Simulation studies show a reasonable type I error control and an excellent power of the proposed method compared to its counterparts. We further show the utility of the method by applying it to two data sets: the Human Liver Cohort and the Alzheimer Disease Neuroimaging Initiative data set, and novel genes are identified. Our method has broad applications in other fields in which the interest is to evaluate the joint effect (linear or nonlinear) of a set of variants.Genome-wide association studies focusing on a single phenotype have been broadly conducted to identify genetic variants associated with a complex disease. The commonly applied single variant analysis is limited by failing to consider the complex interactions between variants, which motivated the development of association analyses focusing on genes or gene sets. Moreover, when multiple correlated phenotypes are available, methods based on a multi-trait analysis can improve the association power. However, most currently available multi-trait analyses are single variant-based analyses; thus have limited power when disease variants function as a group in a gene or a gene set. In this work, we propose a genome-wide gene-based multi-trait analysis method by considering genes as testing units. For a given phenotype, we adopt a rapid and powerful kernel-based testing method which can evaluate the joint effect of multiple variants within a gene. The joint effect, either linear or nonlinear, is captured through kernel functions. Given a series of candidate kernel functions, we propose an omnibus test strategy to integrate the test results based on different candidate kernels. A  Methods on genome-wide association studies (GWAS) are mostly focused on single variant  analysis with a single phenotype, the so-called single-variant single-trait analysis. Increasing evidence shows that pleiotropy, the effect of one gene on multiple phenotypes (often correlated), plays a pivotal role in many complex traits . For exaFor a multi-trait analysis, one commonly applied method is the one-way multivariate analysis of variance (MANOVA) . UnfortuThese limitations motivated the development of gene- or pathway-based association analysis aimed at improving the statistical power and gaining novel insight into disease etiology . FirstlyMost reports in the literature on multi-trait analysis are focused on a single-variant analysis, which shares the same limitation as described for the single-trait GWAS. Although methods for gene-based analysis focusing on a single trait have been developed, multi-trait analysis focusing on genes or gene sets is largely under-developed. There is a pressing need to develop a gene-based method for a multi-trait analysis.p-value. This idea, however, could inflate the type 1 error rate due to the greedy process of kernel selection. We recently proposed a nonparametric KBT testing procedure which relaxes the distributional assumption required in most KBT methods  method is gaining much popularity recently due to its power and flexibility in capturing potential nonlinear effects . The pow methods . The asyp is relatively small. In this work, we borrowed the same idea but relaxed the large p assumption required for the normal approximation and proposed an omnibus testing procedure when multiple candidate kernels are available. Obtaining a p-value needs almost negligible computation and can be extremely fast. When extending the method to a multi-trait analysis, we adopted a Fisher p-value combination (FPC) method with correlated dependent variables, as proposed by Based on empirical studies, the approximation method could be underperformed when We conduct extensive simulation studies to evaluate the type I error control and power and further compare it with its counterparts. We demonstrate the performance of our proposed method through two real data applications of the Human Liver Cohort (HLC) study and the Alzheimer Disease Neuroimaging Initiative (ADNI) study. The results tell which genes are specific to a single phenotype or contributed to a common genetic construction of multiple phenotypes. Our OMGA method enriches the literature of genome-wide gene-based multi-trait association analysis and has broad applications in other fields where the interest is to evaluate the joint effect (linear or nonlinear) of a set of variants.To model the association between a gene and a quantitative trait, we consider the following semiparametric model ,Yi is the response variable for the i-th individual, n is the sample size, α is the effect corresponding to Wi = T, a vector of H-dimensional covariates containing variables such as age and gender, xi = T is a vector of a p-dimensional SNP set in a given gene where p can be large, h(⋅) is an unknown function that captures the joint effect of multiple variants in a given SNP set, and εi is the random error with mean 0 and variance σ2. Here, we relax the error distribution assumption for the error term which does not have to follow a normal distribution.where H0: h(⋅) = 0, while adjusting for the effects of covariates. h(⋅) is modeled as a random effect and h(⋅)∼N where τ2 is the variance and K is a kernel matrix which measures the similarity between individuals across multiple SNP variants. However, the normality assumption on h(⋅) limits its power when this assumption is violated. To relax this assumption, Following model (1), assessing the effect of multiple variants in a given SNP set  is equivalent to test the hypotheses Yi = μ + αTWi + εi; Kθ. In practice, the choice of kernel function for Kθ depends on the underlying relationship between SNPs and the disease response. For example, a linear kernel is applied if the relationship between multiple SNP variants and the disease response is linear, and a Gaussian or polynomial kernel can be applied if a nonlinear relationship between multiple SNPs and the disease response is assumed. Several widely used kernel functions include the linear kernel Kθ = exp(−||Xi−Xj||2/θ). These kernels will be our candidate kernels in the simulation and real data analysis.where m is the eigenvalues and ϕm(⋅) is the orthonormal eigenvectors of the kernel K. For any positive integer k, let Tn follows a chi-square distribution, i.e.:Let V1 with H = I−n−1J as a projection matrix. Then, an asymptotic α-level test rejects the null ifwhere where B = HKH. Then, the p-value of Tn can be obtained.where ∘ represents the Hadamard product, The method described above works for a given kernel function. There are various kernel functions available to use. For example, if a linear relationship is assumed, then one can apply a linear kernel, while a Gaussian kernel can be applied when potential nonlinear relationship exists. Thus, the power of the proposed test statistic largely depends on the choice of the kernel function. If the optimal kernel function that captures the underlying true relationship cannot be determined, the testing power will suffer. In practice, the true relationship is generally unknown, so does the choice of the kernel function.L candidate kernels denoted by K1,K2,⋯,KL,, we can apply the proposed method and get the corresponding p-value denoted by p1, p2,…pL. These L kernel functions can come from a wide range of choices, such as the linear kernel, the Gaussian kernel, and the polynomial kernel. Then, we can transform the L p-values by a Cauchy transformation and combine the transformed p-values to form a new statistic π} follows a Cauchy distribution. Then, the p-value of TO can be approximated byIf p-value method. In addition, it works well under different correlation structures. Thus, when the underlying true relationship is unknown, if the choice of the kernel function is rich enough, we can always achieve good power regardless of the underlying disease gene action mode. More importantly, this method is computationally fast and robust to different dependence structures between p-values  = μ and Var(T) = σ2. Then, δ and τ can be computed as δ = σ2/2μ and τ = 2μ2/σ2. Here we adopt the method proposed by d-dependent p-values. The variance σ2 can be calculated asWhen the  freedom . For corpothesis . Let E(Tjk = cov{−2log(pj),−2log(pk)}. jk based on which we can estimate σ2 [please refer to 2 and μ]. An R package implementing the method can be found at https://github.com/jjyang2019/FisherCombinationStat. Then, based on the estimators of μ and σ2 for the gamma distribution parameters, the overall testing p-value of T can be calculated asLet δp-values, multiple testing adjustment such as FDR can be applied to claim the significance of a gene.The number of the gene-level test is much smaller than the number of the SNP-level test. After obtaining the gene-level https://github.com/SAONLIB/RMMLR. For the MANOVA analysis, the association between each SNP in a gene and multi-trait is implemented with the MANOVA function in R. The minimum p-value in a gene is recorded as the gene-level p-value.To evaluate the statistical power and the type 1 error rate of the proposed method, we conducted extensive simulation studies to compare the proposed method (OMGA) with some existing methods. Specifically, we compared with the method of multivariate multiple linear regression (RMMLR) proposed by https://sourceforge.net/projects/episimsimulator/. We simulated correlated quantitative phenotypes with the following model:The genetic data were simulated to mimic the real structure of a gene through the software EpiSIM . The sofi = T is a d-dim random error vector generated from a multivariate normal distribution with mean 0 and covariance Σ; Yi = T is a d-dim-dependent trait vector; Zi1∼N and Zi2∼Ber(0.6) are two independent covariates; Xi = T is a p-dim SNP genotype vector in a gene. Under all scenarios, we simulated genes with different dimensions, i.e., p = 50 and p = 100, and with different sample sizes, namely, n = 100, 200, and 400. For the number of traits, we assumed d = 5. The correlation between traits was assumed to be p = 0.3 and 0.8, with the purpose to evaluate the impact of correlation on the testing power. In each scenario, we applied 1,000 simulation replications.where ϵh(⋅) = 0] by the proportion of results that incorrectly rejected the null hypothesis. To evaluate the power, we set up four different scenarios for the h(⋅) function and recorded the proportion of results that rejected the null hypothesis. Under scenario A, we assumed that h(x) = 0.3x2 + 0.6x4−0.07x8.We assessed the type 1 error rates under the null hypothesis [i.e., To mimic the situation where a large number of SNPs influence the traits, we assumed the following model:SM consists of a predefined set of 10 SNPs with main