it interacts with the TOR pathway and modulates lifespan [rdgA was associated with stronger effects in animals reared on the DR diet than on AL , and almost undetectable on the AL diet , is of unknown biochemical function but is annotated with a FYVE domain which may bind phosphatidylinositol 3-phosphate (PI3P) [rdgA, schlank, and hwt, and the cohort of additional phospholipid metabolic genes in which we detected enriched association signal , is knoene LAG1 . Comprom species . Howeverpoptosis , 75 and poptosis , 76, 77 e (PI3P) , as welle (PI3P) . Future huntingtin, reminiscent of the weight loss seen in human Huntington’s patients [htt knockdown flies, our study provides a first compelling rationale for refuting the hypothesis that weight loss results from huntingtin loss of function. Our data leaves open the question of how native htt acts as a negative regulator of body mass and starvation resistance. Conceivably, its metabolic function could be mediated by circulating leptin and adiponectin [huntingtin nulls [huntingtin knockdown zebrafish [htt lay the groundwork for tests of mechanistic hypotheses centered around this key human disease gene.Our results also reveal a novel metabolic function for fly patients , 51 and patients –88. The patients , 89. As ponectin , 89 and/in nulls  and the ebrafish , expedieschlank, rdgA, and htt on diet-dependent traits, and we have uncovered a panel of additional candidates for future analyses. Alongside these novel genetic discoveries, our experimental design sets a precedent for the use of gene-by-diet and cross-phenotype association tests in fruit fly GWAS.We have conducted genome-wide scans for variants associated with starvation resistance, body mass and composition and their response to changing diets. We have validated the effects of Drosophila Stock Center [DGRP lines were obtained from the Bloomington k Center . Fly husk Center .To measure starvation resistance for a given line, an isogenic population of 100 non-virgin female flies was reared on either DR (0.5 % yeast) or AL (5 % yeast) food from the day of eclosion, with 25 flies per vial. After 10 days, flies were switched to starvation media (agar providing water but containing no nutrients), and deaths of flies were counted three times daily until all flies died; we then tabulated the average time to death across this isogenic population for use in statistical genetics analyses below. One biological replicate  was assayed for 159 DGRP strains and two biological replicates  for another 12 strains.schlank RNAi we sampled schlank flies at 14 days after eclosion to allow enough time to observe a change in body weight and body composition. This whole-fly homogenate was subjected to two technical replicates of both the StanBio Triglycerides LiquiColor® Test (Cat# 2100-225) and the Glucose Liqui-UV® Test (Cat# 1060-500). The measurements were normalized to body mass [For body mass, glucose and triglyceride measurements for a given line, an isogenic population of 15 seven day old non-virgin female flies was weighed in groups of 3 flies and then homogenized in 200 μl PBS and frozen. In contrast to the constitutive RNAi experiments, for adult-induced ody mass . One bioWe filtered out cases in which variation between replicates for a given DGRP strain was >20-fold greater than the median intrastrain variation  and subjected all remaining measurements to genetic analysis as detailed below.2total - σ2intrastrain)/ σ2total, using only the DGRP lines for which replicate measurements were carried out. For σ2total for a given trait, we calculated the variance across all phenotype measurements for all such lines. Separately, for a given DGRP line we calculated the variance in a given trait across biological replicates; we then calculated the average of these variances across lines as our measure of σ2intrastrain.Broad-sense heritabilities in Additional file Drosophila homologs, and then filtered for human genes with entries in the Online Mendelian Inheritance in Man database [We used DGRP release 2 genotypes and FlyBase R5 coordinates for gene annotations , 93. Fordatabase . All DGR1 x genotype + β2 x diet + β3 x genotype x diet + intercept. Nominal p-values denoted as “genotype” in Table 1 = 0, and those denoted as “interaction” report the probability that β3 = 0. To avoid the potential for false positives at a given nominal cutoff owing to p-value inflation, we calculated false discovery rates via permutation as follows: for a given permutation i, we randomized phenotype values across DGRP lines, retaining the true diet assignment, and on this permuted data set we carried out single-trait association tests for each marker in turn as above. We counted the number of markers ni that scored above a given p-value threshold t. We tabulated the false discovery rate at t as the ratio between the average ni across ten permutations and the number of markers called at t in the real data.For a given trait and marker, we used the complete cohort of average phenotype measurements across all replicates, from flies of all DGRP lines reared on both diets, as input into an association test via ordinary least squares regression using the statsmodels module in Python . The linWe carried out cross-phenotype association tests for starvation resistance and body mass; starvation resistance and triglyceride levels; and starvation resistance and glucose levels as follows. We used the phenotype measurements for a given trait pair from flies of all DGRP lines reared on a given diet, and genotype at a given marker, as input into the R package SMAT . False dp-value threshold t as follows. We tabulated the number of loci ntrue with SMAT significance at or exceeding t in at least one trait pair. Next, a permuted assignment of genotype to strain was used as input into a SMAT calculation for each trait pair in turn, yielding the number of loci nperm with SMAT significance at or exceeding t in at least one trait pair for this permutation. We took the ratio between the average of nperm, across 10 permutations, and ntrue as the multiple testing-corrected FDR across trait pairs. At t = 1.27E-08, corresponding to the SMAT p-value attained in the real data for our least significant SMAT hit, rdgA  biological processes as follows. Given the results from a single-trait or cross-phenotype association scan across markers as above, we first tabulated the single best-scoring marker for every gene tested. We then used the ranked list of these genes as input into GOglm, which tests for GO term enrichment in a ranked list without arbitrary thresholding into significant and insignificant genes, and corrects for gene length effects . Only GODrosophila Stock Center [rdgA we compared a previously characterized transposon insertion mutant [For a given candidate gene, we used functional validation strategies that enable the study of a line in which the gene is perturbed as a comparison with an isogenic control of the same background. For this purpose, for each gene we acquired a strain harboring a UAS-driven RNAi construct  from VDRk Center , and we k Center  or an RUk Center . Strainsn mutant  to a bacTo confirm RNAi-mediated knockdown in a given line in Additional file htt and CG43921, and day 14 for schlank and rdgA. For body mass, significance in a given diet was tested by t-test, and interaction between the genetic perturbation and diet was tested by ANOVA. Starvation resistance assays were performed as on DGRP strains (see above); each trace in main and supplementary figures reports a representative experiment from among 2–5 biological replicates of 100 non-virgin female flies per condition. Lifespan assays used 200 non-virgin female flies per condition, 25 flies per vial, changing media every 2 days. For lifespan assays all knockdowns were induced only in adult flies. Each trace in Additional file We used knockdown and mutant strains to test candidate genes’ roles in body mass, starvation resistance and lifespan. Genotypes of control and experimental strains are listed in Additional file


