Genomic prediction models for multi-year dry matter yield, via genotyping-by-sequencing in a composite training set, demonstrate potential for genetic gain improvement through within-half sibling family selection.Lolium perenne L.) is a key source of nutrition for ruminant livestock in temperate environments worldwide. Higher seasonal and annual yield of herbage dry matter (DMY) is a principal breeding objective but the historical realised rate of genetic gain for DMY is modest. Genomic selection was investigated as a tool to enhance the rate of genetic gain. Genotyping-by-sequencing (GBS) was undertaken in a multi-population (MP) training set of five populations, phenotyped as half-sibling (HS) families in five environments over 2 years for mean herbage accumulation (HA), a measure of DMY potential. GBS using the ApeKI enzyme yielded 1.02 million single-nucleotide polymorphism (SNP) markers from a training set of n = 517. MP-based genomic prediction models for HA were effective in all five populations, cross-validation-predictive ability (PA) ranging from 0.07 to 0.43, by trait and target population, and 0.40–0.52 for days-to-heading. Best linear unbiased predictor (BLUP)-based prediction methods, including GBLUP with either a standard or a recently developed (KGD) relatedness estimation, were marginally superior or equal to ridge regression and random forest computational approaches. PA was principally an outcome of SNP modelling genetic relationships between training and validation sets, which may limit application for long-term genomic selection, due to PA decay. However, simulation using data from the training experiment indicated a twofold increase in genetic gain for HA, when applying a prediction model with moderate PA in a single selection cycle, by combining among-HS family selection, based on phenotype, with within-HS family selection using genomic prediction.Perennial ryegrass (The online version of this article (10.1007/s00122-017-3030-1) contains supplementary material, which is available to authorized users. Genomic selection (GS), introduced by Meuwissen et al. , describhttp://faostat3.fao.org), approximately 68% is used for pastoral agriculture. Pastures based on temperate forage species play a significant role within these agricultural systems with, for example, an estimated 80% of cow’s milk derived from temperate grassland agriculture  (2n = 2x = 14) is the principal source of nutrition for ruminant livestock grazed in temperate-intensive pastoral agricultural systems, including New Zealand. Like most forage species, perennial ryegrass is obligately outcrossing and both natural and synthetic populations are genetically heterogeneous and characterised by high levels of heterozygosity  in advanced perennial ryegrass populations in a commercial breeding programme, integrating multi-year phenotypic data from multiple locations, and including assessment of different data and statistical models for prediction. Our general approach was to construct genomic prediction models for parent plants using herbage accumulation (HA) data, as a measure of DMY potential, from sown plots of their half-sibling (HS) progenies. The literature on GS incorporates a wide-ranging selection of statistical models for determining GEBV’s. This includes GBLUP  through to Bayesian, shrinkage and machine-learning alternatives  strain. Full detail of population development is provided in Supplementary material. Trials were sown with maternal HS seed harvested from 517 maternal parents. Six trials were sown at three New Zealand sites: Ruakura , Aorangi  and Lincoln . Trials were sown in the Southern Hemisphere autumn or spring of 2013 (Supplementary Table S1). The unit for evaluation of HS families in the trials was a 1-m sown row of plants , hereafter referred to as a plot. Plots were sown with 25–30 cm spacing between plots and 30 or 50 cm gaps at the end of the plots, depending on the trial. In the aligned breeding programme, HA measured in this type of plot was positively correlated (r = 0.77–0.83) with DMY in larger (1.5 × 5 m) plots .A training set was composited from five perennial ryegrass breeding populations  from the Grasslands Innovation Ltd breeding programme, all of which were infected with the same fungal endophyte  was grazed by sheep every 2 weeks through the summer period in 2014–2015 and 2015–2016. The other trial  was also grazed but only when plants had reached the 2–3 leaf growth stage (see below). Mechanical mowing was used to defoliate under-grazed areas to a residual height of 5 cm, where needed. At the Lincoln site, one trial was STD and the other  was managed as STD except that it was watered by rainfall plus irrigation to approximately 40 mm of water weekly. All trials used a row–column experimental design with three replicates. Within each of the six trials, populations were blocked and families randomised in three replicates within these blocks. Repeated check lines were planted within and across replicate blocks. In all trials, soil fertility levels were adjusted to ensure nutrients were not limiting plant growth. Nitrogen was applied (15–30 kg N/ha) at each defoliation. Superphosphate fertilizer (8.8 kg P/ha) was applied in late autumn each year.To assess DMY potential, HA was measured by cutting plots to a height of 5 cm. Harvested foliage was dried (80 °C for 48 h) and weighed to obtain HA as g DM per plot. Up to nine HA harvests were completed between summer 2014 and autumn 2016 in each trial (Supplementary Table S1). These were timed to occur at least once in summer, autumn and spring in a given year. However, not all seasons at all sites were sampled each year, due to sub-optimal growth conditions at certain times resulting in insufficient plant material for harvest (Supplementary Table S1). HA harvests were completed when plots were at the 2–3 leaf-growth stage, typically 3–4 weeks regrowth after the prior defoliation (dependent on season and site). The same defoliation management was used outside of when HA measurements were made.Days-to-heading (DTH) was assessed at two sites (Ruakura and Lincoln) during spring 2015, using the Ruakura STD and Lincoln IRR trials. Both trials were closed to grazing from early September. Days-to-heading (DTH) was recorded as days from 1 November, with observations starting on that day and repeated every 2–3 days for the next 35 days. DTH was recorded when there were at least five heads in a plot that were fully emerged and these heads were appearing uniformly along the plot. Further detail of trial treatments are provided in Supplementary material.Data were analysed using the linear mixed model option in GENSTAT GenStat . AnalyseP > 0.05) genetic variation for six of seven seasonal HA determinations completed (Supplementary Table S1), and so was not used. DTH data from the Ruakura and Lincoln sites were analysed as average performance across two sites, to generate an across-site assessment designated Comb DTH.Average HA, merging data from all individual harvests, was used for developing genomic prediction models. This was undertaken within- and across-sites and treatments, with ten HA traits produced: Rua STD (average HA in the Ruakura STD treatment); Rua SEV (average HA in the Ruakura SEV treatment); Aor STD ; Aor SEV ; Lin STD ; Rua STD + SEV (average HA over both treatments at Ruakura); Aor STD + SEV ; Comb STD ; Comb SEV (average HA across both SEV treatments); and Comb STD + SEV . The Lin IRR trial showed no significant  analyses were based on best linear unbiased predictors (BLUP’s) (White and Hodge R), the upper limit of the degree of genetic determination  in the hn2 estimation; σε2, experimental error; nr, number of replicates. The denominator in Eq. σgy2, genotype-by-year; σgh2, genotype-by-harvest; σgt2, genotype-by-treatment; σgI2, genotype-by-site, and their associated divisors: ny, number of years; nh, number of harvests; nt, number of treatments; nl, number of sites.For the MP analyses, variance components were used to estimate HS family mean repeatability  BLUP matrix was carried out using a hierarchical agglomerative complete linkage procedure with squared Euclidean distance as a measure of dissimilarity Wishart . The Har® dsDNA Assay Kit . DNA concentrations were normalised to 20 ng/μl and subsequently used for GBS library preparation. GBS libraries were generated following the methodology of Elshire et al.  and ligated to a unique barcoded adapter and a common adapter (99 ng). A total of six libraries were developed in 96-plex which included a blank and a common positive control sample. Each library was passed through a Pippin Prep™ DNA size selector  to isolate fragments between 193 and 313 bp, which were then sequenced on two lanes of an Illumina HiSeq 2500  at AgResearch Invermay, New Zealand.DNA was isolated from approximately 100 mg of fresh leaf blade + pseudostem tissue for 577 training set mother plants, using a high-throughput method based on that described by Whitlock et al.  with mode et al. , with 10Hordeum vulgare genome (version 082214v1.27) to form ryegrass pseudochromosomes. Non-genic regions of the H. vulgare genome were masked prior to alignment to ensure alignment by gene synteny. Ryegrass contigs were aligned to the H. vulgare reference genome using Lastz version 7.0.1  and genotypic  data were available.A number of statistical models have been developed for prediction of breeding or phenotypic values, and approaches can be collated into two categories, parametric and non-parametric  and is defined as, y = μ + Xu + e, where y is the n × 1 vector of genotype BLUP’s (estimated in stage 1), μ is the n × 1 vector of grand mean, X is the n × m design matrix and u is the m × 1 vector of random marker effects with u ~ N, where G is the n × n ‘genomic relationship matrix (GRM)’, and e is the n × 1 vector of random errors with e ~ N, where I is the n × n identity matrix. With M = {mij} representing the n × m marker matrix, G ∝ MMT and was calculated as G = ZZT/(2∑jpj(1 − pj)), where Z is the  adjusted SNP scores with elements (mij − 2pj), for ith individual (genotypes) and jth SNP, and pj is the ‘minor allele frequency’ of the jth SNP. The GBLUP modelling was implemented using the ‘rrBLUP’ package  exceeds the number of observations (genotypes), we needed to resort to ‘shrinkage’-based regression. A commonly used approach for genomic prediction is the ‘ridge regression’ model (denoted by RR), where a shrinkage parameter λ needs to be estimated. We used the package ‘glmnet’  Breiman , for GEBThe predictive ability (PA) of the models  was assessed via cross-validation. Here, the data were split into training and validation sets. We undertook two assessments of the MP-based models to estimate their PA: (1) within the breeding programme as a whole and (2) for each of the individual populations, Pop I–V.For (1) we considered a tenfold cross-validation, where phenotypic (BLUP) data and corresponding genotypic (SNP marker based) data of the 517 individuals were randomly divided into ten subsets of similar size. Note here that the validation set was composed of individuals from all five populations. Models were fitted on the training set  and the GEBV’s predicted for the validation set (remaining subset). The PA of the models was computed as the Pearson’s correlation coefficient between predicted values (GEBV’s) and observed values (BLUP’s). For this set of cross-validations, bias of the different statistical methods for prediction was also assessed by measuring the slope of the