Recent advances in genome sequencing and imputation technologies provide an exciting opportunity to comprehensively study the contribution of genetic variants to complex phenotypes. However, our ability to translate genetic discoveries into mechanistic insights remains limited at this point. In this paper, we propose an efficient knockoff-based method, GhostKnockoff, for genome-wide association studies (GWAS) that leads to improved power and ability to prioritize putative causal variants relative to conventional GWAS approaches. The method requires only Z-scores from conventional GWAS and hence can be easily applied to enhance existing and future studies. The method can also be applied to meta-analysis of multiple GWAS allowing for arbitrary sample overlap. We demonstrate its performance using empirical simulations and two applications: (1) a meta-analysis for Alzheimer’s disease comprising nine overlapping large-scale GWAS, whole-exome and whole-genome sequencing studies and (2) analysis of 1403 binary phenotypes from the UK Biobank data in 408,961 samples of European ancestry. Our results demonstrate that GhostKnockoff can identify putatively functional variants with weaker statistical effects that are missed by conventional association tests. The authors present GhostKnockoff, a method for genome-wide association studies which can be applied to enhance existing and future studies to identify functional variants with weaker statistical effects that might be missed by conventional association tests. Conventional genome-wide association studies (GWAS) are based on marginal association models that regress an outcome of interest on a single genetic variant at a time, using Bonferroni correction for the number of independent tests to control the family-wise error rate (FWER). Although this approach based on marginal test statistics has successfully discovered many disease-associated variants, its statistical power can be suboptimal, and it often identifies proxy variants that are only correlated with the true causal variants2.Recent advances in genome sequencing technologies and improvement in genotype imputation accuracy enable large-scale genetic studies with hundreds of thousands of samples and tens of millions of variants. The ultimate goal of such studies is to provide a credible set of putative causal variants that could lead to novel targets for the development of genomic-driven medicine. However, our ability to identify causal genetic variants and to translate genetic discoveries into mechanistic insights and drug targets remains limited at this point4. Second, because of the polygenic nature of complex traits, inclusion of loci of small effects improves the predictive power of polygenic risk scores (PRS) for many traits5. Third, although the effect sizes of such loci are small in populations, they can still provide important biological insights. In particular, their effect on molecular phenotypes can be large and they can lead to effective drug targets (e.g. statins)6. However, small effect loci are difficult to distinguish from noisy loci, especially with suboptimal marginal association tests commonly used in GWAS.Multiple lines of genetic research suggest that small effect risk loci that currently lie below the genome-wide significance threshold even in large GWAS can be informative to understand complex phenotypes. First, the widely used polygenic models for complex phenotypes are based on the idea that heritability can be explained by a large number of loci, each with small or infinitesimal effects8. Unlike marginal association testing in GWAS, the knockoff-based inference performs genome-wide conditional tests that account for linkage disequilibrium (LD) thereby reducing false positive findings due to LD confounding. It provides rigorous control of the false discovery rate (FDR), i.e. the expected proportion of discoveries which correspond to truly null hypotheses. The idea of the knockoff-based inference is to generate synthetic, noisy copies (knockoffs) of the original genetic variants that resemble the true variants in terms of preserving correlations but are conditionally independent of the disease phenotype given the original variants. The knockoffs serve as negative controls for the conditional tests to select significant genetic risk loci and to attenuate the confounding effect of LD. Unlike the conventional Benjamini-Hochberg procedure that does not account for LD, the knockoff framework appropriately accounts for arbitrary correlations among the conditional tests while guaranteeing control of the FDR9.Knockoff inference is a recently proposed statistical framework for variable selection in high-dimensional settings7, Sesia et al.10, Sesia et al.11, He et al.12 and Sesia et al.13. These showed that controlling FDR can be more powerful to identify causal variants with weaker effect sizes relative to conventional GWAS, under the assumption of a polygenic model. In particular, they demonstrated that the variants identified by the knockoff inference are more likely to be the causal ones. Despite these appealing features, individual level data needed for the knockoff generation are often not available in large meta-analyses GWAS; instead, summary statistics that do not contain individual identifiable information are usually available. Furthermore, the high computational and memory cost needed to generate individual data knockoffs represents a major bottleneck to achieve its full potential. Finally, unlike for the traditional GWAS, there is currently a lack of standardized, efficient pipelines to facilitate the application of knockoff-based inference to genetic studies.Several knockoff-based methods have already been proposed for genetic studies including Candès et al.GhostKnockoff, to allow efficient knockoff-based inference using freely available GWAS summary statistics for enhanced locus discovery and genome-wide prioritization of causal variants. Methodologically, we show that for the conventional score test in genetic association studies, one can directly generate the knockoff feature importance score per variant without the need to generate individual-level knockoffs for hundreds of thousands of samples. The method requires only summary statistics  from conventional GWAS while retaining the useful features of knockoff-based inference. The method additionally allows meta-analysis of studies with arbitrary sample overlap. We demonstrate its performance in empirical simulations and two applications: (1) meta-analysis study of Alzheimer’s disease (AD) aggregating five genome-wide association studies, three whole-exome sequencing studies and one whole-genome sequencing study; (2) analysis of 1403 individual binary phenotypes from UK Biobank data on 408,961 samples with European ancestry. These analyses demonstrate the appealing properties of the proposed method for robust discovery of additional loci and ability to localize putative causal variants at each locus. Additional discoveries made by the proposed method are further supported by functional enrichment analyses and single-cell transcriptomic analyses. The method is computationally efficient and required only 5.45 h on one central processing units (CPU) to analyze genome-wide summary statistics from the nine AD studies.In this paper, we propose a novel method, 7. Although the Z-scores above are derived from a generalized linear model, it is worth noting that knockoff inference holds without the explicit model assumption. Unlike conventional score test or permutation analysis, knockoff-based inference performs conditional tests that account for linkage disequilibrium and controls FDR. It tests against hypothesis We assume a study population of The knockoff generation in step (1) can be computationally intensive. The main contribution of this paper is to show that for this particular form of feature importance score , one can directly generate the knockoff feature importance score per variant without the need to generate individual-level knockoffs for hundreds of thousands of samples. Our method takes simple Z-scores as input and retains many useful features of knockoff-based