Besides, compared to LDpred that makes use of LD information, EB-PRS also achieved 37.9%, 33.6%, 8.6%, 36.2%, 40.6% and 10.8% relative improvements. We note that our method is not the first method leveraging effect size distributions. Here we first justify our method by presenting theoretical optimal property over existing methods in this class of methods, and substantiate our theoretical result with extensive simulation results. The R-package EBPRS that implements our method is available on CRAN.Genetic risk prediction is an important problem in human genetics, and accurate prediction can facilitate disease prevention and treatment. Calculating polygenic risk score (PRS) has become widely used due to its simplicity and effectiveness, where only summary statistics from genome-wide association studies are needed in the standard method. Recently, several methods have been proposed to improve standard PRS by utilizing external information, such as linkage disequilibrium and functional annotations. In this paper, we introduce EB-PRS, a novel method that leverages information for effect sizes across all the markers to improve prediction accuracy. Compared to most existing genetic risk prediction methods, our method does not need to tune parameters nor external information. Real data applications on six diseases, including asthma, breast cancer, celiac disease, Crohn’s disease, Parkinson’s disease and type 2 diabetes show that EB-PRS achieved 307.1%, 42.8%, 25.5%, 3.1%, 74.3% and 49.6% relative improvements in terms of predictive  Genetic risk prediction is of considerable importance in human genetics. Calculating polygenic risk score (PRS) is the most commonly used approach due to its simplicity as well as the computational efficiency. Many PRS calculation methods have been proposed for accurate prediction by borrowing information from external panels or datasets. Here, instead of external information, we propose a novel PRS method leveraging internal information, namely the effect size distributions, to improve prediction accuracy. Neither parameter tuning nor external information is needed for our method. Extensive simulations and real data applications demonstrate that our method has substantial improvement over existing methods in terms of prediction accuracy. The onset of common diseases results from the combined effects of genetic and environmental factors. The initial objective of genome-wide association studies (GWAS) is to identify genetic variants, such as single nucleotide polymorphisms (SNPs), that are associated with human diseases. In the past decade, GWAS have identified tens of thousands of genetic associations . These ip-value thresholding. The observed effect sizes of selected SNPs, which can be directly extracted from summary statistics, are used as weights. Hence, only GWAS summary statistics are needed to calculate PRS, which is attractive since summary statistics are more accessible than individual-level genotype data due to potential privacy and data sharing concerns. In the following, we only focus on the PRS methods utilizing GWAS summary statistics.Calculating polygenic risk score (PRS) is a common genetic risk prediction approach because of its simplicity and computational efficiency. PRS sums the number of risk alleles among a set of SNPs, weighted by their effect sizes estimated from a certain cohort. We can regard PRS as the estimated genetic liability to a disorder or a trait . The staTo further improve prediction accuracy, several methods have been proposed to utilize other information, such as LDpred (and LDpred-inf) that models the LD information extracted from a reference panel ; AnnoPreIn this article, we explore whether we can improve the standard PRS method without using information from external panels or datasets. We give a positive answer to this question in this article by proposing EB-PRS, a novel PRS approach based on Empirical Bayes theory, borrowing information across markers to improve prediction accuracy. Instead of using a prespecified prior distribution in standard Bayesian modeling, the Empirical Bayes approach estimates the prior distribution from the data. Here we first utilize the GWAS summary statistics to infer the overall distribution of effect sizes and then leverage this distribution to improve the standard PRS method by minimizing the prediction error.Our method does not need to tune parameters, avoiding the use of training data to select the best performing parameters.Compared to other improved PRS methods such as LDpred and AnnoPred, we do not need external panels or datasets.We note that we are not the first one proposing to utilize effect size distributions for PRS calculations. Some methods in this category also have no tuning parameters or external input, such as the methods proposed in So and Sham (2017)  and Mak Compared to the existing genetic risk prediction methods, our method has the following advantages:We demonstrate the better performance of our method through both simulations and real data applications to six complex diseases including asthma (AS), breast cancer (BC), celiac disease (CEL), Crohn’s disease (CD), Parkinson’s disease (PD), and type 2 diabetes (T2D).m = 10, 000 and the causal SNP proportion was set to 0.1. For each SNP, its allele frequency was simulated from a uniform distribution U and its effect size was drawn from a point-normal mixture distribution, i.e., μ ∼ 0.9δ0 + 0.1N. We further set the prevalence of the disease κ to be 1%. To explore the relationship between the prediction performance of our method and the sample sizes of training datasets, we varied the sample size from 2,000 to 8,000. We first set the control-to-case ratios (CCRs) to 1 in the training datasets. In order to simulate under a setting consistent with real data, we also performed simulations with lager CCRs (ranging from 2 to 4).We first performed simulations to investigate the performance of our method when the markers are independent. In these simulations, we fixed the number of independent SNPs to p-value threshold of the P+T method was varied among {1, 5e − 01, 5e − 02, 5e − 03, 5e − 04, 5e − 05, 5e − 06}. We simulated 100 controls and 100 cases as our testing dataset. For each individual in the simulated testing dataset, the PRSs generated from the EB-PRS, P+T, So et al.’s and Mak et al.’s methods were calculated. We evaluate the prediction performance by using both the squared correlation between the PRSs and the observed phenotypes (predictive r2), and the area under the receiver operating characteristic (ROC) curve (AUC). For the P+T method, we report the results with the best performing parameters. We ran experiments in each setting 10 times and compared the average performances of four methods. r2 of EB-PRS, P+T and the method from So et al. Results for using biobank-level sample sizes are in r2 and AUCs for the four methods in different settings are summarized in Because SNPs were simulated independently, there is no need to consider LD among SNPs in this scenario. Therefore, we will only compare our method with a simplified P+T method in which the pruning step is not carried out. The a = b = 0.8. The results of the simulation experiment are shown in N. The results showing the performance of different methods in divergent effect sizes can be seen in r2 under different CCRs in Supplementary Population genetics data suggest that there are more SNPs with low minor allele frequencies (MAF) than those with high MAF . To mimiβ) for associated SNPs were assumed to follow a normal distribution N. The phenotype of each individual was generated according to the following formula:In order to evaluate the performance of our method for depenent SNPs , we conducted simulations based on individual-level genotype data accessed from the database of Genotypes and Phenotypes (dbGaP) , 14  , breast n0 = 41, 335 and n1 = 16, 003) [n0 = 70, n1 = 966) [n0 = 15, 056, n1 = 6, 333 and m = 871, 743) [n0 = 2, 891, n1 = 1, 689) [n0 = 2, 574 and n1 = 1, 843) as the testing data. For T2D, we trained the model on summary statistics from the Diabetes Genetics Replication and Meta-analysis consortium  [n0 = 517, n1 = 662) [For AS, we trained the model using summary statistics from the GABRIEL Consortium, which was a meta-analysis of 23 studies, including 10,365 persons with physician-diagnosed asthma and 16,110 unaffected persons. There were 535,060 SNPs in the released summary statistics. We tested the performance utilizing samples from the study phs000490 in the dbGaP, with 515 cases and 875 controls . For BC,1 = 966) , in whic71, 743) . Individ 1, 689) . For PD, 1, 689) . We used12, 171)  and test1 = 662) . There wp-value. EB-PRS attained significant improvement in prediction accuracy over P+T for AS , BC , CEL , CD , PD , and T2D .For these six diseases, EB-PRS outperformed all other methods, including the unadjusted PRS, P+T, LDpred-inf, LDpred, So et al.’s and Mak et al.’s methods. Even without external information or datasets, the performance of our method was better than best performing LDpred for all diseases. Here, we build two logistic models, one fits PRSs derived from one method only, while the other one fits PRSs derived from two methods. Then we use the likelihood ratio test to compare the difference of the prediction accuracy and report the corresponding r2 of all seven methods to six diseases. Each plot corresponds to a specific disease and the left column indicates the predictive accuracy of EB-PRS. We can see that EB-PRS always outperformed the other six methods. Specifically, evaluated by predictive r2, EB-PRS respectively achieved 307.1% (for AS), 42.8% (for BC), 25.5% (for CEL), 3.1% (for CD), 74.3% (for PD), and 49.6% (for T2D) relative improvements over P+T. Meanwhile, EB-PRS had 37.9% (for AS), 33.6% (for BC), 8.6% (for CEL), 36.2% (for CD), 40.6% (for PD), and 10.8% (for T2D) relatively improvement than LDpred. We also show the AUC values in In general, unadjusted PRS and LDpred-inf (without parameter tuning) performed poorly in all six datasets. Compared to methods which need to tune parameters , our method also achieved better performance in all six datasets. These indicate the distinct advantage of our method: it can achieve noteworthy performance without tuning any parameters or incorporating external information.In this article, we have considered predicting an individual’s genetic risk for complex diseases using summary statistics, which may prove helpful for both disease prevention and clinical decision. The PRS approach is widely used in genetic risk prediction because of its simplicity and efficiency, and a number of PRS methods have been proposed to improve prediction accuracy. Almost all these improved methods are based on borrowing information from external panels or datasets, such as the LD information, annotations or other GWAS datasets studying genetically correlated traits. In this paper we have proposed an improved PRS method by utilizing effect size distributions based on Empirical Bayes theory. No parameter