effect, and SN contains a set of 30 SNP pairs with interactions. Both {αk,k ∈ SM} and {βkk′, ∈ SN} were generated from a uniform distribution with Unif , and were fixed for all simulation replicates once generated. Under scenario C, we set CM = 0.02 and CN = 1.8, which gave a combination of weak main effect and relatively strong interaction effect. Under scenario D, we set CM = 3.8, and CN = 0, with a pure main effect model. The four scenarios with their corresponding mean functions are summarized here:where Scenario A: Nonlinear effecth(x) = 0.3x2 + 0.6x4−0.07x8Scenario B: Linear effectScenario C: Weak main but strong interaction effectsh(x) = 3.8∑k ∈ SMαkxkScenario D: Pure main effectsp = 0.3 are shown in The power simulation results for the case with p = 0.8. Compared with the p = 0.3 case, the power of RMMLR and MANONA decreased, while our proposed method can still maintain a comparable power as the p = 0.3 case. Note that the MANOVA method implemented here uses a minimum p-value approach among multiple SNPs to denote a gene-level p-value. The simulation result echoes the work of p-value method performs the worst among the three methods that the authors compared in their simulation study.In summary, the simulation results clearly demonstrate that the proposed omnibus test method can maintain a reasonable type I error control while having better power than the other two methods under different scenarios. This is because the proposed omnibus testing method can efficiently capture a linear or a nonlinear relationship between multiple variants in a gene and multiple phenotypes. In practice, the underlying true disease–gene relationship is never known. This makes our proposed omnibus test method particularly attractive in real application since it does not put any model assumption. As long as the choice of kernel functions is rich enough, the omnibus test can achieve its power advantage against the other methods which only function well under the desired model assumption.https://www.synapse.org/#!Synapse:syn4499. The HLC study aims to explore the genetic architecture of gene expressions in human liver. There are a total nine phenotypes of P450 enzymes  from unrelated liver samples of Caucasian individuals. The samples were removed if their genotype and phenotype information were missed, and the final data included in our study contained 170 individuals. DNAs were genotyped by the Illumina 650Y SNP and Affymetrix 500K SNP genotyping arrays. SNPs with a minor allele frequency (MAF) less than 5% were removed. The total number of SNPs that remained was 312,082, which were further mapped into 11,579 genes using tools from the NCBI website ftp://ftp.ncbi.nih.gov/snp/.To demonstrate the power and the applicability of our approach, we applied the proposed method OMGA together with RMMLR and MANONA to a HLC study data set, which can be downloaded from The cytochrome P450s compose a superfamily of monooxygenases which are critical for anabolic and catabolic metabolism in almost all living organisms . With itp-values for the six traits and applied the p-value combination method to get a gene-based multi-trait p-value. In the multi-trait analysis, we also applied the RMMLR and the MANONA methods. The Q–Q plot of the single-trait analysis is shown in p-value inflation was observed. Q–Q plot of the multi-trait analysis.For each individual trait, we first conducted a marginal gene-based single-trait analysis with the omnibus KBT. Then, we integrated the –6. This leads to no significant genes in our analysis. Here, we only listed a few top genes with p-value less than 6 × 10–5 as suggestive significance. In the single-trait analysis, the top genes for each trait are HAUS8 and IRS12 for CYP1A2, TRAPPC10 for CYP3A4T, TARID and FUNDC2 for CYP2C9, and PAPLN for CYP2A6. No genes pass the suggested threshold for trait CYP2B6 and CYP2C8 . For the multi-trait analysis, we listed in TARID, TRAPPC10, and HAUS8 were also in the list of single-trait analysis. Gene ATAD3C is not shown in the top list of the single-trait analysis. This may be due to the low power of the single-trait analysis. If we ignore the correlation information among the six enzyme traits and only focus on a single-trait analysis, we may miss some discoveries. For the top four genes by OMGA, the p-values by RMMLR and MANOVA are all quite large. This could be due to the potential complex functional relationship between the genes and the traits. RMMLR and MANOVA were not designed to capture those complex relationships.If we use the genome-wide gene-level Bonferroni correction, the threshold to claim a significant gene level significance is 4.3 × 10ATAD3C has been reported in literature to be associated with aldosterone metabolism and P450 enzyme  is a central nervous system degenerative disease with insidious onset and chronic progress and has affected over 5.5 million Americans, especially among the elderly over the age of 65 years. ADNI provides pre-calculated volumes of five cortical regions including entorhinal, hippocampus, ventricles, midtemp, and fusiform. Brain atrophy is a typical clinical symptom among AD patients . StudiesAPOE4 alleles as the covariates. The Q–Q plot of the gene-based single-trait analysis is shown in p-value inflation was observed. Also, there is no strong indication of significant signals either. Then, we carried out the multi-trait analysis which can more accurately reflect the brain atrophy in AD patients. We also applied MANOVA and RMMLR methods for multi-trait analysis. The Q–Q plot of the multi-trait analysis results by OMGA is shown in p-value inflation.We first conducted the marginal single-trait analysis with the proposed gene-based omnibus kernel testing approach. We log-transformed the volumes of the five cortical regions and took the age, education level, gender, and –5 in SNORA30 and TLR4) that were not in the single-trait analysis list but showed up in the multi-trait analysis list are highlighted in bold font in p-values by OMGA are uniformly smaller, indicating the power of OMGA by taking both linear and nonlinear effect into consideration.Again no significant genes were identified based on the genome-wide gene-level Bonferroni threshold. Here, we listed the top 12 genes based on a suggestive threshold of 5 × 10RBM45, known as the RNA-binding motif protein 45 or developmentally regulated RNA-binding protein-1 (Drbp1), has been shown to be associated with the degenerative neurological changes in AD patients (UPK1B has been shown to be cooperated with CD9 and CD81 and is directly involved in the pathological process of AD (TLR4 reduces microglial activation, increases Aβ deposits, and exacerbates cognitive deficits in a mouse model of AD (TLR4 and CD14 were closely related to AD (TLR2 and TLR4 on the peripheral blood mononuclear cells of AD patients (For the 12 genes associated with multi-trait of brain atrophy in AD patients, some of them have been reported in the literature. For example, gene patients . Gene UPss of AD . Mutatioel of AD . A studyed to AD . Others patients . These ep-value can be quickly computed with the asymptotic results, making the method computationally attractive. Second, it can capture a potential nonlinear effect within genes by using a nonparametric KBT procedure. By incorporating different kernel functions, potential linear or nonlinear genetic effects can be captured and tested. When a given series of candidate kernel functions is available, the omnibus testing procedure is robust against misspecification of kernel functions. Moreover, it is built upon the Cauchy transformation and is computationally fast (Increasing evidence has shown that, for correlated phenotypes, multi-trait analysis can significantly increase the power of association analysis e.g., . Given tlly fast . Thus, tWe conducted extensive simulation studies to evaluate the type I error control and the power of the proposed method. The results show that the proposed OMGA method can maintain a reasonable type 1 error rate and achieve great power compared to other popular methods such as MANOVA and RMMLR. Furthermore, the omnibus testing procedure incorporating different kernels performs as well as if the underlying true genetic function is correctly specified. Thus, the method is safe to apply in real applications regardless of the underlying disease function, making the method practically attractive.p-values to assess the joint association. The method developed by p-values have to take the correlation information into consideration. Otherwise, the results can be biased. Ideally, the first framework should be preferable since it models multiple traits simultaneously in one joint model. On the other hand, the second framework has its advantages. For example, it can be computationally less expensive and ease theoretical evaluations. Especially with the proposed method in this work, the second framework can be a better choice since the asymptotic evaluation of the joint association statistics can be theoretically challenging or may not even be feasible.For multi-trait analysis, there are two different frameworks proposed. One is to jointly model multiple traits as a multivariate response and further assess their association with SNP variants. This framework can directly take correlation information into consideration. Methods for such type of multi-trait analysis include the RMMLR and the MANOVA methods as discussed in this work and many others (e.g., https://github.com/yamin-19/OMGA.Our method can be easily applied to a genome-wide pathway-based multi-trait analysis. It is known that genes usually do not work alone. For example, cellular pathways and complex molecular networks are often more directly involved in the progression and the susceptibility of diseases. Thus, a pathway-based analysis can shed light on the mechanics of complex diseases. On the other hand, the current study only focused on quantitative multivariate phenotypes. It can be extended to qualitative response variables or a combination of qualitative and quantitative phenotypes. However, the extension is non-trivial and will be studied in our future investigation. The R code that implements the method can be found in GitHub at https://www.synapse.org/#!Synapse:syn4499. The ADNI dataset can be accessed through http://adni.loni.usc.edu/.The HLC dataset can be downloaded at YD implemented the method and drafted the manuscript. TH derived the kernel testing method. RF, SL, and HC were involved in the simulation and data analysis. YC conceived the idea, designed the study, and drafted the manuscript. All the authors read 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.