inference, except for the flexibility to incorporate more sophisticated (non-linear) machine learning algorithms.For a multiple-knockoff-based inference where each genetic variant is paired with mentclass2pt{minimp-values from different statistical models  and from different tests . In such cases, we can apply GhostKnockoff to Z-scores obtained by an inverse normal transformation of p-values multiplied by the direction of effect, i.e., p-values were computed using tests with valid type I error rate. For example, for studies with related samples, the p-values can be computed using a mixed model that accounts for sample relatedness, such as GMMAT14, SAIGE15 and fastGWA-GLMM16. We further discuss the robustness of GhostKnockoff in the Discussion section.GhostKnockoff was derived for a particular form of Z-score described above. In practice, we may obtain 18. The choice 17.Suppose Z-scores from Our proposal for meta-analysis of possibly overlapping studies via knockoffs is to mimic a pooled mega-analysis, by revising the knockoff generation to account for the possibility of duplicated samples. We first consider a scenario where all studies in the meta-analysis are homogeneous and have a shared LD structure. In the meta-analysis setting we compute the knockoff Z-scores asNext, we consider a more general scenario where there are 11 and He et al.12. Note that both the HMM method and the SCIT method for individual level knockoff generation has a model complexity p-values efficiently for biobank scale data. The proposed method can leverage other analytical tools that efficiently compute variant-level Z-scores.GhostKnockoff is computationally efficient. Empirically, it only required 11.5 hours on average with one CPU to analyze a phenotype from the UK Biobank, and 5.45 hours to meta-analyze the nine AD genetic studies. This is significantly faster than the existing knockoff methods that require individual level data, which can take several days as reported in Sesia et al.19. We restricted the sampling to individuals with >80% European ancestry (estimated by SNPWeights v2.1 using reference populations from the 1000 Genomes Consortium21). For each replicate, we randomly drew individuals for two overlapping studies with 2500 individuals per study and 2000 genetic variants randomly selected from a 1Mb region near the APOE region . We then restricted the simulation studies to variants with minor allele counts > 25 and to variants that are not tightly linked. We considered three levels of sample overlap: 0% (independent), 25% (moderate) and 50% (high), with 0%, 25% and 50% samples in each study being present in the other study. Details on the simulation studies can be found in the “Methods” section.We performed simulations to empirically evaluate the performance of GhostKnockoff, which include: (1) comparing knockoff inference based on summary statistics vs. knockoff inference based on individual level data; (2) evaluating the proposed method that accounts for sample overlap; (3) comparing multiple-knockoff inference vs. single knockoff inference; (4) comparing knockoff inference vs. conventional marginal association tests in terms of the prioritization of causal variants. Note that the power comparisons between knockoff FDR control and usual FWER control in a genome-wide setting have been extensively studied by Sesia et al. (2020) and He et al. (2021), and therefore we did not focus on these existing comparisons in this paper. Instead, our simulation study focuses on method comparison in a local region. We simulated genetic data directly using whole-genome sequencing (WGS) data from the Alzheimer’s Disease Sequencing Project (ADSP). The ADSP WGS data (NG00067.v5) are jointly called by the ADSP consortium following the SNP/Indel Variant Calling Pipeline and data management tool (VCPA)22. This is because the detection threshold of the knockoff filter , respectively) with the second-order knockoff generator proposed by Candès et al. that requires individual-level data . We also extend the second-order knockoff generator to the multiple knockoff setting and include it in the comparison . The methods that require individual level data were applied to an oracle pooled dataset that only contains unique samples. For a fair comparison, all methods are based on the same feature importance scores, i.e. the squared Z-scores from a marginal score test for association. We present the results in Fig. Second, we compare GhostKnockoff-M (target FDR = 0.1) with conventional marginal tests used in GWAS, adjusted by Bonferroni correction for FWER control  or Benjamini-Hochberg procedure for FDR control . We show results for the setting with 25% sample overlap. Since the FDR control is more liberal than the FWER control, we focus on the prioritization of causal variants in this simulation study. For each replicate, we calculate the proportion of identified variants being causal (1-FDR) for each method. We observed that the causal proportion for GhostKnockoff-M is substantially higher than for conventional marginal tests, because GhostKnockoff-M performs a conditional test, and therefore can properly account for LD Fig. . FurtherFinally, we compare multiple knockoff inference (GhostKnockoff-M) with single knockoff inference (GhostKnockoff-S) in terms of the randomness due to sampling knockoff copies, referred to as stability of knockoff inference. We show results for the setting with 25% sample overlap. We fixed the genotype data and phenotype data, and repeatedly performed knockoff inference. For each replicate, we computed the W-statistic for each variant. Then we calculated the standard deviation of the W-statistics per variant to quantify the variation due to sampling knockoffs. The multiple knockoff procedure shows less randomness due to sampling knockoffs compared to single knockoff inference Fig. .We have also performed additional comparisons with other existing knockoff generators that require individual level data, including the knockoff generator for Hidden Markov Models (HMMs) proposed by Sesia et al. 2019) with number of states S = 50, and the sequential knockoff generator proposed by He et al. (2021). We observed similar results as in comparison with the second-order knockoff generator above  The genome-wide meta-analysis of clinically diagnosed AD and AD-by-proxy  by Jansen et al.24; (3) The genome-wide meta-analysis of clinically diagnosed AD  by Kunkle et al.25; (4) The genome-wide meta-analysis by Schwartzentruber et al.26, aggregating Kunkle et al. 2019 and UK Biobank based on a proxy AD phenotype; (5) In-house genome-wide associations study of 15,209 cases and 14,452 controls aggregating 27 cohorts across 39 SNP array datasets, imputed using the TOPMed reference panels27;  Two whole-exome sequencing analyses of data from The Alzheimer’s Disease Sequencing Project (ADSP) by Bis et al.28 , and Le Guen et al.29 ; (8) In-house whole-exome sequencing analysis of ADSP ; (9) In-house whole-genome sequencing analysis of the 2021 ADSP release30 . All studies focused on individuals with European ancestry. We used LD matrices estimated using the high coverage whole-genome sequencing data of the expanded 1000 Genomes Project31. Due to the relatively small sample size of the 1000 Genomes Project  used to estimate the LD matrices, we restrict the analyses to common and low-frequency variants with minor allele frequency >1%.We applied GhostKnockoff to aggregate summary statistics from nine overlapping large-scale array-based genome-wide association studies, and whole-exome/-genome sequencing studies. Specifically, the studies include (1) The genome-wide survival association study performed on 14,406 AD case samples and 25,849 control samples by Huang et al.We present the estimated study correlations LRPPRC (leucine-rich pentatricopeptide repeat motif containing protein) and APP (Amyloid beta precursor protein) have support for their possible involvement in AD from multiple studies32. Furthermore, Hosp et al. (2015) identified LRPPRC as a preferential interactor of APP carrying the so-called Swedish mutation (APPsw), which causes early-onset AD33. Among the new