The objectives of the study were to evaluate reproductive performance and selection response through genetic trend of community-based breeding programs (CBBPs) of Bonga sheep.Reproduction traits data were collected between 2012 and 2018 from Bonga sheep CBBPs. Phenotypic performance was analyzed using the general linear model procedures of Statistical Analysis System. Genetic parameters were estimated by univariate animal model for age at first lambing (AFL) and repeatability models for lambing interval (LI), litter size (LS), and annual reproductive rate (ARR) traits using restricted maximum likelihood method of WOMBAT. For correlations bivariate animal model was used. Best model was chosen based on likelihood ratio test. The genetic trends were estimated by the weighted regression of the average breeding value of the animals on the year of birth/lambing.The overall least squares mean±standard error of AFL, LI, LS, and ARR were 375± 12.5, 284±9.9, 1.45±0.010, and 2.31±0.050, respectively. Direct heritability estimates for AFL, LI, LS, and ARR were 0.07±0.190, 0.06±0.120, 0.18±0.070, and 0.25±0.203, respectively. The low heritability for both AFL and LI showed that these traits respond little to selection programs but rather highly depend on animal management options. The annual genetic gains were −0.0281 days, −0.016 days, −0.0002 lambs and 0.0003 lambs for AFL, LI, LS, and ARR, respectively.Implications of the result to future improvement programs were improving management of animals, conservation of prolific flocks and out scaling the CBBP to get better results. The total sheep population in Ethiopia was estimated at 31.30 million with 9 breeds .The breeBonga sheep, one of the well-known and largest breed of Ethiopia, is characterized by long and wide fat tail with tapering and twisted end, both male and female are polled, short and smooth hair, mainly convex facial profile of male and predominantly light red coat color. The breed is known by its docile temperament, good fattening potential, fast growth and prolificacy .To improve productivity of local breeds, crossbreeding based on imported sires has been followed for many years though with little success . TherefoReproductive performances of sheep together with, survival and growth traits are important determinants of productivity . The breAs has been indicated above, Bonga CBBP started in 2009 and through the upscale program an additional 14 CBBP were established since 2012. Frequent updating the genetic parameter estimate through evaluation is important and an integral component of breeding program. Therefore, the objectives of this study were to evaluate the genetic trend for reproductive traits and to estimate genetic parameters which help for optimization of the programs.The study was conducted in four districts, namely Adiyo, Gesha, Shisho-Ende, and Tello, of Kaffa zone of Southern Nation Nationalities People Region, Ethiopia. The area is characterized by mixed crop-livestock production system. It has one major rainy season that extends from May to October and a dry season that lasts from October to April . The altAmong the 14 CBBPs, five  were established in 2012 while the remaining were during 2014. Selection of male lambs is being carried at two stages: screening of heavy weaners at weaning (3-month) followed by selection at six months of age (post weaning) by using their estimated breeding values (EBV). When the Bonga CBBP started, selection was carried out at six months. However, because of fast growth potential of the breed, it was noted that many lambs are sold before they reach the selection age. Therefore, the two-stage selection was implemented to keep the best ram lambs within the flock. Candidate lambs which had horn, short tail or black coat color were culled regardless of their EBVs.Flocks being indoors at night in pens made up of bamboo walls and by any locally available corrugated roofing materials whereas, some farmers kept their flock around homestead at night. Flocks were tethered especially adult male and females during crop cultivation period. Therefore, main feed resource was pasture but additionally crop residue and kitchen leftovers were used. Feed availability and abundance vary with rainfall patterns. Comparatively huge amount of feed was available in the rain season whereas feed was less in both quality and quantity during the dry season.Performance and pedigree data for this study were collected from the breeding database of out-scaled Bonga sheep CBBPs. The reproductive performance data used for this study included age at first lambing (AFL), lambing interval (LI), annual reproductive rate (ARR), and litter size (LS). Annual reproductive rate refers the number of young produced per breeding ewe female per year and it was calculated as: ARR = (365×LS)/LI. The detailed data structure and number of records for studied traits was indicated in First, the data were checked for pedigree structure using pedigree viewer then Proc Univariate in Statistical Analysis System (SAS)  was emplCo(variance) components, genetic parameters and breeding values (EBVs) were estimated by restricted maximum likelihood fitting an animal model using WOMBAT software . The folXb+Z1a+eModel 1: y = Xb+Z1a+Z3pe+eModel 2: y = Xb+Z1a+Z2m+e with Cov = 0Model 3: y = Xb+Z1a+Z2m+e with Cov = AσamModel 4: y = Xb+Z1a+Z2m+Z3pe+e with Cov = 0Model 5: y = Xb+Z1a+Z2m+Z3pe+e with Cov = AσamModel 6: y = X, Z1, Z2, and Z3 are the incidence matrices of fixed effect, direct additive genetic effect, maternal genetic effect and animal permanent environmental effect for LI, LS, and ARR but permanent environmental effect of the dam for AFL. A is the numerator relationship matrix between animals, and σam covariance between direct and maternal genetic effects. According to El Fadili et al [Where, y is n×1 vector of observations for each trait, b is a vector of fixed effects , a, m, pe, and e are vector of random effects for direct additive genetic effects, maternal additive genetic effects, animal permanent environmental effect and residual effects, respectively. li et al  the (co)a2, σm2, σpe2, σc2, σam, and σe2 are direct additive genetic variance, maternal