P-values on the -log10 scale with the gene structure and LD matrix. Importantly, IntAssoPlot is designed to plot GWAS results with LD calculated from genotypes different from those in GWAS analysis. IntAssoPlot provides a powerful visualization tool to gain an integrated insight into GWAS results. The functions provided by IntAssoPlot increase the efficiency by revealing GWAS results in a publication-ready format. Inspection of the output image can provide important biological information, including the loci that passed the genome-wide significance threshold, genes located at or near the significant loci, and the extent of LD within the selected region.Genome-wide association study (GWAS), exploring the historical and evolutionary recombinations at the population level, is a major method adopted to identify quantitative trait loci (QTL) for complex traits. However, to summarize GWAS results, gene structure, and linkage disequilibrium (LD) in a single view, multiple tools are required. It is tedious to generate these three results and manually put them together; moreover, it may eventually lead to inaccuracies. On the other hand, genotype markers are usually detected by DNA- and/or RNA-Seq. For GWAS analysis based on RNA-Seq, markers from DNA-Seq provide more genetic information when displaying LD. The currently released software package does not have this function for an integrated analysis of LD, using genotypic markers different from that in association analysis. Here, we present an R package, IntAssoPlot, which provides an integrated visual display of GWAS results, along with LD and gene structure information, in a publication-ready format. The main panel of an IntAssoPlot plot has a connecting line linking the genome-wide association  During the past few years, a sufficient number of molecular markers and availability of fast and accurate variance component estimation methods have made GWAS an ideal tool to detect genetic relationships with complex traits . HoweverTo efficiently visualize GWAS results, packages such as LocusZoom, cgmisc, Ldlink, and Assocplots have been developed . LocusZoWe, therefore, developed an R package called IntAssoPlot, which would not only display the relative significance loci, gene structure, and linkage disequilibrium matrix derived from marker dataset (which is same or different from that for GWAS), but would also draw a connecting line to link them in one panel without the need for further manual arrangement. Additionally, IntAssoPlot is designed to show GWAS results at a single gene level, displaying not only information related to significant loci and linkage disequilibrium structure, but also that related to the detailed genetic structures of the significant loci.1, and reshape2  with the rest, LD heat map matrix, highlighted selected marker, and linking line , right border (end position), genome annotation file, GWAS result, and genotype file are required. The main panel of IntAssoPlot contains three layers and connecting lines. The upper layer shows 2) and RStudio (an integrated development environment for R3) should be downloaded and installed on the computer system. Currently, IntAssoPlot is hosted on GitHub. To download and build IntAssoPlot from GitHub, an R package devtools is required. Importantly, IntAssoPlot also imports some other R packages. When launching R, the depended packages, devtools, and IntAssoPlot can be installed using the following commands in R environment:R )> BiocManager:install)> devtools:install_github)To generate images by IntAssoPlot, there are two steps: (1) data input, (2) generate the image. Basically, IntAssoPlot needs three types of data, including association mapping results, gene annotation file, and genotype file, of which we have included detailed examples of these data in IntAssoPlot. When reading data into the R environment, R function read.table can be used. Below, we provide a detailed case study to illustrate the usage of IntAssoPlot.We present the features of IntAssoPlot and provide an example of the resulting plot  using prr2 or D′) include lead SNP LD (leadsnpLD in IntAssoPlot) and triangle LD (triangleLD in IntAssoPlot). While the lead SNP LD function calculates LD of the most significant or user-provided loci with the others, the triangle LD function calculates the matrix of each pairwise LD from the specified region. All LD values are colored according to the specified color scale, which can be further modified, allowing the package to fit into broader applications  the chromosome start and stop positions  or (2) aications . Currentications . The outications  by settiications , thus reNotably, according to the input, linking lines and association signals can be selected and highlighted , respect® CoreTM i7-6700K processor and Windows 10 operation system, it was found to take less than 30 s to generate the integrated image, hence demonstrating the efficiency and performance of IntAssoPlot. However, <3 min will be consumed to print the image in the R environment. In Generally, generating an image by the function IntGenicPlot requires very limited time. However, for integrated visualization of GWAS results on a regional scale, the time is limited by the number of markers and the samples required to display the LD matrix. In the current example , we haveP-values on a -log10 scale, the genome annotation, and the LD matrix, calculated from genotypes same or different from those in GWAS analysis. Inspection of the output image could reveal: (1) the extent of LD within a region with the most significant associated variants, providing important biological evidence to infer the candidate gene, (2) the most significantly associated genetic feature located within the candidate gene, and (3) the LD between the loci, demonstrating the mechanism of functional variation for further experimental validation.At present, it is difficult to summarize GWAS results, genomic context, and linkage disequilibrium (LD) in a single view. The currently available tools cannot integrate, analyze, and display LD using genotypic markers different from those in association analysis. Therefore, we were prompted to present IntAssoPlot, an R package, aimed to solve these challenges. The output image of an IntAssoPlot plot, which is in a publication-ready format, draws a line connecting the https://github.com/whweve/IntAssoPlot.Functions in IntAssoPlot are designed to be user-friendly, with attention to the quality of visualization, owing to the characteristics of R programming language. Documentation, outlining the detailed functionality, and parameter usage of each function, is available for each of the functions in IntAssoPlot. Detailed examples of the usage of IntAssoPlot have been created based on the analysis of data from a previously reported study on the genetic basis of maize drought tolerance . The Inthttps://github.com/whweve/IntAssoPlot.The datasets generated for this study can be found in the FH, SD, and HW contributed to implementation, documentation, and manuscript writing. FQ contributed to conception, project design, oversight, and manuscript review. All authors read 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.


Brassica oleracea L.), and the second is a data set from a multilocation diallel cross trial in maize (Zea mays L.) without reciprocals. With SASHAYDIALL, diallel experiments conducted in single sites can be analyzed to estimate various genetic parameters, and this analysis is extended over locations or environments to assess genetic effect × environment interaction. SASHAYDIALL is user-friendly software that provides detailed genetic information from diallel crosses involving any number of parents and locations.Different methods of diallel crossing are commonly used in plant breeding. The diallel cross analysis method proposed by Hayman is particularly useful because it provides information, among others, on additive and dominance effects of genes, average degree of dominance, proportion of dominance, direction of dominance, distribution of genes, maternal and reciprocal effects, number of groups of genes that control a trait and exhibit dominance, ratio of dominant to recessive alleles in all the parents, and broad-sense and narrow-sense heritability. In this paper, we fully describe a SAS-based software SASHAYDIALL for performing a complete diallel cross analysis based on Hayman’s model with or without reciprocals. We demonstrate the use of SASHAYDIALL with two data sets; one is a published diallel cross data set with reciprocals in cabbage ( THE DIALLEL CROSS, made by crossing a set of genotypes in all possible combinations, is one of the most popular mating designs used in plant breeding. There are variations of the diallel depending on whether the parents and reciprocals are evaluated together with the F1s. Different methods of diallel cross analysis were developed by Jinks and Hayman (H2) and narrow-sense (h2) heritability.d Hayman , Hayman d Hayman , 1954b, d Hayman , and Gard Hayman . The mosd Hayman , in whicd Hayman  methods d Hayman  method od Hayman  and descd Hayman , 1954b aHordeum vulgare L.)      Merr.]     Jinks, , triticaSpecialized software has been developed for Griffing’s diallel analysis  and parent–offspring covariance (Wri) of individual arrays, (iv) calculation of the mean variance  estimation of the genetic components.Considering that an “array” refers to all the crosses involving a particular parent, the steps required to carry out Hayman’s diallel analysis are (i) ANOVA to detect genetic variation among the genotypes, (ii) creation of the array of means in the diallel table, (iii) calculation of the expected variance (VP); the variance among family (Vr)  means within an array; the mean value of Vr over all arrays (ith array and their nonrecurrent parent (Wr), and the mean value of Wr over all arrays (D), and dominance gene effects (H), and the distribution of genes (F) are defined as:In Hayman’s method of diallel cross analysis, six variances and covariances are calculated from the data set. These are the variance among parents (D = 4Σuvd2H1 = 4Σuvh2H2 = 16Σu2v2h2F = 8Σuv(u − v)dhu and v are the frequencies of increasing and decreasing alleles, respectively, and u + v = 1, d represents the gene’s contribution to the fixable or additive genetic variation, and h is the difference between the heterozygote and the mid-homozygote values , VL11 (mean variance of arrays), VL10 (variance of the array means), and WL010 (mean covariance of array means) , b (dominance genetic effects), c , and d  , b2 , and b3 (test of dominance deviation that is unique to each F1)  components, respectively  and sth column , m is the grand mean of the diallel table, rj is mean deviation from the grand mean due to the rth parents, l is mean dominance deviation, rl is further dominance deviation due to the rth parent, rsl is the remaining discrepancy in the rsth reciprocal sum, rk is average maternal effect of each parental line, and rsk is the variation in the rsth reciprocal differences , l = b1 (mean dominance deviation), rl = b2 , rsl = b3 , rk = c , and rsk = d   and covariances (Wri), calculation of the four second-degree statistics, and testing the adequacy of the additive–dominance model using a t test. Estimates of genetic parameters including D, H1, H2, F, H2, h2, and the average degree of dominance, among others, are computed by SASHAYDIALL. The heritability estimates (H2 and h2) are computed using the formulae given by Mather and Jinks  graph is also plotted. These computations are performed for a single site and across locations or environments, depending on the data set. The SASHAYDIALL program is not computationally intensive.As a first step, a general ANOVA of the data using both PROC MIXED and PROC GLM (for single and across locations or environments) is executed to detect differences among genotypes. The SASHAYDIALL program will then ran ANOVA for the diallel table in presence or absence of reciprocals. The main effects in the ANOVA are tested for significance using both their interaction with replication and the residual as the error terms, and output for both cases is provided. The main effects can be tested against the residual if the error variances are homogenous ;0 then Env=1;if varnum=rc=close(dsid);drop dsid rc;RUN;%global Y Parent1 Parent1 replication genotype Env;%macro testVAR(var);%let dsidvar=%sysfunc(open(&var));%let nvars=%sysfunc);%mend testVAR;%mend listsVAR;Data DIALLEL;set DIALLEL (rename=(&varsvar));Genotype=compress(Parent1||”x”||Parent2); /*make a list of genotypes*/RUN;PROC SORT data=DIALLEL; /*sort data in the file*/ by Env Parent1 Parent2 Replication;PROC MEANS data = DIALLEL mean noprint;/*calculate trait means*/by Parent1 Parent2;var Response;output out = tmp1 (drop = _type_ _freq_) mean= Response;*----------------------------------------------------**General ANOVA for the response variable**----------------------------------------------------**The statements below are for execution of ANOVA for the trait of interest as specified by the user**---------------------------------------------------*;PROC MIXED data=DIALLEL method=type3 noinfo noitprint;class Env REP Parent1 Parent2 Genotype;Model Response = Env Genotype Genotype*Env;random REP(Env);ods output type3=allc;ods output ClassLevels=niv /**/;ods listing exclude FitStatistics ClassLevels type3 tests3 covparms;RUN;*---------------------------------------------------**ANOVA according to Hayman’s method**----------------------------------------------------*1s according to Hayman  Replication Parent1 Parent2 Parent1*Parent2 Env Env*Parent1 Env*Parent1 Env*Parent1*Parent2/ss3;RUN;*----------------------------------------------------**Creation of data set for each parent**----------------------------------------------------**The next set of macros are used to create a data set for each parent in the diallel**---------------------------------------------------*;matrixmacro ;1 %to &P;%do i=data C&I;set MY;if P1=&i OR P2=&i;rename MY=C&i;drop P1 P2;%if &i=2 %then %do;data all;merge C1 C2;%end;%if &I>2 %then %do;data all;merge all C&i;%end;%end;%*----------------------------------------------------*V0L1)**Variance of the mean of arrays ;v0l1=(ssq(meanX) - ((sum(meanX)##2)/&Pro1))/ **Covariance between parents and their offspring ;Wr=j;end;Wr[i]=(sum(W) - (sumX[i] # sumDIAG/&Pro1))/ – HO: b = 0**Testing the significant of b from unity (1) – HO: b =1**Testing the significance of *----------------------------------------------------**The next set of statements are used to test significance of slope from 0 and 1*b0=b/se;1-b)/se;b1=;Wri=(Vr # v0l0)##(MeanWr=sum(Wr)/&Pro1;MeanVr=sum(Vr)/&Pro1;Wrei=MeanWr-(B#MeanVr)+(B#Vr);1#MeanVr)+(1#Vr);Wreiprime=MeanWr-;vfcp = j;Vrqrt=quartile(Vr);Intercept=MeanWr-(B#MeanVr);free MeanWr MeanVr;Graph=Wr ?