genes, TREM1, CYP3A7, SIGLEC11, IL34, RBCK1, C16orf92, WWOX are within 1MB of novel loci reported in recent studies by Wightman et. al. (2021)34 and Bellenguez et al.35.We present the results of the meta-analyses of the nine studies in Fig. p-value. We present the results for FDR = 0.05 and FDR = 0.10 in Supplementary Table To validate the results from the knockoff inference, we adopted an alternative strategy when an independent replication study is not available. Specifically, we applied the method to a subset of samples and show that the identified variants are also replicated when we increase the sample size. We considered GhostKnockoff analysis of Kunkle et al. 2019), Schwartzentruber et al. (2021), and all nine studies. Note that data from Kunkle et al. (2019) is a subset of Schwartzentruber et al. (2021); Schwartzentruber et al. (2021) is a subset of the meta-analysis. We considered the replication of genetic variants. A genetic variant is replicated if the same variant is also identified in the larger study with the same direction of effect and a smaller 9, SchwarAt FDR=0.05, we observed that 338 out of 385 (87.8%) variants by GhostKnockoff analysis of Kunkle et al. (2019) are also replicated in the analysis of Schwartzentruber et al. (2021); 447 out of 634 (70.5%) variants identified by GhostKnockoff analysis of Schwartzentruber et al. (2021) are also replicated in the proposed meta-analysis of all nine studies. At FDR = 0.10, 370 out of 448 (82.6%) variants identified by GhostKnockoff analysis of Kunkle et al. (2019) are also replicated in the analysis of Schwartzentruber et al. (2021); 510 out of 724 (70.4%) variants identified by GhostKnockoff analysis of Schwartzentruber et al. (2021) are also replicated in the proposed meta-analysis of all nine studies. Overall, we conclude that the proposed GhostKnockoff , though systematically different from the conventional GWAS, is a valid approach to make reproducible genetic discoveries.Finally, we present the results based on sample size weighted combination as opposed to the proposed optimal weights in Supplementary Fig. 36. We performed the DEG analysis stratified by 14 cell types, spanning major brain cell types  and cell types that reside in the vascular, perivascular, and meningeal compartments, including endothelial cells, pericytes and smooth muscle cells, fibroblasts, perivascular macrophages and T cells. We adjusted for age, batch, cellular detection rate, and for within-sample correlation by including sample dummy variables as covariates. We used this fixed effect model instead of a random effect model because the number of clusters is small relative to the total number of cells. Among the 50 proximal genes, 38 had expression measurements in the scRNAseq dataset. We considered p-value threshold 0.05 for suggestive signals and a more stringent Bonferroni correction 0.05/38 = 0.0013 for significant signals .For the proximal genes (nearest genes to the lead variant) corresponding to the 50 loci identified at FDR 0.10 in Fig. p-value) vs. log2 fold change) in Fig. p < 0.05) in at least one cell type, a significantly higher proportion compared with the background genes , similar to the proportion for the proximal genes identified at FDR = 0.10. We also observed that the DEG signals are more pronounced for the genes identified by GhostKnockoff compared to background genes , showing a strong enrichment of DEG signals for the proximal genes that reside in the loci identified by GhostKnockoff.We show the scRNAseq results . In this analysis, GhostKnockoff reduces to a knockoff inference based on summary statistics from a single study. We collected existing Z-scores calculated by Zhou et al. (2018) using SAIGE, a method that controls for case-control imbalance and sample relatednessp-value threshold We aim to illustrate two properties of GhostKnockoff inference that are systematically different from a conventional GWAS analysis. First, GhostKnockoff controls for FDR while conventional GWAS controls FWER; Second, GhostKnockoff performs a conditional test while conventional GWAS performs a marginal association test. We expect that the more liberal FDR control will lead to more associated loci, but the conditional test will reduce false positive findings due to LD confounding at each locus. For each phenotype, we count the number of independent associated loci, i.e. loci more than 1Mb away from each other. Within each locus, we count the number of genetic variants passing the FDR 0.1 threshold. We compare GhostKnockoff results and results from conventional GWAS using SAIGE . The presence of tightly linked variants can diminish the power to identify the causal ones. The current implementation applied a hierarchical clustering of genetic variants prior to the analysis and then randomly selected one variant in each cluster. Although this strategy ensures that each variant has a representative variant included in the analysis, the statistical power can be suboptimal when the underlying causal variant is not selected. Alternatively, the group knockoff filter which groups variants and thus requires exchangeability at the group rather than variant level can be usedp-values in the original study are deflated or inflated, the meta-analysis results can be biased subsequently. In addition, the dependency factor for knockoff generation was derived based on sample overlapping. In practice, we found that the analysis based on this dependency factor reasonably reflects other factors, but the theoretical guarantee will require future investigations.We focus on sample overlap because it is one of the main sources of study correlation, but the method can be more general to quantify study correlation due to other factors such as data generation, genotype coverage, imputation, and phenotype definition. In fact, the proposed estimation of study correlation is valid if the correlation of genome-wide Z-scores is correctly inferred. Our proposed method for estimating the correlation is data driven. If other factors increase/decrease the correlation, we think that the data-driven estimation will remain valid. However, we do require that i-values from different datasets are valid, and correctly reflecting the same disease-genetic association. If the We note that GhostKnockoff was derived for a particular form of Z-score, where both features and outcomes are standardized with mean zero and standard deviation one, and samples within each study are assumed independent. In practice available Z-scores can be based on different statistical models  and different tests . Using empirical simulation studies, we observed that GhostKnockoff is robust to such variations Fig. . IntuitiOur meta-analysis method is based on the second-order knockoff generator, which was initially developed for Gaussian distribution and then shown to remain empirically robust to certain deviations if the estimated second-order moments are sufficiently close to those of the underlying distribution.The proposed knockoff-based inference using summary statistics attempts to mimic the inference based on individual-level data. For single-knockoff, we show in Supplementary Materials that the two methods are equivalent if we directly generateThis way, we can directly simulate the knockoff Z-scores from a multivariate normal distribution. For a given dataset, the knockoff Z-scores will follow the same distribution as those calculated based on generating individual-level knockoffs. Therefore, the summary statistics-based knockoff generation retains the properties of knockoff-based inference.When 62. We show in Supplementary Materials that the multiple-knockoffs counterpart for a Z-score can be directly generated byHere we extend the single-knockoff approach to the case with multiple knockoffs where the original feature and multiple knockoffs are simultaneously exchangeable62. In the multiple knockoff scenario, After the knockoff Z-scores are generated, we calculate the feature importance score as the element-wise square of Z-scores,7. Instead, it is a function of the exact knockoff statistics that obey the “flip sign” property in the context of multiple knockoff inference. We use