tuning is needed, and no external panels or datasets are needed to be input. We have shown that our method outperformed the standard P+T method, as well as recently proposed methods in So et al. (2016) and Mak et al. (2017) in both simulations and real data analysis. Furthermore, compared to methods utilizing LD information from a reference panel, our method also achieved superior performance on all diseases including AS, BC, CEL, CD, PD, and T2D. One reason for the good performance is that we leverage the global information of effect sizes and the other reason is that we theoretically construct the optimal PRS in terms of minimizing the prediction error.Note that both So et al.’s and Mak et al.’s methods also use effect size distribution to improve PRS. We show the theoretical superiority of our method over these two methods. So et al. used the square root of the explained liability as the effect size, which is not the optimal one in terms of minimizing prediction error. Besides, the effect size estimated from Tweedie’s formula has already been weighted by local true discovery rates, a further multiplication can make the effect sized over-shrinked. Meanwhile, their method needs to specify the prevalence for each trait, which may be difficult sometimes.z, i.e., the selection of reference alleles. Second, the K-component mixture assumption for effect size of associated SNPs is consistent with the empirical observations from GWAS of many common diseases [Some may argue that why we use parametric mixture model instead of non-parametric Tweedie’s formula in effect size estimation. First, in our model, we use symmetrical prior for the effect size, which makes the estimated magnitude invariant with the sign of diseases –26. Thirdiseases .Although our method can achieve better performance without tuning any parameters and utilizing external information, its performance may be improved with external information, for example, the LD information. Also, in order to increase the prediction accuracy to a larger extent, we may improve our method by combining other available datasets in the future, such as annotations or other GWAS summary statistics studying genetically correlated traits.A basic assumption underlying all PRS methods is that the training and testing datasets are homogeneous and sampled from the same population. If they come from different populations, the allele frequencies of SNPs will be different, together with the causal variants and their effect sizes. In the case, we expect a worse prediction performance , 29. In m is the total number of genotyped SNPs, xi is the genotypic value, and βi is the log-odds ratio (OR) of the i-th SNP. The log-OR is a measure of the effect size defined in the following formula:fi0 and fi1 are the reference allele frequencies among controls and cases, respectively. If the SNP is not associated with disease, then βi = 0.Generally speaking, EB-PRS aims at minimizing the prediction error by leveraging estimated distribution of effect sizes. Assuming that the SNPs are independent, we can show that the optimal PRS (in terms of achieving the best classification accuracy) isβ, which is the minimizer of the Bayes risk under the distribution estimated from the data. The estimators can be directly derived from GWAS summary statistics.In practice, the true values of effect sizes are usually unknown, and need to be estimated from the data. In our method, we use the Empirical Bayes approach to estimate m SNPs genotyped in a GWAS. For each SNP, there are usually two different alleles. We denote one of them as the reference allele, and use the number of reference alleles to code the genotype of the SNP for each individual. For SNP i , the genotypic value is denoted by xi . We use x to represent the vector of genotypic values across m SNPs of an individual and y the disease status of the individual, where y = 1 if the individual has the disease and y = 0 otherwise.Suppose that there are With a multiplicative model and low prevalence, the genotypic value of each SNP follows binomial distribution as:κ is the disease prevalence, and βi is the true value of the log-OR for the i-th SNP.If all SNPs are assumed to be independent, based on R(α(x)|x) for all x:l ∈ {0, 1} and α0 when α1 when P(y = 1|x) > P(y = 0|x), i.e.,β is exactly the log-OR. That is, if we define a polygenic risk score Our objective is to find the decision rule minimizing the overall Bayes risk:S is a function of the parameters βi . To derive the PRS in practice, we can use GWAS summary statistics to estimate these parameters.The constructed optimal polygenic risk score βi by plugging the observed log-OR, the estimated effect sizes will tend to be inflated for SNPs with large values of estimated results. This phenomenon is commonly known as the “winner’s curse”. Here, we adopt the Empirical Bayes approach to address the issue of the selection bias as it is more robust to the winner’s curse [If we simply estimate ’s curse , 31. Alsn0 and n1 are the number of control and disease subjects, respectively, and n = n0 + n1. Given the standardized effect size z-scores is Zi|μi ∼ N. Recent GWAS results suggest that, among all disease-associated SNPs, there are many more SNPs with small effect sizes than those with large effect sizes [π0 is the proportion of non-associated SNPs (0 ≤ π0 ≤ 1) and δ0 is the distribution with point mass at zero. Here we use a K-component Gaussian mixture distribution as the slab, in which the proportion of SNPs in the j-th associated component is πj . The corresponding local true discovery rate is the probability that the hypothesis z-value, and it can be calculated as follows:ϕ(⋅) and fj(⋅) are the probablity density functions of N and With this prior specification, the posterior expected effect size of an SNP under each alternative hypothesis isβi is the optimal estimator for minimizing the Bayes risk. Therefore, we estimate βi as follows:The posterior expectation of π0, π1, ⋯, πK) and  in the above mixture model. In practice, the null proportion π0 is always much larger than the proportions in the alternative components. To take advantage of this prior information, we first add a Dirichlet prior  to proportions . We use the following strategy to infer the value of α. First, we set α to a reasonable value   and Mak i. If no confounders are considered in the regression, then The unadjusted PRS is the summation of genotypic values weighted by the corresponding estimated effect sizes from the marginal logistic regression, i.e.,p-value thresholding. The method first prunes SNPs according to a given threshold for squared correlation coefficients (r2) between different SNPs. Then it further filters the SNPs with a p-value cutoff in marginal association tests. In this article, we set LD clumping r2 to 0.1 and vary the p-value cutoff values from {1, 5e − 01, 5e − 02, 5e − 03, 5e − 04, 5e − 05, 5e − 06}. In the following comparison experiments, we will report the prediction results of the P+T method with the optimally tuned parameters.The P+T method generates PRS based on a subset of independent SNPs obtained via informed LD-clumping  and p-vaD denotes the LD matrix, n is the sample size of the GWAS, I denotes the identity matrix, and w represents the corresponding standardized genotype.The LDpred-inf method estimates the causal effect sizes under an infinitesimal model, where LD among SNPs is considered. The assumption for the causal effect size is π0 is a parameter that needs to be specified by users. Here, we set π0 from {1, 3e − 01, 1e − 01, 3e − 02, 1e − 02, 3e − 03, 1e − 03, 3e − 04, 1e − 04, 3e − 05, 1e − 05}, which are the default values recommended in LDpred. In the following comparison experiments, we will report the best prediction results with the optimally tuned parameters.LDpred is an extension of LDpred-inf, which makes use of a point-normal prior instead of normal prior to estimate causal effect sizes. To calculate the posterior expectation of causal effects, Markov Chain Monte Carlo (MCMC) is used, and the proportion of causal effects μ is non-parametrically estimated by using the Tweedie’s formula:f(z) is the estimated probability density function of z-values. Then the explained liability of each SNP is assessed based on estimated μ. The final effect size is estimated using the square root of explained liability weighted by the corresponding local true discovery rate, i.e.,So et al. proposed to construct PRS by using the following three steps to calculate the effect size of each SNP. Firstly, the standardized effect size μ without conditioning alternative hypothesis Since we have theoretically shown that the true log-OR is the optimal effect size for constructing PRS in terms of prediction accuracy, using the square root of explained liability will decrease the performance. In addition, Tweedie’s formula evaluates the posterior expecation of Mak et al. proposed to construct PRS by directly using the observed effect size weighted by ltdr, i.e.,As we pointed out before, the observed effect size suffers from the winner’ curse. The shrinkage estimator derived from Empirical Bayes theory is a better choice in terms of overcoming the winner’s curse and minimizing the Bayes risk.S1 Tabler2 and AUCs are highlighted in boldface.The highest mean (XLSX)Click here for additional data file.S2 Tabler2 and AUCs are highlighted in boldface.The highest mean (XLSX)Click here for additional data file.S3 Tabler2 and AUCs are highlighted in boldface.The highest mean (XLSX)Click here for additional data file.S4 Tabler2 and AUCs are highlighted in boldface.The allele frequencies follow uniform distribution in the training and testing data. The highest mean (XLSX)Click here for additional data file.S5 Tabler2 and AUCs are highlighted in boldface.The results are the average of 10 times simulations. The highest mean (XLSX)Click here for additional data file.S6 TableThe simulations were based on an Intel Xeon processor with 2.50GHz. The shortest time is highlighted in boldface.(XLSX)Click here for additional data file.S1 Fige + 05. The error bar indicates the standard deviation of predictive r2 across 10 times simulations.Here the control-to-case ratio is set to one. EB-PRS always outperformed the other methods. So et al.’s package will produce errors when the sample size is above 3(TIF)Click here for additional data file.S2 Figr2 across 10 times simulations.Here the control-to-case ratio is set to one. EB-PRS always outperformed the other methods. The error bar indicates the standard deviation of predictive (TIF)Click here for additional data file.S3 Figr2 across 10 times simulations.Here the control-to-case ratio is set to one. EB-PRS always outperformed the other methods. The error bar indicates the standard deviation of predictive (TIF)Click here for additional data file.S4 Figr2 across 10 times simulations.Here the control-to-case ratio is set to one. EB-PRS always outperformed the other methods. The error bar indicates the standard deviation of predictive (TIF)Click here for additional data file.