/?/ Vr ?/?/ Wri ?/?/Wrei?/?/Wreiprime;qrt=Wriqrt?/?/Vrqrt;*---------------------------------------------------*;*----------------------------------------------------**Estimation of genetic components of variation**----------------------------------------------------*D, F, H1, H2, and E**The next set of statements are for estimating E=ems;D=v0l0-E;0 then D=0;if D < 2#v0l0)-(4#w0l01)-(2#(&Pro1-2)#E/&Pro1);F=+(4#v1l1)-((3#&Pro1-2)#E/&Pro1);H1=v0l0--(4#v0l1)-(2#E);H2=-(4#(&Pro1-1)#E/(&Pro1##2));SH2=#(1/(&Pro1-1))#((ssq(Wr-Vr))-((sum(Wr-Vr)##2)/&Pro1));S2=, c, and d. The components a, b, c, and d are tested for significance using both their respective interaction with replication and the residual as the error term in the ANOVA. The user has to decide which output to use for interpretation, although Hayman  generated by SASHAYDIALL is similar to that presented in D, H1, H2, F, and h2) and their SEs are computed by SASHAYDIALL to allow for a test of significance. The Wr –Vr graphs plotted by SASHAYDIALL  show the distribution of dominant and recessive genes among the parents, and these graphs are similar to those presented by Tanaka and Niikura  for DTA at each location. Significance of component b indicates presence of dominance for this trait.Hybrids without their reciprocals from a 13-by-13 maize diallel cross together with their parental inbred lines were evaluated at three locations in Kenya. The hybrid trial with 78 diallel hybrids and two check hybrids was laid out as an 8-by-10 α  lattice, whereas the parental trial with 13 parents and two check inbred lines was laid out as a three-by-five α  lattice with two replications. Days to anthesis  were recorded for the hybrids and inbred lines and the data analyzed using SASHAYDIALL. Results of the general and genetic effects ANOVA by location and across locations are presented in 2). In this example, genetic components D, H1, H2, and h2 were all significant, and dominance genetic variance was larger than additive genetic variance across locations. Significance of both D and H components suggests that DTA is controlled by both additive and dominant effects. Furthermore, an estimate of the number of groups of genes that control DTA and exhibit dominance and heritability (broad and narrow sense) are provided among others (Wr) and variance of the F1 hybrids is shown in the Wr − Vr graph, which gives the ranking of inbred lines for frequency of dominant alleles for DTA across locations  .The genetic parameters for DTA are estimated by SASHAYDIALL across locations  and for ocations  and indiDiallel mating designs provide important genetic information useful in a breeding program. The SASHAYDIALL program described in this paper is based on models for analysis of a diallel developed by Jinks and Hayman  and Hayma, b, c, and d is tested using both the pooled error and block interaction as the error terms  and environmental (E) components are computed for single and multiple locations together with their SEs, which enables a test for their significance.The SASHAYDIALL program is user friendly, as the user only needs to specify the location and name of the file with data to be analyzed, provide the variables required for the analysis, and indicate whether to analyze data from single or multiple locations. Breeders typically evaluate progenies from diallel crosses in multiple locations, and SASHAYDIALL can handle analysis of such data easily. The analytical procedure in SASHAYDIALL is automated, as the program automatically detects the number of parents in the diallel cross data set and presence or absence of reciprocals and computes the number of genotypes. The significance of genetic components h2 and H2, mean degree of dominance, and the number of groups of genes that control the trait of interest are computed to aid in the interpretation of the inheritance of a trait by the breeder. The Wr − Vr graph that provides an insight into the order of dominance and an estimate of the proportions of dominant to recessive alleles among the parents is generated. The Wr and Vr output can be used in other software to generate the Wr − Vr graph with the limiting parabola, which is not provided for in this program. The plot of Wr + Vr against Yr generated by SASHAYDIALL can give an indication of the effect of dominant or recessive alleles on expression of a trait.Estimates of In summary, the SASHAYDIALL program was written to provide user-friendly, freely available analytical software for Hayman’s diallel analysis. SASHAYDIALL has an advantage that the user does not have to indicate the number of parents, as this is automatically detected and the program can analyze data from multiple environments. The SASHAYDIALL program generates comprehensive output that is easy to understand for proper genetic interpretation of the inheritance of a trait by the breeder. This program should revive the nterest in application of Hayman’s  method ohttp://hdl.handle.net/11529/10548045). The data set used for the maize diallel example and corresponding output will be provided on request.The SASHAYDIALL program described in this paper was developed and tested in SAS version 9.4 (SAS Institute, Click here for additional data file.


The allelic diversity of primitive germplasm of fruit crops provides a useful resource for introgressing novel genes to meet consumer preferences and environmental challenges. Pre-breeding facilitates the identification of novel genetic variation in the primitive germplasm and expedite its utilisation in cultivar breeding programmes. Several generations of pre-breeding could be required to minimise linkage drag from the donor parent and to maximise the genomic content of the recipient parent. In this study we investigated the potential of genomic selection (GS) as a tool for rapid background selection of parents for the successive generation. A diverse set of 274 accessions was genotyped using random-tag genotyping-by-sequencing, and phenotyped for eight fruit quality traits. The relationship between ‘own phenotypes’ of 274 accessions and their general combining ability (GCA) was also examined. Trait heritability influenced the strength of correspondence between own phenotype and the GCA. The average (across eight traits) accuracy of predicting own phenotype was 0.70, and the correlations between genomic-predicted own phenotype and GCA were similar to the observed correlations. Our results suggest that genome-assisted parental selection (GAPS) is a credible alternative to phenotypic parental selection, so could help reduce the generation interval to allow faster accumulation of favourable alleles from donor and recipient parents. The first approach increases the frequency of desirable genes and can help develop ‘pre-bridging’ germplasm, which can later be used as a pollen source for making crosses with elite lines2.Growing demand for nutrient-rich foods, increasing biotic and abiotic risks in fruit production, and evolving consumer preferences require development of novel cultivars. The narrow genetic base of advanced genetic material generally inhibits introduction of new traits, hence utilising wild or semi-wild genepools as sources of genetic variation is a common breeding practice. Introduction of novel genes/traits from exotic germplasm have been achieved through two main strategies3, so most efforts have focussed on introgression of major genes (e.g. disease resistance) using a PBC strategy where foreground selection is carried out using marker assisted selection (MAS) and the resistant seedlings are then planted in the orchard for fruit quality and other trait evaluation5. PBC often results in ‘linkage drag’ (i.e. linkage between the gene of interest and undesirable genes that are inherited together from the donor parent), so repeated PBC with elite parents is applied to minimise the non-desirable genomic content of the donor parent in selected seedlings. In addition to the foreground MAS for major genes, a marker-based background selection (which involves selection of only those resistant seedlings that have inherited the least proportion of donor genome) can also be incorporated in a PBC breeding strategy9.Pre-breeding of fruit crops germplasm using recurrent selection is very rare10. Alternatively, a transgenic early flowering approach for the introgression of fire-blight resistance from the wild apple ‘Evereste’, showed that five breeding cycles could be completed within seven years9. However, transgenic plants are still regulated in many countries, so this strategy cannot be used for commercial cultivar breeding at the moment.The breeding cycle length for outbred perennial fruit crops is long , so pre-breeding generally takes decades to develop parents suitable for crossing with elite lines. Agro-technical (e.g. growth chamber) methods have been suggested to reduce the juvenility period12 and commercial cultivar breeding13. In GS-based parental breeding schemes, deleterious variation can be deselected to increase favourable allele frequencies irrespective of their origin, thus minimising linkage drag12. Numerous traits of interest could potentially be controlled by multiple genes, so GS would be ideal for introgressing traits of higher genetic complexity relatively faster than conventional breeding16.Genomic selection (GS) has been shown to be an effective tool to reduce the cycle length for pre-breeding17. Given the long time it takes to obtain progeny-based performance, fruit breeders continue with this current practice, accepting the known risks. Schlathölter et al.9 proposed using GS to identify parents for the next generation, but the efficacy of genome-assisted parental selection (GAPS) has not yet been fully established for pre-breeding programmes of perennial fruit crops. GAPS would help shorten the parental breeding cycle, so the main objectives of this study were to evaluate: (1) the correlation between seedlings own phenotype and progeny-test performance ; (2) the accuracy of GAPS to predict own phenotype and GCA.Estimated breeding values (EBV) are commonly used to rank individuals in a breeding programme. An individual’s own phenotype (e.g. phenotypic records on a seedling) is one indicator of its EBV. Alternatively, EBV of an individual/seedling can be obtained from the performance of its progeny. In pre-breeding programmes of perennial fruit crops, own phenotype of seedlings is generally used for selection of parents for the next generation. However, own phenotype may not be a reliable indicator of EBV, especially for low-heritability traits, which could lead to sub-optimal parental selection18. An open-pollinated (OP) family represented seeds (which were pollinated by random pollen) harvested from a female parent. There was no passport data available on female accessions, and majority of these accessions belong to the domesticated species Malus × domestica. Seedlings were grown on their own roots, and after phenotypic evaluation for adaptation and fruit quality traits, a subset of