it as a convenient and intuitive representation of the magnitude of association. We present the exact knockoff statistics that obey the “flip sign” property and the corresponding knockoff filter in the “Methods” section.Variants with We define the threshold for the knockoff filter asIn addition, we define the Q-value for a variant with statistics Suppose Z-scores from Given independence between studies, The same knockoff filter procedure as before can be applied in this setting.The principle for meta-analysis of overlapping studies is to mimic a pooled mega-analysis where the knockoff generation should be revised to account for the presence of possibly duplicated samples. One sufficient condition for a valid knockoff inference is that for a sample that is present in more than one study its knockoff version for different studies should be identical instead of being independently generated for each study.Let The number of duplicates per sample is typically unknown. We propose an approximation of We propose a technique based on the proposed knockoff framework to identify study correlations due to sample overlap. The method requires GWAS summary statistics only and it naturally accounts for LD. Specifically, we first calculate the study correlation matrix63. We calculate effective sample size asWe then estimate 17.A common approach in meta-analysis is to sum Z-scores and weight them properly based on sample sizes, i.e.Suppose there are which means that it can be generated by the weighted summation of the knockoff Z-scores generated for each individual group.When meta-analyzing studies with overlapping samples, we would like to down-weight studies that are largely overlapping with others. In general, the proposed meta-analysis approach can be written aswk ≥ 017. It is a convex optimization problem with a unique solution which can be efficiently solved by standard software such as the CVXR package in R. With the proposed weights, we revise the calculation above of the dependency factor asWe note that this is similar to the optimal weights proposed by Lin and Sullivan (2009), except for the additional constraint It is worth noting that the form of Another possible and often overlooked complication in meta-analyses of genetic studies is the unequal coverage of variants across studies due to different genotyping platforms and/or different imputation panels for individual studies, which results in the presence of “study-specific” rare variants (MAF < 0.01) that are measured in only some of the studies. One suboptimal solution is to only include variants measured across all studies. Alternatively, to maximize the power of genetic discovery, all variants may be included in the meta-analyses. In the presence of study-specific rare variants, we propose to calculate the overall Z-score and its knockoff counterpart asAlthough the knockoff method helps to prioritize causal variants over associations due to LD, it is difficult or impossible to distinguish causal genetic variants from highly correlated variants. The presence of tightly linked variants can diminish the power to identify the causal ones. We applied a hierarchical clustering of genetic variants prior to the analysis, where variants in the same cluster have a pair-wise correlation APOE region  in the ADSP study. We then restricted the simulations to variants with minor allele counts >25 to ensure stable calculation of summary statistics . Since the simulations here focus on method comparison to identify relevant clusters of tightly linked variants, we simplify the simulation design by keeping one representative variant from each tightly linked cluster. Specifically, we applied hierarchical clustering such that no two clusters have cross-correlations above a threshold value of 0.75 and then randomly choose one representative variant from each cluster to be included in the simulation study. To simulate multiple causal variants, we randomly set 10 variants in the 1Mb region to be causal, with a positive effect on the quantitative/dichotomous trait as follows:For each replicate, we first generated two overlapping studies  with genetic data on 2000 common and rare genetic variants randomly selected from a 1Mb region near the Further information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


Combining ability studies under low soil P conditions provides useful information on the inheritance of important traits to improve soybean for low P tolerance. The study aimed at determining the combining ability and gene actions of biomass yield and root traits in soybean under low phosphorus conditions. Nine parental genotypes and their 36 half diallel F2/F3 progenies were evaluated at two locations in Ethiopia on soils of low P availability. Highly significant (P<0.01) general combining ability (GCA) were found for all the traits and specific combining ability (SCA) for root dry weight and root fresh weight; while the SCA effects of all the rest of the traits were significant (P<0.05). The higher relative contributions of GCA over SCA revealed the preponderance of additive gene action in the inheritance of biomass yield, root dry weight, biomass dry weight, root volume, and root fresh weight with respective relative GCA:SCA contributions of , , , , and ; while the narrow-sense heritability was high (34.3%) only for biomass yield. Hardee-1 displayed significant (P<0.05) and positive GCA effects for most of the studied traits, and several crosses involving this parent showed superior performances. The traits i.e., biomass yield, biomass dry weight, root volume and root fresh weight showed highly (P<0.001) correlation with grain yield. Thus, breeding programs aiming to improve soybean for biomass yield and root traits under low-P condition can use Hardee-1 as a parent. Glycine max L. Merril) is one of the world’s most economically important legumes and oilseeds, and its global production and yield have increased considerably in the last three decades [Soybean  is among the essential soil nutrients required in large quantities for crop growth and development, throughout their life cycle, especially during the reproductive and seed development stages. However, most tropical and sub-tropical soils that lack proper fertilization and manuring treatments do not contain sufficient readily available P to meet the high demands of the crop, especially during certain periods of the growing cycle . Thus, c-1 [In soybean, low P stress is more detrimental than other nutrient deficiencies, toxicities or diseases; however, it is difficult to select high P efficient soybean varieties based on phenotypes. The soybean demand for P reaches the maximum during pod and seed development , 18, as -1 . Phospho-1 . Suman [-1 of forage from soybean [Soybean is primarily produced for grain purpose, however, in the 1800’s or before world war-II it used to be cultivated mainly for forage purposes in the United States , 4. More soybean . Varieta soybean . One IITPlant root traits play important roles in increasing soil P availability and acquisition and adaptation to soil P deficiency. Root characteristics such as high root biomass, length and volume enable the plants to occupy greater soil volume and enhance P acquisition by plants . Root di‐P can grow better under low‐P conditions, and understanding the genetic mechanisms of low‐P tolerance will not only facilitate identifying the relevant genes, but also helps in developing low‐P tolerant cultivars [Combining ability studies provide valuable information that helps in making decision on the choice of parental line and allows understanding the gene action influencing trait inheritance resulting in greater efficiency in soybean breeding programs . Plants ultivars . Breedinultivars , 25. Eveultivars , their b-1) applied P conditions. The parental line, H 3, was received from Mozambique Agricultural Research Institute, was specifically identified for its low P tolerance. All the parental lines used in this study had been tested in yield trials for over three years and in at least six locations in each year and showed good performance and adaptability for the mid-altitude and high rainfall