Interest in selection for milk yield and thermotolerance in cattle has grown, since heat stress has caused great losses in milk yield. However, few studies on how to carry out concurrent selection are available. Milk yield was analyzed by traditional methods, including heat stress indicators, in genetic evaluation. The results showed that the best sires for milk yield are not the best for heat tolerance, and only a small proportion of individuals have the aptitude for joint selection. Despite a small population fraction allowed for joint selection, sufficient genetic variability for selecting more resilient sires was found, which promoted concomitant genetic gains in milk yield and thermotolerance.Intense selection for milk yield has increased environmental sensitivity in animals, and currently, heat stress is an expensive problem in dairy farming. The objectives were to identify the best model for characterizing environmental sensitivity in Holstein cattle, using the test-day milk yield (TDMY) combined with the temperature–humidity index (THI), and identify sires genetically superior for heat-stress (HS) tolerance and milk yield, through random regression. The data comprised 94,549 TDMYs of 11,294 first-parity Holstein cows in Brazil, collected from 1997 to 2013. The yield data were fitted to Legendre orthogonal polynomials, linear splines and the Wilmink function. The THI (the average of two days before the dairy control) was used as an environmental gradient. An animal model that fitted production using a Legendre polynomials of quartic order for the days in milk and quadratic equations for the THI presented a better quality of fit (Akaike’s information criterion (AIC) and Bayesian information criterion (BIC)). The Spearman correlation coefficient of greatest impact was 0.54, between the top 1% for TDMY and top 1% for HS. Only 9% of the sires showed plasticity and an aptitude for joint selection. Thus, despite the small population fraction allowed for joint selection, sufficient genetic variability for selecting more resilient sires was found, which promoted concomitant genetic gains in milk yield and thermotolerance. Dairy breeding programs have traditionally focused on selection for milk yield. This intense selection has increased sensitivity to environmental changes in animals. Climate and variability in climate have negatively affect milk yield due to impacts on metabolic efficiency and immune responses . CurrentGarcia et al.  observedAccording to Sigdel et al.  and AnsaBrazil has a diverse climate, from warm and dry/humid to cold and humid climates, due to a wide variation in longitude, latitude, and altitude in its territory and the effects of coastal, continental vegetation . In addiDifferent thermotolerances are found between and within dairy cattle breeds. The selection of animals within a breed is an alternative when crossbreeding is not feasible. Physical sizes, metabolic rates and productive levels have been associated with thermotolerance .Ravagnolo and Misztal  describeThe evaluation of decreases in milk yield per THI-unit increase from a determined threshold is a method for predicting the relationship between production and climate conditions . The THISeveral hypothetical models and fitting equations have been proposed to estimate the effect of heat stress. A combination of methods allows the identification of the best methodology for explaining the variation in genetic and non-genetic components within an environmental gradient. This enables critical genetic analysis and the reduction of the negative effects of heat stress on dairy cattle performance and impacts the dairy production chain.In this context, the objective of this study was to identify the best model for characterizing environmental sensitivity in Holstein cattle in Brazil, using the test-day milk yield combined with temperature–humidity index data from public weather stations, and identify sires genetically superior in terms of heat tolerance and milk yield through random regression models.Bioclimatic data from 18 weather stations  were obtained from the Instituto Nacional de Meteorologia. The stations were located within 60 km of the evaluated farms. The temperature–humidity index (THI) was calculated according to the equation described by the National Research Council—NRC :THI = [ was calculated by the difference between the daily maximum and minimum temperatures (°C). The DTV was found to range from 2 to 25. The numbers of test-day milk yield records by the THI and DTV are shown in The THI and DTV daily averages used were calculated based on averages of two days (one and two days before the test-day milk yield records), as described by Negri et al. .The test-day milk yield (TDMY) data, provided by the Associação de Criadores de Gado Holandês de Minas Gerais (ACGHMG), consisted of records of Holstein cows at first lactation in the state of Minas Gerais, Brazil (19°55′ S–43°57′ W), from 1996 to 2015.Records of animals with ages at calving <18 or >48 months, days in milk (DIM) <5 or >305 days, and milk yields <4 or >44.8 kg were excluded from the data set. Only healthy animals with at least four TDMY records during lactation were used for analysis. The minimum size of each contemporary group  was three animals. Records of daughters of sires with at least one daughter in at least three herds were included in evaluation.Considering these criteria, a total of 94,549 TDMY records from 11,294 first lactations of Holstein cows, with a mean test-day milk yield of 25.81 kg, from 129 herds, collected from 1997 to 2013, were analyzed. This database was fitted to all the evaluated models. The pedigree file included 32,409 animals. The structure of the dataset after editing is shown in Five models (M1 to M5) and three fitting equations were used to analyze the TDMY records: the Wilmink parametric function (WL) , linear t (described below the models), and DIM with 60 classes  were fixed effects. The fixed curve (described below the models), additive genetic and permanent environmental functions were regressed to the THI, using the LP (4th order), LS (4 knots) and WL.Model 1 (M1): The contemporary group, milking frequency (two and three times a day), variable t were fixed effects. The fixed curve, additive genetic and permanent environmental functions were regressed: the DIM using the LP (4th order), and to the THI using the LP (2nd order); to the DIM using LS (4 knots) and to the THI using LS (3 knots); to the DIM and THI using the WL.Model 2 (M2): The contemporary group, milking frequency and variable t were fixed effects. The fixed curve, additive genetic and permanent environmental functions were regressed: to the DIM using the LP (4th order), and to the THI and DTV using the LP (2nd order); to the DIM using LS (4 knots), and to the THI and DTV using LS (3 knots); to the DIM, THI and DTV using the WL.Model 3 (M3): The contemporary group, milking frequency and variable t and DTV  were fixed effects. The fixed curve, additive genetic and permanent environmental functions were regressed: to the DIM using the LP (4th order), and to the THI using the LP (2nd order); to the DIM using LS (4 knots), and to the THI using LS (3 knots); to the DIM and THI using the WL.Model 4 (M4): The contemporary group, milking frequency, variable t and DIM with 60 classes  were fixed effects. The fixed curve, additive genetic and permanent environmental functions were regressed: to the THI and DTV using the LP (2nd order); to the THI and DTV using LS (3 knots); to the THI and DTV using the WL.Model 5 (M5): The contemporary group, milking frequency, variable t was defined to estimate the decreases in milk yield caused by heat stress (HS). The threshold for HS used was a THI of 74, based on Negri et al. [A dummy variable i et al. . TherefoThe fixed curves considered in all the models were defined by the age classes—1 (18 to 25 months), 2 (26 to 27 months), 3 (28 to 29 months) and 4 (30 to 48 months)—combined with calving season subclasses—1 (rainy: October to March) and 2 (dry: April to September)—totaling eight fixed curves. The residual variance was considered homogeneous in all the models .y is the vector of observations; X, Z and W are the incidence matrices for the fixed effects(b), additive genetic random regression coefficients (a), and permanent environmental random regression coefficients (p), respectively; A is the additive genetic numerator relationship matrix based on pedigree information; and I is an identity matrix. G0 and P0 are the (co)variance matrices of the additive genetic and permanent environmental random regression coefficients, respectively, and