regression of GEBV on BLUP.For each trait and each SNP marker data, five replicates of the cross-validation scheme were considered , enabling computation of empirical standard errors of PA and ensuring that results obtained were not due to random partitioning of data. Five replicates were deemed sufficient after it was determined that expanding to ten replicates made no difference to variability or PA . To warrant precise comparisons, the four different statistical models were fitted in exactly the same cross-validation partitions. To compare similarities of these models across all chosen traits, a simple ANOVA with two factors (genomic prediction method and trait) was employed. The PA’s computed separately for each of the five tenfold cross-validation sets were considered as response.For , estimatc) from one cycle of selection using conventional phenotypic HS family selection (HSF), against a GS strategy (ApWFgs-HS). The GS strategy simulated combined among-family selection based on phenotype and within-family selection using genomic prediction. The simulation used ‘real’ data generated from training population phenotyping trials, specifically: Rua STD for Pop II (n = 108 HS families), based on HA data from eight discrete harvests over a period of 27 months. This trait was chosen as it was based on the most complete set of seasonal data in the study (Supplementary Table S1). Pop II was selected as the best-performed population in this environment  in addition to the PA of 0.27 estimated by cross-validation for Rua STD in Pop II  was fixed at 1.40 (top-ranked 20% of families) for HSF and all ApWFgs-HS simulations, while three different within-family selection intensities were tested at each PA for ApWFgs-HS: kw = 2.67 , kw = 2.27  and kw = 2.06 . The estimation of genetic gain using within-family genomic selection was based on a modification of the equation proposed by Casler and Brummer . SNP calling was conducted jointly for all populations, Pop I–V. Initial filtering yielded 1,093,464 SNPs across all populations and this was reduced to 1,023,011 following an additional filter for Hardy–Weinberg disequilibrium (HWdiseq > − 0.05). The mean missing rate per SNP of this subset was 0.24 and the mean read depth 2.94. The overall MAF distribution of the selected SNPs is shown in Supplementary Figure S2.S) of dimension 566 × 566 was derived using the KGD analysis package, based on the set of 1,023,011 SNPs. Multidimensional scaling (MDS) was applied to its distance matrix (1 − S), revealing the structure amongst the five individual populations of the MP training set . The rates of decay varied amongst the populations. Pop III was characterised by the shortest extent of LD (r2 = 0.25 at 366 bp), followed by Pop II (477 bp) and the remaining populations had longer LD—Pop I (1506 bp) Pop IV (1750 bp) and Pop V (1100 bp). These observations align with what is understood about the breeding history of two of the contrasting populations. Pop I was based on only six pair crosses between randomly selected individuals from two cultivars, whereas Pop III originated with contributions from a larger number and greater diversity of parents—a polycross of 80 randomly selected individuals from six different cultivars. After advancement to F2, both underwent multiple cycles of selection prior to their inclusion in the MP training set.A summary of results from linkage disequilibrium (LD) analysis of the five individual populations in the MP training set is shown in Fig. Data from 28 seasonal HA harvests (Supplementary Table S1) were used to derive estimates of average HA within each site and treatment combination, and across site and treatments. Nine discrete HA traits were generated and variance components (Table n = 517 HS families) significant (P < 0.05) σg2 amongst families was indicated for seven of the HA traits as well as DTH estimated across two environments (Comb DTH) (Table P > 0.05) σg2 for HA traits Comb STD  or Comb STD + SEV . Significant genotype-by-location (σgl2) and genotype-by-treatment (σgt2) interactions  and the same trend was observed for hn2 in individual populations. Further description of variance components for both the MP training set and individual populations, including genotype-by-environment interactions, as well as R and hn2 values, are provided in Supplementary material.For the MP training set . For KGD, GBLUP and RF a full set of 1,023,011 SNPs were used in the models. Due to computational limitations, only a smaller set of 249,546 SNPs was able to be used for RR.r for Comb DTH was 0.50. Amongst HA traits, there was substantial variation in PA, ranging from Lin STD (mean r = 0.12 over the four methods), Aor STD (0.21), Aor SEV (0.24), Rua STD (0.27) up to Rua SEV (0.30). Combining data from certain sites and/or treatments generated higher PA: amalgamation of standard and severe treatment HA data from the Ruakura trials (Rua STD + SEV) had a mean PA of r = 0.43 and combining data from the severe grazing treatments at Aorangi and Ruakura (Comb SEV) resulted in a mean PA of r = 0.36.The highest PA amongst traits, determined as the Pearson’s correlation between observed phenotype (BLUP) and GEBV, was for Comb DTH Fig. . Across R.Amongst HA traits and Comb DTH there were small Fig.  but signr in the individual populations was consistent with that observed in the full MP training set , Aor STD , Aor SEV , Rua STD  and Rua SEV ; and higher for Comb DTH  and HA traits where data were merged from more than one environment, Rua STD + SEV  and Comb SEV . No one of the five populations ranked consistently highest for PA across all traits  to those estimated using the largest SNP dataset (1.02 M). A comprehensive summary of the effects of missing SNP data rate and read depth, by statistical method, is provided in Supplementary Table S3.The influence of SNP density on PA was investigated to a limited extent. SNP datasets of different sizes were generated Table  but thisGc when using a genomic prediction model to select the top-ranked individuals by GEBV within the best 20% of HS families (ApWFgs-HS), as compared to randomly selecting individuals within those families (HSF). HSF in Pop II achieved ∆Gc of 6.02% for the Rua STD HA trait, with a single selection cycle. Applying genomic prediction to select the top individuals within the best 20% HS families resulted in ∆Gc increasing from 6.02% to a minimum of 7.89%, assuming the lowest genomic PA (0.10) and lowest selection intensity . This increased to a maximum ∆Gc of 18.18% when the highest PA (0.50) and selection intensity  combination was applied. This range is equivalent to a 31–202% improvement in ∆Gc by applying ApWFgs-HS over HSF. The effect of using a higher selection intensity was amplified as PA increased, as seen by the relative slopes of the three selection intensity lines  occurred in environments where frequent summer defoliation was applied. Severe grazing during summer, through the imposition of short grazing intervals and/or low grazing height, can lead to loss of plant vigour in ryegrass pastures , alfalfa  and switchgrass . High PA (up to r = 0.58) for Comb DTH, almost twice that of within-environment HA traits, is in agreement with studies in other monocot plant species . In dairy cattle, where robust comparison of pure-against multi-breed approaches has been completed, the experience from various studies is of either a small increase or no change in PA when using a multi-breed training set for predicting GEBVs within a single breed. The efficacy of a multi-breed training approach was influenced by trait architecture and the statistical model used  than PA observed in the training set as a whole. Given the small size of the individual populations, it is difficult to compare MP-based prediction models with within-population models, as cross-validation correlations in the latter could only be based on very small validation sets; when we investigated this we observed nearly half within-population models yielded Perennial forage species are generally bred for broad adaptation, as the market for cultivars adapted to specific environments is considered too small to justify development costs  were, nevertheless, achieved in the current study in two cases where data were successfully pooled across environments, Comb SEV and Rua STD + SEV. The higher PA that resulted from pooling data in these cases may be a consequence of underlying genetic correlation between environments, effectively increasing the number of measurements per genotype and the reliability of the HS-family BLUP’s for those traits, which has implications for the design of future training experiments that utilise these trial formats.Higher PA’s  and high-selection intensity. In a practical breeding sense, 3 years of field evaluation could be used to phenotype and rank HS families, enabling selection of the best families. The phenotypic data generated in the field phase would also be used, in conjunction with maternal parent genotypic data, to generate a genomic prediction model that is then applied for the within-HS family selection component. Because GS occurs within the same generation used to train the prediction model, erosion of PA over more than one cycle of selection (see below) is not a factor in this situation.As described by others  that favour the ability of GBLUP methods to capture genetic relationship information in the SNP dataset. Expansion to a larger training set, based on a single population, may identify differences in PA of different analytical approaches in ryegrass. This should include the application of Bayesian methods, which were not assessed here, but which were found to be superior to GBLUP in achieving high PAs when using a multi-breed training set  model persistence and efficacy over more than one selection cycle from the training generation and (b) transferability of the constructed models to populations unrelated to the training set. Sown rows, used in this training experiment instead of larger plots, have been shown to be correlated with sward yield and persistence in large rectangular plots (1.5 m × 5 m) in a ryegrass breeding programme . Nevertheless, validation of the genomic prediction models described here will require that experimental synthetic developed by GS are assessed in larger plots and future genomic selection training systems should ideally use larger plot formats that more closely resemble on-farm swards.MF conceived the study, designed and coordinated the training experiment, completed statistical analysis of phenotypic data, contributed to development of GBS protocols and wrote the paper. SG evaluated and applied genomic prediction statistical models and imputation methods. MC developed an informatics pipeline for GBS data analysis and completed GBS data analysis for the training set. ZJ designed the field trials, statistically analysed phenotypic data and completed simulations. TB completed the linkage disequilibrium analysis. SE conceived the study, established field trials and statistically analysed phenotypic data. AG developed GBS protocols and RT co-developed and applied GBS protocols. RM compiled the ryegrass reference genome used for supporting GBS. BB wrote the grant and contributed to project execution. JS, CF, DR, JT and PR were in charge of field trials at different locations and acquired the phenotypic data. SG, MC, ZJ, TB, SE, AG, RM, PR and BB all contributed to writing the paper.Supplementary material 1 (DOCX 1408 kb)Below is the link to the electronic supplementary material.