soybean growing agro-ecologies of the country. While being among the parental lines, the released varieties  might serve as standard checks for the tested genotypes in this experiment. The nine parental lines were crossed in a 9 x 9 half diallel mating scheme. The diallel experiment was conducted using F2/F3 progenies due to inadequate quantities of seeds in the F1.The parental lines  used in The diallel trials consisting of 45 genotypes (parents and progenies) were grown at two locations, i.e., Assossa , and Metu  in Western Ethiopia in a 5 x 9 alpha lattice design with two replications. The two experimental sites were known for their strongly acidic reddish-brown soil with low P availability . Each plBefore the experiment, three soil samples were collected from the top layer (0–20 cm) of the fields in each of the study locations. The soil samples were submitted to the soil laboratory of Jimma Agricultural Research Center for the different analyses. Bray II method was used for P analysis, while Kjeldhal method for N, flame photometry for K and Walkley and Black method was used to determine organic carbon (OC) and organic matter (OM). Other soil parameters such as pH, exchangeable acidity, Al and H were also determined for the soil samples. Results of the soil analysis at the experimental sites (Assosa and Mettu), where this research was conducted are presented in Data were collected for biomass yield and other root traits at R6 growth stage of the crop, including biomass yield (gm): the weight of fresh above ground shoot biomass samples collected from five representative plants, while biomass dry weight (gm), which is the weight of oven dried above ground shoot biomass collected from five representative sample plants. Other root parameters collected from five randomly selected representative plants included: root fresh weight (gm) the fresh weight of root samples, root dry weight (gm) which is the weight of oven dried root samples, root length (cm) the mean length of the central longest tap roots, and root volume (ml) the volume of water displaced from a measuring cylinder by the roots.Analysis of variance for the individual locations was performed for each of the traits, and highly significant differences were found among genotypes for all the studied traits. Test of homogeneity of error variances of the individual locations (Assossa and Mettu) was performed for all the traits as suggested in  and therX = the population mean, gi = the general combining ability effect of the ith parent, gj = the general combining ability effect of the jth parent, Sij = the specific combining ability effect of the cross between ith and jth parents, such that Sij = Sji, (gL)ijk = the interaction effect, if general combining ability of ith parent with Kth locations, (gL)jk = the interaction effect of general combining ability of jth parent with Kth locations, (SL)ijk = the interaction effect of the specific combining ability with locations, and eijk is the residual associated with ijkth observation. The formula provided in [Where, vided in , 32 were2σ2gca is the variance of GCA and σ2sca is the variance of SCA. Since the total genetic variance among F1 hybrids is equal to twice the GCA component plus the SCA component, the closer the ratio is to unity, the greater the predictability of a specific hybrid’s performance based on GCA alone [CA alone , 34. PeaThe analysis of variance revealed highly significant (P<0.01) differences among the genotypes (G), environments (E) for all the studied biomass yield and root related traits . SimilarThe mean performance of 66 crosses and nine parental lines evaluated under low P conditions are presented in Estimates of GCA effects of root traits for the nine soybean parental genotypes evaluated under low P conditions are presented in Among the crosses, Hardee-1 x H-3, Davis x Clark 63 K, Alamo x SCS-1 showed significant negative SCA effects for root length, whereas Alamo x Clark 63 K showed significant positive SCA effects for root length . SimilarThe relative contributions of GCA and SCA, and narrow sense heritabilities of the studied root and shoot biomass traits were presented in The correlation analysis revealed a strong, highly significant positive association of grain yield with biomass yield (0.79), biomass dry matter yield (0.74), root weight (0.70), root fresh weight (0.57). Similarly, grain yield showed significant (P<0.05) association with root dry weight, while no association was found with root length . The corThe 6.07 and 8.40 ppm P levels recorded for Assosa and Mettu experimental sites, respectively, were far lower than the optimal P levels. The optimum level of P reported for soybeans was 15 ppm and soil P levels should be maintained between 15 and 30 ppm . AccordiSignificant differences observed among the parental genotypes as well as in the progeny populations for all the studied traits in the present study might be as a result of the high genetic variation created in the progeny populations that may allow the genetic improvement of the populations for the studied biomass yield and root related traits for low P tolerance. The presence of genetic variability is of prime importance for good genetic progress in improving a trait in a selection program. The use of parental genotypes from diverse sources in the crossing might have contributed to the observed significant differences and high genetic variations among the crosses and progeny populations. Similarly, highly significant differences among parents and progeny populations were also reported for grain yield, 100-seed weight, pod length, days to maturity and plant height under low P conditions . SignifiThe relative importance of GCA and SCA was examined by expressing it as the ratio of additive variance to the total genetic variance. The closer this ratio was to unity, the greater the predictability based on GCA alone . The ratCrowford was identified as the best performing parent based on the mean values for most traits, followed by SCS-1 and Hardee-1. GCA effects for all the traits varied significantly among the parental genotypes and between environments for biomass dry matter yield and biomass yield. Hardee-1 showed significant positive GCA effects for biomass dry matter yield, root volume and biomass yield; while Alamo displayed significant negative GCA effects for root dry weight, root length, root volume, root fresh weight and biomass yield. In a recent study, Hardee-1 was reported possessing significant positive GCA effects for grain yield, number of seeds per pod, pod length, plant height and pod number; while Alamo showed significant negative GCA effects for hundred seed weight, pod length, and plant height . Hardee-Average heritability estimates were categorized as high, medium and low with respective values of 5–10%, 10–30%, and 30 to 60%, that represent different crops and across locations and seasons , 51. AccA half-diallel experiment involving nine parental genotypes and their F2/F3 progeny populations was conducted at two environments under low P soil conditions. The results revealed wide genetic variability among the parental genotypes and progeny populations used in the study. Both the GCA and SCA effects were significant, indicating the importance of both the additive and non-additive gene actions in the inheritance of the traits. Among the parents, Hardee-1 was the best general combiner for root traits, yield and yield-related traits, and hence the best parent to improve soybean for low P tolerance. High narrow sense heritability and high relative contributions of GCA over SCA was found for biomass yield, indicating the importance of additive gene effects in the inheritance of this trait, and recurrent selection in the segregating population would be the best approach to improve the trait for low-P tolerance. The high and positive correlation of biomass yield with grain yield indicates that improving biomass yield can help improve the productivity of soybean under low P conditions. More importantly, soybean biomass can greatly help improve the forage yield and value of soybean as an alternative animal feed to Alfaalfa and other forage crops.