R is the (co)variance matrix of the residual.Random regression models (RRM) were used for analysis. Henderson’s mixed model equations  for RRM e is the vector of the residuals, and all the other terms were previously defined. The genetic (Σ) and environmental (Φ) (co)variance matrices for time points can be obtained as follows (assuming the same function for factors):T is a matrix of independent covariates for all time points  associated with the model and function used.All the genetic analyses were performed with an animal model, using the REMLF90 program . Considep is the number of parameters in the model), and Schwarz’s Bayesian information criterion (BIC = −2logL + p log (λ), where log (λ) is the natural logarithm of the sample size (or dimension of y) and p is the number of parameters in the model). The BIC is more rigid than AIC. The model with the lowest value for both criteria was the one with the best fit.The quality of fit was evaluated considering non-nested models and penalties, according to the number of parameters to be estimated. The following criteria were used: the maximum likelihood estimation (−2logL), Akaike’s information criterion  and environmental gradient  information, according to the equationi (coefficients corresponding to DIM and THI) and j and DIM k.The estimated breeding value (EBV) of an animal The top 1% and 5% dairy Holstein sires (with at least 20 daughters) for EBV_TDMY and EBV_HS were sampled to represent the resilience of the animals, considering the DIM and THI scale .Considering only the THI, approximately 31% of all the TDMY records were obtained under heat-comfort conditions (<THI 74) and 69% were under HS conditions. The data show that the milk yield tended to decrease as the THI was increasing. The mean and standard deviation of the TDMY were 28.57 ± 1.8 kg for THI < 74, and 23.95 ± 1.9 kg for THI > 74.Approximately 46% of all the TDMY records were obtained at DTV within heat comfort conditions (<DTV 13), and 54% were in HS conditions. The mean and standard deviation of the TDMY records were 27.33 ± 1.3 kg for DTV < 13 and 24.94 ± 0.4 kg for DTV > 13. The phenotypic value tended to decrease as the DTV increased. However, slope is more representative for assessing the THI effect.Five models that used the LP to fit fixed and random curves showed better quality of fit . The besAIC includes the complexity and predicted ability of the data to fit the model, and is linked to the BIC due to the probability function. However, the BIC penalizes models more because of the number of parameters. Thus, the quality of fit (AIC and BIC) indicates the same model, confirming that the chosen model is the most appropriate.The overall heritability estimate for the TDMY regressed to the THI ranged from 0.15 to 0.21 when using the LP equation , while fThe heritability estimated as a function of lactation in M4 using the LP (best fit) weighted by the THI and DIM, after the THI threshold (THI = 74), showed a decrease . The envThe fixed effects solution (BLUE) for DTV shows that an increase in the variation temperature is reflected in a decrease in milk yield . The fixClasses: DTV 2 to 6 = class 1; DTV 7 to 11 = class 2; DTV 12 to 16 = class 3; DTV 17 to 21 = class 4; DTV 22 to 25 = class 5.The existence of additive genetic variability for the slope of the environmental gradient indicated the presence of G×E interaction . Some ofApproximately 9% of the sires were resilient to changes in the THI, considering their EBV for TDMY and HS tolerance; however, approximately 30% showed probable plasticity. This allows the selection and formation of a resilient lineage with good productivity.The reranking of sires was confirmed by the Spearman rank correlation coefficients, comparing the genetic evaluation for TDMY and thermotolerance . TherefoThe database, in which 90% of the records were measured under heat-stress conditions, showed that the traditional model (which does not consider heat stress) is inefficient for estimating the EBV when animals are under heat stress. Thus, considering two situations, when sires are considered equally in heat comfort (THI = 74) and in heat stress (THI = 84), sires with less than 40 daughters are the most penalized, and their EBVs are underestimated .The effect of the genotype-by-environment interaction is minimized and the traditional methodology is not biased when a sire has more than 101 daughters in several herds. However, some breeders intensively use high EBV_TDMY, and others use them less often. This unequal contribution to adaptive values makes the estimates biased.Most dairy cows in Brazil are kept in open barns and in grazing systems ,24,25. MClimate changes may increase heat-stress levels in dairy cows; thus, these environmental phenomena, which frequently cause droughts, heat waves, storms and floods, should be considered . IncreasThese changes justify and foster research that evaluates the effects of climate variables on animal production, mainly regarding genetic breeding, in which the effects are cumulative and long term. In addition, the use of heat stress indicators collected from public weather stations, rather than directly from farms, has been widely explored for inclusion in genetic evaluation. According to Lee et al. , the evaLegendre polynomials are more widely used for these evaluations ,31,32,33A low number of observations of extremes of lactation may affect the prediction coefficients of functions fitted through random regression . The samThe sooner HS is detected, the greater the chances of keeping more resilient animals in production and, consequently, the more productive they are in different heat conditions. According to Aguilar et al. , the genBrügemann et al.  emphasizThe use of random regression to detect G × E fits a variance–covariance structure of repeated measures along a gradient for traits such as the TDMY . SimilarSelecting sires only by EBV_TDMY, disregarding the herd rearing system, technological level and bioclimatic conditions of a region, may compromise the genetic gain of herds. Moreover, investments in high-merit genetic material from animals evaluated in highly technological environments should not be recommended for farmers in environments with low technological investments. An ideal curve would be a high and constant EBV_TDMY under different THIs; however, few animals presented this desired profile. Thus, considering the needs for breeding of each herd is important for more quicky increasing the TDMY or tolerance to HS. Each sire has a thermotolerance slope limit, as shown by the difference between the curves, which allows the better targeting of sires for different uses, according to farmers’ demands.The results shown in This high variability indicates that the apparent genetic merit of sires for milk yield may change depending on the environment, generating great concern about genetic evaluation and the choice of sires, which can be affected by this dependence. Phenotypic and genetic parameters are dependent on the population and environment, and can have different magnitudes, resulting in heterogenous variations. Thus, changes in variances and the covariance would promote changes in important parameters, such as heritability, repeatability and correlations, which may result in incorrect choices of selection methods adopted in a breeding program.in loco: the creation of a selection index for the simultaneous selection and targeting of mating to develop a tolerant lineage. However, it requires attention to avoid estimation biases. Negri et al. [According to Santana et al. , the flai et al.  pointed The existence of genetic variation for sensitivity to heat stress allows for the selection of genetically resilient animals.The most adequate selection methodology for improving heat tolerance without decreasing productivity includes diurnal temperature variation as a fixed effect and regresses data to the temperature–humidity index and days in milk.Legendre polynomials should be used to ensure better predictions of the estimated breeding value and determine the genetic effect of heat stress through random regression models.Antagonism between the test-day milk yield and heat stress was confirmed, and enabled the use of heat tolerance as a selection criterion for improving animal thermotolerance and productivity simultaneously. The development of selection indexes weighted by technological levels or sire summaries that include information on the environmental gradient could be viable solutions. The selection and development of more thermotolerant lineages is a more attractive option than the development of selection indexes.