Hanwoo beef is known for its marbled fat, tenderness, juiciness and characteristic flavor, as well as for its low cholesterol and high omega 3 fatty acid contents. As yet, there has been no comprehensive investigation to estimate genomic selection accuracy for carcass traits in Hanwoo cattle using dense markers. This study aimed at evaluating the accuracy of alternative statistical methods that differed in assumptions about the underlying genetic model for various carcass traits: backfat thickness (BT), carcass weight (CW), eye muscle area (EMA), and marbling score (MS).Accuracies of direct genomic breeding values (DGV) for carcass traits were estimated by applying fivefold cross-validation to a dataset including 1183 animals and approximately 34,000 single nucleotide polymorphisms (SNPs).Accuracies of BayesC, Bayesian LASSO (BayesL) and genomic best linear unbiased prediction (GBLUP) methods were similar for BT, EMA and MS. However, for CW, DGV accuracy was 7% higher with BayesC than with BayesL and GBLUP. The increased accuracy of BayesC, compared to GBLUP and BayesL, was maintained for CW, regardless of the training sample size, but not for BT, EMA, and MS. Genome-wide association studies detected consistent large effects for SNPs on chromosomes 6 and 14 for CW.The predictive performance of the models depended on the trait analyzed. For CW, the results showed a clear superiority of BayesC compared to GBLUP and BayesL. These findings indicate the importance of using a proper variable selection method for genomic selection of traits and also suggest that the genetic architecture that underlies CW differs from that of the other carcass traits analyzed. Thus, our study provides significant new insights into the carcass traits of Hanwoo cattle.The online version of this article (doi:10.1186/s12711-016-0283-0) contains supplementary material, which is available to authorized users. Bos taurus coreanae) is an indigenous cattle breed in Korea that has been intensively bred for meat during the last 30 years  were used to identify genotyping errors (302 SNPs). Missing genotypes were imputed using BEAGLE [A total of 1679 animals were genotyped using the Illumina BovineSNP50 K (n = 959) and HD 777 K n = 720) Beadchips . Common SNPs between the 50 K and 777 K SNP chips were selected which resulted in 43,852 SNPs. All animals with more than 10% missing data (N = 68) and those with an inconsistency between pedigree and genomic relationships (N = 5) were excluded from further analyses. Phenotypic records were available for 1183 of the remaining 1606 animals that were genotyped  follows a normal distribution In the BayesL method, the prior distribution for  follows :\documenith SNP. In the BayesC method, the value of The prior distribution for r et al.  where \dThe DGV for each animal in the validation set was estimated as the sum of the cross-product of animal genotype and the estimated SNP effect over all SNPs.i; ith SNP; To confirm results of Bayesian analyses, a single-marker regression was run by using the Wombat software  with the−6) was used, where N is the number of SNPs used for the analyses.To adjust for multiple testing, a Bonferroni-corrected threshold of 0.05/N . Four subsets were used as training populations (≈946) and the fifth subset as a validation sample (≈237). The animals for the various subsets were selected randomly, except that paternal half-sibs were always placed in the same subset . Cross-vi. Genomic heritability  . Due to ent}α=2) , we consThe expected accuracy of the genomic prediction r et al. , i.e. \deLln4Nel  and (2) Me2=2NeL , where \The pedigree-based estimates of variance components for the carcass traits are in Table We used the average extent of linkage disequilibrium (LD) in the genome to estimate effective population sizes at various times in the past. Estimates of mentclass2pt{minime et al. , who alse et al.  and also and Kim  estimatez et al.   for CW, while for the other traits, the differences in MSE between the methods were trivial [see Additional file The predictive performance of the models depended on the trait analyzed. The three methods performed similarly for BT, EMA and MS traits, whereas for CW BayesC clearly outperformed GBLUP and BayesL. This indicates that the infinitesimal model holds for BT, EMA and MS but not completely for CW. In other words, BT, EMA and MS traits would be controlled by several genes, each with a small effect, whereas one or more individual genes would have a large effect on CW. These findings were confirmed by the single-marker method used for the GWAS analysis, which detected genome-wide significant SNPs on chromosomes 6 and 14 for CW but not for MS, BT and EMA [see Additional file lue Fig. .Fig. 3AcWolc et al.  pointed Our results support a previous study on Hanwoo cattle by Lee et al.  that aimf et al.  found thr et al.  obtainedr et al.  showed tIn spite of their high heritabilities, prediction accuracies for BT and MS were lower than those for CW and EMA Table a, 2a, whod Table . The proσg2/σa2) . Our res2 Tables , 4 for aThis finding may explain the lower prediction accuracies obtained for BT and MS compared with EMA and CW, in spite of their higher heritability. In addition, it was expected that the DGV for MS would be more accurate than those for BT because MS had a higher heritability Table , possiblThe low genomic heritabilities achieved for BT and MS indicate that more animals (with genotypes and phenotypes) are necessary to accurately estimate the effects of SNPs compared with CW and EMA. We also observed that the SNPs on the 50 K SNP chip could not capture all the genetic variability for those traits (BT and MS). Therefore, a high-density SNP chip could be used to adequately assess LD and potentially capture a larger proportion of the additive genetic variance than the medium-density chip . In order to investigate the performance of SNP density, 570,969 SNPs were imputed from the 50 K chip. Our findings indicate that the genomic variance In general, the realized accuracies of DGV for the four carcass traits, regardless of the method used, were low compared with results from other studies , 25, 50.ion size , 59. Usiion size  observedion size . This coion size  than in An alternative for improving prediction accuracy for Hanwoo cattle, with a deep pedigree, is to apply single-step GBLUP (ssGBLUP) , 74. In As shown in Fig. L/ln4Nel  but greaMe2=2NeL . Our resMe2=2NeL  who repoHayes et al.  pointed s et al.  recommens et al. , it seems et al.  assumes The performance of the statistical methods used depended on the trait analyzed. The results showed a clear superiority of BayesC compared with GBLUP and BayesL for CW, whereas for the other traits all methods performed similarly. The prediction accuracy of DGV for CW using BayesC was around 7% higher than that obtained with the GBLUP and BayesL methods. This indicates the importance of using a proper variable selection method for genomic selection of traits. In addition, the results also suggest that the genetic architecture underlying CW may differ from that underlying the other carcass traits. This could be due to the fact that BT, EMA and MS seem to be controlled by several genes, each with a small effect, whereas for CW, there are probably several individual genes that each have a large effect. Overall, our results provide the first information for implementing genomic prediction in Hanwoo beef cattle.