P < 0.05). Ewe maternal index had no quantifiable impact on lambing ease, carcass conformation, or fat, the health status of the ewe or lamb, ewe barren rate, or ewe live weight. Lambs born to rams of superior terminal index produced heavier lambs from preweaning onwards, with a reduced day to slaughter (P < 0.05). Lambing traits, lamb health, and carcass characteristics of the progeny did not differ between sires stratified as low or high on the terminal index (P > 0.05). Results from this study highlight that selecting either ewes or rams of superior maternal or terminal attributes will result in an improvement on pertinent performance traits of the national sheep flock, resulting in greater flock productivity and profitability.Genetic evaluations provide producers with a tool to aid in breeding decisions and highlight the increase in performance achievable at the farm level through genetic gain. Despite this, large-scale validation of sheep breeding objectives using field data is lacking in the scientific literature. The objective of the present study was to evaluate the phenotypic differences for a range of economically important traits for animals divergent in genetic merit for the Irish national maternal and terminal sheep breeding objectives. A dataset of 17,356 crossbred ewes and 54,322 progeny differing in their maternal and terminal breeding index recorded in 139 commercial flocks was available. The association of the maternal index of the ewe or terminal index of the ram and a range of phenotypic performance traits, including lambing, lamb performance, ewe performance, and health traits, were undertaken. Ewes excelling on the maternal index had higher litter sizes and produced progeny with greater perinatal lamb survival, heavier live weights from birth to postweaning and reduced days to slaughter ( Sheep systems are traditionally operated as low input with low-profit margins, therefore, strategies are required to improve farm sustainability and profitability ; the usehttps://www.sheep.ie/). In total, performance data were available on 17,356 crossbred ewes and 54,322 progeny.Performance data from 139 commercial flocks across a range of animal-specific events including lambing ; lamb performance ; ewe performance records ; and animal health  recorded between October 2018 and June 2021 were extracted from the Sheep Ireland database  slaughtered between 60 and 365 days of age. For each weighing event, each lamb was allocated to a contemporary group of flock-date of weighing. For all carcass traits, lambs were allocated to a contemporary group of abattoir-date of slaughter. Across all lamb performance traits, only contemporary groups with at least five records were retained.Lamb live weight was recorded at three time points: preweaning, weaning, and postweaning  by produEwe live weight was defined as the weight of a female who had at least one recorded lambing event; only recorded ewe live weights between 30 and 130 kg were retained . Ewe litDag score was measured by trained technicians on a five-point scale as 1 = fecal soiling and dags covering the breech area and extending down the hind legs towards the pasterns to 5 = no fecal soiling . Dag scoAcross all traits, data were also available on dam age number (or ewe age for traits of the ewe herself). Ewe or dam age was classified into five categories as 1, 2, 3 (3 to 5), 4 (6 to 8), and 5 (≥9). Age of the ewe or dam at first lambing was categorized as lambing either: 1) between 8 and 18 months of age, or 2) between ≥ 18 and 28 months of age as per The maternal and terminal breeding indexes . For all models the index, either maternal or terminal, was considered on a categorical scale .For the lambing traits, the model employed was:ijklmmo is the dependent variable of lamb birth weight, lamb survival, or lambing ease; µ is the population mean; CGi is the effect of the contemporary group ; EweAgej is the age category of the ewe ; BirthTypek is the birth type of the litter ; Sexl is the sex of the lamb ; o is the maternal index of the dam or the terminal index of the sire ; and eijklmmo is the residual term.where YFor lamb performance and health traits, the model employed was:ijklmmopqrs is the dependent variable of lamb weight ; carcass  or health (lamb lameness and dag score) trait; µ is the population mean; CGi is the effect of contemporary group ; EweAgej is the age category of the ewe ; BirthTypek is the birth type of the litter ; RearTypel is the rearing type of the litter ; Sexm is the sex of the lamb ; Agen is the age of the lamb at recording ; r is the covariate of the EBV for the dependent variable of the lamb’s sire  or dam ; and Indexs is the maternal index of the dam or the terminal index of the sire . When the dependent variable under investigation was carcass conformation, fat, or age at slaughter the model also included: Monthp is the month of birth (p = January to May) and CarcWtq is the covariate of actual carcass weight of the lamb. Across all models, eijklmmopqrs is the residual term.where YFor ewe traits, the model employed was:ijklm is the dependent variable of ewe litter size, barren rate, ewe live weight, or ewe lameness score; µ is the population mean; CGi is the effect of the contemporary group ; EweAgej is the age category of the ewe ; AFLk = age at first lambing (k = 8 and 18 months of age or ≥ 18 and 28 months of age); m is the maternal index of the ewe ; and eijklm is the residual term.where YAll 139 commercial flocks operated a spring lambing production system, with a median lambing date of 2nd April. The average lambing difficulty score was 1.45 and 1.52 in singleton and multiple litters, respectively . The preP < 0.05) no clear trend was observed across the five maternal index strata. The maximum difference in lambing ease observed between the five strata was 2.79% and 1.76% for single and multiple litters, respectively (P < 0.05), with a difference of 0.98% observed between ewes of the low and high maternal index strata. Greater lamb birth weights were associated with ewes of higher maternal indexes . However, across all the lambing traits no obvious trend was noted across sires stratified on terminal index, with no difference observed between sires stratified as low and high on terminal index for any of the lambing traits . Carcass fat did not differ by ewe maternal index  were observed between the ewe maternal index strata, but no clear trend was observed across the five strata.Relative to ewes in the low maternal stratum, lambs from ewes in the high maternal stratum were heavier at preweaning (+0.39 kg), weaning (+0.80 kg), and postweaning (+0.99 kg) and had a shorter number of days to reach slaughter , and the weight difference between lambs born to rams in the low and high terminal index strata increased with lamb age (P < 0.05). No difference was observed in the carcass fat score of lambs based on the terminal index of the sire (P > 0.05). Carcass conformation score tended to reduce based on a terminal index of the sire, with a 0.05 lower carcass conformation score associated with lambs born to sires in the high terminal index stratum relative to lambs of sires in the low terminal index stratum (P < 0.05).Greater preweaning, weaning, and postweaning weights were associated with lamb born to rams of a higher terminal index (lamb age . Lambs bP < 0.05), with a +0.17 greater litter size associated with ewes of high maternal index, relative to ewes of low maternal index (P > 0.05). Although differences were observed in ewe live weight across the five stratifications of ewe maternal index (P < 0.05), the differences were biologically small (ranging from 0.07 to 0.71 kg), and no clear trend was observed across the five strata for maternal index.Litter size differed by ewe maternal index .Dag score and ewe lameness differed by ewe maternal index .Dag score differed by sire terminal index  impact on lambing performance traits. This in itself is noteworthy given that the terminal index is selecting for heavier lambs (at least from preweaning onwards), coupled with the negative relationship reported between lamb (birth) weight and lambing difficulty and dystocia  suggestsThe number of lambs born and reared has been highlighted as one of the key drivers in flock productivity and profitability both nationally  and inteP < 0.01) were observed (results not presented). For example, a (favorable) 1.25% difference in perinatal lamb survival was observed between animals in the top and bottom 20% EBV for perinatal lamb survival; similarly, a 7.61% and 2.27% difference was observed in the proportion of lambs that required assistance at lambing for the EBV for single and multiple lambing ease, respectively. These results highlight that the genetic evaluations that underpin the breeding objectives are yielding favorable results but that the breeding objectives may require some additional research, including the potential revision of the economic weightings assigned to these traits. This also suggests if producers are selecting an animal based on a particular trait such as health or ewe barren rate, then they should focus on the animal’s individual EBV in combination with the overall breeding objective.Differences were not detected or no clear trend was observed across the five strata investigated in the current study on either the maternal or terminal indexes in a number of different parameters including health traits (lameness and dag score), carcass characteristics (conformation and fat score) and ewe barren rate . These traits  have been introduced to the national breeding objectives relatively recently  and therResults from this study highlight that selecting animals based on either the maternal or terminal breeding objective will simultaneously result in greater animal performance and productivity for a number of pertinent traits. Although the magnitude of differences on individual traits observed in the present study was generally small the accumulation of these differences to overall farm profitability warrants further investigation to assess the true potential of the national genetic evaluations to improve the national flock productivity and profitability.txac099_suppl_Supplementary_AppendixClick here for additional data file.