The identification of gene–gene and gene–environment interaction in human traits and diseases is an active area of research that generates high expectation, and most often lead to high disappointment. This is partly explained by a misunderstanding of the inherent characteristics of standard regression‐based interaction analyses. Here, I revisit and untangle major theoretical aspects of interaction tests in the special case of linear regression; in particular, I discuss variables coding scheme, interpretation of effect estimate, statistical power, and estimation of variance explained in regard of various hypothetical interaction patterns. Linking this components it appears first that the simplest biological interaction models—in which the magnitude of a genetic effect depends on a common exposure—are among the most difficult to identify. Second, I highlight the demerit of the current strategy to evaluate the contribution of interaction effects to the variance of quantitative outcomes and argue for the use of new approaches to overcome this issue. Finally, I explore the advantages and limitations of multivariate interaction models, when testing for interaction between multiple SNPs and/or multiple exposures, over univariate approaches. Together, these new insights can be leveraged for future method development and to improve our understanding of the genetic architecture of multifactorial traits. So far, this quest has been quite unsuccessful and the large number of methods that have been developed to improve detection  on a quantitative outcome Y. For simplicity I assume in all further derivation that E is normally distributed with variance 1, and G and E are independents. The simplest and most commonly assumed underlying model for Y when testing for an interaction effect between G and E is defined as follows:βG is the main effect of G, βE is the main effect of E, βGE is a linear interaction between G and E, and ε, the residual, is normally distributed with mean and variance σ2 set so that Y as mean of 0 and variance of 1 (so the absence of the intercept term in the above equation). One can then evaluate the impact of applying linear transformation of the genotype and/or the exposure when testing for main and interaction effects. For example, assuming E has a mean > 0 and G is defined as the number of coded allele in the generative model, Y can be rewritten as a function of Gstd and Estd, the standardized G and E:βG′, βE′, and βGE′ are the main effects of Gstd and Estd and their interaction. Relating the standardized and unstandardized equations, we obtain (supplementary Appendix A):μG, σG, μE, and σE are the mean and variance of G and E, respectively. Hence, the estimated main effects of Gstd and Estd not only scale with the variance of G and E but can also change qualitatively if there is an interaction effect (i.e. the direction of the effect can change). In comparison, the interaction effect βGE′ remains qualitatively similar, however, because βGE′ does not scale with σGE the variance of the interaction term but with the variance of G and E, the interpretation of the relative importance of the interaction effect can change (see Section Consider an interaction effect between a single nucleotide polymorphism (SNP) G and E has the most biological sense can only be discussed on a case by case basis  to Y. When G and E are centered, the interaction term has a positive contribution to the most extreme subgroups  and a negative contribution to the opposite heterogeneous subgroups  of the magnitude of the genetic and environmental effects , an interaction effect will appear more and more as a sole genetic effect . Overall, coding schemes that can be related through linear transformations are mathematical equivalent . However, coding scheme should not be overlooked because of this equivalence, and as shown in the example of Figure Which coding scheme for Clayton, . Yet, itcts Fig. B. Hence,will be an extrapolations beyond the observed range of experience”  of the predictors of interest. Assuming all effects are small, so that σ2 the residual variance is close to 1, these ncps can be approximated by (see supplementary Appendix B):The power of the tests from the interaction model and from a marginal genetic model defined as E in the marginal genetic model has a minor impact on ncpmG.Note that in such scenario adjusting for the effect of G (ncpmG) and the interaction test (ncpGE) are invariant with the coding used in the model tested, while the significance of the test of the main genetic and exposure effects can change dramatically when shifting the mean of G and E. Second, as illustrated in Figure ncpG=ncpmG×σE2/(μE2+σE2), so that testing for βmG will be much more powerful that testing for βG if the mean of E is large, although there is no interaction effect here. When the generative model includes an interaction effect only (βG=βE=0 and βGE≠0), we obtain ncpmG=ncpGE×μE2/σE2. Again, the marginal test of the genetic effect can be dramatically more powerful than the test of interaction effect although the generative model includes only an interaction term but no main effect.The above equations indicate first that the significance of the marginal test of Y (where variance explained for a predictor X is defined as βX2/σX2) but inducing no marginal genetic effect . It induces uncertainty on the estimation of the predictor effects, which decreases the significance of the estimates in the interaction model. With increasing intercorrelations between predictors it becomes impossible to disentangle the effects of one predictor from another, the standard errors of the effect estimates becoming infinitely large and the power decreases to the null , E (rE2), and G×E (rGE2) to the variance of the outcome using the estimates from the standardize model, in which the interaction term is independent from G and E (supplementary Appendix D):In genetic association studies the proportion of variance explained by an interaction term is commonly evaluated as the amount of variance of the outcome it can explain on top of the marginal linear effect of the interacting factors , times its marginal (or zero‐order) correlation with the outcome cor, i.e. rXi2*=βXi×cor.Still, this is a strong limitation when the goal is not prediction but to understand the underlying architecture of the trait under study and to evaluate the relative importance of main and interaction effects from a public health perspective. Lewontin  linear transformation of predictors other than Xi. It also has convenient additivity properties as it satisfies the condition rG2*+rE2*+rGE2*=rmodel2 (supplementary Appendix D), so that the overall contribution of the predictors is the sum of their individual contribution, and for example the cumulated contribution of multiple interaction effects can easily be evaluated by summing rXi2*. The Pratt's index also received criticisms .By definition, s Bring, , in partrXi2* can be expressed as a function of the estimated effects, the means and the variances of E and G (supplementary Appendix D), and can be derived using estimates from a standard regression model:From a practical perspective, As showed in Figure Table 2.4Using statistical technics such as the Pratt index can provide clues on the importance of interaction effects; however it does not help in mapping interaction. Increasing power mostly relies on two principles: increasing sample size, and leveraging assumptions on the underlying model. The case‐only test, which assumes independence between the genetic variant and the exposure, and a two steps strategy that select candidate variants for interaction test based on their marginal linear effects, are good examples of the later principle , their variances (σβG2 and σβGE2) and their covariance γ (supplementary Appendix E). By accounting for γ the joint test recovers most of the power lost by the univariate test of the main genetic and interaction effect :βG′′ and βGEcent.i′′ are the effects of G and G×Ecent.i. Such a test is robust to non‐normal distribution of the exposure, and modest correlation (<0.1) between the genetic variant and the exposures, but sensitive to moderate correlation (>0.1) between exposures . Hence, one can perform meta‐analysis of a joint test including multiple interaction effects using existing software simply by centering exposures. In brief one would have to perform first a standard inverse‐variance meta‐analysis to derive chi‐squares for the l+1 terms from the model considered, and then to sum all chi‐squares to form a chi‐square with l+1df. Importantly, centering the exposures will be of interest only when testing jointly multiple interactions and the main genetic effect. In comparison, the combined test of multiple interaction effects can be simply performed by summing chi‐squares from each independent interaction test or from interaction test derived in a joint model. As previously, the validity of this approach relies on independence between the genetic variant and the exposures, and between the exposures. Finally, a more general solutions that should be explored in future studies would consists, as proposed for the analysis of multiple phenotypes , derived as the weighted sum of the risk alleles. Several interaction effects have been identified using this strategy . Of course, in a realistic scenario, a number of non‐interacting SNPs would be included in the GRS, diluting the overall interaction signal and therefore decreasing power. However, the gain in power for the multivariate approaches can remain substantial even when a large proportion of the SNPs tested . Alternatively, others have used weights proportional to the marginal genetic effect of the SNPs, assuming the magnitude of the marginal and interaction effects are correlated. Obviously, the relative power of each of these weighting schemes depends on their relevance in regard to the true underlying model. Finally, applying GRS‐based interaction tests implicitly supposed a set of candidate genetic variants have been identified. The current rationale consists in assuming that most interacting variants also display a marginal linear effect and therefore have focused on GWAS hits, however other screening methods can be used (Aschard, Zaitlen, Tamimi, Lindstrom, & Kraft, A number of strategies can be used for the weighting scheme. Assuming equal effect size of all interaction effects, one should weight each SNP by the inverse of their standard deviation (3r2 if the interaction term was removed from the model. Here, I argue for the use of new approaches and analytical strategies to address these concerns. This includes using methods such as the Pratt index to evaluate the relative importance of interaction effects in genetic association studies. These methods can highlight important modifiable exposures influencing genetic mechanisms, which could be neglected with the existing approach. Regarding detection, and besides increasing sample size, increasing power to detect interaction effects in future studies will likely mostly rely on leveraging additional assumptions on the underlying model. In the big data era, where millions of genetic variants are measured on behalf of multiple environmental exposures and endo‐phenotypes, this means using multivariate models. A variety of powerful statistical tests can be devised assuming multiple environmental exposures interact with multiple genetic variants. As showed in this study, the application of such approaches can dramatically improve power to detect interaction that can be missed by standard univariate tests. While these methods comes at the cost of decreased precision—i.e. a significant signal would point out multiple potential culprit—they can identify interaction effects that would potentially be of greater clinical relevance that univariate pairwise interaction (Aschard et al., Advancing knowledge of how genetic and environmental factors combine to influence human traits and diseases remains a key objective of research in human genetics. Ironically, the simplest and most parsimonious biological interaction models—those in which the effect of a genetic variant is either enhanced or decreased depending on a common exposure—are probably the most difficult to identify. Furthermore, the contribution of such interaction effects can be dramatically underestimated when measured as the drop in Understanding the strengths and limitations of standard statistical methods is a major key to overcome today's challenges for the identification of interaction effects in human traits and diseases. By deciphering the basic principles of interaction tests, this perspective aims at providing a comprehensive guideline for performing interaction effects analyses in genetic association studies, and opening the path for future method development.Additional Supporting Information may be found online in the supporting information tab for this article.Appendix A: Effect estimates from standardized and unstandardized predictorsAppendix B: Non‐centrality parameters for marginal and interaction modelsAppendix C: Variance‐covariance for the GxE term and its estimated effectAppendix D: Derivation of the Pratt indexAppendix E: Joint test of main and interaction effectsAppendix F: GRS‐based test, joint test and univariate test of multiple interaction effectsFigure S1. Linear interaction effect across different coding schemesFigure S2. Power comparison for linear regressionFigure S3. Power comparison for logistic regressionFigure S4. The Pratt index across multiple interactionsFigure S5. Joint test of main genetic effect and multiple interaction effects in a linear regressionFigure S6. Joint test of main genetic effect and multiple interaction effects in a logistic regressionFigure S7. GRS‐based statistic and meta‐analysis of single SNP estimates in linear regressionFigure S8. GRS‐based statistic and meta‐analysis of single SNP estimates in logistic regressionClick here for additional data file.