c. 500 seedlings representing genetic diversity of the first-generation population, were identified. These 500 selections were propagated onto ‘M9’ rootstock and planted in duplicate at the Havelock North research orchard of Plant & Food Research for further assessment and long-term conservation. Nearly 350 (70%) of these accessions were used as parents to create a second generation, with each parent being involved, on average, in two crosses. The second generation comprised c. 10,000 seedlings; of these about 200 accessions (20%) were used as parents to create a third generation3. Outstanding accessions from this pre-breeding programme have been used in Plant & Food Research’s cultivar/parental development programmes.A recurrent selection based pre-breeding programme was initiated during the early 1990s when about 35,000 apple seeds representing 500 open-pollinated families were imported from different countries into New Zealand3), soluble solids content , crispness , juiciness , astringency  and titratable acidity . The average value of six fruits were used to represent each phenotype of each accession. Further details of harvesting and assessment protocol were reported previously3.A set of 274 accessions was chosen for this study, taking completeness of own phenotypic data as well as progeny-test data into consideration. Own phenotypes of each accession were recorded, and their GCA performance was obtained based on the phenotypes of their progenies. Because of the time it takes for progeny testing, own phenotypes and progeny performance were observed over different years. Six fruits from each plant were assessed over two consecutive years. Fruit were harvested when judged mature based on a change in skin background colour, and when the starch pattern index was between 2 and 3 using a scale from 0 (full starch) to 7 (no starch). Six fruits from each plant were harvested each fruiting season over 2 consecutive years, and were stored for 42 days at 0.5 °C, then a further 1 day at 20 °C before evaluation. The phenotypes used for this study included fruit weight , russet coverage , fruit firmness  were obtained with a hand-held 1 Hole Plier Punch sterilised by dipping in ethanol for about 1 min, followed by distilled water for ~15 s, then dried out with lint-free tissues. The leaf discs were placed in a 1.5-mL micro-centrifuge tube containing lysis buffer and RNase A. The leaf sample was ground by hand with a sterile plastic pestle until most of the tissue was disintegrated. The sample was processed as instructed by the vendor, except that the final elution of DNA was done twice, with 1 h of incubation for each elution event. Both eluates were combined and quality assessed on a Fragment Analyzer (Genomic DNA High Sensitivity kit). DNA preps with a Genomic DNA Quality number equal or larger than 6.4 were considered acceptable . The average concentration was 15 ng/µL .19. After confirming that enough amplicon template could be obtained from this range of DNA concentrations, all DNA samples were processed and random tagged genotyping-by-sequencing (rtGBS) libraries prepared using the restriction enzyme BamHI. This enzyme was chosen after screening 10 restriction enzymes bioinformatically and later experimentally, according to the calculation sheet provided by the Gene Pool at the University of Edinburgh (http://genomics.ed.ac.uk/) by Mark Blaxter’s group, and uploaded in protocols.io (https://www.protocols.io/view/genotyping-by-sequencing-gbs-library-protocols-kzmcx46/abstract).As a test to verify that the observed range of DNA concentration would produce random-tagged DNA for library preparation, a set of 64 preps representing such range was amplified by PEP-PCR (Primer extension pre-amplification) and enriched by TD-PCR (touch down) as described by Hilario et al.Two quality control steps were implemented: the first after random-tagging the DNA, and the second after amplifying the rtGBS library. Any samples that did not produce a library were repeated. Once all samples produced a library, five pools were prepared by combining a maximum of 56 libraries per pool. The pools were concentrated and quantified by fluorescence before and after size selection using a 3% agarose gel (250–650 bp). The sized fragments were assessed by gel electrophoresis, quantified by fluorescence and sent to Australian Genome Research Facility (AGRF), Brisbane, for sequencing. Each pool of rtGBS libraries was sequenced in one lane, on the Illumina HiSeq2000 platform, in single-end mode.20. First of all, 64-base long unique tags were extracted from the compressed fastq file for each pool through ‘FastqToTagCountPlugin’ with a minimum count of 3. Tags from the five pools were merged with ‘MergeMultipleTagCountPlugin’ to create the overall tag count table, then converted to Fastq format with ‘TagCountToFastqPlugin’. Afterwards tag sequences were mapped to Malus_x_domestica.v1.0-primary genome21 using Bowtie222 with parameters ‘--very- sensitive --end-to-end’ in multi-thread mode. The Sequence Alignment Map (SAM) file was converted to Tags on Physical Map (topm) format using ‘SAMConverterPlugin’ followed by ‘ModifyTBTHDF5Plugin’ to achieve HDF5 format for rapid accessing of large datasets. In the meantime, Tags by Taxa (TBT) data in HDF5 format were created from all the raw sequencing files together with the tag count table using the SeqToTBTHDF5Plugin. To speed up variant calling, we ran the TagsToSNPByAlignmentPlugin for each pool against each Malus chromosome in parallel. Single nucleotide polymorphisms (SNPs) called on the same chromosome from different pools were merged with MergeDuplicateSNPsPlugin, while duplicate samples were combined with MergeIdenticalTaxaPlugin. The combined SNPs were filtered using GBSHapMapFiltersPlugin with a minimum site coverage (-mnScov) 0.9, minimum taxa coverage (-mnTCov) 0.8 and minimum minor allele frequency (-mnMAF) 0.05. The missing SNP genotypes were imputed using BEAGLE23 through the R package Synbreed24.Sequencing data were downloaded from AGRF and data integrity confirmed with md5sum. Data quality was checked with FastQC-0.11.2. Barcode ligation proficiency and enzyme digestion efficiency were verified with fastq-multx in ea-utils.1.1.2-537 package in two steps: sample barcodes (sequence trimmed after de-multiplexing) and BamHI residue sequence (not-trimmed), both with a minimum phred score of Q20. For genotyping, we used the TASSEL3 pipeline25y is the vector of observations, b is the vector of fixed effects ; a, p and e are vectors of random additive genetic effects, permanent environment effects, and residual effects, respectively. The matrix X is the incidence matrix for the fixed effects and Z is the incidence matrix relating observations to seedlings. The associated variances with the random effects, a, p and e were 26 was used to obtain best linear unbiased prediction of additive effects (BLUP-BV) of each accession for each trait. These BLUP-BVs were later used for GS model development.As the measurements of own phenotypes of 274 accessions were repeated over two successive years, the following individual-tree mixed linear model (MLM) accounting for permanent environment effect was used for each trait:h2) of each trait were obtained as the ratios of additive variance For each trait, the GCA of all 274 accessions was obtained from phenotypes of their offspring. Individual-tree MLM Eq.  was usedy is a vector (274 × 1) of BLUP-BVs for a given trait; μ is an intercept, 1n is a vector of 1 s; Z is a design matrix relating observations to accessions, g is a vector of genomic breeding values with a normal distribution; g ~ N. The records in one subset were in-turn set to missing values and were predicted using the model developed from the remaining 10 subsets, until phenotypes in all subsets were predicted. This 11-fold cross-validation scheme was repeated 20 times, and the prediction accuracy was calculated as the correlation between observed BLUP-BV and predicted genomic breeding value (GEBV) in the validation set. In addition, correlations between GEBV and GCA were also obtained in each validation set. Equation About 5000 offspring (derived from cross-pollination) and 274 parents were phenotyped: the distribution of phenotypes in these two groups is presented in Supplementary Fig. Initially, about 50 K SNPs were obtained following the filtering criteria described in the Methods section. SNPs were subsequently discarded using these criteria: more than 10% missing data; minor allele frequency (MAF) < 5%; and SNPs separated by one bp. As a result, a total of about 6400 high-quality SNPs, varying from 246 SNPs on LG16 to 594 SNPs on LG15, were retained , based on progeny test data, varied from 0.15 (for CRISP and JUIC) to 0.50 (AVFW). After AVFW, fruit firmness was the second most heritable (0.41) trait, followed by ASTR (0.26) and RUSS (0.21)  Fig. . Estimat21) Fig. . FurtherAccuracy of genomic predictions of own phenotype (i.e. correlation between GEBV and BLUP-BV) is shown in Fig. The average correlation between predicted own performance (GEBV) and GCA was higher than 0.50 for AVWT, FIRM and ASTR; and between 0.30 and 0.50 for RUSS, SSC and TA; and between 0.25 and 0.30 for CRISP and JUIC  could be followed by marker-based background selection to identify seedlings with high genomic similarity to the elite lines29.A key goal of creating pre-bridging germplasm is to evaluate and exploit the available genetic variability using recurrent selection cycles, to generate advanced genetic material suitable as parents for cultivar development populations30.Genomic-similarity based selection could ensure the high recovery of genomic content of the recipient lines when using a high-density genotyping platform. However, in most pre-breeding programmes, the major goal is not necessarily to capture the recipient’s genomic background, but to build on some specific economically important traits. High genomic similarity may not necessarily deliver high phenotypic similarity to the elite parent, hence GS models, derived using genotype and phenotypes, would provide a more efficient and targeted approach for background selection. Thus, GS would lead to desired genetic improvement of target traits relatively faster than using genomic-similarity based selection33, but the current applications of GS in perennial fruit crops are generally aimed at skipping Stage 1 seedling evaluation so that candidates for Stage 2 evaluation can be identified based on GEBV—hence reducing the cultivar development timeline by at least five years13. Although, the candidates selected for Stage 2 testing could also be used as parents of the next generation, it is suspected that their worthiness as parents could be compromised mainly because of recombination events.GS would be a more efficient strategy for background selection, especially for complex traits, as favourable alleles from the donor and recipient lines can be targeted across the whole genome. Accuracy of GS studies in apple and pear cultivar breeding were encouraging36. Relatively smaller training population sizes and lower average pairwise genomic relatedness would have contributed to lower prediction accuracies than those reported earlier for the same traits13.The results that relationship between own phenotype and GCA was highly correlated with the square-root of trait heritability, suggested that heritability expresses the reliability of phenotypic value as a guide to the breeding value. For this reason, the determination of heritability of breeding target traits is one of the first objectives in breeding programmes. The accuracy of predicting phenotypes of our 274 accessions was 0.58 for the least heritable trait (CRISP) and 0.75 for the most heritable trait (AVWT). Trait heritability, genetic architecture of the trait, and genetic relatedness between the training and validation sets, are among the key factors influencing the accuracy of genomic predictions25. Nevertheless, pre-breeding programmes of perennial fruit crops (e.g. apple and pear) use seedlings’ own phenotypes for background selection of parents of the next generation. Our results suggest that parental selection based on genomic prediction of own phenotypes would be similarly accurate as this conventional selection. Hence, GS approach would obviate the need for costly and time-consuming phenotypic screening for background selection in pre-breeding programmes. Linkage disequilibrium between pairs of loci would decay over successive backcross cycles, which could require recalibration of GS model every couple of generations.This study showed that the degree of correspondence between own phenotype and progeny-based performance (i.e. GCA) was strongly influenced by the heritability i.e. for low-heritability traits, own phenotype could be a poor indicator of GCA37, and a GE-GS combination was also proposed for pre-breeding schemes to develop climate-smart crops38. GE is still a controversial technique, so for the foreseeable future GS-based pre-breeding schemes could improve efficiency in introgressing favourable polygenic traits of donors into high-quality recipient lines whilst also minimizing linkage drag11.A combination of genome editing (GE) techniques (e.g. CRISPR-Cas) and GS has been shown to significantly enhance the response to selection in animal breeding schemesIn parental breeding programmes of various fruit crops, MAS is commonly used to screen seedlings for monogenic traits (e.g. disease resistance) and then selection for fruit quality traits is carried out based on field phenotypes. Results from this study showed that GS is a credible alternative to phenotypic selection, so for parental breeding of perennial fruit crops we suggest a two-stage selection might be employed—where MAS is used for foreground selection for monogenic traits and GS is used for background selection for fast recovery of the best genomic content of the donor and recipient parents. Prospective parents selected based on MAS and GS could then be propagated in fast-growth chambers to facilitate early transition from the juvenile to the adult phase. Such turbocharged regimes could reduce the breeding cycle of some fruit crops  to two years, compared with the seven years of a conventional scheme.Supplementary Fig S1