additive genetic variance, animal permanent environmental variance, maternal permanent environmental variance, direct-maternal genetic covariance, and residual variance, respectively. Id and In are identity matrices of an order equal to the number of dams and the number of lambs, respectively.Where, σ2a) and additive maternal (h2m) heritability, ratio of animal permanent environmental variance with phenotypic variance (pe2) and ratio of maternal permanent environmental variance with phenotypic variance (c2) were calculated as ratios of estimates of additive direct (σa2), additive maternal (σm2), animal permanent environmental (σpe2), and maternal permanent environmental (σc2) variances to the phenotypic variance (σp2), respectively. Total heritability was calculated according to the following equation [Estimates of additive direct (hequation :am) was estimated as the ratio of the estimates of the σam to the product of the square roots of the estimates of σ2a and σ2m [The genetic correlation between direct and maternal genetic effects (r and σ2m .g) between traits were estimated as the ratio of the estimates of the genetic covariance between the traits 1 and 2 to the product of the square roots of the estimates of genetic variance for trait 1 and genetic variance for trait 2.The genetic correlation  was estimated according to Mokhtari et al :2a = additive genetic variance; σ2pe = animal permanent environmental variance σ2p = phenotypic variance.Where, σTo determine the most appropriate model likelihood ratio tests (LRT) was used. The significance of model comparison was done from univariate analysis of animal models with and without including the effects as a random effect and compared the final log-likelihoods (Maximum log L) by chi-square distribution for α = 0.05 with one degree of freedom . An effe2 statistic with degrees of freedom equal to (pf–pr). Where LRT = Log likelihood ratio test, L(x)f = maximum likelihood for full model, L(x)r = maximum likelihood for reduced model, Pf = number of parameter for full model, and Pr = number of parameter for reduced model. If the chi-square distribution value is significance at (p<0.05) the full model is best fit the data [The LRT was distributed as a χthe data .The overall least squares mean±standard error (SE) and coefficient of variation of AFL for Bonga ewes were 375±12.5 days and 19.8%, respectively . Age at The overall least squares mean±SE of LI of Bonga sheep was 284±9.9 days. It was influenced by lambing year, CBBP cooperative, dam parity and season of lambing (p<0.05), however, the influence of lambing type was non-significant . The LI The overall least squares mean±SE of Bonga sheep was 1.45±0.010 and the coefficient of variation was 36.62%. The percentages of twins and above were 40.13%. Litter size was significantly influenced by CBBP cooperative and dam parity (p<0.001) but non-significant for lambing year and lambing season . PerusalThe overall least squares mean± SE of ARR was 2.31±0.050 lambs/ewe/yr and the coefficient of variation was 38.84%. Annual reproductive rate was significantly affected by lambing year, CBBP cooperatives, dam parity and lambing season (p<0.01) . The resImportance of including both or one of each of additive maternal genetic or animal permanent environment effect on direct animal genetic effect was tested using LRT to determine the most appropriate model fitting the dataset . Inclusi2a) for AFL, LI, LS, and ARR, respectively. These values accounted for 6.57%, 6.38%, 16.66%, and 25% of the total variance indicating limited contribution of additive effect. The ratio of animal permanent environmental variance to phenotypic variance was higher for repeatable traits  which were 0.51, 0.37, and 40, respectively. This indicated that improving the animals’ environment would result an improvement of these traits. This permanent effect is an environmental effect that contributes permanently to individual’s phenotype and is constant across repeated measures and which is not transmitted to across generation. For example intrauterine environment stimuli may impact foetal development and this permanently affects phenotype performance later in life [The estimates of (co)variance components and resulting genetic parameters for reproductive traits along with estimated maximum likelihood values for six models for each trait are presented in  in life .Direct heritabilities from selected models for AFL, LI, LS, and ARR were 0.07±0.190, 0.06±0.120, 0.18±0.070, and 0.25±0.203, respectively. The heritability of LI and AFL  was low Bivariate analysis revealed negative genetic correlation (−0.66±0.03) between AFL and LS but positive for phenotypic correlation (0.03±0.052). This indicated that a fast growing ewe lamb has the ability to achieve a higher prolificacy rate. The higher the ovulation rate, the more oocytes will be available for fertilization during the estrous and therefore increases the possibility of a larger litter . CorrelaThe estimate of repeatability of LI, LS, and ARR was 0.57, 0.54, and 0.65, respectively, for Bonga sheep. High repeatability indicates that culling of animals based on performance in single or only few initially available records could be done. The result was much higher than Horro sheep for LS 0.12  and PeliGenetic trends of different reproductive traits in Bonga sheep  were estDifference in heritability estimates obtained from the different models suggests that model choice is an important aspect for obtaining reliable parameter estimates to be used in prediction of breeding values. Heritability estimates for age at first lambing and lambing interval were low indicating difficulty of improving these traits through direct selection because these traits are highly influenced by environment. Therefore, improvement of such traits could be made through manipulation of production management to reduce environmental influence. The possible reason for negative trend of litter size may be a greater emphasis for improving body weight and litter size being negatively correlated with body weight. Therefore, this trait needs special attention for either on-farm or on-station conservation for prolific flocks.