Theobroma cacao L.) trees share the many challenges of breeding long-living perennial crops, and genetic progress is further constrained by both the limited understanding of the inheritance of complex traits and the prevalence of technical issues, such as mislabeled individuals (off-types). To better understand the genetic architecture of cacao, in this study, 13 years of phenotypic data collected from four progeny trials in Bahia, Brazil were analyzed jointly in a multisite analysis. Three separate analyses  were performed to estimate genetic parameters from statistical models fitted on nine important agronomic traits . Genetic parameters were estimated along with variance components and heritabilities from the multisite analysis, and a trial was fingerprinted with low-density SNP markers to determine the impact of off-types on estimations. Heritabilities ranged from 0.37 to 0.64 for yield and its components and from 0.03 to 0.16 for disease resistance traits. A weighted index was used to make selections for clonal evaluation, and breeding values estimated for the parental selection and estimation of genetic gain. The impact of off-types to breeding progress in cacao was assessed for the first time. Even when present at <5% of the total population, off-types altered selections by 48%, and impacted heritability estimations for all nine of the traits analyzed, including a 41% difference in estimated heritability for yield. These results show that in a mixed model analysis, even a low level of pedigree error can significantly alter estimations of genetic parameters and selections in a breeding program.Breeding programs of cacao ( Theobroma cacao L. is a small understory tree native to the Amazon estuary , witches' broom (Moniliopthora perniciosa), cacao swollen shoot virus, and frosty pod/moniliasis (Moniliophthora roreri)   individual tree selection through vegetative propagation and (2) production of sexual families by open and controlled pollination Soria, . While bParticularities of cacao propagation, management and physiology give rise to unique challenges for breeding. These include, among others, the presence of genetic self-incompatibility in many populations, temporal variability in the genetic control of diverse traits and their phenotypic expression, diverse modes of vegetative and sexual reproduction, and a lack of consistent standards and methods in evaluating resistance Dias, . FurtherLinear mixed model (LMM) methodology, using restricted estimation maximum likelihood (REML) allows for reliable prediction of additive and genotypic effects  despite the often unbalanced nature of phenotypic data  in Barro Preto in the state of Bahia, Brazil . We estimated genetic parameters such as heritability, dominance ratio, genetic correlation, and genetic gain for the different traits and created for each genotype a ranked index according to weighted breeding values. The identities of all trees from a single trial (PT08) were validated with a 96 SNP off-typing marker set to determine the presence of mislabeled accessions, and genetic parameters were calculated both with and without off-types included. Hence, the two main objectives of these analyses were: (1) to increase our understanding of the genetic architecture of different traits through a multi-site analysis, and (2) to understand the impact of off-types on the estimation of genetic parameters, genetic gains and selections within a breeding program.Genetic material from four progeny trials  was used for this study. The trials were planted between 2000 and 2009 and evaluated from 2003 to 2015 Table . The objPhytophthora-infected pods (%PP) was a cumulative measure of pod loss due to black pod rot (Phytophthora spp.), calculated monthly. The percentage of witches' broom-infected pods (%WBP), a measure of pod loss due to witches' broom (M. perniciosa), was calculated monthly. The percentage of pods due to other losses (%OL) is a ratio of the pods lost to other stresses besides Phytophthora spp. and witches' broom, including pest damage from rats and birds, and was also measured once per month. The vegetative brooms (VB) parameter included a count of vegetative brooms per tree caused by witches' broom; these were counted and removed on an annual basis. All of the above traits were measured in all trials, except vegetative brooms that was not obtained for trial PT03, and seed index, which was not obtained for trial PT07. For trial PT08 only, measures of vigor were included when the trees reached 6 years of age. This consisted of stem diameter  measured for each tree at a height of 30 cm aboveground, and height  measured as the distance from the base of the tree to the first jorquette. Note that cacao plants follow a dimorphic growth form, exhibiting orthotropic development until a certain developmental stage when they produce a jorquette and develop plagiotropic fan shoots.Phenotypic data were collected on yield components and resistance to pests and diseases. Yield  was defined as total dry bean weight, obtained from monthly wet bean weight measurements converted to dry bean weight, by multiplying with the coefficient of 0.4  interactions on different traits. The four trials included in the multisite analysis are located within the two farms of MCCS, and were evaluated during different time intervals between 2003 and 2015 ; as is the random effects vector of interaction of individuals with site, with as ~ MVN; f is the random effects vector of family, with f ~ MVN; fs is the random effect vector of interaction of family with site, with fs ~ MVN; ps is the random effects vector of plot within-site, with ps ~ MVN; and e is the random vector of errors, with e ~ MVN. X1, X2, Z1, Z2, W1, W2, and W3 are all incidence matrices, 1 is a vector of ones and I are identity matrices of their corresponding size. The matrix A is the numerator relationship matrix for individuals calculated using the corrected pedigree . Dps and De are block diagonal matrices where the different sites have their own independent ith plot and error term component, where a2 being the additive variance, σas2 the genotype within site variance, σf2 the family variance, σfs2 the family within site variance, B) additive genetic correlation across the four sites was calculated as Narrow-sense heritability was calculated as The estimated breeding values (BV), which represent deviations from the overall mean phenotypic values, were obtained from the multisite analysis described above. These were later converted into predicted values by adding to each BV an overall phenotypic mean. In the case of yield, a back-transformation was implemented over these predicted values to express it in its original units. Finally, for each of traits predicted values were standardized  for the construction of an index for clonal selection. Here, economic weights were assigned to each trait with the primary objective of advancing yield and a second objective of increasing resistance to witches' broom. This index was constructed using the standardized values of the traits Yd, PI, and VB with weights equal to 0.7, −0.15, and −0.15, respectively. The negative values are required to decrease the response of PI and VB. The genetic gains from selections were calculated as the ratio of the mean phenotype plus the breeding value for the top 1 and 5% of individuals for each trait divided by the phenotypic mean plus the overall average breeding value.Leaf punch samples were collected from all trees in the field and outsourced to LGC Genomics  for fingerprinting by KASP™ genotyping. A 96 SNP offtyping marker set was used to fingerprint all progeny and parents used in PT08. This marker set can reliably distinguish between closely related individuals, and has been used widely for offtyping in cacao breeding programs ; f is the random effects vector of family, with f ~ MVN; p is the random effects vector of plot, with p ~ MVN; and e is the random vector of errors, with e ~ MVN. X, Z, W1 and W2 are incidence matrices. All other terms were previously defined.A single-site analysis of PT08 was fitted to determine the effect of off-types on estimation of genetic parameters. The single-site analysis used a similar structure as the multisite analysis with the following LMM:The single-site models from PT08 were fit first with all individuals, and then with off-types removed through the pedigree to determine the impact of these individuals on the estimation of genetic parameters. Later, genetic gains were obtained by dividing the predicted values for each genotype by the trial average, and were calculated using a 1% selection intensity according to the weighted index described earlier. Genetic gains were calculated first from the complete dataset of all individuals and then the dataset with off-types excluded.A) additive genetic correlations were estimated by running a pairwise bivariate analysis model across the different pairs of traits. This was based on a model that considered the same terms as above but, in addition, a heterogeneous correlation structure was considered for the all random effects, including the error term. Standard errors of heritability, dominance ratio and genetic correlations were