Apolipoprotein A-IV (apoA-IV) has been observed to be associated with lipids, kidney function, adiposity- and diabetes-related parameters. To assess the causal relationship of apoA-IV with these phenotypes, we conducted bidirectional Mendelian randomization (MR) analyses using publicly available summary-level datasets from GWAS consortia on apoA-IV concentrations , kidney function (estimated glomerular filtration rate (eGFR), n = 133,413), lipid traits , adiposity-related traits , waist-hip-ratio ) and fasting glucose . Main analyses consisted in inverse-variance weighted and multivariable MR, whereas MR-Egger regression and weighted median estimation were used as sensitivity analyses. We found that eGFR is likely to be causal on apoA-IV concentrations . Triglyceride concentrations were also causally associated with apoA-IV concentrations , independently of HDL-C and LDL-C concentrations . Evaluating the inverse direction of causality revealed a possible causal association of apoA-IV on HDL-cholesterol . Whether a measurable trait is a causal risk factor or a marker acting as an indicator for the presence of a disease or its severity, is one of the key questions in biomedical research6. To act as a biomarker for a certain disease, causality is not strictly required, since a biomarker can be regulated as a response to a disease and/or an associated trait already in a very early stage of the disease. It can therefore act as a disease predictor without being causally involved in the pathogenesis of the disease. Moreover, the association between a biomarker and a disease may be confounded by measured or unmeasured factors that distort their relationship. However, establishing causality between a measurable trait and a disease is crucial to understand the pathophysiological mechanisms.Apolipoprotein A-IV (apoA-IV) has been discussed as a biomarker and /or risk factor for cardiovascular diseases, kidney disease and diabetesDisease endpoints are often detected using continuous surrogate markers (e.g. fasting glucose as marker for impaired glucose metabolism leading to diabetes) or are influenced by many other intermediate phenotypes, which might better represent the causal pathway leading to a disease than the disease state itself. With this motivation in mind, we evaluated the causal relation of apoA-IV with disease-related, continuous surrogate markers and intermediate phenotypes for which evidence from observational association studies or functional experiments proposes a functional link with apoA-IV.7. Its physiological role is not fully elucidated, yet. It participates in reverse cholesterol transport9 and plays an important role in relieving peripheral cells of an overload of cholesterol11. It has anti-atherogenic properties13 and low concentrations were found to be associated with cardiovascular outcomes such as coronary heart disease or acute coronary syndrome16. About 30% of the phenotypic variance has been shown to be genetically regulated17. In a recent genome-wide association study (GWAS) meta-analysis we have identified two variants within the APOA5-A4-C3-A1 cluster and one variant in the KLKB1 gene to be associated with apoA-IV concentrations17. Furthermore, the lead APOA4-SNP was shown to be associated with HDL cholesterol (HDL-C) concentrations. Other variants within the APOA5-A4-C3-A1 cluster have also been shown to be associated both with HDL-C, but also with triglyceride (TG) concentrations20. In addition, a TG genetic score was found to be associated with apoA-IV concentrations17. Studies in animal models, genetic association studies and studies evaluating disease progression argue for apoA-IV as the driving factor influencing satiety, adiposity, glucose concentrations and chronic kidney disease28. On the other hand apoA-IV concentrations have also been shown to change following food intake, gastric bypass surgery or weight loss30. Those findings warrant further investigation in causal associations and especially in the direction of the effects between apoA-IV and lipid levels, adiposity, diabetes-related parameters and kidney function. Recent developments in genetic epidemiology using genetic markers as proxies for a trait help estimate causal associations with a disease outcome through a Mendelian randomization approach31.ApoA-IV is a glycoprotein, which is a component of triglyceride-rich and high-density lipoproteins but it also circulates free in human plasma32.Such causal effects are usually very small. Therefore, single studies are often underpowered. However, results of genome-wide association studies are increasingly made publicly available. Harnessing summary-level data, Mendelian randomization analyses then reach sufficient statistical power to yield more precise causal effect estimates36. Furthermore, a GWAS meta-analysis on apoA-IV concentrations has been published recently17.For all of the already mentioned apoA-IV-associated and disease-related traits, large genome-wide association studies are available, in which dozens of genetic variants have been identifiedTherefore, we conducted a bidirectional two-sample Mendelian randomization analysis to assess the causal relationship of apoA-IV concentrations with HDL-C, LDL cholesterol (LDL-C), TG, fasting glucose (FG) as well as body-mass-index (BMI), waist-hip-ratio adjusted for BMI (WHR), and estimated glomerular filtration rate (eGFR). Herein, lipid levels, adiposity-related traits, glucose and eGFR were considered as risk factors on apoA-IV concentrations as outcome variable. We complemented the analysis by investigating the inverse association of whether apoA-IV is causally associated with the same traits. We applied different sensitivity analyses to account for presence of potential pleiotropy.A graphical overview of the design and studies used in our investigation is given in Fig. Table An overview about the characteristics and the meta-analysis results of the 71 HDL-SNPs, the 58 LDL-SNPs and the 40 triglyceride-SNPs can be found in Supplementary Tables HDL-C levels (in SD) with the log-transformed apoA-IV concentrations resulting in a causal estimate of βMR-IVW = 0.0341 . This is the same SNP that we planned to exclude as a sensitivity analysis due to its close proximity to the APOA4 gene (see Methods). After exclusion of this SNP, the effect became non-significant  attracted our attention as it harbored a potential bias due to its low level of precision , approximately 50 kb downstream of APOA4, and shows r2 < 0.3 with SNPs in APOA4  reported in GTEx for BUD13, ZPR1 and all apolipoprotein genes in the APOA5-A4-C3-A1 gene cluster were not in linkage disequilibrium (LD) with rs964184 . Together this suggests that rs964184 is neither in LD with SNPs in the APOA4 gene nor with any known eQTL in the gene cluster, but presents modest LD with SNPs in APOA5. It is therefore unlikely that rs964184 has a direct effect on apoA-IV concentrations and it would be too conservative to exclude it from the analysis. It is also not surprising that the exclusion of the 23 SNPs, which are included in the SNP sets of the other traits or in LD with SNPs of the other traits, resulted in a non-significant causal estimate. Among these 23 SNPs were the most informative SNPs, i.e. SNPs with the highest effect on TG and therefore also on apoA-IV. Not even half of the triglyceride SNPs remain, which is primarily due to being in LD with HDL-C SNPs. The multivariable method is the most useful method to account for this interrelation with other lipid traits by simultaneously keeping the most informative SNPs. Therefore, we additionally excluded only SNPs that were in LD with SNPs from the non-lipid traits, but adjusted for HDL-C and LDL-C. Using this method, the causal estimate from triglycerides on apoA-IV remained statistically significant. Nevertheless, this relationship has to be interpreted with caution. Further studies are needed to confirm this potentially causal association of TG and apoA-IV.The second main finding was that TG causally affects apoA-IV, even after adjusting for HDL-C and LDL-C. However, in the sensitivity analysis excluding the potentially pleiotropic SNP rs964184, the causal effect calculated using the MR-IVW method resulted in a statistically non-significant estimate. In this setting, this was not surprising, as this SNP was the one with the highest effect size on both TG and log(apoA-IV). However, it is only mandatory to exclude this SNP from the analysis, if it violates the instrumental variable assumption. This would be the case, if it influenced apoA-IV concentrations directly or through an endogenous variable that is different from the exposure. It was not identified to be pleiotropic by the applied statistical methods (gtx-package), though. Although being located within the 19. Besides, a study investigating the LDL-C lowering response to different diets found that the apoA-IV protein isoforms modulate the LDL-C lowering response to a diet39. However, we demonstrated recently in a study with more than 13,000 individuals, that the genetic variants that are the molecular basis for the apoA-IV isoforms do not have an effect on apoA-IV concentrations. In the data at hand, the MR-IVW method and the MR-Egger regression revealed a statistically significant positive causal estimate, but the effect vanished after adjustment for the other lipid traits. It is therefore conceivable that the effect of both HDL-C as well as LDL-C on apoA-IV concentrations is triggered primarily by the association with TG. Furthermore, 5 SNPs are present in all three lipid datasets  which might also influence this result. The exploration of the reverse causation, i.e. whether apoA-IV influences HDL-C, resulted in a significant finding, showing an inverse causal direction. However, this result is triggered mainly by one SNP in the APOA4 gene (rs1729407). This SNP was associated with both apoA-IV concentrations as well as HDL-C. Since it was the top signal in the GWAS on apoA-IV concentrations17 but not genome-wide significantly associated with HDL-C18, although conducted in a much higher sample size, it is conceivable that it exerts an effect primarily on apoA-IV. However, a direct effect on HDL-C cannot be excluded which would violate the exclusion-restriction assumption of Mendelian randomization. Given that apoA-IV is an important component of the HDL-C particle42, a causal effect of apoA-IV on HDL-C level is possible and partly supported by our data, but has to be considered with caution.The investigation of HDL-C and LDL-C as causal factors influencing apoA-IV concentrations yielded inconsistent results. In previous genetic studies, several loci have been associated with apoA-IV as well as HDL-C and LDL-C21 and in humans26. In addition, the administration of apoA-IV resulted in reduction of food intake and genetic association studies have found associations between polymorphisms within the APOA4 gene and adiposity-related traits28. Although these findings argument in favor of apoA-IV as a risk factor, it has also been shown that apoA-IV is decreased following weight loss and/or gastric bypass30. Despite the epidemiological and also functional studies linking adiposity-related traits to apoA-IV, we could not find a causal effect in one or the other direction. One reason for that might be that – despite the already huge datasets and the high number of associated SNPs – the power is still insufficient to detect a causal effect from especially WHR as exposure on apoA-IV as outcome variable. To be detectable in our analysis with a power of 80%, the causal effect of WHR on apoA-IV would have to be that high, that it explains at least 15% of the phenotypic variance of apoA-IV  and also with 2 h glucose levels4. Experimental studies and APOA4 knockout mice have also shown that apoA-IV has a glucose-lowering effect44. Therefore, we would have expected to find a causal association of the apoA-IV SNPs  on fasting glucose. In this case, apoA-IV would have to explain only more than 0.48% of the phenotypic variance of fasting glucose to have a power of 80%. Still, we could not find a causal association with any of the methods used in any of the investigated directions. Not finding a significant association does not exclude the possibility that