Large-scale phenotype data can enhance the power of genomic prediction in plant and animal breeding, as well as human genetics. However, the statistical foundation of multi-trait genomic prediction is based on the multivariate linear mixed effect model, a tool notorious for its fragility when applied to more than a handful of traits. We present MegaLMM, a statistical framework and associated software package for mixed model analyses of a virtually unlimited number of traits. Using three examples with real plant data, we show that MegaLMM can leverage thousands of traits at once to significantly improve genetic value prediction accuracy.The online version contains supplementary material available at (10.1186/s13059-021-02416-w). New high-throughput phenotyping technologies hold promise for a revolution in data-driven decisions in plant and animal breeding programs , 2. For However, efficiently incorporating high-dimensional phenotype data into breeding decisions is challenging. Whenever two traits are genetically correlated, joint analyses can improve the precision of variety evaluation . HoweverThe multivariate linear mixed model (MvLMM) is a widely-used statistical tool for decomposing phenotypic correlations into genetic and non-genetic components. The MvLMM is a multi-outcome generalization of the univariate linear mixed model (LMM) that forms the backbone of the majority of methods in quantitative genetics. The MvLMM was introduced over 40 years ago , and hasp>>n approach of genomic prediction methods–with algorithmic innovations recently developed for LMMs. In the three examples below, we demonstrate that our algorithm maintains high predictive accuracy for tens-of-thousands of traits, and dramatically improves the prediction of genetic values over existing methods when applied to data from real breeding programs.Here, we describe MegaLMM (linear mixed models for millions of observations), a novel statistical method and computational algorithm for fitting massive-scale MvLMMs to large-scale phenotypic datasets. Although we focus on plant breeding applications for concreteness, our method can be broadly applied wherever multi-trait linear mixed models are used . MegaLMM dramatically improves upon existing methods that fit low-rank MvLMMs, allowing multiple random effects and un-balanced study designs with large amounts of missing data. We achieve both scalability and statistical robustness by combining strong, but biologically motivated, Bayesian priors for statistical regularization–analogous to the n genotypes and t traits /2+t free parameters, and any direct estimation approach is computationally demanding because it requires repeatedly inverting these matrices (an MegaLMM fits a full multi-trait linear mixed model (MvLMM) to a matrix of phenotypic observations for K un-observed (latent) traits called factors (fk) to represent the causes of covariance among the t observed traits. We treat each latent trait just as we would any directly measured trait and decompose its variation into the same fixed, random and residual components using a set of parallel univariate linear mixed models  to avoid over-fitting covariances, and ii) shrinkage on the factor sizes to avoid including too many latent traits. This two-dimensional regularization helps the model focus only on the strongest, most relevant signals in the data.Together, the set of parallel univariate LMMs and the set of factor loading vectors result in a novel and very general re-parameterization of the MvLMM framework as a mixed-effect factor model. This parameterization leads to dramatic computational performance gains by avoiding all large matrix inversions. It also serves as a scaffold for eliciting Bayesian priors that are intuitive and provide powerful regularization which is necessary for robust performance with limited data. Our default prior distributions encourage: i) shrinkage on the factor-trait correlations , the, the18])We combine this efficient factor model structure with algorithmic innovations that greatly enhance computational efficiency, drawing upon recent work in LMMs –22. WhilGenomic prediction using MegaLMM works by fitting the model to a partially observed trait matrix, with the traits to be predicted imputed as missing data. MegaLMM then estimates genetic values for all traits (both observed and missing) in a single step Fig. B.Arabidopsis thaliana accessions , to evaluate the accuracy and time requirements for trait-assisted genomic prediction–a classic example of an applied use of MvLMMs–across a panel of existing software packages. We created datasets with 4 to 20,842 “secondary” traits with complete data, and used these data to predict the genetic values of a single randomly selected “focal” gene with 50% missing data.We used a gene expression matrix with 20,843 genes measured in each of 665 Despite the limited number of independent lines in this data set, adding up to ≈200 secondary traits improved the genomic prediction accuracy of MegaLMM and two other Bayesian methods: MCMCglmm and phenix , as long as enough factors are specified to capture the majority of the covariance among traits, adding additional latent factors does not lead to over-fitting  with a kernel based on the cross-product of hyperspectral reflectances across all wavelengths and time points (termed the H matrix). We replicated these results, achieving a prediction accuracy of ρg=0.58 (HBLUP method). These authors also proposed a multi-kernel model combining the K and H kernel matrices, although they only applied this to cross-treatment genotype-by-environment predictions. We found that applying this multi-kernel method to the within-environment data resulted in additional accuracy gains (ρg=0.64) . Second, because the RKHS model had the highest performance among univariate predictions, we implemented an approximate RKHS method in MegaLMM based on averaging over three kernel matrices )While MegaLMM works well across a wide range of applications in breeding programs, our approach does have some limitations.on the fly using efficient routines for low-rank Cholesky updates. We also do not currently suggest including regressions directly on markers and have used marker-based kinship matrices here instead for computational efficiency. Therefore as a stand-alone prediction method, MegaLMM requires calculations involving the Schur complement of the joint kinship matrix of the testing and training individuals which can be computationally costly.First, since MegaLMM is built on the Grid-LMM framework for efficient likelihood calculations , it doesSecond, MegaLMM is inherently a linear model and cannot effectively model trait relationships that are non-linear. Some non-linear relationships between predictor variables (like genotypes) and traits can be modeled through non-linear kernel matrices, as we demonstrated with the RKHS application to the Bread Wheat data. However, allowing non-linear relationships among traits is currently beyond the capacity of our software and modeling approach. Extending our mixed effect model on the low-dimensional latent factor space to a non-linear modeling structure like a neural network may be an exciting area for future research. Also, some sets of