TM apparatus.In recent years, the meat industry is looking with increased interest at the implementation of non-invasive new tools for predicting the final quality of dry-cured hams and monitoring ham aging. The selection of raw meat and the control of the salting procedure to predict the quality of dry-cured hams are of primary importance for meat processors. The identification of genetic markers associated with ham traits and related to different aptitudes of the thighs towards salting phases and weight losses is a primary goal for the Italian pig production chain. This paper addresses the need for investigating the associations between genomic markers and ham traits obtained through the application of non-invasive technologies for monitoring hams before and during the salting process. To our knowledge, this is the first study investigating the markers and genes associated with ham traits obtained through the use of Ham InspectorSemimembranosus muscle ultimate pH, ham weight and lean meat content, adsorbed salt) of the corresponding thighs, undergone PDO ham process in three different plants, were measured, using a fast and non-invasive technology. Green ham weight and lean meat percentage influenced the estimated salt content and the weight loss during salting, even if the processing plant greatly affected the variability of the measured ham traits. The genomic data were obtained with the GeneSeek Genomic Profiler (GGP) 70k HD Porcine Array, using the slaughter day and the sex of the animals in the statistical analyses. The phenotypic traits were associated with the genotypes through GenAbel software. The results showed that 18 SNPs located on nine porcine chromosomes were found to be associated with nine phenotypic traits, mainly related to ham weight loss during salting. New associations were found between markers in the genes Neural Precursor Cell Expressed Developmentally Down-Regulated 9 , T-Cell Lymphoma Invasion and Metastasis 2 , and the ham quality traits. After validation, these SNPs may be useful to improve the quality of thighs for the production of PDO dry-cured hams.Protected Designation of Origin (PDO) dry-cured hams production is greatly dependent on raw meat quality. This study was performed to identify genetic markers associated with the quality of dry-cured ham. Carcass traits of 229 heavy pigs belonging to three commercial genetic lines were registered . Phenotypic traits ( Semimembranosus muscle (SM) pH and drip loss [The production of Protected Designation of Origin (PDO) Parma and San Daniele hams plays an economic role of primary importance in the Italian pig production chain  and reprrip loss ,13, and rip loss . Most ofrip loss ,15, but In recent years, different non-invasive technologies based on X-rays or near-infrared (NIR) spectroscopy were investigated as quality control techniques in the ham industry . MagnetiThis work aims to investigate the variability of green ham traits in a sample of 229 commercial hybrid heavy pigs during salting and the genomic regions associated with the measured phenotypes. These regions will be singled out through a Genome-Wide Association Study (GWAS), which will allow identifying DNA markers and candidate genes associated with phenotypic characteristics of the fresh hams measured during the first stages of the ham processing. The identified SNPs might be of interest to improve ham yield after salting and the quality of the finished product. The identification of genetic markers associated with the quality of the thighs for PDO dry-cured hams can offer new helpful tools for the highly innovative pig production chain.The samples and hams used in the present study were obtained from the slaughtering of commercial heavy pigs intended for human consumption, and thus the present research did not need approval from a research ethics committee. The heavy pig hybrids were slaughtered in commercial abattoirs in four slaughter days between March and July 2018. The animals were slaughtered in compliance with the European rules  on the pA total of 229 fresh hams were collected from carcasses classified as “U”, “R”, and “O” in compliance with Commission Implementing Decision, 2014/38/EU ,24. A saThe pH of fresh hams was measured in SM with a Hamilton glass electrode probe attached to a portable pH meter . Homogeneous sets of hams in terms of muscle pH at 24 h post-mortem (pHu) ranged between 5.50 and 5.90 were used for each plant.Then, all fresh hams underwent traditional salting for Italian dry-cured ham, based on a two-step addition of salt , followiTM apparatus . The system based on electromagnetic induction (MI) technology generates a signal with an amplitude depending on the ham lean amount and salt content, estimated using a proper calibration [The lean amount of green hams and the salt content of the salted ones were determined by the Ham Inspectoribration ,18.Two hundred and twenty-nine fresh hams were scanned with the MI system set in the “RAW” mode, installed at each plant. The lean amount expressed as a percentage of ham weight was estimated by using previously developed predictive models reported in Simoncini et al. . This moAll scanned hams were tempered at 3 ± 0.5 °C and temperature tested with the thermometer Ebro TFX 410 Pt1000  inserted into SM muscle (5 cm depth) to avoid possible drifts of MI signal, associated with variations in sample temperature.The weight of the fresh hams as well as their weights during the salting process  was recorded by the MI apparatus in order to calculate the corresponding weight losses, expressed as percentage loss of fresh ham weight.All statistics of phenotypic traits were obtained by SPSS version 22.0 software platform ; normal distribution of data was investigated before statistical analyses. The boxplot procedure was applied to present the distribution of measured lean percentage of hams, differently labeled according to the EUROP grid (lean carcass grading). Data of ham traits were analyzed using Generalized Linear Model (GLM) procedure; the models included the processing plant and the sex of the pigs respectively, as fixed factors. These factors were included in the model since they are known to affect ham quality . The Leahttp://www.lgscr.it/ENG/index.html) where the genotype analyses were also performed. For the genotyping, the GeneSeek® Genomic Profiler-GGP-70k HD Porcine chip  containing 68516 SNPs was used using the procedures indicated by the company. The SNPs were mapped using Sus scrofa Genome Assembly Build 11.1 . The sex of the animals  was obtained on the basis of the genotypes for the sex chromosomes. The genotypic data were filtered using gPLINK  [p-value < 0.001); all the individuals with more than 10% missing genotypes and with Identity by State (IBS) > 90%. After filtering, 54,569 SNPs and 169 individuals were retained. The large number of excluded animals (n = 60) was because their IBS was above the threshold set at 90%. The association analyses were carried out using polygenic_hglm and qtscore functions implemented on the GenAbel package according to the procedure described in Nicolazzi et al. [p-values of the associations between ham traits and SNPs were corrected for the “deflation” factor, as reported by GenAbel. Markers were considered significant with corrected p-values below the chromosome-wide significant threshold . Candidate genes were identified on the basis of their location (the nearest gene to the significant marker) and biological role. In order to find possible splice sites or motifs with biological relevance, the sequences flanking the intronic variants found associated with ham traits were submitted to the Tomtom tool in MEME Suite version 5.3.0 [http://meme-suite.org/). The found motifs are ranked based on their Bonferroni significance  for the found match between the query sequence (or its complementary) and the motif in JASPAR CORE 2014 database.The collected SM samples were used for the genomic analyses. DNA extractions were carried out using a standard protocol by an outsource laboratory   and GenAon 1.07)  discardion 1.07)   than those estimated from the EUROP classification of the corresponding whole carcass.The class R, corresponding to an estimated lean % of the carcass in the range 45 to 50% is the most abundant (n = 110) compared to classes O  and U . In the current study, the lean % of the hams scanned by Ham InspectorAll fresh hams were processed in three different manufacturing plants in accordance with tutelary regulations of Parma ham ,24.The results of GLM analysis including “processing plant” and “sex” as fixed effects and their interaction are summarized in p < 0.001) were detected. In particular, processing plant 1 handles the heaviest hams between the tested plants (15.1 kg), and hams leaner (62.7%) than plant 3 (60.6%). This condition affects salting weight losses, yielding higher values at the end of salting for plant 1 compared to other plants. The salt % predicted in ham lean content after both salting steps differed significantly between processing plants (p < 0.001), reporting greater values for plant 3 and 2, respectively (Differences in the measured ham traits between processing plants (ectively .p < 0.001) and their weight loss after the first (p < 0.05) and at the end of the salting . The higher lean % of green hams from females caused higher weight losses during salting, and higher values of salt content at the end of salting (2.60%) if compared to barrows (2.53%). As for the salt content at the end of salting, the interaction between processing plant and sex was significant (p < 0.05): the three plants differed regardless of the sex of the animal, but in the case of females the salt values were higher than in barrows.The sex of the pigs generated differences for the lean % of green hams (p < 0.01) and the weight loss at the end of salting . The weight of green hams was negatively correlated with salt content after the first salting in all tested processing plants , green ham weight and ham weight at the end of salting , and between ham weight after first and at the end of salting .The results of the Pearson’s correlation analysis performed between ham traits measured in each processing plant are reported in g plants , whereasp-value significant at the chromosome-wide level, reported in bold in Sus scrofa chromosome 18 (SSC18). Green ham lean % showed an association with a region on SSC4 at 2 Mb, where the marker ASGA0016987 is located. This SNP is an exon variant of a non-coding transcript (ENSSSCT00000066959.1), and most of the genes comprised in the flanking region are non-coding genes. Green ham weight, ham weight after first salting, and ham weight at the end of the salting showed an association with the same two markers, namely CASI0010463 and WU_10.2_14_144250775. The first is located on SSC15 at 12 Mb, in an intron of the gene Neurexophilin 2 (NXPH2). WU_10.2_14_144250775 is an intergenic variant in a region characterized by high gene density, on SSC14 at 132 Mb. Two SNPs were significant for ham weight loss after first salting: ASGA0031014, an intron variant of the gene Neural Precursor Cell Expressed, Developmentally Down-Regulated 9 (NEDD9), and WU_10.2_10_74620421, a variant in a non-coding transcript on SSC10. Salt content at the end of salting showed two markers displaying a chromosome-wide significant association. The first (INRA0000796) is located on SSC1 at 13 Mb, and is an intron variant of the gene Regulator of G Protein Signaling 17 (RGS17); the second (ASGA0102337) is