there still exists one: apoA-IV and fasting glucose might still be causally related with each other but the true effect might be smaller than what can be detected with our data. The other possibility to explain this non-significant finding might be that the observed association of apoA-IV with glucose is confounded by other factors that influence both traits.Counter-intuitively, we found no causal association of fasting glucose with apoA-IV and vice versa. This should not be a problem of power like for the adiposity-related traits, as the effect that could be detected with the given data is even smaller than for TG and eGFR. Already much is known that links glucose with apoA-IV. Diabetics have been found to have significantly higher apoA-IV levelsUsing summary-level data of all SNPs that have been shown to be genome-wide significantly associated with their respective traits as instrumental variables, is both a strength but also a limitation of our study. By using summarized data, a higher power can be achieved than in single studies. The availability of dozens of associated SNPs that were identified in more than 100,000 participants does not guarantee to get a high power for the Mendelian randomization analysis, though. For the adiposity-related traits as risk/protective factors for apoA-IV, the instrumental variables do not explain much of the variation in these traits. Therefore, to be able to find a causal association of a reasonable size, further SNPs would have to be identified that can be used to increase the variance explained on BMI and especially WHR. For the lipid traits, however, our applied methods based on summarized data achieved a high power enabling the detection of very low causal effects. Nevertheless, not only high power is necessary for Mendelian randomization analysis but also the choice of valid instruments. To be a valid instrumental variable, a SNP should be associated only with the respective risk/protective factor. For the correlated traits HDL-C, LDL-C and TG, there is substantial overlap of the SNPs, which makes it extremely difficult to discriminate the instrumental variables for each of the lipid traits correctly from each other. The exclusion of all instrumental variables that were found to be associated with at least two of the three lipid traits would lead to a substantial loss of strength for the Mendelian randomization analyses. However, we checked for possible pleiotropy of the SNPs using appropriate statistical methods and adjusted for the effects of the other lipid traits to find independent causal effects. Still, the interpretation of the identified causal effects remains difficult.Another limitation which arises from using summary-level data is that observed effect sizes cannot be derived from directly and thus, if not obtainable from the literature, cannot be compared with the estimated causal effects. Although we only investigated causal relationships for which there is already sufficient evidence of either observational association or functional experiments, direct comparison of observational and causal estimate is only possible if it is on the same scale. All GWAS meta-analysis data we used for our analyses are derived from either log-transformation or inverse normal transformation. However, such transformations are hardly ever done in observational epidemiological studies. Results from functional wet-lab experiments can certainly not be transferred into observational estimates.To summarize, our data revealed an inverse causal association of kidney function (eGFR) on apoA-IV. Furthermore, investigating the lipid traits suggested a causal involvement of primarily triglyceride levels on apoA-IV concentrations. The causal effects of HDL-C and LDL-C on apoA-IV are hard to discriminate from each other and from the effects triggered by TG. Our results also argue for a causal, inverse association of apoA-IV concentrations on HDL-C, which however have to be interpreted with caution due to potential presence of pleiotropic effects of the genetic markers.For all evaluated disease-related traits and apoA-IV, SNPs were selected and summarized results were taken from the most recent and most comprehensive GWAS, which were conducted primarily in cohorts of European ancestry. A graphical overview of the design and studies used in our investigation is given in Fig. 45. Four control sera with different concentrations were run on each plate in double measurements for control purposes throughout the entire project. The intra- and interassay coefficients of variation were 2.7% and 6.0%, respectively45.For all participating studies, quantification of plasma apoA-IV was done in the same laboratory . It was based on a double-antibody enzyme-linked immunosorbent assay using an affinity-purified polyclonal rabbit anti-human apoA-IV antibody for coating and the same antibody coupled to horseradish peroxidase for detection. Plasma with a known concentration of apoA-IV was used as the calibration standardIn Mendelian randomization analyses, instrumental variables should meet certain requirements to minimize weak instrument bias.et al.33. Using this formula, the percentage of phenotypic variance explained by the instrumental variables (SNPs) can be estimated as th SNP on the risk factor The strength of the instrumental variables (SNPs) used for the Mendelian randomization analysis was assessed using the explained variance (R²). R² was calculated according to Pattaro 2 < 0.1) were included in this analysis . This corresponds to an F statistic > 30 for each single variant46. In the Mendelian randomization literature a threshold of F < 10 has typically been used to define a “weak IV” (the Staiger-Stock rule48). Since we are using a combination of several genome-wide significant SNPs, weak instrument bias is negligble.The F-statistic is typically used to judge on the validity of instrumental variables. However, it cannot be calculated in this setting, where only summary-level data are available. However, only genome-wide significant SNPs that are independent from each other , a sample size of 188,577 is assumed for the lipid analysis etc. Table . Given \The Mendelian randomization analyses were performed bidirectional. In the first run, apoA-IV was considered as an outcome variable whereas lipids, eGFR, BMI, WHR (adjusted for BMI) and fasting glucose levels were considered as exposures. In the second run, apoA-IV was the exposure variable and the other phenotypes  and fasting glucose levels) were used as outcomes.Before any analysis, the SNP-exposure and SNP-outcome association estimates have all been oriented towards an increase in the exposure trait.et al.46. Causal estimates based on this method are notated as βMR-IVW. The MR-IVW estimate can also be interpreted as a weighted regression from the effect estimates of the exposure SNPs on the estimates of the outcome of the same SNPs (removing the intercept).For the main Mendelian randomization analysis, the SNP-exposure and SNP-outcome estimates were combined using the inverse-variance weighted (MR-IVW) method as proposed by Burgess MR-Egger).The MR-Egger regression: assesses directional pleiotropy by borrowing from the same principles of testing for small study bias in meta-analysis .The exclusion of possible pleiotropic SNPs based on the gtx package in R .For the lipids: the multivariable Mendelian randomization adjusting for the effect estimates of the other lipid phenotypes  in the gene-exposure association estimates), sensitivity analyses were performed, where different methods were used to detect possible pleiotropy and also to account for it:50 was used to investigate whether there is directional bias caused by pleiotropy. Directional bias means that the pleiotropic effects of genetic variants are not balanced about the null and are drawn into one direction. This regression is an adaption of the standard Egger regression which is used to analyze small study bias in the meta-analysis literature. The intercept obtained from the MR-Egger regression gives an estimate of directional bias and the slope coefficient provides an estimate of the causal effect, which is consistent even when all the genetic variants are invalid instrumental variables with respect to pleiotropy50. To assess whether the MR-Egger regression estimates might be biased through a violation of the NOME assumption, an adaption of the I² statistic 51 was calculated and the corrected MR-Egger estimate was computed using the method of Simulation Extrapolation (SIMEX)51.MR-Egger regressionet al.52. In this method, the ratio estimates of the SNP-exposure and SNP-outcome association estimates are ordered and weighted by the inverse of their variance. The weighted median estimator is then the median of these estimates, according to the weights. This estimator is consistent if at least 50% of the weight comes from valid instrumental variables. Although the MR-Egger regression method allows all the instrumental variables to be invalid, the weighted median estimation approach offers the advantages of an improved precision compared to the MR-Egger regression. Therefore, both methods were used to assess whether pleiotropy had influenced our results.Additionally to the MR-Egger regression, the weighted median estimator was calculated as proposed by Bowden 54. This assumption was tested by a goodness of fit test using the function “grs.filter.Qrs” in package “gtx” in R . This function performs a stepwise downward model selection in which SNPs are iteratively removed from the risk score until the heterogeneity test is no longer significant at the specified threshold (pthreshold = 0.05). SNPs showing a deviation from this assumption are therefore potentially not mediated completely by the exposure and were excluded in a further sensitivity analysis. This was only the case, however, for one HDL-C SNP. In a second approach used to account for possible pleiotropy, we looked up whether there are either any overlapping SNPs in the different SNP selection datasets or SNPs in LD with each other. To find the proxies for each SNP, we used SNiPA55 with the 1000 Genomes Phase 3 v5 variant set and an LD-threshold of r² > 0.8. If overlaps were found, these SNPs were excluded. For the lipids, we followed two different approaches. First, we excluded all SNPs that were found in any other SNP selection dataset, no matter which trait. Second, we excluded only those SNPs that were found in other non-lipid SNP selection datasets . In this case, an adjustment for the other lipid traits using multivariable Mendelian randomization was included as described below, to adjust for the lipid traits as well. This second approach was performed due to the huge SNP overlap between the different lipid traits.In two further sensitivity analyses, all SNPs that were assumed to have pleiotropic effects were excluded. In Mendelian randomization analyses, bias due to pleiotropy only occurs when the SNPs are associated with other phenotypes, which also influence the outcome variable or are independently associated with the outcome variable itself. If this is not the case and there is also no direct effect of the SNPs on the outcome variable, the effect of the SNPs on the outcome is mediated completely by the intermediate variable. Then, the causal effects of all SNPs individually should rather be homogeneous and approximate the true unknown causal effect of the exposure variable on the outcomeet al.57. In this approach the gene-outcome associations are regressed on all the gene-risk factor associations simultaneously in a multivariable regression model, using the SNPs associated with the risk factor of interest.For the lipid traits, we also performed a multivariable Mendelian randomization adjusting each lipid-apoA-IV causal estimate by the estimates of the SNP-lipids association not under consideration . For this, an extension to the inverse-variance weighted method was used, as proposed by Burgess In the case where apoA-IV acted as the exposure variable, only two  or three (for fasting glucose) SNPs were available for the MR analysis. Here, all four sensitivity analyses were not applicable or meaningful and therefore only the MR-IVW method was applied.As four different “trait blocks” including correlated traits were analyzed, a p-value of 0.05/8 = 0.00625 was considered as significant.http://snipa.helmholtz-muenchen.de/)55 using 1000 Genomes phase 3 data and superimposed to UCSC Genome Browser hg19 using modified scripts from58. Expression QTL data for rs964184 and for all genes in the APOA5-A4-C3-A1  cluster was retrieved from GTEx 59.LD structures and pairwise SNP correlations were retrieved from SNiPA (Supplementary text, tables and figures