traits may not have low-rank correlation structures that are well-approximated by a factor model. For example, certain auto-regressive dependence structures are low-rank but cannot efficiently be decomposed into a discrete set of factors.Nevertheless, we believe that in its current form, MegaLMM will be useful to a wide range of researchers in quantitative genetics and plant breeding.Beyond the examples we show in this work, the scalability and statistical power of MegaLMM can open up new avenues for innovation in genomic prediction applications across the fields of quantitative genetics–both in breeding programs as we have described here and, potentially, in human genetics. Genomic prediction is also used for the calculation of polygenic risk scores for complex human traits and diseases . MegaLMMWe have focused here on simple scalar phenotypes: the expression of a single gene, the total grain yield, and individual measures of agronomic performance. However, many important traits in plants, animals, and humans cannot easily be reduced to a scalar value. Examples include time-series traits such as growth curves , metabolBR2 and BF2 by adapting the prior structure. This will be further explored in future manuscripts.MegaLMM should be straightforward to extend to more flexible genetic models including the Bayesian Alphabet family of mixture priors on marker effect sizes. These effects can be incorporated into the parameters Lastly, we have only focused on Gaussian MvLMMs, in which observations are assumed to marginally follow a Gaussian distribution. However, many other types of data require more flexible models. It should be possible to extend MegaLMM to the broader family of generalized LMMs. These approaches model the relationships among predictor variables in a latent space, which is then related to the observed data through a link function and an exponential family error distribution. More generally, link-functions could be any non-linear function of multiple parameters such as a polynomial or spline basis, or a mechanistic model. In this case, we would model the correlations among model parameters on this link-scale and then use the link-function to relate the latent scale variables to the observed data. Extending MegaLMM to accommodate such generalized LMM structures would require new sampling steps in our MCMC algorithm (see Methods), but we do not see any conceptual challenges with this approach.MegaLMM is a flexible and powerful framework for the analysis of very high-dimensional datasets in genetics. Multivariate linear mixed models are widely used for analyzing correlated traits, but have been limited to a maximum of a dozen or so traits at a time by the curse of dimensionality. We developed a novel re-parameterization of the MvLMM that allows powerful statistical regularization and efficient computation with thousands of traits. When applied to real plant breeding objectives, MegaLMM efficiently leverages information across traits to improve genetic value predictions. Our open-source software package will enable users to apply and extend this method in many directions, opening up new areas of research and development in breeding programs.n×t matrix Y represent observations on t traits for n observational units . A general MvLMM takes on the following form Multivariate linear mixed models (MvLMMs) are widely used to model multiple sources of covariance among related observations. Let the X is a n×b matrix of “fixed” effect covariates with effect sizes matrix B,U is an r×t matrix of random effects for each of the t traits, with corresponding random effect design matrix Z, and E is a n×t matrix of residuals for each of the t traits.where X and Z, and different priors on B,U and E. The distinction between “fixed” and “random” effects in Bayesian mixed models is not well-defined because every parameter requires a prior. However, we use the following distinction here: “fixed” effects are covariates assigned flat  priors or priors with independent variances on each coefficient; “random” effects, in contrast, are grouped in sets that can be thought of as (possibly correlated) samples from a common population distribution. Generally, “fixed” effects are used to model experimental design terms such as blocks, time, sex, etc, genetic principal components, or specific genetic markers; while “random” effects are used to model genetic values, spatial variation, or related effects.MegaLMM uses this formulation to accommodate a large number of designs through different specifications of An important feature of MegaLMM is that multiple random effect terms can be included in the model. We specify this as Zm is an n×rm design matrix for a set of related parameters with corresponding coefficient matrix Um. For example, U1 may model additive genetic values for each individual, while U2 may model spatial environmental effects for each individual. The distribution of each random effect coefficient matrix is M, among-row covariance Km and among-column  covariance Gm. We assume that both Zm and Km are known, while Gm is unknown and must be learned from the data. Note that Km must be positive semi-definite, while Gm is positive-definite. The covariance among different coefficient matrices is assumed to be zero.where each In is the n×n identity matrix and R is an unknown t×t positive-definite covariance matrix.To complete the specification of the MvLMM, we assign the residual matrix the distribution U and E are correlated. This means that data from individual traits (columns of Y) cannot be treated independently. Maximum-likelihood approaches for fitting MvLMMs  compute the full (or restricted) likelihood of Y, which involves calculating the inverse of an nt×nt matrix many times during model optimization. This is computationally prohibitive when n and/or t are large  when t is large. This means that Gm and R are not identifiable in many datasets and estimates require strong regularization.Fitting Eq.  is challe.g., MTG compute Gm and R were diagonal matrices, the t traits would be uncorrelated. Fitting Eq.  to be correlated due to the shared dependence on Λ, this is not necessarily the case. When any diagonal element of any ΨFx matrix is set to zero, the corresponding row of Λ does not contribute to that term. If at least t linearly independent rows of Λ contribute to each matrix, then any set of positive-definite matrices can be represented as above. Therefore, we can represent any set of positive-definite matrices Gm and R with our model as long as K>=t(M+1).Although these equations appear to imply that our mixed effect factor model constrains Λ for multiple covariance matrices, we can save parameters in the model. From a biological perspective, shared factors provide a biologically realistic explanation for correlations among traits. If we consider the columns of F to be K traits that simply have not been observed, then it is reasonable to propose that each of these traits is regulated by the same sources of genetic and environmental variation as any of the observed traits.Of course, the reason that we parameterize our model in this way is that we do expect some correlation among the genetic and residual covariance matrices. From a statistical