The growth traits of broilers have significant economic value in the chicken industry, and many QTLs affecting growth traits have been identified, especially on chromosomes 1, 4, and 27, albeit with large confidence intervals that potentially contain dozens of genes. To promote a better understanding of the underlying genetic architecture of growth trait differences, specifically body weight and bone development, in this study, we report a nine-generation AIL derived from two divergent outbred lines: High Quality chicken Line A (HQLA) and Huiyang Bearded (HB) chicken. We evaluate the genetic architecture of the F0, F2, F8, and F9 generations of AIL and demonstrate that the population of the F9 generation sufficiently randomized the founder genomes and has the characteristics of rapid linkage disequilibrium decay, limited allele frequency decline, and abundant nucleotide diversity. This AIL yielded a much narrower QTL than the F2 generations, especially the QTL on chromosome 27, which was reduced to 120 Kb. An ancestral haplotype association analysis showed that most of the dominant haplotypes are inherited from HQLA but with fluctuation of the effects between them. We highlight the important role of four candidate genes  in bone growth. We also retrieved a missing QTL from AIL on chromosome 4 by identifying the founder selection signatures, which are explained by the loss of association power that results from rare alleles. Our study provides a reasonable resource for detecting quantitative trait genes and tracking ancestor history and will facilitate our understanding of the genetic mechanisms underlying chicken bone growth.The advanced intercross line (AIL) that is created by successive generations of pseudo-random mating after the F The Huiyang Bearded chicken (HB) is a Chinese meat-type breed with a long history , which is characterized by its slow growth, high meat quality, and muff and beard phenotype ; currentm mating . The pop9 generation, body weight was measured at hatching and every other week until 12 weeks of age. During weeks 4–12, the shank length and shank circumference were also measured every 2 weeks. Boxplots for each phenotype were generated to scan for outliers. Individuals that were further than 1.5 times IQR away from the upper or lower quartile of the boxplots were removed. Descriptive statistics of the phenotypes are provided in For the F0, F8, and F9  libraries were prepared and sequencing was performed on a Illumina Nextseq500 sequencer. The TASSEL-4.0 GBS analysis pipeline was used to discover SNPs. Using VCFtools (0.1.17), the raw GBS SNP filter criteria was set to: –maf 0.05 –max-alleles 2 –min-alleles 2 –minDP 5 –minGQ 98 –max-missing 0.2  that failed to meet the following criteria were removed: individual call rate (>0.9), individual SNP call frequency (>0.9), and minor allele frequency (MAF > 0.05). All the genomic coordinates of the SNPs were uniformly converted to the chicken reference genome Gallus gallus, version 5.0 (Ensembl release 94). After that, we kept 161,376 GBS SNPs for 16 HQLA, 14 HB, 185 F8, 602 F9 individuals, and 43,472 Chip SNPs for 492 F2 individuals.We employed GBS SNPs of F, and F9  and Illund F9   of the candidate SNP to be tested for association, x is the SNP genotype indicator variable, g is the polygenic effect , and e is the residual. The GWAS statistical model of body weight included the sex and batch as discrete covariates and hatch weight as a quantitative covariate. For shank traits, body weight at the same age were also included as a covariate, because we focused on QTL scans which are associated with bone growth. A quantile-quantile (Q-Q) plot generated in CMplot1 was used to assess the potential impact of population stratification (r2 >0.3.The mixed linear model (MLM) approach was used for the GWAS of the F (v1.92) . The basfication . Bonferrfication . QTL intFst (population differentiation-based), to investigate the signatures of selection between HQLA and HB. The XP-EHH and iHH value at each locus were estimated by The selfscan program (v1.2.0a)  , Tajima’s D (frequency spectrum-based), and v1.2.0a) , and the(0.1.17)  with a wA haplotype-based association analysis was performed in the ∼120 Kb fine-mapped QTL region on GGA27 using the following model:Y = Xβ + Zu +eY is a column vector containing the SL10 of the F9 individuals. X is the design matrix including the coding for the sex of the birds. For each specific interval, there are n haplotypes for m individuals constructed by several SNPs. Z is the design matrix (m × n) containing each haplotype count  of each individual. β is a vector that estimates the fixed effect of sex, u is a column vector that estimates the allele substitution effects for each haplotype, and e is the normally distributed residual.where 0 population as the ancestor population, RFmix was used to evaluate the local ancestral source of individuals in the F9 generation. To determine the haplotype window size, we set conditional random field spacing (# of SNPs) (-c) to 9 based on the results of LD with r2 = 0.2 as the critical value, and generations since admixture (-G) set to 9. Other parameters were left as default.The RFmix software (v2.03)  is based9 generation  decays in HQLA were significantly faster than those in HB, which is consistent with the ancestral cross history of HQLA , supporting the suitability of the F9 population for high-resolution mapping.LD (r of HQLA . The F2 2)  were lost compared to the F0 GBS data. Considering the distribution of minor allele frequencies (MAFs)  than F0 (22.46%). This pattern shows that the AIL population still experiences a slight genetic drift and bottleneck between F0 and F9.We used GBS SNPs to estimate the nucleotide polymorphisms (π) in each population (except F2)  and the 2) . HQLA shs (MAFs) , a high 9 individuals. All traits have a high phenotypic and genetic correlation, especially between the same traits at different periods. The correlation between SC and BW at different periods is higher than the correlation between SL and BW , we identified a large major QTL mainly affecting body weight at GGA1: 168.6–171.7 Mb (Q1) and a small major QTL mainly affecting shank development at GGA27: 3.60–3.72 Mb (Q2)  and SL10 at GGA27: 3,608,297 bp (p = 6.1 × 10–8). Q1’s confidence interval was 25-fold that of Q2, partly because the recombination rate of GGA27 (12.05 cM/Mb) was 4.9-fold that of GGA1 (2.44 cM/Mb)  . These Qanalysis . The mos4 cM/Mb)  and the 4 cM/Mb) . The broFst method. However, one must carefully evaluate the results of selection signals since small sample sizes may introduce large drift effects. Hence, we combined our GWAS results with the Animal Quantitative Trait Loci Database2 to conduct a further screening of each selection signal interval. By comparing the growth traits associated QTLs with the candidate selection interval obtained by at least one method, we identified a total of 10 clear selection signal intervals (S1–S10), four of which occurred mainly in HQLA and six of which occurred in HB , and has been reported to be significantly associated with chicken body weight in different populations, such as White Leghorn × Rhode Island Red cross  was identified by 34 GBS SNPs and aggregated using chhiking . It is dchhiking  (the mos9). Tracing back to the F0 generation, we confirmed three HQLA-origin haplotypes , four HB-origin haplotypes , two shared haplotypes (gray), and three recombination haplotypes (orange)  were identified to have statistically independent associations with SL10 at a 5% False Discovery Rate (FDR) threshold. The haplotypes tagged by these 4 SNPs were estimated; in total, 12 haplotypes were detected (MAF > 0.01 in F(orange) .n = 95), 0.08 ± 1.22 cm (n = 201), -1.53 ± 0.64 cm (n = 151), respectively. The results showed that HQLA carries the main length increasing alleles, and heterosis does not commonly exist in crosses of AB. Next, the additive haplotype substitution effects on SL10 were estimated. There was a gradient distribution of haplotype allele effects between decreasing SL10 by 1.57 cm and increasing it by 2.38 cm  and higher density markers . We highlighted the fine-mapped QTL on the GGA27 derived from GWAS, haplotype association, and local ancestry inference, which implicated four candidate genes corroborated by extant human, mouse, and chicken genetic data.Crosses among well-characterized strains are a mainstay of modeling organism genetics. We reported a running chicken AIL that was generated by crossing HQLA × HB, which was differentially bred for fast growth and slow growth prior to subsequent intercrossing. Systematic characterization of the genetic architecture of AIL makes it possible to evaluate the suitability of different genomic situations for GWAS. Overall, the F0 generation, even though the four males were full siblings, and the 12 females were either half or full siblings, in the HQLA and HB founders, which is very different from the inbred AIL line of mice (9) than broiler × Fayoumi AIL (60% SNPs with MAF < 0.05 in F18 and F19)  . Moreoveand F19)  reportedpulation , which ipulation  than thepulation . In addiancestry  using thancestry .0 still reduces the false positive rate of the selection signal to some extent, which allows all candidate intervals to be further studied based on their association with other phenotypes. Secondly, we showed a typical example of failing to replicate prior results on GGA4, which we explained by the loss of GWAS power that results from rare alleles. This result demonstrated that local diversity may be lost, even if two founder strains generally maintain large phenotypic/genotypic differences, which is also a major performance difference between AIL and MAGIC. Besides, this study used ∼160 K SNPs, which means that a very large sample size which not available currently is required to meet the multiple testing correction of detecting epistatic QTLs. Therefore, a comprehensive analysis of interaction between directional epistasis and mutation effects will also be a very interesting issue to be explored in the near future.We also presented a joint analysis of GWAS, and selective sweep of this AIL was able to comprehensively extract more genomic features. Firstly, although we cannot rule out the effect of genetic drift on the selection results, the diversity of F2 finding  belongs to a family of RNA-binding proteins implicated in mRNA localization, turnover, and translational control  also has been recognized in the last decade as an important contributor to bone remodeling and is necessary for optimal bone quality  genes. We focused on the narrow QTL on GGA27 that contains fewer genes, and we highlighted some genes that are noted by the existing literature for their role in the corresponding traits. This result finely replicated the F finding  and is c finding  and Peki finding . The lea control . The IGFult life . Moreoves by 15% . Glucose quality . GIP sti quality . It is p quality . In shor2 generations, especially the QTL on chromosome 27. Further, we highlighted the important role of four candidate genes  for bone development. We also identified a missing QTL on chromosome 4 via the joint analysis of GWAS and a selection signature analysis, which demonstrated the local limitations of this population but can be remedied by a multidimensional analysis. Overall, our study provides a promising resource for this field of study and will facilitate our understanding of the genetic mechanisms underlying chicken bone growth.In summary, the HQLA-HB-AIL chicken, which balanced the avoidance of rare alleles with the requirement for rapid linkage disequilibrium (LD) decay, is a reasonable resource for detecting quantitative trait genes. This AIL yielded a much narrower QTL than the F10.6084/m9.figshare.12581063.v1. The phenotype data can be found in All data are published and can be found in The animal welfare committee of the State Key Laboratory approved all animal care and experimental procedures for Agrobiotechnology of China Agricultural University with approval number SKLAB-2014-06-07.XH, CL, HQ, NL, and YW conceived and designed the experiments. YW and XC performed the experiments. YW, LB, and CZ analyzed the data. YW, LB, XC, JR, and ZH contributed reagents, materials, and analysis tools. YW wrote the manuscript. DS, HQ, CL, XC, and XH provided comments on the manuscript. All authors contributed to the article and approved the submitted version.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.