an intron variant of the gene GRAM Domain Containing 1B (GRAMD1B), located on SSC9 at 50 Mb. Eleven markers showed less significant associations with the ham traits, with adjusted p-values comprised between the chromosome-wide significance level and the threshold of 5.00 × 10−5  or completely lacking . The weights of fresh thighs and hams after first and at the end of salting were associated with the same markers, namely CASI0010463 and WU_10.2_14_144250775. Furthermore, the marker ASGA0026341 showed an additive genetic effect on both ham weights after first salting and at the end of salting. In fact, the AA animals for this marker showed lower ham weights than GG pigs  harboring several binding sites recognized by Forkhead box O (FOXO) transcription factors , and an estimation of salt amount adsorbed in the lean part during the salting stages. The use of Ham InspectorTM in three processing plants qualified for the production of PDO Parma ham provided the phenotypic data and information to perform the GWAS. At present, green hams allowed to be processed into PDO Parma hams are those labeled as U, R, and O according to the EUROP grid, with a few specific exceptions [TM was higher than the lean % of the corresponding carcasses estimated from EUROP grading. Thus, the thigh lean % given by Ham InspectorTM and the carcass lean % obtained from EUROP grading provide different information. This is anyway expected, because ham is a lean cut, with a higher lean % than that of the corresponding EUROP carcass class. The measures estimated by Ham InspectorTM about the lean-to-fat ratio of each thigh proved to be crucial to homogenously group hams during processing [The development of new technologies enabling a fast and non-invasive measure of green ham potential to be processed into typical dry-cured ham is a goal for pig production chain and PDO ham producers. In the last decade, technologies such as those based on X-rays have been studied , with thceptions . In the ocessing . Processocessing . As can ocessing . Currentocessing .−5. The most significant association was found between pHu and the WU_10.2_18_17949287 marker, which is located in an intergenic region of SSC18, harboring the genes Plexin A4 (PLXNA4), and Muskelin 1 (MKLN1). This association signal with the PLXNA4 region could support the findings reported by Bordbar et al. [PLXNA4 gene harbored 18 SNPs significantly associated with muscle development in the Simmental breed. Despite this strong association, no clear biologic evidence supporting the PLXNA4 role in bovine muscle development was found [With the aim of finding genomic regions and candidate genes associated with the green ham weight, lean %, salting losses, and contents of adsorbed salt, we used sex and slaughter day  as fixed effects in the GWAS model. GWAS indicated eight markers significant at the chromosome-wide level, and eleven with a Pc1df below the threshold of 5.00 × 10r et al.  in Simmeas found . The pHuT-Cell Lymphoma Invasion And Metastasis 2 (TIAM2). Among the identified associations, the H3GA0000815 marker showed the clearest additive effect, with the GG animals showing a higher lean % than those with the AA genotype. The lower frequency observed for the GG genotype in our samples suggests that the favorable allele G may be used in selection schemes to increase lean mass deposition in the pig breeds used for the production of PDO hams. Interestingly, the TIAM2 gene was found in a previous study to be located in a region displaying a selective signature in a Duroc pig population [TIAM2 gene and its roles in pig muscle development is still mostly unknown.Thigh lean % was associated with the marker H3GA0000815 located in an intronic region of the gene pulation . This gepulation . Cell mipulation . Despitepulation , to dateCalmodulin 1 (CALM1), which encodes for one of three calcium-binding calmodulin proteins. CALM1 mediates the control of a large number of enzymes, ion channels, aquaporins, and other proteins through calcium-binding, and controls also the transport of glucose and other sugars in hepatic cells [Longissimus muscle of pigs with a high deposition of intramuscular fat [The variability of green ham weight, and ham weight after first salting and at the end of the salting period showed to be associated with the same markers, indicating a pleiotropic effect of these mutations. The LSM estimated for these markers were concordant among the measured traits, with the same genotypic class displaying higher estimated LSM for the weights of the fresh thigh and the ham after first salting and at the end of salting. This pattern was expected given the degree of shared variability between these three traits, as demonstrated by their high and positive phenotypic correlations, indicating that the higher the weight of the fresh thigh, the heavier are the same hams after first salting and at the end of salting period. Ham weights at the first salting and at the end of salting were significantly associated with the two markers ASGA0026341 and WU_10.2_7_118557013. An additive effect was found for both these markers, which are located in intergenic regions on SSC5 and SSC7, respectively. This is not surprising, since the literature indicates that the majority of GWAS peaks are located in non-coding or intergenic regions , and mayic cells . Its genular fat , suggestNEDD9, which codes for a focal adhesion protein that acts as a scaffold to regulate signaling complexes important in cell attachment, migration, and invasion [NEDD9 is essential for the Transforming Growth Factor β (TGF-β) signaling pathway [NEDD9 in TGF-β signaling, it is, therefore, possible that changes in its gene sequence may affect also TGF-β signaling and the differentiation of mesenchymal stem cells during muscle development. Furthermore, NEDD9 is known to take part in the inhibition of primary cilia formation during embryogenesis [NEDD9 may take part in this complex signaling pathway related to muscle and adipose tissue development in embryogenesis. Interestingly, the marker ASGA0031014 fell into an intronic region harboring several sequences recognized by FOXO transcriptional regulators. In particular, this intronic variant is located in a site matching the motifs recognized by FOXO1, FOXO3, and FOXO4 transcription regulators, suggesting that changes in this sequence may also affect the ability of those transcription regulators to recognize this binding site. This hypothesis seems to be supported in the literature, which indicated that NEDD9 gene expression was found to be regulated by another forkhead box member (FOXC1) [FOXO1 has a major role in the regulation of skeletal muscle differentiation and fiber type specification in mammals [The ham weight loss after first salting was found to be associated with ASGA0031014, on SSC7. The alleles for this marker show a significant additive effect and balanced genotype distributions in the considered sample. The most favorable genotype for this locus was GG, which displayed the lowest weight losses during processing. This mutation is an intron variant of the gene invasion , as wellinvasion . Some st pathway ,50. More pathway ,52. Due ogenesis . Primaryogenesis , adipogeogenesis . In our ogenesis , and NED (FOXC1)  and that mammals . Taken tNeurexophilin 2 (NXPH2) gene. A Run of Homozygosity (ROH) region was found in the NXPH2 gene in Valdostana Black Pied and Valdostana Chestnut bovine breeds [NXPH2 in livestock traits related to muscle development and production efficiency. However, this gene has never been studied before in pigs and the limited knowledge of the NXPH2 gene does not permit to reach a complete interpretation of the associations found for this gene in the present study. Another marker associated with green ham weight, ham weight after first salting, and ham weight at the end of salting is WU_10.2_14_144250775. This marker results to be unmapped in the latest release of the Ensembl database [Acyl-CoA Dehydrogenase Short/Branched Chain (ACADSB), H6 Family Homeobox 2 (HMX2), H6 Family Homeobox 3 (HMX3), and BUB3 Mitotic Checkpoint Protein (BUB3). The sequence comprising ACADSB, HMX2, HMX3, and BUB3 is highly conserved between mammals [GRAM Domain Containing 1B (GRAMD1B) gene. This gene codes for a cholesterol transporter that mediates non-vesicular transport of cholesterol from the plasma membrane to the endoplasmic reticulum [GRAMD1B gene expression in muscle was found associated with obesity in the mouse model [GRAMD1B sequence may also influence salting and maturation traits. However, the possible effect of this gene on ham quality traits needs confirmation with studies in larger samples.In addition to these markers, other mutations were associated with the ham traits, even though they did not present significant additive effects. Among the markers associated with the ham weights at the first and at the end of the salting steps is CASI0010463, an intron variant of the e breeds . This evdatabase , while i mammals , suggesteticulum ,62. GRAMse model . As fat NEDD9 could be of particular interest for further studies and for implementing selection schemes aimed at improving ham yields after the salting steps. Further studies including a greater number of hams and different processing conditions are needed to strengthen the investigated associations.To our knowledge, this is the first study describing significant associations between porcine candidate genes and ham traits, measured in a non-invasive way using a Magnetic Induction System. This on-line and non-invasive technology allows the estimation of green ham lean % and the salt content in the salted ones, on a great number of hams during processing. The GWAS identified several markers associated with the measured traits, and SNPs in candidate genes related to the neuromuscular junction, and muscle development during embryonic stages were found associated with lean % and ham weights. Among the markers associated with ham traits, the marker located in


Endurance competitions are carried out across the countryside worldwide, where the adapted physical and metabolic conditions of the horses are essential to satisfactorily end the competition. Horse breeding programs usually use the rank and time to improve the performance of horses in competitions. It is also relevant to analyse the placing trait i.e., whether or not a horse finishes the race. The discontinuous nature of rank and placing traits require special methodologies to deal with them. Here we have used 6135 endurance records from 1419 horses, with a pedigree containing 10,868 animals, to develop a multitrait model with a new free software tool (GIBBSTHUR). The obtained results suggest that it is possible to ignore the race time and use rank and placing to perform the genetic evaluation in endurance horse populations.The racing time and rank at finish traits are commonly used for endurance horse breeding programs as a measure of their performance. Even so, given the nature of endurance competitions, many horses do not finish the race. However, the exclusion of non placed horses from the dataset could have an influence on the prediction of individual breeding values. The objective of the present paper was to develop a multitrait model including race time (T), rank (R) and placing (P), with different methodologies, to improve the genetic evaluation in endurance competitions in Spain. The database contained 6135 records from 1419 horses, with 35% of the records not placed. Horse pedigree included 10868 animals, with 52% Arab Horses. All models included gender, age and race effect as systematic effects and combined different random effects beside the animal and residual effects: rider, permanent environmental effect, and interaction horse-rider. The kilometers per race was included as a covariate for T. Heritabilities were estimated as moderately low, ranging from 0.06 to 0.14 for T, 0.09 to 0.15 for P, and 0.07 to 0.17 for R, depending on the model. T and R appeared mostly as inverse measures of the same trait due to their high genetic correlation, suggesting that T can be ignored in future genetic evaluations. P was the most independent trait from the genetic correlations. The possibility of simultaneously processing the threshold, Thurstonian and continuous traits has opened new opportunities for genetic evaluation in horse populations, and much more practical genetic evaluations can be done to help a proper genetic selection. Horse breeding programs present particularities that differ from other classical livestock breeding programs, which require breeders to make an additional effort to develop useful tools, specifically for horses. Among horse breeding programs, rank endurance competitions are an example of the difficulties genetic evaluation can present. For example, as in many other performance competitions, often only the final position of the horse is registered, thus