perspective, when it is reasonable (given the data) to use the same row of K latent traits (F) are the key drivers of all phenotypic co-variation among the t observed traits (Y). These latent traits may not account for all variation in the observed traits. But, by definition, this residual variation  is unique to each trait and uncorrelated with the residual variation in other traits.In Eq. , the K lΛ.The intuitive structure of the mixed effect factor model , and compatibility with efficient computational approaches. For the variance components, we use the non-parametric discrete prior on variance proportions we previously introduced in GridLMM  that appWe use a carefully constructed MCMC algorithm to draw samples from the posterior distribution of each model parameter. We gain efficiency in both per-iteration computational time and in effective samples per iteration through careful uses of diagonalization, sparse matrix algebra, parallelization, and integration . In particular, our algorithm synthesizes and extends several recent innovations in computational approaches to linear mixed models , 22, 57.We demonstrate MegaLMM using three example datasets.Arabidopsis thaliana accessions. We downloaded the data from NCBI GEO  and andArabiNCBI GEO . We down project  and subst=2 to t=24,175 genes by randomly sampling. We selected one gene as the “focal” trait in each dataset, masked 50% of its values, fit the model in Eq. , we rotated the input data by pre-multiplying by the eigenvectors of K so that the input relationship matrix was diagonal. Since this matrix rotation is only possible with complete data, we again used the two-step multi-trait prediction approach . We. We64]. K calculated with the A.mat function of rrBLUP as in [GBLUP: implemented using the R package rrBLUP , with thUP as in .Bayesian Lasso (BL): implemented using the R package BGLR [% missing data, and imputed the remaining missing genotypes with the population mean allele frequency. We used the default prior parameters for the Bayesian Lasso in BGLR, and collected 9,000 posterior samples with a thinning rate of 5 after a 5,000 iteration burnin.age BGLR . We firsD). We also used the default theta.seq parameter to automatically choose the scale parameter of the Gaussian kernel.RKHS: implemented using rrBLUP. We used the same thinned and imputed genotype dataset as for the BL method to calculate a genomic distance matrix . We ran MegaLMM with K=100 factors, “default” priors  at a thinning rate of 2, discarding the first 1,000 iterations as burn-in.MegaLMM-GBLUP: we modeled the combined trait data d in Eq.  using a D based on its mean (squared) value, and placed a uniform prior on the set of scaling factors h={1/5,1,5}, which we implemented by calculating three corresponding relationship matrices K1,…,K3 and by specifying three random effects in Eq.  at a thinning rate of 2, discarding the first 1000 iterations as burn-in.MegaLMM-RKHS: we implemented multi-trait RKHS regression model using the “kernel-averaging” method proposed by . We stans in Eq. . We agaiMegaLMM-GBLUP-CV1: we repeated the MegaLMM-GBLUP method above, but this time without partitioning the trait data. Instead, we masked both the grain yield and the 620 hyperspectral band data from the testing set so all lines in the training data had complete data. Predictions of the genetic values were calculated identically to above.We compared eight methods for predicting the GY trait based on the genetic marker and hyperspectral data. The first five were “standard” methods using state-of-the-art models for genomic prediction. The final three were new models implemented within the MegaLMM framework. g could be estimated accurately in the testing partition. This cross-validation algorithm was repeated 20 times with different random partitions.We used cross-validation to evaluate the prediction accuracy of each method. We randomly selected 50% of the lines for model training, 50% for testing, and masked the GY observations for the testing lines. We fit each model to the partially-masked dataset and collected the predictions of GY for the testing lines. We estimated prediction accuracy as g traits . BLUPs wWe used data on maize hybrids from the Genomes-To-Fields Initiative experiments to demonstrate how MegaLMM can leverage genetic correlations across locations in multi-environment trials. We downloaded the agronomic data from the 2014-2017 field seasons from the CyVerse data repository  and corr% of hybrid-site-year combinations were observed across each of the four BLUP matrices. We then used four methods to predict the BLUPs of hybrids that were not grown in each trial: GBLUP (univariate): missing values were imputed separately for each site:year using the mixed.solve function of the rrBLUP package.GBLUP (env BLUPs): genetic values for each hybrid were assumed to be constant across all site-years. We estimated these in two steps. In the first step, we estimated hybrid main effects treating lines as independent random effects using lme4, with site:year included as a fixed effect. In the second step, we estimated genetic values using the mixed.solve function of the rrBLUP package.Y using K as a relationship matrix.phenix: we used phenix to impute missing observations in Y, with K=50 factors and “default”. Here, we partitioned Y into 4 sets based on year to minimize the number of missing observations to condition on during the MCMC. We collected 1000 posterior samples of imputed values MegaLMM: we fit the model specified in Eq.  to the fA total of 2012 non-check hybrids with phenotype and genotype data from 108 trials  were available. We selected four representative agronomic traits: plant height (cm), grain yield (bushels/acre), days-to-silking (days), and the anthesis-silking interval . For each trait in each site-year, we calculated BLUPs for all observed genotypes using the R package lme4  with RepWe estimated prediction accuracy of each method using cross-validation. For each of 20 replicate cross-validation runs per model, we randomly masked 20% of the non-missing BLUPs, and then calculated the Pearson’s correlation between these “observed” values and the imputed values of each method. Pearson’s correlation is appropriate as an estimate of genomic prediction accuracy in this case because different plants were used in each trial, so there is no non-genetic source of correlation among site-years that may bias accuracy estimates.Additional file 1Supplemntary Methods. Expanded description of the prior distributions and derivation of the MCMC algorithm used in MegaLMM [Figure S1. Prediction accuracies for each target gene expression trait relative to MegaLMM. Figure S2. Prediction accuracies for each target gene expression trait as a function of dataset size. Figure S3. Accuracy of covariance estimates in simulated data. Figure S4. Sensitivity of MegaLMM to changes in K. Figure S5. Performance of single-trait and multi-trait genomic prediction for wheat yield across 20 experiments. Figure S6. Relationship between genetic correlation and benefit of MvLMM across Genomes2Fields site-years. Table S1. Default hyperparameters for user-customizable prior distributions. MegaLMM –76. FiguAdditional file 2 Review history.