Several factors such as genotype, environment, and post-harvest processing can affect the responses of important traits in the coffee production chain. Determining the influence of these factors is of great relevance, as they can be indicators of the characteristics of the coffee produced. The most efficient models choice to be applied should take into account the variety of information and the particularities of each biological material. This study was developed to evaluate statistical and machine learning models that would better discriminate environments through multi-traits of coffee genotypes and identify the main agronomic and beverage quality traits responsible for the variation of the environments. For that, 31 morpho-agronomic and post-harvest traits were evaluated, from field experiments installed in three municipalities in the Matas de Minas region, in the State of Minas Gerais, Brazil. Two types of post-harvest processing were evaluated: natural and pulped. The apparent error rate was estimated for each method. The Multilayer Perceptron and Radial Basis Function networks were able to discriminate the coffee samples in multi-environment more efficiently than the other methods, identifying differences in multi-traits responses according to the production sites and type of post-harvest processing. The local factors did not present specific traits that favored the severity of diseases and differentiated vegetative vigor. Sensory traits acidity and fragrance/aroma score also made little contribution to the discrimination process, indicating that acidity and fragrance/aroma are characteristic of coffee produced and all coffee samples evaluated are of the special type in the Mata of Minas region. The main traits responsible for the differentiation of production sites are plant height, fruit size, and bean production. The sensory trait "Body" is the main one to discriminate the form of post-harvest processing. The search for specialty coffee is growing both in the Brazilian and worldwide markets. The production of good quality coffee depends on several factors. Among these, the genotype, environment, and post-harvest processing of coffee are described in the literature as fundamental factors for a better final quality product –3.Brazil has a great diversity of coffees, environments, and technological levels of production. These different influences affect the responses of important traits manifested in the coffee produced. Among the several coffee-producing municipalities, those located in the state of Minas Gerais, obtain good results in coffee quality concourses, which guarantees in the market space and added value to the product . A wide The price of coffee is related to the size of the bean, according to Cheng et al.  small beConsumers of high-quality coffee may prefer the genotype with species labeling  or the production environment  . Thus, tBecause of this wide variation, to which coffee activity can be submitted, it is important to identify the main plant traits that are most affected by these changes, since some genotypes may show better patterns in specific environments , 17, 18.Data collected in plant breeding studies often present a multi-trait multi-environment structure. However, these data are rarely analyzed in a combined analysis. Although combined analysis is a better representation of reality, it requires more complex models . TogetheFor that, statistical models can be used to discriminate genotypes according to their production variation. However, not all discrimination statistical models are efficient when there are non-linearly separable problems . Also, sComputational intelligence is widely consolidated in computing and engineering areas with a high potential to circumvent discriminatory problems . MachineIn this context, the present study proposes to evaluate the efficiency of statistical methods and machine learning models for discriminating environments through multi-traits  of coffee genotypes. Additionally, it was intended to identify the main traits responsible for the variation of genotypes according to production sites and post-harvest processing.The field experiments were installed in three municipalities located in the Matas de Minas region, in the state of Minas Gerais, Brazil: Senhora de Oliveira, Araponga, and Paula Cândido. The study was carried out on private land, the owner of the land gave permission to conduct the study on this site. No specific permissions were required for activities in these locations. There is mutual trust between researchers and producers, where the researchers provide raw materials for production and the producers provide the sites to evaluate the experiments. The field studies did not involve endangered or protected species.The experiments consisted of a randomized complete block design, with three replications, and 50 plants per plot. The samples of fruits collected in the municipality of Araponga were divided into two parts according to the type of post-harvest processing . Thus, these samples together with samples from the other two locations resulted in the combination of four groups of environmental factors. The particularities of each environment were described in At each environment, ten cultivars and one elite progeny Arabica coffee trees were evaluated, with different levels of rust resistance. The field experiments were conducted according to standard technical recommendations for arabica coffee cultivation , 43, excThirty-one morpho-agronomic and post-harvest traits were evaluated. The morpho-agronomic traits, evaluated before harvest, were: Vegetative vigor, fruits maturation cycle (AMC), fruits maturity uniformity (MU), mature fruit size (FS), severity of cercosporiosis (Cer) and rust (Rust), plant height (PH), top (TopD) and stem diameter (StemD); the post-harvest traits were: Production (Prod), defect percentage (DefP), defects, sieves , moca grains , sieve bottom (SB); and sensory attributes—fragrance/aroma (FragAr), taste, acidity, body, clean cup, sweetness, uniformity, aftertaste (Aft), balance, and overall impression .Vegetative vigor was assessed by assigning scores according to a visual scale that ranged from 1 to 10, in which the score of 1 corresponds to plants with reduced vegetative vigor and marked symptom of depletion, and 10 to plants with marked vegetative growth of the branches, productive and without apparent symptoms of nutritional deficiencies or diseases . The MU Severity of cercosporiosis (Cer) and rust (Rust) were carried out in the peak months of the disease in the field (between March and July), in individual plants of the useful plots with scores from 1 to 5 for immune, resistant plants, moderately resistant, moderately susceptible and susceptible, according to criteria recommended by Fazuoli . PH was 2, in a suspended terrarium built with stainless wire mesh (2 mm2 mesh) and 7 cm tall wooden sides. The second sample from the Araponga site, together with the samples collected at the Senhora de Oliveira and Paula Cândido sites, were peeled in a Pinhalense model DPM-02 n° 928 sample peeler, driven by a 0.5-hp liter electric motor. After peeling, remaining husk residues, grains broken during the operation, and eventually drilled were removed from the samples. Then, the samples of peeled coffee were packed in plastic buckets of 20 L capacity, for demucilation through natural fermentation, for 24 hours (pulped coffee). Posteriorly of the fermentation period, the grains in parchment were washed in clean water, rubbing them against each other manually, under running water, and spread in the sieves like afore-mentioned, similar to the natural coffee.To evaluate the maximum potential of the behavior quality offered by the genotypes, the fruit samples were composed only of fruit in the cherry stage, since completely mature. The fruits of lower density, pips, and badly granulated were eliminated from the samples. One of the fruit samples from the Araponga environment was sent to the drying process  in sieves with an area of 1 m-1 was performed by approximation of values, considering the average yield of 480L of “field coffee” for each 60 kg bag of green coffee, which corresponds to the average yield adopted in all regions. Thus, bean production was evaluated in 60-kg bags of processed coffee per hectare (bg ha-1). In the drying process, the grains were spread on the sieves for drying in full sun, until the grains reached 11% moisture (bu). After drying, natural coffee beans with the endocarp attached were kept in double-leaf Kraft paper bags for a rest period of 30 to 40 days, to standardize the moisture content of the grains. Posteriorly this period, the samples were processed and conditioned in impermeable plastic bags and sent for tests physical of grain and sensory quality of the drink.The production of processed coffee was evaluated in liters of “field coffee”  per plot, between May to July. After that, conversion of the volume of coffee collected to bags haThe sieve classification was also carried out from 300g of samples. Flat coffee beans were classified by the percentage of retention in sieves from 14 to 19 . The coffees beans were classified in flat and mocas, evaluated as a percentage of retention of each sieve and with grains retained at the bottom of the sieve. Defects, intrinsic and extrinsic, were classified by the sum of the number of defects found in 300g of the sample, according to the Official Brazilian Classification Table . DefP coSensory analysis of the drink was performed by three tasters and according to the Specialty Coffee Association of America , using aInitially, the hypothesis was formulated that there would be differences between the environments that could be revealed, posteriori, by the formation of clusters based on information from individuals, whose variation between performances would be determined by the macro-differences of the environments. The individuals were grouped according to the Kohonen Self-Organizing Map (KSOM) machine learning technique.KSOMs are an unsupervised learning neural network method that detects similarities between entry patterns through a competition process , 49, 50.In another approach, the hypothesis was formulated that there would be, a priori, differences between individuals provided by the differences between the four environments. The