complicating the genetic evaluation process. By definition, if the rank trait is analyzed as if it was a continuous variable, it implies a uniform distribution within a race if the rank is expressed over the number of participants. Unfortunately, the reality is that the number of participants varies and sometimes not all of the animals are available, thus leading to a right skewed distribution . FortunaEndurance competitions are long distance races that vary from 40 km to 160 km per day. The competition can reach more kilometers, but in this case several days are needed to finish the race. This type of competition is carried out across the countryside, where the adapted physical and metabolic conditions of the horses are essential to finish the race. Horses can be excluded after veterinary controls when they exceed a determined heart rate or certain metabolic parameters or lameness during the endurance exercise. A good animal for endurance performance would be a strong animal achieving a good position, but one that is also veterinary protected. Obtaining good positions and keeping in the race might be opposed features. The Spanish Arab Horse Breeder Association (AECCA) is currently developing a breeding program aimed at improving endurance performance. This selection objective is common in other crossbreeds such as Anglo-Arab, Hispano-Arab and Caballo de Deporte Español in Spain. However, endurance competitions are open to other breeds with very different breeding objectives.The race time and the ranking at the finishing line are traits commonly used for endurance horse breeding programs as a measure of their performance. Given that race time or speed is highly correlated with the ranking trait, they are frequently used in the genetic evaluations as alternatives, and they also have a more suitable Gaussian distribution ,10. An aThe Thurstonian methodology has proved to be the most suitable method to study genetic evaluation of rank in endurance horse competitions in Spain; it was validated using a univariate model for rank . The modThe total data set consisted of 6135 records from 1419 horses , aged between 5 and 24 years . Most ofThe number of different riders in the data set was 1018 and the average number of different riders riding the same horse was 1.7. In total, 45% of the horses were ridden by two different riders or more. In addition, the average number of different horses ridden by a rider was 2.5, and 50.8% of riders rode at least two different horses. The rider–horse interaction or match effect had an average of 2.4 records across 2550 levels.Pedigree was traced back by using the information from the corresponding pure Studbooks. Pedigree information for genetic evaluation totaled 10868 animals: 52% Arab Horses, 18% Thoroughbred, 12% Pura Raza Español, 10% Anglo-Arab, 2% Caballo de Deporte Español and 6% other breeds. This pedigree was built by completing the genealogy of participant animals until the maximum known generation. In order to measure the pedigree completeness, the equivalent complete generations were computed for each participant. The mean of equivalent complete generations for participating horses was 7.1 for Arab Horses, 3.5 for Thoroughbred, 5.9 for Anglo-Arab and 3.8 for Caballo de Deporte Español. This parameter was computed with ENDOG4.8 .The following traits were jointly analyzed: Race Time in hours (T); Placing, with two thresholds, 1 not placed and 2 placed (P); and Rank race (R) traits. The unplaced horses were considered as missing values for T and R traits. The genetic parameters were estimated for these three traits using a different methodology for each of them. A Bayesian procedure was applied by fitting a classical mixed linear method for T, a threshold method for P, and a Thurstonian method for R.I is the phenotypic record for race time or the liability for placing and rank, X is the incidence matrix of systematic effects, Z the incidence matrix of animal genetic effects, W the incidence matrix of permanent environmental effects, Q the incidence matrix of the rider effect, N the incidence matrix of match effects, b the vector of systematic effects, u the vector of direct animal genetic effects, p the vector of permanent environmental effects, r the vector of rider effects, m the vector of match effects and e the vector of residuals. In addition to the complete model shown in the equation above, all of the model combinations, ignoring one or two effects from p, r and m, were also fitted.The general mixed model equation applied across methods including all the possible random effects was:Three different methodologies were jointly considered depending on the trait:I contained the race time of the horses in hours as a continuous variable. However, vector I was assumed to be the liabilities for an underlying variable, as described below for the P and R traits. Note that for the T trait, the lower the performance, the better the horse.For the T trait, vector Threshold model methodology, also called probit ,12,13 waA Thurstonian model was fitted for R. Under this methodology, ranks were renumbered for the animals registered for each race. The statistical analysis was performed with a specific Bayesian approach designed for Thurstonian models suggested by Gianola and Simianer . A ThursTN) as:n − 1 and n + 1 for the competing horses in the respective previous and next qualifying positions in a race; nμ and The liability of the race winner was set to 0. The liability for any other horse n in a race was calculated by using the following truncated Gaussian distribution , age  and race event as systematic effects. Race effect had different levels according to the traits because race time was not recorded in all races. This race effect was included as the even effect to account for all of the common environmental circumstances of the horses competing together and correcting their differences between events, including class and difficulty of the competition of the race, and also the mean level of competitors, as non random participation occurs. All horses qualified in some races showed: a total of 731 levels were fitted for T, 797 for P and 1275 for R. Distance in km of the race was also fitted as a covariate for the T trait, with a range from 60 to 160 km.All of the models accounted for ten genetic groups according to the origin of the founder. The use of genetic groups is indicated when there are different populations of origin with presumably different means, as is the case in . The genA global model including all the random effects was fitted, but also it excluded one or two of the additional random effects besides additive genetic and residual, which were fitted.We used the GIBBSTHUR software  that is Total chain lengths of 2,000,000 samples for each analysis were defined, with a burn-in period of an additional 100,000 and a thinning interval of 100.The means and standard deviations of the marginal posterior distributions of heritabilities are given in Depending on the model being considered, heritabilities were estimated as rather low, ranging from 0.06 to 0.14 for T, 0.09 to 0.15 for P, and 0.07 to 0.17 for R. Regarding genetic and other correlations between random effects, T and R mostly appeared as inverse measures of the same trait since these correlations ranged from −0.97 to −0.99 across models and effects. P was the most independent trait since the genetic correlations of P with T ranged from −0.03 to −0.16 and of P with R from 0.07 to 0.20. This pattern was similar across effects except for the match effect when correlations were from −0.39 to −0.44 with T, and from 0.42 to 0.49 with R. This result shows that a good horse-rider match affects both qualifying for a race and in a good position. This favorable combination did not happen when the rider or the horse effects were analyzed independently.When fitting all the random effects, the interaction between the horse and the rider, known as the match effect , had a similar magnitude of importance to the heritability component for all the three traits . The permanent effect  also had a similar importance for T and R, but was insignificant for P. The rider effect  was the most important among the random effects for T and R, but again mostly insignificant for P, for which the match effect was the most important.The standard deviations of the estimated parameters were low for heritabilities and for the ratios of additional random effects (0.02 to 0.04) and moderate for correlations (0.18 to 0.28), but larger for permanent environmental effect (0.28 to 0.39).Regarding reduced models, excluding one or two random effects , they always increased the heritability of the traits. Excluding the permanent environmental effect increased the heritability of both T and R by 49%, but only 19% for P, and excluding the rider effect increased the heritability of T by 39%, R by 42%, but only 9% for P. However, excluding the match effect barely increased the heritability of both T and R with 2%, but P increased by 28%.When two effects were simultaneously excluded, heritability became even higher. For P, the model fitting only the match effect performed similarly to the model that fitted the rider effect and the permanent effect as two separate effects; both models had similar heritability estimates showing that the match effect incorporates the sum of both the rider effect model and the permanent effect model. There was a different pattern for T and R, heritability estimates were more than twice those of the complete model for both traits when only match effect was included, showing a confusion between rider and permanent effect with the additive genetic effect. Keeping the rider or permanent effect in the model obtained lower heritabilities than keeping the match effect, but absorbing the residual, which is an important part of the non fitted random effects.Solutions for the complete model, including all the random effects, were analyzed to make inferences from effects. The estimate of the corresponding covariate for distance showed that horses took on average 69.4 s per additional kilometer. Regarding the gender influence, Analyzing the genetic evaluation from horse competitions is an issue that presents additional particularities for endurance races. The goal for genetic evaluations is to breed animals with special abilities to win races or to score relevant positions in races. However, the direct use of such position scores does not always provide the best information to genetically select animals . Apart fAnother particularity of endurance races is the veterinary control that can disqualify horses: 35% of the horses were disqualified because of heart rate, metabolic problems, limb problems such as lameness, and other veterinary reasons  . This diA study was done to analyze race time, ranking, and placing simultaneously in a multitrait animal model considering the last two traits as threshold traits. The ranking trait involved eight different categories, grouping all individuals ranking higher than six within the 7th category, and grouping the non placed individuals within the 8th category ,24. In tGarcía-Ballesteros et al.  demonstrFitting different additional random effects besides residual and additive genetic effects has always been a topic of debate ,27. The There are still other difficulties in the genetic evaluation of endurance. One of them is that although genetically connected, the participating horses are from different breeds and crosses. This implies having to consider different origins with genetic levels; it is, therefore, advisable to use genetic groups in the models . The genThe solutions for the gender effects  showed tThe pattern of age solutions  implies The agreement across traits for gender effect, age solution, and correlation between traits for rider–animal interaction shows that a combination of a good rider and gelding animal competing at eleven years old is best for better performance.From all of the gathered information, genetic evaluation would be best done for P under a threshold model and for R under a Thurstonian model methodology. The development of open source modifiable software is an important advance for this purpose of genetic evaluation . The chaSummarizing, the development of a free software application to deal simultaneously with threshold, Thurstonian and continuous traits will open a new world to the genetic evaluation of horse populations. Moreover, genetic evaluations can be done to achieve better genetic selection. This new tool was successfully applied in endurance horse competitions in Spain and the genetic parameters estimates are reported here. The selection for ranking and placing traits seem sufficient to carry out appropriate genetic selection processes, but an analysis involving continuous traits, such as conformation or physiological variables, remains feasible for future changes in selection objectives.