approximated using the delta method.In addition, for the PT08 data, trait-to-trait, or type-A  was low across all trials, ranging from 3.1 to 7.7%, while witches' broom pods (%WBP) ranged from 5.7% in PT02 to over 20% in PT03 and PT08. Pods lost from other pests and diseases (%OL) was also higher in the two most recent trials (PT03 and PT08). The higher pest and disease incidence is reflected in the percentage of healthy pods (%HP), which was more than 80% for PT07 and PT02 but the percentage decreased to 53.6 and 56.8% for PT03 and PT08, respectively. The trial average of vegetative brooms (VB) removed annually ranged from 1.3 (PT07) to 5.9 (PT02). Differences in phenotypic values between the different trials reflect differences in the families tested, trial size, and duration as well as site-specific effects such as differences in disease pressures, and helped to provide measures of G × E on the traits evaluated  provides a measure of G × E interaction on the trait. Type-B correlation values range from −1 to 1, with scores close to ±1 indicating high stability across environments. Type-B additive correlations were high across all traits, and yield-related traits in particular were extremely stable, ranging from 0.81 (%HP) to 1 (SI). This corresponds to the high heritabilities of the different yield components. GxE was highest for witches' broom-related traits, which had lower stability across sites. Type-B correlations ranging from 0.37 for VB to 0.76 for %WBP.Understanding genetic correlations between sites  provides a measure of pleiotropy and can be useful for indirect selection of correlated traits. There existed a strong genetic correlation between SI and PI (−0.81), but much lower correlations between both of these traits and Yd (−0.25 ± 0.17 and −0.12 ± 0.18). The weighted index used in our selections included PI and Yd as the yield components. This would allow for indirect selection of SI based on the strong correlation with PI. The low correlations between yield components and total yield support the inclusion of overall yield and an index (pod or seed index) within a breeding program. The strong correlation (−0.72) between %HP and %WBP suggests that witches' broom is driving most of the disease related losses in the trial, relative to %OL (−0.64). The correlation between %WBP and VB, which represent different stages of the same infection was only 0.27, with a large standard error. Of the two measures, %WBP was more informative of the impact to productivity, with a correlation of −0.61 with Yd and −0.72 with %HP. Of the vigor measures, D had low correlations with all other measures, including Ht. The trait Ht had strong correlations with %WBP (−0.5), Yd (0.39), and PI (0.37). This could correspond to more productive surface area along the main trunk for pod growth in cacao, a cauliflorous crop. The trait %HP showed strong genetic correlations with both yield components and disease related traits, despite having a low heritability itself.An understanding of genetic correlations between traits  out of the 3,516 individuals of PT08 were classified as off-types Figure . The inces Table .In this study, four trials were analyzed in a multisite analysis to evaluate the genetic architecture of 10 traits, and make selections from the trial PT08 using a weighted index. Also, a single-site analysis was performed for trial PT08 after using molecular markers to identify and remove off-types to determine the magnitude of impact that pedigree errors have on the estimation of genetic architecture. Our findings build upon previous studies in cacao and other crops and will be relevant for informing future breeding strategies for cacao. In addition, we identify both promising selections for clonal testing, and promising potential sources of resistance to witches' broom.Few prior studies have established narrow-sense heritability estimations for cacao. In our multisite analysis, pod index (PI) exhibited the highest heritability of all traits evaluated (0.64 ± 0.1), and showed a high stability across sites as well (0.96 ± 0.05). It had a high genetic correlation with seed index (−0.81 ± 0.07), and only a moderate correlation with yield (−0.25), making both traits good targets for selection. The heritability obtained for PI falls between previous reported heritabilities of 0.14 , and showed high stability across sites as well (0.76 ± 0.22). PT08 progeny with the top 1% BVs for this trait all came from a single cross between two PT02 selections: MC-08005, a cross between CCN-51 and GU-171c, and MC-08047, a cross between IP-128 and COCA-3370/5. On average, the genetic gain for trees from this cross showed a 47% reduction in %WBP compared to the trial mean. Vegetative brooms showed a low narrow-sense heritability in the multisite analysis and low stability, suggesting a strong effect of environment. High variability in vegetative brooms have been demonstrated in field trials, ranging from 0 to 90 brooms  to be much lower than any of the reports in the cacao literature. Nonetheless, this still resulted in altering index selections by 48%, and altering expected genetic gains across all traits included in the analysis from 2% (%HP) to 34% (Yd). At the time of publication, records were not available on the origins of the NA-33 in the germplasm collection at MCCS; however, a literature search revealed a 99.7% genetic similarity based on RAPD markers between NA-33 held at BAL plantation in Malaysia, suggesting that the off-type may be widespread in global collections (Figueira, While the applications of mixed models and BLUP estimations using REML can greatly improve estimations in cacao breeding, this study shows that uncorrected pedigree errors can alter estimated BLUPs, heritabilities, and genetic gains, for diverse traits, and impede breeding progress by altering selections. The failure of selections to meet expectations can affect farmer confidence and ultimately impede the adoption and use of molecular tools and technologies in breeding (Padi et al., All relevant data are within the paper and supplementary files.JM, SG, and AD: designed the analysis; AD: wrote the manuscript; SR and J-PM: oversaw the collection of field data and AD, SG, DL, CS, and GM: analyzed the data. All authors offered revisions and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Most of the genome-wide association studies (GWASs) for human complex diseases have ignored dominance, epistasis and ethnic interactions. We conducted comparative GWASs for total cholesterol using full model and additive models, which illustrate the impacts of the ignoring genetic variants on analysis results and demonstrate how genetic effects of multiple loci could differ across different ethnic groups. There were 15 quantitative trait loci with 13 individual loci and 3 pairs of epistasis loci identified by full model, whereas only 14 loci (9 common loci and 5 different loci) identified by multi-loci additive model. Again, 4 full model detected loci were not detected using multi-loci additive model. PLINK-analysis identified two loci and GCTA-analysis detected only one locus with genome-wide significance. Full model identified three previously reported genes as well as several new genes. Bioinformatics analysis showed some new genes are related with cholesterol related chemicals and/or diseases. Analyses of cholesterol data and simulation studies revealed that the full model performs were better than the additive-model performs in terms of detecting power and unbiased estimations of genetic variants of complex traits. Elevated level of cholesterol increased risk of cardiovascular disease including coronary heart disease, stroke and peripheral vascular disease. Moreover, it has also been linked to diabetes and high blood pressure. Several association studies with different approaches were previously performed to analyze cholesterol trait for a number of different populations12et al. showed constructing genetic relationship matrix by excluding the chromosome that being tested, might improve analysis resultsQTXNetworkUsefulness of multi-loci approaches compared to single locus approaches were largely described in QTL mapping era67891011121314151617E-A), Chinese-Americans (C-A), African-Americans (A-A), and Hispanic-Americans (H-A). Four different association approaches were used: full model and multi-loci additive model through QTXNetwork, single locus linear mixed model approach through GCTAPLINKIn this study, we analyzed total cholesterol of multi-ethnic populations that including European-Americans  of extracted set of SNPs using full model approach to reveal complex genetic architecture of trait. We plotted results of cholesterol data analyses by using full model and multi-loci additive model approaches in Two distinct steps were used to complete cholesterol data analyses. At first, we extracted a set of SNPs that were significantly identified through 1D, 2D and 3D scan by GMDR-GPU module and then used a linear mixed model approach to explore and build up an optimum model of genetic architecture of trait. Actually, the first step is a filtering step that assists to reduce computational time for further analysis. In the second step, we tested for experimental-wise statistical significance  less than 1 × 10−5 using full model approach (10PEW > 5) additive effects were detected for 11 QTSs. C/C of rs478442 near gene APOB (Apo lipoprotein B) had the most significant additive effect (10PEW > 47), while T/T of rs629301 in gene CELSR2 had another most significant additive effect (10PEW > 34). In addition to additive effect, QTS rs629301 also had significant ethnic specific dominance effects negative for E-A population  and Hispanic American (H-A) cohort in addition to its additive main effect. That implies the additive effect of QTS rs6465748 was significantly different in these two ethnic groups as compared to other two groups, whereas additive effect was the smallest for A-A population  identified for cholesterol with experimental-wise approach , Fig. 1.aa), additive × dominance (ad), and dominance × additive (da). The significant additive × additive epistasis interaction (10PEW > 13) was from A/A of rs12246594 in gene SORCS1 × G/G of rs12595211 in gene ETFA. SORCS1 encodes one family member of vacuolar protein sorting 10 (VPS10) domain-containing receptor proteins, located at chromosome 10q25.1. Variants of SORCS1 gene have been reported associate with type-2 diabetes26283031ETFA is located on chromosome 15q24.3 that participates in catalyzing the initial step of the mitochondrial fatty acid beta-oxidation. Negative epistasis interactions between rs2264802 in gene SKAP2 and rs9548318 in gene UFM1 had highly significant additive × additive (10PEW > 26) and additive × dominance (10PEW > 12). SKAP2 encodes protein contains an amino terminal coiled-coil domain for self-dimerization, a plecskstrin homology (PH) domain required for interactions with lipids at the membrane. Positive epistasis effects were detected between rs478442 near APOB and rs7694118 near PCDH10  for candidate genes detected using full model approach. Biopubinfo is a search engine for tracing public biological information mainly covers data from life sciences and medical sciences, and includes a concept ontology database derived from several sources . The candidate genes corresponding to detected QTSs were used as seeds for searching related pathway, functions, genes, chemical and drug information, protein-protein interactions, gene-disease association etc. CELSR2, SKAP2, ETFA and UFM1) with chemical cyclosporine, whereas cyclosporine has significant relationship with blood cholesterol levels and cause of increasing blood cholesterolBioinformatics analyses were applied by using APOB and CETP with cholesterol; genes CETP and MMP13 with chemical chloranium, chloride ion and hydrochloric acid; genes MMP13 and ETFA with formic acid and formyloxidanium  population. For GCTA analysis, GRM was additionally used to control genetic relatedness. We separately analyzed cholesterol data for two subsequent Examinations (Exam-1 and Exam-3) of MESA population. Genomic inflation factors (λGC). which were calculated based on median of Chi-square distribution of whole-genome P-values, were 1.02 and 1.03 for Exam-1 and Exam-3 respectively after adjusting the population stratification by 10 principle components (PCs). Again, Q-Q plots of the GWASs P-values from PLINK and GCTA analyses showed good-fit to the uniform distribution . For ribution . TherefoGCTA analysis, we used MLMePLINK and GCTA analyses. By setting “--indep-pairwise 50 5 0.75” option in PLINK v1.07, we removed the SNPs of high LD (r2 > 0.75) with the extracted set of SNPs, and calculated the approximate number of the independent tests. After the LD based pruning, there were 458,716 SNPs and therefore Bonferroni corrected threshold for genome-wide significance at α = 0.05 level of significance was −log10P = 6.96.For PLINK, however none of the dominance effects were genome-wide significant. Therefore, we recalculated the effects of all SNPs for additive effects only, and detected only two loci for Exam-1 and one locus for Exam-3, respectively with genome-wide significant for additive effects. Number of non-missing individual observations was larger in Exam-1 (N = 5277) as compared to Exam-3 (N = 4572), and therefore the power of SNP detection was better in Exam-1 as compared to Exam-3. The QTS rs629301 (−log10P = 12.10) located at chromosome-1 and the QTS rs478442 (−log10P = 6.97) located at chromosome-2 was genome-wide significant for Exam-1 (10P = 8.37) was genome-wide significant for Exam-3  for the both Exams . The significance of the candidate QTSs in both Exams might refer their robustness of associations with cholesterol data.We inspected additive and dominance effects using r Exam-1  and onlyr Exam-3 . Analysith Exams . Remarka10PEW > 34) but low significant additive by ethnic interaction effect (−log10PEW > 2.70), whereas detection powers were 100% for additive effect but only 15% for additive by ethnic interaction effect. Full model approach can obtain unbiased estimates of parameters and produce only small FDR (3.7%) under the simulated scenario-I.Under the simulated scenario-I, calculated powers of detecting loci using full model were high or moderate for most of the loci (Table S4). Again, calculated powers of detecting effects were high or moderate for most of the effects corresponding to loci . Full mo2 > 0.85) with the true loci, might be representative of true loci. We observed most of the false loci were very near to the true loci and had similar effect size. If we consider the false loci as the representative of true loci, then false discovery rates were close to zero for the full model and multi-loci additive model. However, multi-loci additive model identified more nearby false loci as compared to the full model. Again, estimation of genetic parameters was biased upwards or downwards for some loci  identified in real data analysis using single locus approaches (Tables S2~S4). Calculated powers for others SNPs were quite low and mostly not detectable using single locus approaches . Therefore, over controlling also can decrease power for detecting true QTSs. By comparing loci detection powers of different approaches, it was revealed that full model approach is more powerful to dissect genetic architecture of complex traits .Under scenario-II, we assume causal markers are controlling simulated traits in additive fashion with their additive and additive by ethnic interactions. In this case, both full model and multi-loci additive model could provide unbiased estimate of genetic parameters (Table S5). False discovery rate was also similar for these two approaches, 4.85% for full model approach and 3.96% for multi-loci additive model approach. Under this scenario, additive model identified all ethnic specific genetic effects that support our hypothesis (Table S5). Because, under this scenario additive model approach did not have extra noise rather than random errors in estimating parameters. Detection powers were similar for full model and multi-loci additive model approaches. Under this scenario-II, single locus approach of GCTA for Exam-1 data, but only one SNP was detectable with genome-wide significance. It was suggested that there might have some other causal loci controlling the cholesterol trait of MESA population.Genetic effects of multiple loci might