veracity of this hypothesis was evaluated through an Apparent Error Rate (AER).This procedure was adopted with the assumption that the environment whose genotypes belong to is known information. Thus, the consistency of the discrimination of environments was verified using the linear discriminant analysis of Fisher  and AndeFor the construction of the Multilayer Perceptron network (MLP), the Levenberg-Marquardt algorithm of feed-forward propagation with Bayesian regularization (trainbr function in MATLAB) was used to avoid the overfitting problem . The MatThe activation function used was the hyperbolic tangent sigmoid,  another . The modThe Radial Basis Function (RBF) is a type of network considered hybrid, that is, it presents the first stage unsupervised, to grouping the data and, later, a supervised step to capture the pattern obtained. In the first stage of training, the K-means method was used. The number of K groups was given by the number of environments . In the second stage, the training is carried out similarly to that performed in the MLP networks, that is, supervised .The architecture of the RBF is of the feedforward type with one input layer, one intermediate layer, and one output layer . For theThe purpose of analysis using tree-building algorithms is to determine a set of logical conditions (split) ’if-then’ that allows for accurate classification or prediction of cases, known as classification and regression tree models (C&RT) . ClassifThe mathematical background used for the classification tree was defined according to Krasteva et al. :n observations in a parent node P and there are J classes labeled as P1, P2, P3, …, Pj. Let nj be the number of individuals in the class j, where j is evaluated environment. The relative proportion j individuals in the node is denoted by pj. Each binary split si produces two child nodes–left (L), which contains nL individuals and right (R) with nR individuals, such that nL + nR = n. The child nodes contain the relative proportions j individuals in the child nodes are denoted by PjL and PjR. The notation i(p) is further used as a generic notation of impurity, formulated in the present study, based on entropy or maximum deviation reduction to minimize the mean square error. Entropy or maximum deviation reduction is given as:There are pj = 1 class j, then the node is said to be pure, since it contains individuals of only one class (environment). When the entropy is maximized, pj is uniform, then the node is least pure because it contains equal proportions of individuals from each environment. The “tree” and “ISLR” R packages were used for this procedure [When the entropy of a node is zero, rocedure , 61.The basic idea of Bootstrap aggregation or Bagging is to create several similar data sets by resampling (bootstrapping) and regression trees that are performed without pruning and averaging , 62. SomZ = {, , …, }, obtaining the prediction x. Bagging averages these predictions over a collection of bootstrap samples, thereby reducing its variance. For each bootstrap sample Z*b, b = 1, 2, …, B, we fit our model, giving prediction f1(x), f2(x), …, fB(x)). Each model is used as an individual classifier. A new individual will be allocated to the most common class among the predictions of the individual B classifiers [Suppose a training data model ssifiers . The bag1, y1), x, y2, …, xi, yi). The “true” bagging estimate is defined by Denote by The number of trees to grow was fixed as 500. To carry the Bagging, the “randomForest” R package was used .Random forest  is similTo make a classification of new point x:Let p being the number of variables. The “randomForest” R package were used for this procedure [The number of trees to grow were fixed as 500 and number of individuals selected at each tree node was given rocedure .ht(x)) and the individual classifier ht(x) at each iteration [ht(x) have low classificatory power, but when used together H(x), they present good results [In Boosting, bias is reduced by repeatedly readjusting the weights of the training samples, by focusing on ‘‘difficult” examples from previous samples . Boostinteration . The ind results , 66. The results .In The performance of those methods has been verified using the testing database. Also, k-fold cross-validation procedure was used to mitigate the bias caused by the random selection of the data , 69. Themj is the number of genotypes from the environment Al that were classified in another environment Al′, where l′ = l and l = 1, 2, …, 4 environments; considering: nl is the number of genotypes related to the Al environment.The apparent error rate (AER) measures the efficiency of the methods to classify individuals correctly in the previously established environments. AER was determined by the ratio between the number of wrong classifications and the total number of classifications, according to Cruz et al. :AER(%)=Final AER for each method was given by the average of the 10 replicates and for the comparison of efficiency and definition of the methodology with the best classification power was performed the Scott-Knott test, at a 5% probability.The calculation of the relative importance of the traits was carried out according to the specific technique of the methodology (s) with the best classificatory power. The importance analysis of traits was performed through the technique indicated by Fischer . For eacAnother technique utilized to obtain the importance of traits, not yet studied in other articles and proposed in the present work, is the randomization of each trait at the input of the network. In this way, the randomized trait loses its relationship with the output trait. If this randomization results in a reduction in the efficiency of the network, it implies that the randomized trait is important in printing the final result, according to the magnitude of the reduction in efficiency resulting after its randomization. This proposal is in the Genes software .AERmod) can be compared with the apparent error rate (%) of the complete network prevision (AERcom), to obtain the magnitude of the effect of the input trait for each test set. The magnitude of the effect of the input trait j was given by the sum of the magnitudes in the test sets performed  of each trait, according to the equation below:RIj is the relative importance of trait j in percentage; AERmod (j) is the apparent error rate of the model modified with the randomization of trait j; AERcom is the apparent error rate of the complete model; i = number of repetitions (test set), ranging from 1 to 10; and j = number of traits, ranging from 1 to 31.Each input trait the apparent error rate (%) of the modified network prevision  for all genotypes in different environments. Similar results were found by Gamonal et al. , when evThe clusters formed by the pattern recognition analysis performed by the Kohonen self-organizing maps (KSOM) method were not efficient in revealing the grouping of the individuals in their respective assessment environments . Thus, eIn James et al.  had alreFischer and Anderson discriminant analyzes were compared with machine learning models, according to the apparent error rates for the test data set, considering the 10 repeats . The disBased on the confusion matrix presented in As the individuals from the Araponga—Natural and Araponga—Pulped environments present redundant values for the pre-harvest traits, the results found by the confusion matrix , reinforUnlike the results obtained in this study, when using neural network modeling and Fisher discriminant analysis for selection among sugarcane families, Peternelli et al.  found thCarica papaya L) [Studies carried out on the diversity of papaya accessions (apaya L)  and studapaya L) , showed apaya L) . It is iThe analysis of the importance of the variables was evaluated only for the PMC and RBF models since they presented better results. For this, two strategies were considered based on the results of neural networks. The first was indicated by Fischer , each exA cut-off point was created on the axis of relative importance, where only the traits that presented values of relative importance greater than 15%, on average in the four quadrants of The phenotypic traits: plant height, mature fruit size, and production, together with the sensory trait body, they were mainly responsible for the discrimination of environments . These pPulped coffee had the highest score for the body attribute . BesidesMature fruit average size increased as the altitude of the production site was higher. In this way, Araponga presented larger fruits, followed by the fruits produced in Senhora de Oliveira, and finally, the Paula Cândido, a site of lower altitude . The altIn Paula Cândido the height of the plants was 1.831m (± 0.139). The greater density of plants can influence their growth due to phototropism . This co-1), followed by the productivity in Araponga (57.71 bg ha-1) and Senhora de Oliveira (21.64 bg ha-1)  . These rThe morpho-agronomic traits maturity uniformity, top diameter, cercosporiosis, and rust severity presented a little contribution to the process of classifying individuals according to the different production sites . This shSimilarly, the sensory traits acidity and fragrance/aroma also made little contribution to the process of classifying individuals in environments . These rMachine learning models are able to discriminate coffee samples submitted to different environments and post-harvest processing more efficiently than linear statistical methods. However, among the various models used, the artificial neural networks of Radial Basis Function and Multilayer Perceptron presented a lower apparent error rate average  and, thus, proved to be the most efficient.Finally, the analyzes demonstrated the presence of environmental and post-harvest processing effects in the expression of traits, which reflects in a multivariate way in the productive traits of the coffee tree and its final product. By the techniques of the importance of traits making trait value to zero and randomizing the trait value, based in artificial neural networks, the main traits responsible for the differentiation of production sites were: fruit size, plant height, and production; in addition to the sensory trait “Body”, which was fundamental to discriminate the type of post-harvest processing.