The genetic etiology of human lipid quantitative traits is not fully elucidated, and interactions between variants may play a role. We performed a gene-centric interaction study for four different lipid traits: low-density lipoprotein cholesterol (LDL-C), high-density lipoprotein cholesterol (HDL-C), total cholesterol (TC), and triglycerides (TG).n = 12,853 to n = 16,849 depending on lipid phenotype) and a replication phase with ten independent cohorts totaling up to 36,938 additional samples. Filters are often applied before interaction testing to correct for the burden of testing all pairwise interactions. We used two different filters: 1. A filter that tested only single nucleotide polymorphisms (SNPs) with a main effect of p < 0.001 in a previous association study. 2. A filter that only tested interactions identified by Biofilter 2.0. Pairwise models that reached an interaction significance level of p < 0.001 in the discovery dataset were tested for replication. We identified thirteen SNP-SNP models that were significant in more than one replication cohort after accounting for multiple testing.Our analysis consisted of a discovery phase using a merged dataset of five different cohorts  contains supplementary material, which is available to authorized users. For this study, we perform several analyses to identify and validate genetic interactions associated with circulating lipid levels. Our motivation for studying the contribution of interactions to lipid levels is three-fold. First, dyslipidemia have a large impact on human health. Circulating lipid levels, such as high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C), total cholesterol (TC), and triglycerides (TG), are associated with risk for various common disease traits including cardiovascular disease . Cardiov, as most individuals were genotyped using a cardiovascular gene-centric array and we filtered before interaction testing, the considerations about interaction do still apply [p-value from the main effect term in a regression model) using bona fide index lipid signals derived from existing GWAS. A limitation to the main effect filter approach is that SNPs involved in true interactions with little or no main effects will likely be filtered out. Another approach is to select SNP-SNP models based on knowledge-driven biologically plausible genes/loci, such as selecting SNP pairs in genes shown to physically interact in previous biological experiments (Biofilter) [Here we are trying to identify genetic interactions by searching for statistical interactions. For interpretation purposes, it is important to understand how we define an interaction. Biologically, we are trying to identify genetic variants that alter the phenotype in a manner that is dependent on genotypes at two different loci. For example, an individual may have variants in two different regions of a metabolic enzyme protein that cause triglyceride levels to increase even more than the combined additive effects of the variants. Statistically, we use a likelihood ratio test to assess the significance of including a multiplicative interaction term along with the two main effect terms in a linear regression model. While there has been some debate about the relationship between statistical and biological interactions, there is substantial evidence that this method is robust to the non-linear or interaction effects we are interested in .One of tll apply . One appofilter) .n = 12,853 to n = 16,849 depending on lipid phenotype): Atherosclerosis Risk In Communities (ARIC); Coronary Artery Risk Development in Young Adults (CARDIA); Cardiovascular Health Study (CHS); Framingham Heart Study (FHS); and Multi-Ethnic Study of Atherosclerosis (MESA); from the NHLBI Candidate gene Association Resource (CARe). Models were selected for replication testing based on statistical significance from the discovery set. There were ten replication sets in total with sample sizes between n = 1568 and n = 7504 totaling 36,938 for the replication dataset. We identified models with the most evidence for significant associations with the lipid traits according multiple-testing corrected likelihood ratio test p-value thresholds from linear regression models. We also assessed the number of cohorts in which the models replicated. This study highlights an analysis strategy to explore genetic interactions for complex traits and suggests several replicating interactions for lipid traits.For this analysis, we used both of the aforementioned filter methods to test for interactions. After applying these filters, we identified potential SNP-SNP interactions for each of the lipid traits in a discovery analysis, which consisted of five cohorts merged into one dataset , CARDIA (n = 2319), CHS (n = 4490), FHS (n = 1467), and MESA (n = 5598). Individuals were genotyped using the gene-centric ITMAT-Broad-CARe (IBC) array [L ~ C – H - kT where C is total cholesterol, H is HDL, L is LDL, T are triglycerides, and k is 0.45 for mmol/L (or 0.20 if measured in mg/dl). If TG values were >4.51 mmol/L (>400 mg/dL), then LDL was treated as a missing value. More details for the five merged discovery cohorts are shown in Table The discovery dataset for each of the traits had n ~ 14,000, with each of the cohorts having the following contributions: ARIC (C) array , which wC) array . All of p < 1.0 x < 10−7) were removed from the analysis. After SNP genotyping quality control, 44,750 markers remained. Individuals with SNP genotype missing rates >90% were excluded from the analysis. For cohorts that contained known trios, non-founders (i.e. offspring) were removed. To address unknown or cryptic relatedness, identity-by-descent (IBD) estimates were calculated, and one individual from each pair with pi-hat >0.3 was removed. The TG values were log transformed to improve normality. Four new datasets were created for each of the quantitative lipid traits: HDL-C , LDL-C , TC , and TG .Individuals were genotyped on the ITMAT-Broad-CARe (IBC) array. This array consists of ~50,000 SNPs across ~2100 loci. Selection criteria for SNPs to be included on the IBC array have been described in detail previously . Quality2 > 0.6 using PLINK. SNPs with a main effect p < 0.001 based on a previous GWAS regression analysis were selected for interaction testing [Additional quality control metrics were applied to the individual lipid datasets for each of the statistical analyses. For both the main effect filter and Biofilter analyses, SNPs with missing phenotypes were removed along with variants with minor allele frequency (MAF) < 0.05 or missing genotype rate > 5%. For the main effect filter analysis, SNPs were pruned to remove high levels of SNP correlation, or LD from the data. No LD pruning was done for the Biofilter interaction analyses, as these models are specifically generated using SNPs that are in different genes. This was performed by removing one SNP from all pairs of SNPs with an r testing . We had  testing , 19. Brip -values <0.001 (comparing the full and reduced linear regression models (Eqs. ).To test for SNP-SNP interactions, we used an R script that automatically tests the models according to user input parameters . We testels Eqs. ). We adj2 > 0.8) with model SNPs based on the HapMap European CEPH (CEU) population in 1000 Genomes Project Pilot 1 data (2010 release) using SNAP [The full model consisted of the same SNP and covariate terms as the reduced model, but with an additional multiplicative interaction term for the SNP-SNP model. We generated “proxy” models by identifying SNPs in high linkage disequilibrium (LD)  . The eMEund here .p-value threshold of at least p < 1 × 10−6 was applied by each group. In each of the replication cohorts, population stratification and relatedness were assessed and adjusted for accordingly. All of the individuals in the replication cohorts were of European-American descent. The full details for the QC procedures can be found in the references provided for each replication cohort in Table The minimum variant and sample call rate threshold for all replication cohorts was 0.95 and 0.90, respectively. A Hardy-Weingberg equilibrium test p < 0.001 and all of the corresponding proxy models were tested using the same statistical approach as for the discovery analysis  models tested and for the 10 replication cohorts. We also assessed how many of the 10 cohorts had significant replication for each of the models. These results were visualized using the program SynthesisView [Replication analyses were performed in nine independent cohorts genotyped previously on the IBC array for a range of phenotypes including lipid levels  and the sis Eqs. . The samesisView .Full results from the discovery analysis for all original models selected for replication testing can be found in Additional file p = 0.05. For the MEF analyses, the number of original (non-proxy) models selected for testing are shown as: lipid trait  - HDL-C ; LDL-C ; TC ; and TG . The respective counts for the Biofilter analysis were: HDL-C ; LDL-C ; TC ; and TG . We then calculated the number of model signals that passed the respective thresholds in each cohort   and the number of replication cohorts (further divide by 10) to perform a Bonferroni-like correction equivalent to p-value, where replication was observed in more than one cohort. For the main effect filter analyses, more models passed the selected replication threshold. Also, a number of models showed similar results in more than one cohort. For HDL-C, 17 total models replicated with seven models observed to replicate in at least two cohorts. For LDL-C, two models replicated, both in at least two cohorts. For TC, replication occurred for one model in one cohort. For TG, 11 total models replicated, with four models replicating in at least two cohorts , as shown in Fig. 2 > 0.1) was observed in our data between SNPs in the same replication model.Although we performed LD pruning prior to the interaction analyses, moderate LD remained with rAPOA4, APOA5, APOC3, SIK3, and BUD13. There are complex patterns of moderate to strong LD in this region, and thus bona fide “independent” signals are challenging to delineate. However, for the main effect filter analyses of TG, one SNP (rs180327) appeared in two of the four models that replicated in more than one cohort. Moderate correlation exists between most of the other SNPs except for rs180327 . However, intergenic interactions, such as those that we observed in this study, should not be ignored, as they may contribute to a substantial proportion of the genetic architecture. Our top replicating models for HDL-C consisted of two SNPs in CETP. Many of these model replicated across cohorts with the top replication Due to the complex nature of estimating heritability, we focus on how our results contribute to understanding the genetic architecture and biological underpinnings of lipid traits. First, the estimated heritability of lipid traits has a relatively wide range (40–60%). There is also high variability in results that can come from methods that calculate overall heritability. A recent study found that for certain models, the estimate is extremely inflated and potentially not reliable . FurtherIn our study, we can see the difference in R2 for the full versus reduced model , the main effect filter pipeline would not detect such effects. Also, as our results possibly indicate, strong main effects may create inflated interaction signals. A more appropriate filtering pipeline may use a main effect filter – Biofilter hybrid approach. Another possible filtering mechanism may be one that ranks variables based on potential main and interaction effects simultaneously. Some machine learning methods, such as Random Forests (RF) and artificial neural networks (ANN), are currently being tested for this approach .