differ in different human ethnicity due to various lifestyles and environmental exposures, and therefore analyzing gene by ethnicity interactions might help to reveal better knowledge about complex traits and personalization of treatment after a disease44464749For full model and multi-loci additive model approaches, we used repeated measures from two-year examinations (Exam-1 and Exam-3) for subjects as replications to improve power of detecting small effects of multiple causal loci. Comparisons of full model and multi-loci additive model provide insight of usefulness of full model and the consequences of ignoring dominance and epistasis effects. In simulation study under two different scenarios, we observed that full model approach could obtain unbiased estimation of genetic parameters with only a small fraction of FDR (3.70~4.85%) with repeated measures. Again, under scenario-II, we observed that the full model and multi-loci additive model could obtain unbiased estimates of the genetic parameters with similar FDR, indicating robustness of the full model approach even only additive genetic effects of multiple loci controlling phenotypic traits. Multi-loci additive model provided biased estimates of several genetic parameters, failed to detect several true loci and ethnic specific genetic effects of loci in 100 simulations under the scenario-I, describing the deficiencies of the additive model approach for complex trait analysis.PLINK and GCTA) under two different simulated scenarios. This result could describe the reasons of difference in results of single locus approaches from full model approach in our real data analyses. Separately analyses of data sets for Exams-1 and Exams-3 through PLINK and GCTA can detect only two different loci associated with cholesterol (Table S2 and Table S3). In simulation study, we observed that single locus approach detected QTS rs629301 with high power and QTS rs478442 with moderate power, but detection powers for other loci were negligible. Again, average detection power of multi-loci additive model approach was lower than the full genetic model approach. It was revealed that multi-loci additive model approach failed to detect some QTSs of cholesterol trait due to ignoring dominance and epistasis effects. Therefore, detection power of full model approach could be dramatically increased not only due to using repeated measures but also including dominance and epistasis effects into the model.Detection power of QTSs was very low for single locus approaches  and G1 (ABCG1)ABCA1 gene was reported to be associate with total cholesterol in previous genome-wide association study (GWAS)UMF1 to be associate with plasma lipoprotein levelsSKAP2 and UFM1 genes were detected for additive-by-additive and dominance related interactions in our study, where bioinformatics ontology search showed that they are related through cytoplasm. ETFA (electron transfer flavoprotein A) has functions for multiple acyl-coenzyme A dehydrogenation deficiency (MADD), and is related with lipid storage myopathies (LSMs)vu463) in the ETFA gene has swollen and hyperplastic neural progenitor cells, hepatocytes, and kidney tubule cell as well as elevations in triacylglycerol, cerebroside sulfate and cholesterol levelsAssociation using full model approach identified the variants of three known genes http://www.ncbi.nlm.nih.gov/gap). MESA is a prospective population-based study focusing on characterization of subclinical cardiovascular disease and the risk factors that enable prediction of the progression of CVD55. Study participants of four ethnic groups include 6,500 men and women, nearly in equal numbers, who are aged 45~84 years and free of clinical CVD at baseline, and initially recruited in 2000 from six US communities: Baltimore, MD; Chicago, IL, Forsyth County, NC; Los Angeles County, CA, Northern Manhattan, NY; and St. Paul, MN. The recruited participants are 38% European-American (E-A), 28% African-American (A-A), 22% Hispanic American (H-A), and 12% Asian, predominantly of Chinese descent, American (C-A). More details of sampling design and study procedures have described previously by Bild et al.Multi-Ethnic Study of Atherosclerosis (MESA) data used in this study were downloaded from dbGaP  were used in this studyGMDR-GPUQTXNetwork. And then association mapping was conducted by QTS module of QTXNetwork for detected 707 candidate SNPs. The linear mixed model includes SNP loci effects  as fixed; ethnicity (e) and loci by ethnicity interaction  as random effects,Two distinct approaches were used for genome-wide association analyses of cholesterol trait: generalized multi-factor dimensionality reduction (GMDR) method to scan 714,211 SNPs by 1D for main effects, 2D and 3D for epistasis interactions using module sk is the fixed effect of the k-th individual ; ai is the additive effect of the i-th locus with coefficient QQ, 0 for Qq, −1 for qq); di is the dominance effect of the i-th locus with coefficient Qq, 0 for QQ and qq); aaij, adij, daij and ddij are the digenic epistasis effects with coefficients QQ × QQ and qq × qq, −1 for QQ × qq and qq × QQ, and 0 for others), QQ × Qq, −1 for qq × Qq, and 0 for others), Qq × QQ, −1 for Qq × qq, and 0 for others) and Qq  × Qq, and 0 for others); eh is the effect of the h-th ethnic population ; aeih is the additive × race interaction effect of the i-th locus in the h-th ethnic population with coefficient deih is the dominance × race interaction effect of the i-th locus in the h-th ethnic population with coefficient aaeijh, adeijh, daeijh and ddeijh are the digenic epistasis × race interaction effects in the h-th ethnic population with coefficient εhk is the residual effect of the k-th individual in the h-th ethnic population. In this model, we have constraints for random variables with normal distributions of zero mean and variances where μ is the population mean; The linear mixed model and its distribution can be expressed in matrix notation,y is an n × 1 column vector of phenotypic values and n is the sample size of observations; μ is the population mean, bu is the u-th vector of fixed effects; Xu is the known incidence matrix relating to the u-th fixed effects; ev is the v-th vector of random effects with distribution Uv is the known coefficient matrix for the v-th vector of random effects; where The total heritability is estimated byaa) epistasis, ad) epistasis, da) epistasis, dd) epistasis, aa epistasis by environment interaction heritability contributed by sum of pair-wise aa epistasis by environment interaction effects, ad epistasis by environment interaction heritability contributed by sum of pair-wise ad epistasis by environment interaction effects, da epistasis by environment interaction heritability contributed by sum of pair-wise da epistasis by environment interaction effects, dd epistasis by environment interaction heritability contributed by sum of pair-wise dd epistasis by environment interaction effects.where We also used a multi-loci additive model by ignoring non-additive effects in our study with the following formwith matrix notation and distribution asThe heritability of a multi-loci additive model is estimated byF-statistic test for association analysis. Permutation test was conducted by a total of 2,000 times for calculating the critical F-value to control the experiment-wise type I error (αEW < 0.05). The QTS effects were estimated by using the MCMC (Markov Chain Monte Carlo) algorithm with 20,000 Gibbs sample iterations62258P value  for genetic effects by controlling the experiment-wise type I error (PEW < 0.05) was thus calculated. More details of procedure about the approaches were described in S1 text.The linear mixed model with Henderson method IIIPEW≤ 1 × 10−5) through full model approach. However, this approach also detected some experimental-wise significant effects with PEW < 0.05. In simulation study, we used all perceived effects of loci; because small effects of several variants also might have influence on complex traits. Under scenario-II, we simulated data in similar way as scenario-I nevertheless using perceived genetic architecture of cholesterol trait from multi-loci additive model approach. Therefore, loci truly had only