Thinopyrumn intermedium, IWG) as a perennial grain crop have been ongoing since the 1980’s. Currently, there are several breeding programs within North America and Europe working toward developing IWG into a viable crop. As new breeding efforts are established to provide a widely adapted crop, questions of how genomic and phenotypic data can be used among sites and breeding programs have emerged. Utilizing five cycles of breeding data that span 8 years and two breeding programs, University of Minnesota, St. Paul, MN, and The Land Institute, Salina, KS, we developed genomic selection (GS) models to predict IWG traits. Seven traits were evaluated with free-threshing seed, seed mass, and non-shattering being considered domestication traits while agronomic traits included spike yield, spikelets per inflorescence, plant height, and spike length. We used 6,199 genets – unique, heterozygous, individual plants – that had been profiled with genotyping-by-sequencing, resulting in 23,495 SNP markers to develop GS models. Within cycles, the predictive ability of GS was high, ranging from 0.11 to 0.97. Across-cycle predictions were generally much lower, ranging from −0.22 to 0.76. The prediction ability for domestication traits was higher than agronomic traits, with non-shattering and free threshing prediction abilities ranging from 0.27 to 0.75 whereas spike yield had prediction abilities ranging from −0.22 to 0.26. These results suggest that progress to reduce shattering and increase the percent free-threshing grain can be made irrespective of the location and breeding program. While site-specific programs may be required for agronomic traits, synergies can be achieved in rapidly improving key domestication traits for IWG. As other species are targeted for domestication, these results will aid in rapidly domesticating new crops.Perennial grains could simultaneously provide food for humans and a host of ecosystem services, including reduced erosion, minimized nitrate leaching, and increased carbon capture. Yet most of the world’s food and feed is supplied by annual grains. Efforts to domesticate intermediate wheatgrass ( Zea mays), wheat (Triticum aestivum), and rice (Oryza sativa), providing nearly 60% of human calorie consumption (fao.org). Additionally, 70% of arable land is planted to annual crops (Sorghum bicolor), sunflower (Helianthus), and pulses are in development . Intermediate wheatgrass is native to Eastern Europe and the Mediterranean region  often suggested single or a few genes with large effects , which wWhile original IWG breeding work utilized recurrent phenotypic selection, modern genetic tools have provided breeders with new options. One of the most promising genetic tools for breeding is genomic selection (GS). Proposed by While multiple locations are breeding IWG, there has been limited integration of information between breeding programs. The opportunity to utilize molecular tools like GS across wide environments could open new potentials for faster genetic improvement, specifically by increasing the training population size , integraHordeum vulgare), a multi-environment GS model was shown to increase prediction accuracy 11% over single-environment analysis (Pinus taeda) were relatively consistent across environments as long as the environments were within the same breeding zone. However, in both of these examples many of the lines had true replication, whereas the IWG programs usually have single genotypes due to the challenges of cloning large numbers of individuals. As IWG breeding expands, the ability to combine data across multiple locations and breeding programs with differing, unreplicated, germplasm could be beneficial to increasing the rate of genetic gain.Applying GS to IWG across multiple environments could be a very cost-effective and efficient method to increase IWG breeding gains, but even within annual crops there is limited information about multi-site or multi-environment GS compared to single site GS studies. analysis . ResendeGiven the need for new crops and the challenges associated with developing perennial crops, this study focused on (1) How data from diverse sites and breeding programs could be combined to improve prediction abilities of models for enhanced selection decisions, (2) The ability of GS to accurately predict traits across a range of environments and traits, with emphasis on differences between domestication and agronomic traits, and (3) How insights gained from IWG breeding could be applied to other potential new crops undergoing domestication.Using terminology consistent with –1 of N was applied in April of each year. Weed control in the plant nurseries was primarily done manually with a one-time application of herbicide Dual II Magnum  in April at a rate of 1.2 L ha–1. Experimental genets were surrounded on all sides with IWG plants. While each program is selecting genets for its respective growing region, all original UMN material, i.e., UMN-C1, came from TLI-C3, providing a common genetic link between the programs. All genets were evaluated as single plants with no replication.UMN-C1 consisted of 2,560 genets from 66 half-sib families from TLI-C3 material. Genets were established in the field, St. Paul, MN  in the fall of 2011 with field observations in 2012 and 2013. Additional information about the UMN-C1 population can be found in Field evaluations were completed for several key domestication and agronomic traits including: plant height, spikelets per inflorescence, spike length, spike yield, shattering, seed mass, and free-threshing. Plant height was measured after plants reached physiological maturity and was measured from the ground to the tip of the tallest spike. Shattering was measured on a five point scale, with 0 representing no shattering and 4 representing over 50% shattering by visual observation . Spike lPstI and MspI. Libraries were prepared by multi-plexing 192 samples per GBS library, and all GBS libraries were sequenced on Illumina HiSeq 2500. Single nucleotide polymorphisms (SNPs) were called using the GBS pipeline in Trait Analysis by aSSociation, Evolution, and Linkage (TASSEL) software version 5.2  minor allele frequency greater than 0.01, (2) each SNP was called in 30% or more of the individuals, (3) GBS tags uniquely aligned (one location) to the reference genome to prevent aligning to orthologous sequences, (4) only biallelic SNPs were retained, (5) a minimum read depth of four tags per individual were required to call a homozygote. Using a custom Perl script, homozygotes that had less than four reads per site were set to missing. Heterozygotes were called with a minimum of two contrasting tags. Additionally, any genet that had more than 95% missing SNPs calls was discarded from the analysis, resulting in a final data set of 23,495 SNP loci and 6,199 genets. Any missing genotype calls in the final data set were imputed using Beagle version 4.1 using the default settings .K = 1–10) were evaluated using the admixture model with 100,000 reps and the first 25,000 as burn-in. Ten replicates of each value of K were assessed, with Structure Harvester  was performed on the imputed marker matrix in R . The total variance, V, is defined as G structure accounts for the variation between genets using the realized additive genomic relationship matrix and is defined as G = K where K is the realized additive genomic relationship matrix. K is computed as θMM’ where M is a matrix with n individuals and m columns of markers and θ is a proportionality constant  respectively and ρ is the correlation parameter between rows and columns, respectively. A minimum of 350 observations were recorded from each cycle for use in GS models after adjusting phenotypic data for genetic relationship and spatial location in the field.where constant . The genn rrblup  R packagrrBLUP kin.blup function  were developed to assess prediction ability. Within each cycle, a fivefold cross-validation method was repeated 100 times. For each iteration of the cross-validation, we randomly sampled all of the genets that were in a given cycle, splitting the genets into a training population (80% of genets) and a prediction population (20% of genets). The GS model was fit with the training population using function , with prfunction :y is a vector of observations , W is a design matrix relating genets to observations, g is a vector of genotypic values, and e is a vector of random residuals. The vector of genotypic values, g, is distributed as g ∼N and the BLUP for the respective phenotype. From the GS model, variance components were extracted to calculate genomic heritability using the genetic variance and residual error variance using the formula :h2 is narrow-sense heritability, where psychometric R package  locus and the dominant mutation of the Q gene. The Tg loci has been reported to explain up to 44% of the variation in threshability, and at least five other quantitative trait loci (QTLs) for threshability have been observed in wheat (Br (brittle rachis) locus controls shattering in wheat with two dominant genes and is homoeologous to the Btr loci in barley  two and five generations of selection had occurred for UMN and TLI respectively, allowing for potential population divergence.We evaluated models using a leave-one-out approach for all cycles, which should result in the largest training population available for GS prediction. This leave-one-out strategy insured that the models were not biased by the size or the relationship of the training population  in compaThe results from these models were inconsistent, with the leave-one-out model performing as well as or better the majority of the time. Often breeding program-specific or PCA-specific subsets performed well, but there was no clear pattern to this performance . For exaAs concerted efforts to develop new crops through domestication of crop wild relatives continues for food security and environmental benefits , we haveThese results show that as plant species undergo early domestication, collaboration will accelerate progress, i.e., not every breeding program will have to solve the same domestication problems and that progress can be made across programs. As domestication traits are fixed, breeding programs can work toward developing adapted lines for targeted growing regions. These data provide several potential use cases for breeding programs. If a program is beginning, there appears to be little downside in utilizing training data sets from across programs. As programs mature and have sufficient, data from multiple years and locations, GS models can be developed within programs. This could be especially important for agronomic traits such as spike yield as combining data across programs could result in negative predictions . HoweverOur results show that GS can be a powerful tool in breeding programs, yet GS is not a single, stand-alone solution for quickly developing new crops. While we envision GS improving with larger data sets and new statistical model development, multi-environment predictions are extremely complex. To fully leverage genomic resources, GS should be integrated with phenomic and environmental data. High-throughput phenotyping is an emerging field that is providing dense phenomic measurements  that havDomesticating crop wild relatives is a challenging and time consuming task . PreviouPerennial grains derived from the domestication of wild species hold much promise for environmental and human benefit. To achieve these benefits, specific traits of wild species will need to be modified. Within IWG, free-threshing and non-shattering seed types are two key domestication traits that must be improved for wide-scale adoption. In addition, the economic yield of IWG must be sufficient to incentivize the transition to new crops. Along with fixing key traits for domestication, breeding efforts should also ensure that crops are broadly adapted .The ability to use molecular tools such as GS, combined with modern breeding methodologies, may allow perennial crops and crop wild relatives to compress the 10,000 year selection history of many annual crops into a few decades. While GS predictions for agronomic traits like spike yield were low between breeding sites and environments, significant synergies could be achieved by utilizing collective information about domestication traits. While site-specific or regional programs will be necessary to breed for the best locally adapted genets, progress made toward improving key domestication traits could be shared among all programs. This is especially important for resource-limited programs that are domesticating new crops, allowing improvement for traits that are less environmentally influenced and are essential for domestication. Early domestication work could be carried out by a single program or shared among programs with each program phenotyping a few lines in diverse locations to quickly and efficiently improve key traits. As more programs are initialized for the breeding of IWG, they will be able to identify germplasm that has key domestication traits and be able to focus breeding efforts toward achieving higher site-specific agronomic performance.https://www.ncbi.nlm.nih.gov/bioproject/) BioProject accession numbers PRJNA563706, PRJNA609095, and PRJNA608473. All phenotypic data and scripts for data analysis have been placed in the Dryad Digital Repository (https://doi.org/10.5061/dryad.3j9kd51d9).The genotypic datasets analyzed for this study have been placed in the NCBI Sequence Read Archive (SRA) (JC, LD, and PB conceived experimental ideas and methods. LD, JA, XZ, and PB conducted all field evaluations. LD, JP, PB, and XZ performed DNA extraction and genotyping. JC completed data analysis and wrote the manuscript. All authors read, reviewed, and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.