Rosette morphology across Arabidopsis accessions exhibits considerable variation. Here we report a high-throughput phenotyping approach based on automatic image analysis to quantify rosette shape and dissect the underlying genetic architecture. Shape measurements of the rosettes in a core set of Recombinant Inbred Lines from an advanced mapping population (Multiparent Advanced Generation Inter-Cross or MAGIC) derived from inter-crossing 19 natural accessions. Image acquisition and analysis was scaled to extract geometric descriptors from time stamped images of growing rosettes. Shape analyses revealed heritable morphological variation at early juvenile stages and QTL mapping resulted in over 116 chromosomal regions associated with trait variation within the population. Many QTL linked to variation in shape were located near genes related to hormonal signalling and signal transduction pathways while others are involved in shade avoidance and transition to flowering. Our results suggest rosette shape arises from modular integration of sub-organ morphologies and can be considered a functional trait subjected to selective pressures of subsequent morphological traits. On an applied aspect, QTLs found will be candidates for further research on plant architecture. Understanding the role of environmental conditions on plant development is of increasing importance to counterbalance climate change effects in agricultural species . NaturalRosettes display limited internode extension and generally are comprised of a spiral of leaves, overlapping to a greater or lesser extent . This leShape is a ubiquitous concept in biological research with context dependant morphometrical methodologies , 17. OutHigh dimensional vectors of descriptors need multivariate statistics to discriminate shapes numerically. Particularly, Principal Component Analysis (PCA) , 36 builTo interrogate shape and size variation over populations large enough to reveal associations with the underlying genetics requires measurement techniques that are scalable. Imaging techniques are readily scalable and have been widely used to measure growth rate , 54, 55,QTL mapping experiments leverages the phenotypic variation associated with the standing genetic variation. Biparental crosses estimate linkage between markers , 71 and Advanced mapping populations, like Multiparent Advanced Generation Inter-Cross (MAGIC) , trade tThe use of highly diverse natural accessions increases the opportunity to find trait-associated markers that may not be available in laboratory experimental populations. In particular, the wild-type ecotypes phenotyped in  are the Here, we report machine-assisted acquisition of time-stamped images from MAGIC RILs during their rosette development and we extract a range of morphology descriptors for rosette size and shape variation. We continue the work of  and extePhenotyping was performed on a core set of 485 RILs (3 replicates of each) from the MAGIC population , 97. SeeExperiments were performed in greenhouse chambers at the National Plant Phenomics Centre (NPPC) at IBERS, Aberystwyth University, UK. Seedlings were vernalized for 28 days at 5°C and 8h light/16h darkness cycle. This ensured that all genotypes germinated and flowered within the time course of the experiment.-2 s-1). Plants were imaged, weighed and watered to a predefined target weight of 65% of field capacity, daily, until most plants had flowered.Single seedlings were pricked out into 6 cm diameter pots  and were transferred after 7 days to PlantScreen Phenotyping System  and grown under controlled conditions  was calcor and cor.test from the package stats [H2) was calculated independently at each DAS for all shape descriptors to estimate the proportion of the phenotypic variance explained by genetic variation. Variance decomposition random-effect models were fitted (function lme from the package nlme [ij) as dependent variable, RIL (Ri with I as line number) as a random factor and random residuals (εij) for each replicate plant j as ijP = μ+iR+ijϵ [varcomp from the ape package [H2) for each descriptor was estimated as Vg is the variance among the RILs and Ve is the environmental variance. The general workflow for the data analysis is summarized in Pairwise Pearson’s correlation across descriptors’ averages were calculated at each DAS (function ge stats ). Broad-age nlme ) with phμ+Ri+ϵij . Varianc package . Broad-shappy.hbrem R package. This software was specifically designed for multi-parental population analysis [happy) working out the Identity By Descent (IBD) using a Hidden Markov Model [hbrem) model [hbrem procedure) within an interval where other SNPs pass the genome-wide P-value (from the resampling procedure). A boxplot with allelic phenotypic effect for each founder ecotype was calculated using the hbrem procedure.Each shape descriptor (9 variables) and principal component (9 PCs) were split by DAS and used as input for QTL mapping with the analysis  and prevanalysis . RILs geov Model . For eacm) model  with 19 m) model , 102. Fihttps://github.com/tavareshugo/MagicHelpR). The closest gene to the QTL marker was identified and gene annotations were retrieved from ARAPORT11 [The amount of phenotypic variation explained by each marker was estimated using the package MagicHelpR  increasing daily between 25–35% up to an average of 1180 ± 400 mm2. RIL PRA variation had a min-max range of 385 mm2 at 35 DAS and 2239 mm2 at 44 DAS. Perimeter Length (PL) varied between 15 and 204 mm (mean ± sd: 78 ± 31mm) at 35 DAS increasing to a min-max range between 57 and 694 mm (mean ± sd: 353 ± 95 mm). The PRA-PL correlation  with a similar range afterwards . Compactness correlated negatively with PRA (-48.34% at 35 DAS) changing towards a slight positive correlation (3% at 41 DAS and 27.02% at 44 DAS). Compactness correlated negatively with PL (-65% at 35 DAS moving towards -36% at 44 DAS) .ECC values vary from 0 (a circle) to 1 (a line). At 35 DAS, the rosettes had a range of values between 0.14 and 0.77 (mean ± sd: 0.34 ±0.09) decaying to a min-max between 0.08 and 0.30 (0.16 ± 0.03). ECC correlated negatively with PRA (around 50% on most DAS) and weakly with PL (between -16 and -54%). The correlation between ECC and compactness fluctuated between -32% and +15%. Eccentricity also correlated strongly with Rotational Mass Symmetry (RMS), over 80% between 35 and 38 DAS diminishing towards 60% at 44 DAS and 6% at 42 DAS. Correlation between ECC and roundness convex hull (RCH) was below -80% at all days except -74% at 40 DAS .RMS  is also valued between 0 and 1. A value of 1 means an irregular rosette, either because it is eccentric or it is non-homogeneous. Small values of RMS indicate circular and high-coverage rosettes. RMS had values between 0.32 and 0.93 at 35 DAS (mean ± sd: 0.75 ± 0.1). RMS fluctuated with ample variation along days (min-max range around 0.70) between 0.12 and 0.77 at 44 DAS (mean ± sd: 0.42±0.10) .RCH had low variation across time, with minimum values between 0.70–0.80 at all DAS and maximum values of between 0.92–0.97 with a dynamic range between 0.10 and 0.20. The correlation between RCH and RMS peaked at -66% at 35 DAS and increased towards -22% at 40 DAS and decreased again to -40% at 44 DAS .RND values are between 0, circular rosettes, and 1 asymmetric ones. Rosettes RND ranged between 0.09–0.59 at 35 DAS, decreasing to 0.04–0.38 (mean ± sd: 0.22 ± 0.07 at 35 DAS to 0.13 ± 0.05 at 44 DAS). RND was negatively correlated with PL (below -70%) and with Slender of leaves (SOL) (-77.5% at 35 DAE) decreasing through time (-47% at 44 DAS) .SOL had an unbounded dynamic range from 0 to 289 (in our rosette set). SOL minimum rose from 1.93 at 35 DAS to 4.24 at 44 DAS, and maximum also increased from 21 to 243. SOL had a strong positive correlation with PRA, around 78% at 35 and 36 DAS decreasing to 41% at 44 DAS .RND (50% to 61% from 38 DAS onwards) and negatively with PL (-51% to -67% between 38 DAS and 44 DAS) (Isotropy (ISO) was weakly but positively correlated with  44 DAS) .Heritability values , S2 Fig Principal component analysis , S3 Fig A Bayesian multipoint QTL mapping , 91 was Redundant associations  were filtered out. Most QTLs were found either in the first 4 or in the last 3 DAS . For shaQTL tended to cluster on chromosome 2 at all DAS and mostly for compactness, RND and PL descriptors . QTL at QTL on Chromosome 2  were disThe marker MASC05920 was found in this region with maximum significance level (-log(P) between 10 and 15 according to date and descriptor) found for Compactness, RND and PC2  Tables. log(P) = 12.1) (log(P) = 4.2). This marker is located within the PHYB gene (AT2G18790) encoding for the PHYTOCHROME B gene  . It was  = 12.1) . A QTL oE B gene , a photoE B gene .CPR-5), involved in plant defence (systemic acquired resistance—SAR). Four QTL were found in chromosome 4 associated with RND (AtTIPSY1).Other relevant QTLs were found spread over the other chromosomes. A QTL on chromosome 5 (marker MN5_25963543) explained 8% of the phenotypic variation for RND and Compactness at 44 DAS . Its clowith RND . Three oPlant development occurs throughout the individual lifetime –110 and Extending the strategy previously used to describe shape variation of the 19 parental accessions in , we haveThe MAGIC population has been previously characterised for flowering time, height and fitness , 118 witOur results support the idea that variation in rosette growth and shape involves multiple genes in a hierarchical control. This genetic structure should be able to exploit variable environmental conditions , 120, reShape descriptors were correlated, suggesting ecologically related trait syndromes . TherefoSignificantly associated markers were found using a dynamic QTL approach with a full combination of shape traits and DAS. This method yields up to 180 variables to test, thus increase the analytic effort with respect to single time point and single variable approaches, yet also increase the number of QTLs that would otherwise not be found using these other common strategies, e.g. phenotyping rosette size at the six leaves stage.cpr5 mutants in response to light and altered salicylic acid levels [AtTIPSY1) [The markers found at chromosome 2 form a region with several potential genes related to rosette morphology. A first example is the GPA-1 gene. In yeast, the GPA gene is related to signal transduction in pheromone response pathway . In Arabd levels , 136. AntTIPSY1) .GPA-1 (AT2G26300), a protein kinase receptor like ERECTA (AT2G26330), transcription factors like, PHYTOCHROME RAPIDLY REGULATED1 , or chromo proteins like PHYB (AT2G18790) and hemoproteins, like HO2 (AT2G26550), participating on photomorphology and shade avoidance responses, by regulation of an auxin-responsive gene [Overall, from the 116 markers significantly associated with the rosette shape descriptors, most are located within loci with known or suspected regulatory functions . These wive gene  and simiA. thaliana rosette. Rosette leaf shape varies along the ontogenetic development according to their local environment [This study focuses on the global shape of an organ assemblage, the ironment , 139, e.ironment . Thus, rironment –142. Ourironment , 143. Thironment –147. In ironment  with parironment , 150. FrS1 FigEach line represents a RIL. Bold lines remark 8 random RILS.(TIFF)Click here for additional data file.S2 Fig(TIFF)Click here for additional data file.S3 FigPC1 vs PC2 coloured by DAS .(TIFF)Click here for additional data file.S4 FigIn red ERECTA and PHYB markers. Number in parenthesis besides each marker means the number of times the same marker was identified for all descriptors across time.(TIFF)Click here for additional data file.S5 FigFour QTLs on chromosome 2 at 39, 42 and 43 DAS are shown for roundness, and one QTL for on chromosome 2 at 39 DAS is shown for compactness.(TIFF)Click here for additional data file.S1 TableGrey background cells indicate values between -50% and 50% and red coloured values indicate negative correlations.(XLSX)Click here for additional data file.S2 TableGrey background cells indicate values between -0.5 and 0.5 and red coloured values indicate negative loadings.(XLSX)Click here for additional data file.S3 Tablep-value, percentage of variation.Including the region position of the QTL, the position of the SNP peak, the significance, (XLSX)Click here for additional data file.S4 Tablep-value, percentage of variation.Including the region position of the QTL, the position of the SNP peak, the significance, (XLSX)Click here for additional data file.S5 TableIt contains the closest gene to every SNP peak, its gene annotation, position and the count of combinations DAS and descriptor for which the SNP peak was significantly associated to the marker each gene accession is the closest.(XLSX)Click here for additional data file.S1 DataThree replicates per RIL were phenotyped for the 9 shape descriptors at (XLSX)Click here for additional data file.