additive and additive-by-ethnic interaction effects in scenario-II.Association analyses of cholesterol data by using full model and additive models revealed different results. We conducted Monte-Carlo simulations to perceive possible explanations of differences in results using full model and additive models. Simulated phenotypic data were generated under two distinctive scenarios: (I) simulated traits controlling by additive, non-additive genetic effects and ethnic specific genetic effects; (II) simulated traits controlling by additive and their ethnic interaction effects. We generated data for repeated measures of individuals and analyzed by treating as replications through full model and multi-loci additive model approaches. Under scenario-I, estimated genetic effects of significant loci obtained from full model approach were used as true loci and parameters to generate phenotypic data, and estimated error variance used to generate random errors. In +” or “−” sign at the right side of estimated value, whereas “+” refers overestimation and “−” refers underestimation of parameters  were estimated as the ratio of falsely identified loci with respect to the total number of detected loci for each simulated trait, detection powers of loci were the detection rate of each locus, and detection power of the effects were the detection rate of the effects in 100 simulations. Powers of single-locus additive model approaches were estimated in similar way. We estimated empirical confidence interval of each effects from output of 100 simulations, and described estimation is unbiased if parameter belonging to the empirical confidence interval otherwise estimation is biased. We did not arrange empirical confidence intervals in table, however biased estimates were marked by “rameters .PLINK and GCTA. Only detection power of loci were presented for PLINK and GCTA analyses .Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Although genome-wide association and genomic selection studies have primarily focused on additive effects, dominance and imprinting effects play an important role in mammalian biology and development. The degree to which these non-additive genetic effects contribute to phenotypic variation and whether QTL acting in a non-additive manner can be detected in genetic association studies remain controversial.RUNX2, a candidate gene that has been associated with milk production in mice. When adding non-additive effects into the prediction models, however, we observed little or no increase in prediction accuracy for the eight traits analyzed.To empirically answer these questions, we analyzed a large cattle dataset that consisted of 42,701 genotyped Holstein cows with genotyped parents and phenotypic records for eight production and reproduction traits. SNP genotypes were phased in pedigree to determine the parent-of-origin of alleles, and a three-component GREML was applied to obtain variance decomposition for additive, dominance, and imprinting effects. The results showed a significant non-zero contribution from dominance to production traits but not to reproduction traits. Imprinting effects significantly contributed to both production and reproduction traits. Interestingly, imprinting effects contributed more to reproduction traits than to production traits. Using GWAS and imputation-based fine-mapping analyses, we identified and validated a dominance association signal with milk yield near Collectively, our results suggested that non-additive effects contributed a non-negligible amount (more for reproduction traits) to the total genetic variance of complex traits in cattle, and detection of QTLs with non-additive effect is possible in GWAS using a large dataset.The online version of this article (doi:10.1186/s12864-017-3821-4) contains supplementary material, which is available to authorized users. Both dominance and imprinting play an important role in mammalian biology and development . Though Several studies have been conducted to decompose dominance genetic effects from the total genetic variance of complex traits, theoretically –8 and emGene mapping studies have primarily focused on genetic variants with additive effects. Although many empirical studies have reported non-negligible contributions from non-additive effects to complex traits, QTLs with non-additive effects are still difficult to identify in animal and human gene mapping studies, largely due to the low statistical power in the testing for non-additive effects of individual loci . The larTo empirically address questions related to dominance and imprinting effects of complex traits, we analyzed a large cattle dataset that consisted of more than 40 K Holstein cows with SNP genotypes, pedigree information, and eight yield deviation (YD) phenotypes . Both parents of these cows were also genotyped to phase the parental inheritance of SNPs of the cows. The aims of this study were to estimate the relative contribution of additive, dominance, and imprinting effects to dairy production and reproduction traits, to identify QTLs with dominance or imprinting effects, and to investigate whether adding these non-additive genetic components improves the prediction accuracy of genomic selection in real data.H2 = proportion of total genetic variance in phenotypic variance) was 31.9–38.6% for production traits and 1.4–7.9% for reproduction traits, respectively. The narrow-sense heritability (h2 = proportion of additive genetic variance in phenotypic variance) was 27.2–33.8% for production traits and only 0.8–5.1% for reproduction traits, respectively. Proportions of dominance variance in phenotypic variance were significantly higher (P < 0.05) for production traits (2.5%–4.0%) than for reproduction traits (0.2%–1.1%), but the proportions in total genetic variance are higher for reproduction traits. The variance explained by imprinting effect was very low for all eight traits, <1% of the phenotypic variance for production traits and 1–2% for reproduction traits. However, these imprinting effects were significantly larger than zero for most production and reproduction traits (P < 0.05). Moreover, for reproduction traits that have a low heritability, imprinting effects explained a relatively large portion of the total genetic variance , which were significantly higher than those for production traits (P < 0.05).Using 42,701 Holstein cows with YD phenotypes, SNP genotypes, and two genotyped parents, we decomposed the total genetic value of eight dairy traits into additive, dominance, and imprinting effects, estimating corresponding variance components  based variance decomposition is highly dependent on the assumption of polygenic genetic architecture, as genome-wide SNP genotypes are used with equal weights. Existing GWAS have provided evidence of a polygenic architecture of additive effects in most complex traits . HoweverP = 9.54 × 10−8 and P = 6.33 × 10−8, respectively. BovineHD2300004730 is 71 kb upstream of the RUNX2 gene. The RUNX2 gene has been previously reported to be a novel regulator of mammary epithelial cell fate in development and breast cancer, and it has also been shown that exogenous transgenic expression of RUNX2 in mammary epithelial cells blocked milk production [We performed a whole-genome single-marker scan for additive, dominance, and imprinting effects on all eight traits. To increase computational efficiency, we used a two-step approach to remove polygenic effects from the data: 1) a mixed model with genomic relationship matrices to generate residuals; followed by, 2) a GWAS scan using residuals from the mixed model as the phenotype. Although our two-step strategy has slightly lower power than a single-step mixed model, we identified a novel dominance signal on chromosome 23 that was associated with milk yield  as our target region for fine-mapping using sequence-based imputation. Based on the LD decay pattern between BovineHD2300004730 and nearby variants derived from the sequences of 443 Holstein bulls from the 1000 Bull Genomes project (Run 5.0) , we chos730 Fig. . Using tP-value for dominance effect (8.64 × 10−9) was found at two variants, one in the first intron of RUNX2  and the other between SUPT3H and RUNX2  as a covariate into the