Ovis canadensis): horn length, horn base circumference, and body mass. These traits are of specific concern in bighorn sheep as artificial selection through trophy hunting opposes sexual selection. Specifically, horn size determines trophy status and, in most North American jurisdictions, if an individual can be legally harvested. Using between 7,994–9,552 phenotypic measures from the long-term individual-based study at Ram Mountain , we first showed that all three traits are heritable (h2 = 0.15–0.23). We then conducted a genome-wide association study (GWAS) utilizing a set of 3,777 SNPs typed in 76 individuals using the Ovine Infinium® HD SNP BeadChip. We found suggestive association for body mass at a single locus (OAR9_91647990). The absence of strong associations with SNPs suggests that the traits are likely polygenic. These results represent a step forward for characterizing the genetic architecture of fitness related traits in sexually dimorphic ungulates.Elucidating the genetic basis of fitness-related traits is a major goal of molecular ecology. Traits subject to sexual selection are particularly interesting, as non-random mate choice should deplete genetic variation and thereby their evolutionary benefits. We examined the genetic basis of three sexually selected morphometric traits in bighorn sheep ( A goal of molecular ecology is to identify the genetic architecture underlying traits of ecological relevance . There iSexual selection poses particularly interesting scenarios for fitness-related traits, leading to the so called lek paradox . Under sOvis aries) some breeds have horns while others are polled (lacking horns entirely), and from an agronomic production standpoint there is interest in removing horns from certain breeds (In domestic sheep (n breeds . Soay shn breeds .Bos taurus) (The genetic basis of these differences in horn morphology and development in domestic sheep has been investigated. A single genomic region on chromosome 10 is associated with the presence and absence of horns in domestic breeds  includin taurus) , indicatOvis canadensis) are iconic North American wild sheep named for their large horns. All individuals have normal horns, though males have much larger horns than females. Previous research has shown that horn size and body mass are important for intrasexual competition among males for reproductive access to females  are native, isolated and philopatric. Individual-based monitoring of the population began in 1972 . Most inThis study uses data from animals captured under research protocols that were approved by the University of Alberta Animal Use and Care Committee, affiliated with the Canadian Council for Animal Care (Certificate 610901). We considered three morphological characteristics: average horn length, average horn base circumference, and body mass. Specifically, sheep were weighed to the nearest 250 g with a Detecto spring scale, while horn length  and base circumference were measured to the nearest millimeter with tape. Each trait measurement was standardized to a sex and age specific standard deviation of one . We only considered individuals aged 1 or greater to avoid maternal effects , and pooVp) into that due to additive genetic variation (Va), permanent environmental effects (Vpe), and residual variation (Vr) (Vpe), as well as year of birth (Vyb) and year of measurement (Vy) to account for environmental effects. Thus, phenotypic variation was broken into five components Vp = Va + Vpe + Vy + Vyb + Vr.Quantitative genetic variation in our morphological characteristics was estimated using a series of ‘animal models’. Animal models are linear mixed effects models that incorporate pedigree information along with phenotypic measures to partition phenotypic variation (ion (Vr) . For ourVp explained by the random effect, and its significance tested by comparing a model with the term removed to the full model using a likelihood ratio test with one degree of freedom. From these models, we calculated heritability (h2) of each trait as the ratio of Va∕Vp. We also recorded estimates of individual breeding values (Va), calculated using best linear unbiased predictors (BLUPs), for use in selecting individuals for the association analyses (see below).The three morphological traits were modeled independently using univariate animal models run in ASReml version 3.0 , based o® HD SNP BeadChip an array originally developed for domestic sheep that contains 606,006 loci distributed throughout the domestic sheep genome (p >1.28 × 10−5) in our sample set . Finally, we used VIPER  to account for polygenic effects and individual ID as a random effect to account for repeated measures. In our analyses, the base model had the same structure as that used in the ASREML analyses above. Second, the estimated (co)variance matrix from the first step is used when individual SNPs are tested for association with the phenotype. Specifically, associations are assessed using a linear model and p-values are calculated with a Wald statistic. We fit separate models for horn length, horn base circumference, and body mass.Keff . These estimates were then compared to inter-marker physical distance based on map positions from the domestic sheep genome, and half-length was calculated using a custom script which calculated LD decay rate as in Appendix 2 of We examined gene annotations in the domestic sheep genome near suggestive loci (see ‘Results’). To determine the genomic window within which to search, we estimated the ‘half-length’ of linkage disequilibrium (LD) for our marker set, i.e., the inter-marker distance at which LD decreased to half its maximal value . This vaAverage horn length, horn base circumference, and body mass all showed positive phenotypic correlations, with the magnitude much stronger in males than females . All thrλ) was ≤1, indicating that there was no underlying population structure or other factors which could lead to false positive associations  within a 413,000 bp window on either side of the candidate marker using BioMart  is an order of magnitude less than found in a previous assessment of LD in bighorn sheep from RM  are below the diagonal, while those for males (aged 4) are above the diagonal. Note that we present the sexes separately given the sexual dimorphism in this species, and these ages as they allow consideration of adult phenotypes (removing autocorrelation with age), while avoiding the effects of selective harvest due to trophy hunting in males as measurements are collected before the hunting season and no male younger than 4 years has ever been legally harvested.Click here for additional data file.10.7717/peerj.4364/supp-2Table S2® HD SNP BeadChip an array originally developed for domestic sheep containing 606,006 loci. Marker positions were taken from the domestic sheep genome assembly (version 3.1).Genotyping was done using the Ovine InfiniumClick here for additional data file.10.7717/peerj.4364/supp-3Supplemental Information 1Click here for additional data file.10.7717/peerj.4364/supp-4Supplemental Information 2tped formatted genotypes for use in GWAS analyses.Click here for additional data file.10.7717/peerj.4364/supp-5Supplemental Information 3Click here for additional data file.10.7717/peerj.4364/supp-6Supplemental Information 4Click here for additional data file.10.7717/peerj.4364/supp-7Supplemental Information 5Click here for additional data file.10.7717/peerj.4364/supp-8Supplemental Information 6Click here for additional data file.10.7717/peerj.4364/supp-9Supplemental Information 7Click here for additional data file.