Recent years have seen a push for the integration of modern genomic methodologies with sociological inquiry. The inclusion of genomic approaches promises to help address long-standing issues in sociology , as well as open up new avenues for future research. This article reviews the substantive findings of behavior genetic/genomic research, both from the recent past  and from contemporary genomic analyses. The article primarily focuses on modern genomic methods available to sociologists  and their various applications for answering sociological questions. The article concludes by considering a number of areas to which genomic researchers and sociologists should pay close attention if a consilience between genomic methods and sociological research is to be fully realized. Social scientists have long been interested in understanding what role biology plays in human social traits and behaviors. With the completion of the Human Genome Project at the turn of the twenty-first century and the subsequent advent of genome-wide data and methods, researchers are addressing this question in unprecedented ways. Genome-wide analyses, and particularly the polygenic score (PGS) analysis, have already made significant contributions in the health and life sciences such as medicine and epidemiology, and even the social sciences such as psychology and economics. The use of genomic methods in sociology, albeit growing, has not yet been fully realized. In other words, we agree with Conley and Fletcher , p. 11 tThe purpose of this article is to review the past and current findings that have bearing on sociogenomics work. We will also offer thoughts and predictions about the future direction(s) of sociogenomics research. Thus, this article begins by providing a brief description of the behavior genetic research that preceded sociogenomics, beginning with twin/adoption studies and candidate gene studies. The bulk of the paper will focus on the contemporary era and, in particular, on genome-wide association (GWA) and PGS studies, with special focus turned toward the substantive findings and possible uses of these methods in sociological research. We will then conclude by considering some of the current and future issues that sociogenomics research will need to address in the coming years.Consilience  was explained by genetic influences including characteristics such as temperament and conduct disorder. Furthermore, Polderman et al. , and instead sought to answer the deeper questions of which genes and why—known as the “mechanism elucidation” approach  were associated with the behavioral outcome of interest.Toward the end of the first era of behavior genetic research, scholars aimed to go beyond simply addressing  Tabery, . The secMAOA gene and childhood maltreatment on antisocial behavior in adulthood. In the second study  the possession of genetic risk and (2) exposure to environmental stressors in order for them to manifest.Of particular interest is the phenomenon of gene-environment (G × E) interaction. Simply put, a G × E interaction suggests the effect of the environment depends on genes or, the reverse, that the effect of genes depends on the environment  and other medically-relevant physical traits like body mass index and height. Only a short time later, however, researchers were able to conduct GWA studies on complex traits that were of interest to social scientists. Some recent GWA studies have examined traits such as intelligence  approach has emerged as a useful tool in research of complex social traits and behaviors  interactions. It is useful to think of G × E interactions as functioning two ways. First, genes may be thought of as moderators of environmental associations, wherein the effects of an environmental exposure are conditional upon an individual's genetic makeup. For example, Guo et al.  hypothesA second way to view G × E interactions is to think of environmental exposures moderating the effects of genetic propensities on later outcomes. Schmitz and Conley , for exarGE) has increasingly drawn the attention of social scientists. A rGE occurs when an individual's environmental exposure depends on his/her genotype  can be estimated. This method has also been used to estimate the genomic contribution to human height  can be estimated from both twin/adoption models and genomic methods; however, family-based trait heritabilities have often dwarfed those estimated from genomic data. For example, family-based heritability of height  has been estimated to be as high as 0.80 , while SNP heritability estimates have, until recently, only been estimated at less than half that level  are largely limited to individuals with European ancestry due to an evolutionary phenomenon known as population stratification. Population stratification occurs when systematic differences in allele frequencies  exist between two subgroups within a larger population. These systematic differences between groups can be used to identify an individual's genetic ancestry; however, if a particular phenotype also breaks along ancestral lines , population stratification can lead researchers to assume that these systematic differences are causally related to the phenotype itself  genome-wide data on none-European populations is rare  ignoring numerous segments of the population. These limitations suggest that genomic methodologies may produce a new form of inequality  between groups of different ancestry in the population . As with most regression-based models, GWA studies are designed to discover SNPs that are associated with the mean level of a phenotype; vQTLs, on the contrary, are SNPs that are associated with the variance in a phenotype's expression. Although identifying variance effects across the genome has proven difficult , and one of the most exciting findings to emerge from modern genomics research is that the epigenome is responsive to the environment  of the promoter region of the 5-HTT candidate gene and that this gene was linked to later depression risk. Taken together, these studies suggest there may be something to the idea that our social environments can indeed get under our skin and impact human behavior in ways that challenge the traditional view that biological and social factors can be considered separate spheres of influence. But low statistical power may be a concern.Nonetheless, there several studies that have drawn on epigenetic data in social science research. One such study was conducted by Beach et al. . Using ai et al.  relied oAlso, more recent evidence complicates this narrative by drawing attention to several practical and methodological challenges. Sugden et al.  uncovereN = 2,232). This research team tested for an association between personal victimization experiences and epigenetic markers. They conducted an epigenome-wide analysis (EWA) that attempted to differentiate participants who had experienced victimization and those who had not. If the idea that our environments can become “embedded” and “get under our skin” is right, then we should expect to see epigenetic markers for extremely stressful environmental exposures like victimization. But their analysis failed to identify any epigenetic markers among victims. Marzi et al. (Finally, a similar word of caution was expressed by another group of researchers (Marzi et al., i et al. , p. 517 Consilience, E.O. Wilson envisioned a unification of all branches of knowledge including biology, the humanities, and the social sciences. Likewise, our object in this paper has been the consilience of modern genomic research with the discipline of sociology. Sociogenomics research has experienced its own “jumping together”—the literal meaning of “consilience”—of its two historical approaches perspectives: variance partitioning and mechanism elucidation (Tabery, In his book,  Tabery, . Modern  Tabery, , p. 12, HL, JB, and PT designed the paper. PT, RM, RK, JB, and HL wrote the paper.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.