association test of each of the remaining 651 variants. This analysis revealed that the significant additive associations disappeared while the dominance signals remained  on association P-values and found that poorly imputed variants tended to have a larger association P-value . However, there was no significant difference in prediction accuracy between the models ADD + DOM and ADD + DOM + IMP for the three traits.We compared prediction performance of three models: 1) additive effect only (ADD), 2) additive and dominance effects (ADD + DOM), and 3) additive, dominance, and imprinting effects (ADD + DOM + IMP). Overall, the three models showed similar prediction accuracy and unbiasedness for all the eight traits Fig. , even thThis study provided a systematic view of dominance and imprinting effects through a comprehensive analysis of a large cattle data set, including variance decomposition, GWAS, and genomic prediction. The study of imprinting effects benefited from the large size of the cattle data which included complete pedigree, representing one of the largest pedigrees available in a mammalian species, to infer parent-of-origin of alleles. The current study provided another demonstration of the power of dairy industry-oriented data to facilitate biological research , 26.In general, our results are consistent with previous studies regarding the proportion of phenotypic variance explained by dominance effects for complex traits in cattle  and the In this study, we didn’t observe much improvement of prediction accuracy by including dominance and imprinting effects in genomic selection models. This observation can be attributable to a few things: 1) low heritability of non-additive effects; and 2) lacking of full-sib pairs between reference and prediction populations because full-sibs are the primary source of non-additive relationships but dairy data consist of mostly half-sibs.RUNX2, but it was difficult to distinguish causal variants from linked markers. Due to a very small effective population size and a limited number of haplotypes in the dairy cattle population, our imputation works well, even from 50 k or less SNP data to sequence-level variants, in our fine-mapping association analysis.Using a GWAS approach, we found a dominance association signal and validated it in independent samples. The fine-mapping analysis further confirmed the dominance QTL to be near Our study demonstrated the possibility of identifying non-additive effects in GWAS using a large dataset. Additionally, the power of the two-step GWAS approach was comparable to a full mixed-model based method  phenotypic data. YD phenotypes were adjusted for appropriate covariates, including farm, year, and season effects. Eight traits were analyzed, including milk yield (MY), fat yield (FY), protein yield (PY), somatic cell score , standardized productive life , daughter pregnancy rate , cow conception rate , and heifer conception rate . Since many cows were not measured for all the phenotypes, the final sample size for the eight traits ranged from 12,911 (STPL) to 29,811 , as shown in Table G12 is the genetic value for the genotype 12 with a paternal allele 1 and a maternal allele 2 , R is the overall mean, a is additive effect, d is dominance effect, i is imprinting effect, A is genotypic additive value arising from a, D is genotypic dominance value arising from d, and I is genotypic imprinting value arising from i. Under Hardy-Weinberg equilibrium, eq.  is genotypic additive (dominance) value after centralization. Note that in eq. (2), genotypic additive value (A*) is not independent of genotypic dominance value (D*), or Cov ≠ 0. To address the issue, we can use the extended natural and orthogonal interactions (NOIA) model [R** is the overall mean and β is allele substitution effect. Despite its similarity to eq. , dominance deviation (D**), and genotypic imprinting value (I), respectively.Genetic effects of SNPs can be decomposed into three components , following their evident biological meanings:entclass1pt{minimaentclass1pt{minimaThe differences and relationships between eqs.  and 3)  3) have y) was decomposed into fixed effects (b), genotypic additive value (a), genotypic dominance value (d), genotypic imprinting value (i), and residual (e). Eq.  have been proposed. We used a version with pooled variance across all markers [Zik (Zjk) is the additive genotype code for marker k of individual i (j) as shown in the vector corresponding to a in eq.  and imprinting (P), which are shown as following:H and S are the genotype codes for dominance and imprinting effects as shown in the corresponding vectors in eq. ,H* is the dominance genotype code as shown in the vector corresponding to d in eq. , 1000 + 100 + 100, and 1000 + 1000 + 1000. Simulation for each scenario was repeated 100 times. We fitted model (4) for each simulated data set and compared variance component estimation between the three scenarios.Zk, Hk and Sk are the genotype codes of marker k for additive, dominance and imprinting effects, respectively, as described in eqs. , and ak, dk, and ik are corresponding SNP effects. SNPs were filtered by MAF ≥0.01 and P-value of Chi-square test for Hardy–Weinberg equilibrium ≥1 × 10−6. Association P-values were calculated from t-tests for the three types of SNP effects.To increase computational efficiency, we used a two-step strategy for genome-wide association study, similar to the GRAMMAR approach . First, For association signals with sufficient statistical evidence from the two-step analysis, we further used the full mixed model,RUNX2 signal. The GRM was built using all chip SNPs except those on chromosome 23, which resulted in a leave-one-chromosome-out analysis (LOCO) [P-value were analyzed with model  . We alsoth model  for fat P-value of Chi-square test for Hardy–Weinberg equilibrium <1 × 10−6 and SNPs with an allelic R2 (AR2) <0.05. AR2, reported by Beagle software, is the estimated squared correlation between the most probable alternative allele dose and the true alternative allele dose and serves as a good metric for estimating imputation accuracy [First, we used the sequence data of 443 Holstein bulls from the 1000 Bull Genomes project   (ADD + DOM + IMP), we also considered two reduced models, the additive model (ADD) and the additive-plus-dominance model (ADD + DOM), and compared the prediction performance between the three models. Ten-fold cross validation was used to assess 1) prediction accuracy, defined as the Person correlation between genomic estimated breeding value (GEBV) and phenotype, and 2) unbiasedness, defined as the regression coefficient of phenotype on GEBV in the validation population.We estimated the values of the three effects for individuals in the training population from fitting model (4) in MMAP. The genomic predictions for new individuals can be calculated byAdditional file 1: Table S1.Variance decomposition of breeding value, dominance deviation, and genotypic imprinting value for eight dairy traits. (XLSX 10 kb)Additional file 2: Figure S1.Individual estimates of different components with two variance decomposition models for fat, protein, SCS, STPL, DPR, CCR and HCR. (PDF 115 kb)Additional file 3: Table S2.RUNX2 gene in the validation data set. (XLSX 17 kb)Mixed-model association statistics of 50 SNPs around the Additional file 4: Figure S2.Manhattan plots for associations of SNP effects with fat, protein, SCS, STPL, DPR, CCR and HCR. (PDF 6350 kb)Additional file 5: Table S3.Two-step and full model analysis results for candidate non-additive associations in the discovery data set. (XLSX 17 kb)Additional file 6: Table S4.Full mixed model analysis results for the dominance associations with fat and protein in the validation data set. (XLSX 10 kb)Additional file 7: Figure S3.2 of the sequence based imputation. (PDF 5 kb)ARAdditional file 8: Table S5.A full list of imputed sequence variants showing stronger association with milk than BovineHD2300004730. (XLSX 14 kb)Additional file 9: Figure S4.Association analysis conditional on the additive effect (A) and both the additive and dominance effects (B) of variant Chr23:18,676,057. The vertical blue line indicates the location of Chr23:18,676,057. (PDF 14 kb)