In recent decades, Holstein–Friesian (HF) selection schemes have undergone profound changes, including the introduction of optimal contribution selection , a major shift in breeding goal composition (around 2000) and the implementation of genomic selection . These changes are expected to have influenced genetic diversity trends. Our aim was to evaluate genome-wide and region-specific diversity in HF artificial insemination (AI) bulls in the Dutch-Flemish breeding program from 1986 to 2015.Pedigree and genotype data (~ 75.5 k) of 6280 AI-bulls were used to estimate rates of genome-wide inbreeding and kinship and corresponding effective population sizes. Region-specific inbreeding trends were evaluated using regions of homozygosity (ROH). Changes in observed allele frequencies were compared to those expected under pure drift to identify putative regions under selection. We also investigated the direction of changes in allele frequency over time.Effective population size estimates for the 1986–2015 period ranged from 69 to 102. Two major breakpoints were observed in genome-wide inbreeding and kinship trends. Around 2000, inbreeding and kinship levels temporarily dropped. From 2010 onwards, they steeply increased, with pedigree-based, ROH-based and marker-based inbreeding rates as high as 1.8, 2.1 and 2.8% per generation, respectively. Accumulation of inbreeding varied substantially across the genome. A considerable fraction of markers showed changes in allele frequency that were greater than expected under pure drift. Putative selected regions harboured many quantitative trait loci (QTL) associated to a wide range of traits. In consecutive 5-year periods, allele frequencies changed more often in the same direction than in opposite directions, except when comparing the 1996–2000 and 2001–2005 periods.Genome-wide and region-specific diversity trends reflect major changes in the Dutch-Flemish HF breeding program. Introduction of OCS and the shift in breeding goal were followed by a drop in inbreeding and kinship and a shift in the direction of changes in allele frequency. After introduction of GS, rates of inbreeding and kinship increased substantially while allele frequencies continued to change in the same direction as before GS. These results provide insight in the effect of breeding practices on genomic diversity and emphasize the need for efficient management of genetic diversity in GS schemes.The online version of this article (10.1186/s12711-018-0385-y) contains supplementary material, which is available to authorized users. Genetic variation in (closed) livestock populations is largely driven by the fundamental processes of selection and genetic drift. While selection acts directionally on alleles that have a selective (dis)advantage and on alleles that are ‘hitchhiking’ –3, genetIn Holstein–Friesian dairy cattle (HF), intense artificial selection has been practised over many years. The use of a limited number of elite sires has reduced the effective population to a size ranging from 49 to 115 . This imTraditionally, genetic diversity has been characterised and managed with pedigree-based coefficients of inbreeding and kinship, which refer to the proportion of the genome that is expected to be identical by descent (IBD) within and between individuals, respectively. However, this genealogical approach has several limitations: (1) it strongly depends on pedigree completeness and quality (e.g. ); (2) itG Morgan [G is the number of ancestral generations to the common ancestor from which the segment was derived, this approach may be used to distinguish recent from distant relatedness and move from IBS to ‘realised IBD’ [With the wide availability of dense single nucleotide polymorphism (SNP) data, it has become possible to obtain more accurate estimates of genome-wide inbreeding and kinship and to evaluate diversity for specific regions of the genome –15. Two G Morgan , where Gsed IBD’ . Both IBsed IBD’ , 20, 21.In recent decades, HF selection schemes have undergone profound changes with respect to inbreeding management, breeding goal composition and breeding value estimation. Around the year 2000, optimal contribution selection (OCS) was introduced to maximise genetic gain at a restricted rate of inbreeding . Around The aim of this study was to evaluate genome-wide and region-specific genetic diversity in HF AI bulls from 1986 to 2015, using genealogical, marker-by-marker and segment-based approaches. An important objective was to evaluate whether major changes in the Dutch-Flemish HF breeding program were accompanied by changes in inbreeding and kinship trends. A second objective was to investigate whether observed changes in allele frequency could be attributed to selection, and whether regions under selection could be linked to known quantitative trait loci (QTL). A last objective was to investigate how the direction of changes in allele frequency has evolved over time.A total of 6280 AI bulls with breed fraction  higher than 87.5% HF, born between 1986 and 2015 and genotyped by the Dutch-Flemish cattle improvement co-operative (CRV), were included in this study. Thus, the vast majority of AI bulls in the Dutch-Flemish breeding program were included. Figure n over all known ancestors, with n being the generation number of a given ancestor. The average CGE increased from 9.6 in 1986 to 17.0 in 2015 and was equal to 13.3 when calculated across all years. The average number of completely known generations increased from 4.1 in 1986 to 8.1 in 2015. The generation interval (L), i.e. the average age of parents at the birth of the bulls, was computed per year of birth for bull sires and bull dams separately, and for all parents combined  or CRV custom-made 60 k Illumina panel (versions v1 and v2). Genotypes were imputed to ~ 76 k from the different panels, following Druet et al. , and hapGenome-wide diversity was quantified with genealogical, marker-by-marker and segment-based approaches. Pearson correlation coefficients between genealogical, marker-by-marker and segment-based measures were calculated to compare the different approaches.i or between individuals i and j, were IBD with reference to a base population [calc_grm [Genealogical coefficients of inbreeding  were detected by moving SNP by SNP across chromosomes and testing potential ROH against predefined criteria. The following criteria were used to define a ROH: (1) a minimum physical length of 3.75 Mb, (2) a minimum of 38 consecutive homozygous SNPs , and (3) a maximum gap of 500 kb between two consecutive SNPs. The minimum length of 3.75 Mb was chosen to match the pedigree depth. Given the genetic distance of approximately 1 cM per Mb [G M for ROH derived from a common ancestor G generations ago [Segment-based inbreeding  of the empirical gene drop distribution were considered indicative of selection. To visualise systematic changes over the erratic pattern of individual SNPs, the moving average of 31 adjacent absolute Changes in allele frequency were computed as dropping . In eachGenomic regions with an excess of putative selected SNPs were considered as putative selected regions. For the key regions of interest, we investigated which QTL were known in these regions, using AnimalQTLdb . The comChanges in allele frequency were also computed within each 5-year period as Descriptive statistics for all six genome-wide parameters are shown in Table Pearson correlation coefficients between different genome-wide estimates of inbreeding and kinship per year of birth are shown in Fig. rge Fig. .Fig. 3CoRoughly, genome-wide inbreeding increased from 1986 to 2000, remained rather constant for a decade and then steeply increased from 2011 onwards Fig. . Genome-Genome-wide rates of change per year and per generation for the 1986–2015 period are shown in Table ars Fig. . In factRates of inbreeding and kinship were also computed for periods of 5 years, accounting for the change in els Fig. . In thisAccumulation of inbreeding across the genome was evaluated with ROH-based positional inbreeding coefficients . Correlation coefficients for any two consecutive periods were positive (ranging from 0.08 to 0.26), except for the transition from the 1996–2000 period to the 2001–2005 period (− 0.09).To evaluate the direction of allele frequencies over time, correlation coefficients between the ed Table . Except In this study, we evaluated genetic diversity across the genome of HF AI bulls from 1986 to 2015. An important objective was to investigate whether major changes in the Dutch-Flemish HF breeding program were accompanied by changes in diversity trends. We used genealogical, marker-by-marker and segment-based approaches to compare trends in expected IBD, IBS and realised IBD.Genome-wide rates of inbreeding and kinship and corresponding estimates of 9 to 127 , 40. A sountries .Genome-wide diversity trends showed two breakpoints. The first occurred around 2000, after which levels and rates of inbreeding and kinship temporarily dropped Figs.  and 5. TThe drop in inbreeding and kinship around 2000 followed a shift in breeding goal composition and the introduction of OCS. Although the Dutch-Flemish bull selection index has changed continuously over time, the major shift took place around 2000, when longevity, udder health and reproductive traits were added to the index within a few years’ time Table . The inculations , 40, altulations  suggesteThe steep increase in inbreeding and kinship rates around 2010 coincided with the implementation of GS. From the 2006–2010 period to the 2011–2015 period, there was a two- to four-fold increase in the annual rate of inbreeding. Rates per generation were also considerably higher since the implementation of GS, although the difference was less pronounced due to the decrease in ulations , 48. The of sibs .Estimates of inbreeding and kinship rates in real life HF GS schemes are still scarce. Rodríguez-Ramilo et al.  recentlyparately  indicate to 2012 , which iAn important factor that contributes to the accumulation of kinship in GS schemes is the relationship of selection candidates with the reference population. In GS, genomic EBV (GEBV) are computed from the effects of SNPs, which are estimated in a reference population of individuals with known genotypes and phenotypes . The accSince the implementation of GS, rates of marker-by-marker homozygosity and similarity have been considerably higher (0.7%) than segment-based rates, which in turn have been slightly higher 0.1–0.3%) than genealogical rates. The higher rate for IBS suggests that relatedness due to distant common ancestors is increasing relatively fast compared to relatedness caused by common ancestors in more recent generations. This could be due to the discordance between the way breeding values are estimated and the way diversity is managed. In the current Dutch-Flemish breeding program, breeding values are predicted with genomic BLUP (GBLUP) and are, thus, based on marker-by-marker similarities weighted by allele frequencies . However% than gen et al. , the genn et al. . Thus, cIn this study, genomic diversity was characterised with marker-by-marker IBS and segment-based IBD. Both measures have clear advantages and drawbacks with regard to management. The main advantage of using marker-by-marker IBS in OCS is that it is the most effective in conserving diversity , 55. Howt}HOMSNP , 20, 21.t}HOMSNP . Anotherterature , 60, 61,terature , 18, 20.Selection has played an important role in shaping genetic variation across the HF genome over time. Although the identification of selection footprints was not the primary objective of this study, the regions in Table A10 Fig. , which iOHk Fig. . This coountries , 62, 64.The important role of selection was also apparent from the fact that, in consecutive 5-year periods, allele frequencies changed more often in the same direction than in opposite directions Table . An exceSubstantial differences in }Δp Fig.  and in tmentclass2pt{minimmentclass2pt{minimod Table .An important question that should be raised is how heterogeneity in athogens  or to liathogens , 8. Thisathogens , 66. Altathogens , 68. To athogens . Thus, tathogens , 69.In general, genomic information offers many opportunities to manage genetic diversity and inbreeding more efficiently in the future .Additional file 2: Table S1. Number of QTL extracted from AnimalQTLdb per trait and trait category.Additional file 3: Fig. S2. Moving correlation (of 51 markers) between changes in allele frequency in the 1996–2000 and 2001–2005 periods.Additional file 4: Table S2. Genomic regions of ≥ 7 Mb with strong negative correlation (r ≤ − 0.6) between changes in allele frequency in the 1996–2000 and 2001–2005 periods, and fraction of QTL in these regions per trait category.