Positive genetic correlations were observed between all SNA traits and anterior SL24h, except for clustering coefficient. Our results suggest that selection for an index that combines the eigenvector centrality and clustering coefficient could potentially decrease SL24h and SL3wk compared to selection for each trait separately. This study provides a first step towards potential integration of SNA traits into a multi-trait selection index for improving pigs’ welfare.Social network analysis (SNA) has provided novel traits that describe the role of individual pigs in aggression. The objectives were to (1) estimate the genetic parameters for these SNA traits, (2) quantify the genetic association between SNA and skin lesion traits, and (3) investigate the possible response to selection for SNA traits on skin lesion traits. Pigs were video recorded for 24 h post-mixing. The observed fight and bullying behaviour of each animal was used as input for the SNA. Skin lesions were counted on different body parts at 24 h (SL24h) and 3 weeks (SL3wk) post-mixing. A Bayesian approach estimated the genetic parameters of SNA traits and their association with skin lesions. SNA traits were heritable (h Grouping of unacquainted pigs is a common procedure in commercial farms; however, it results in elevated aggression as animals attempt to establish stable dominance relationships . AggressSeveral traits have been recommended as indicators of aggressive behaviour in pigs . Among tWhilst skin lesion counts provide some indication of pigs’ aggressive behaviour, a significant part of the variance in aggressive interactions is not captured by the number of skin lesions received by individuals . Most prRecently, social network analysis (SNA) of animal behaviour has gained much attention, due to its potential to provide novel insights into the social relationships between individuals for use in the fields of animal welfare science and fundamental ethology ,16. In p2 per pig. Animals were fed dry pelleted food ad libitum from a single space feeder and had constant access to water via a nipple drinker. The animals were the progeny of 82 sires and 217 dams. The total number of animals in the two-generation pedigree was 2427. Animals were distributed into 78 pens, i.e., social groups, each containing 15 animals of the same sex and breed which were formed using 3 animals from each of 5 litters. Animal weights were considered while grouping in order to minimize weight variation within the pen. The average age at mixing of the animals was 71 days (SD 4.5).This study uses the same dataset as described in Desire et al. (2016) and Foister et al. 2018) ,18, whic ,18, whiFresh skin lesions were counted for each body region 24 h post-mixing. One uninterrupted scratch was classed as a single lesion, regardless of length or severity. The body regions were separated into anterior , central (flanks and back) and posterior (hind legs and rump). To avoid including the injuries that occurred before mixing, skin lesions were counted immediately before mixing the animals and subtracted from the number counted 24 h post-mixing. Moreover, fresh lesions were counted again 3 weeks post-mixing as a measure of aggression under stable social conditions. A lesion was considered to be recent if it was vivid red in colour or recently scabbed. The skin lesion records were log transformed (y = loge (x + 1)) to approach the normal distribution. For further detailed information see Desire et al. (2016) .Animals were video recorded for 24 h post-mixing. Each animal that initiated or received an aggressive interaction was registered, including animal identity and type of interaction (fighting and/or bullying), as well as the corresponding duration. Fighting behaviour was defined as aggression that lasted at least one second where both pigs engaged in biting, pushing or head knocking the opponent. The bullying behaviour was defined as when one pig received or delivered aggression with no observable retaliation occurring .The SNA traits considered in this study were derived from Foister et al. 2018) [ [18] usiWhilst betweenness centrality is a continuous trait that assigns to each animal an individual betweenness centrality value, this trait was found to have a highly positively skewed distribution, as often only 1 or 2 individuals in each group have high betweenness centrality, whilst the majority of animals have very low or zero betweenness centrality. Therefore, we also transformed the betweenness centrality to a categorical trait, called “categorical betweenness” with two categories: ‘high’, comprising individuals within the top quartile of the betweenness centrality, and ‘low’, comprising individuals with the remaining 75%. The mean betweenness centrality of the top quartile was 0.13 (with a maximum of 0.4), and for the low betweenness category it was 0.01. Both the continuous and the categorical betweenness traits were included in the genetic analysis to investigate their genetic components.A series of univariate and bivariate analyses were used to estimate the genetic variance components and EBVs of all transformed SNA and skin lesion traits using the following linear animal model:The categorical betweenness and clique membership traits were analysed using the threshold liability animal models with the same fixed and random effects as used in the linear animal model. In the threshold model an unobservable normally distributed variable, i.e., liability, is assumed for each observation. According to this, the observed categorical value is realized depending on whether the liability falls below or above a certain threshold value ,31.0 is the additive genetic (co)variance matrix and I is the identity matrix, and ⊗ represents the Kronecker product of the matrices. C0 is the (co)variance matrix of the environmental pen effects and R0 represents the (co)variance matrix of the residuals. The conditional posterior distributions of co-variance components of G0, C0 and R0 were sampled from inverse-Wishart distributions. The posterior distribution of the genetic and environmental effects was derived from a Markov Chain of 1,000,000 iterations of the parameters, where the burn in of 100,000 was applied to obtain a stationary MCMC distribution and a lag of 20 iterations was applied to reduce the autocorrelations between consecutive iterations. The convergence of the Markov Chain was tested using the algorithms of Raftery and Lewis (1992) [Bayesian analyses using the Markov Chain Monte Carlo (MCMC) method of Gibbs sampling were performed to estimate the models’ parameters using GibbsF90 from BLUPF90 family software  for the s (1992) . PosteriAs the SNA and skin lesion traits were measured on different scales, the EBVs obtained from the analyses were standardized into z-scores, i.e., expressed in terms of standard deviation with a mean of zero. Amongst the non-categorical traits, eigenvector centrality and clustering coefficient emerged as the two complementary SNA traits most closely and antagonistically related to the skin lesions at different body regions and time points in the above analyses. Therefore, to estimate the effect of selecting for these two SNA traits on skin lesions at the individual and pen level, the same method as in Desire et al. (2016)  was chosAs selection for the eigenvector centrality and clustering coefficient traits would be expected to affect the pen’s network structure, therefore, both the average EBV as well as the standard deviation of EBVs at the pen-level, as a measure of diversity for these traits, were calculated. The pens were then ranked based on their average or standard deviation in the EBVs of these SNA traits, and the corresponding average skin lesions for the lowest 20% of pens was calculated.The descriptive statistics for the transformed SNA traits, skin lesion traits and the number of fights and bullying behaviours considered in this study are shown in The marginal posterior distributions and 95% highest posterior density intervals indicate that the heritability estimates for all SNA traits were significantly above zero . The posThe posterior means of the genetic correlations and the HPD95% for SNA traits are shown in The posterior means of the genetic correlations and the HPD95% of SNA traits and skin lesions, recorded 24 h post-mixing, are presented in Animals selected to have EBVs in the lowest 10% for eigenvector centrality (EBVs mean = −2.48 SD) had lower than average EBVs for anterior SL24h (EBVs mean = −1.53 SD), while they had higher posterior SL24, anterior, central and posterior SL3wk a. In conThe phenotypic values for individuals with lowest 10% of EBVs for eigenvector centrality and clustering coefficient largely mirrored those observed on the genetic level for all skin lesions, except for posterior SL3wk for eigenvector centrality a, and ceThe mean EBVs of the skin lesions in the lowest 20% of pens ranked based on the standard deviation of the EBVs for eigenvector centrality, clustering coefficient and eigenvector-clustering index are shown in 2 ranged from 0.11 to 0.66) [2 = 0.04–0.43) [2 = 0.11–0.43) [Few studies have explored the genetic determination underlying SNA traits. Here, the posterior means of the heritability for the SNA traits of aggressive behaviour were low to moderate. To the best of our knowledge, the heritability of SNA traits in pigs have not been previously estimated. However, the heritability estimates found here, except for closeness centrality, are similar to the heritability reported for SNA of aggressive behaviour in different species (hto 0.66) ,23,24,2504–0.43) ,35, and 11–0.43) ,9,12,36.2 = 0.09). This trait measures how close an animal is to all other animals in the network, which reflects the degrees of separation or steps between individuals [2 = 0.59).Closeness centrality showed the lowest heritability estimates among the SNA traits . In contrast, these SNA centrality traits were generally negatively genetically correlated with SL3wk on different body regions. That would suggest that individuals with a genetic predisposition for high centrality immediately after mixing would tend to suffer high injuries on the anterior part of the body at that stage but would tend to have lower injuries in the stable group. A similar trade-off has been previously observed for dyadic aggressive interactions, where reciprocal aggression, in which the recipient of the attack retaliated, showed strong and positive genetic correlations with anterior SL24h (rg > 0.75) and negative correlations with skin lesions in the stable group . Thus, cAmongst all SNA traits, the clustering coefficient was the only trait that was found to be positively genetically correlated with skin lesions at both time points . This would suggest that using the clustering coefficient at mixing as selection criterion may not inflict a trade-off for reducing lesions at different time points or different body parts. However, it also needs to be considered that the clustering coefficient is strongly negatively correlated with all other SNA traits.Except for the clustering coefficient, the genetic correlations between SNA traits with central and posterior SL24h were generally low, with high levels of uncertainty and the 95% highest posterior density intervals spanning a wide range of values both below and above zero. In line with these results, Desire et al. (2016)  found noAlthough genetic correlations are valuable parameters to understand the genetic relationship among traits, the estimation of genetic correlations typically has a high level of uncertainty and requires substantial amounts of data . FurtherConsistent with the strength and direction of genetic correlation estimates, our results showed that animals with low EBVs for eigenvector centrality had low genetic and phenotypic values for anterior SL24h. However, it should be noted that these animals showed high EBVs for the posterior SL24h and SL3wk on all parts of the body a; howeveAt the pen level, the lowest 20% of pens ranked based on the pen average EBVs for eigenvector centrality, clustering coefficient and the eigenvector-clustering index showed the same trend as the individual level . Thus, sSelection for SNA traits could lead to a change in the structure of the network, i.e., the pen, as it could lead to a reduction in the variation in these traits. Therefore, we also investigated the effect of the variation in eigenvector centrality and clustering coefficient traits within the pen on skin lesions. Our findings suggest that the pens with low variation in EBVs for eigenvector centrality and clustering coefficient would have low SL24h and SL3wk at different parts of the body, except anterior SL24h in both traits, and central SL24h for clustering coefficient a,b. On tThe latter results would also suggest that the reduction in the mean index was more important for reducing anterior skin lesions than the index variation around the mean pen level. However, it is necessary to emphasise that selection mainly on the eigenvector-clustering index and secondary on the variation of this index within pen could be used to achieve a reduction in central and posterior SL3wk in the stable group. Moreover, the weighting of the SNA traits within the index could be changed to achieve different correlated responses in lesion traits, as both eigenvector centrality and clustering coefficient are inversely affecting skin lesion traits.Breeding against aggressive behaviour in pigs is challenging. The determination of the appropriate traits to reduce the pen level aggression and skin lesions and choosing which traits are easy to measure in commercial farms are important aspects for improving the welfare of pigs. SNA has shown the potential in providing measures that describe the direct and indirect social relationships between farm animals ,19. AdvaHowever, this study only provides a first step towards potential integration of SNA traits into selection strategies for improving animal welfare by reducing both aggressive interactions as well as resulting injuries. Antagonistic genetic relationships between the diverse SNA traits and skin lesions in different body regions obtained at mixing versus stable groups point towards potential trade-offs between reducing aggression and resulting injuries at different body regions and time points when using SNA traits separately as criteria of selection. However, the effect of this trade-off can be decreased by considering the eigenvector-clustering index, suggested in this study, although further studies are needed to confirm this, and also to better understand the genetic influence underlying group level aggression in different group compositions, environments and production systems.Compared to dyadic behavioural traits, SNA traits describe an individual’s direct engagement in aggressive behaviour in the context of the group’s behavioural structure defined by social interactions between all group members. Previous studies have highlighted that the social genetic effects play an important role in skin lesions resulting from aggressive interactions of pigs at mixing ,42. FurtLastly, SNA traits may enable selection for more socially tolerant or socially skilled pigs that contribute to lower pen level aggression and injuries, thus maintaining high performance in the social environments that prevail on commercial farms. Such selection should be complemented by continued efforts to find commercially feasible management interventions to reduce aggression. However, it is important to consider the association between these behaviour measures and economically important traits, e.g., performance and feeding behaviour traits .Social network analysis could be considered as a promising approach to describe the social interactions underlying harmful aggressive behaviour of animal groups. The results of this study indicate that many relevant SNA traits are moderately heritable and strongly genetically correlated but have different genetic correlations on the outcome of aggressions identified as skin lesions. Thus, the genetic correlations between SNA traits and skin lesions, and EBVs based estimates of selection response at the individual and pen level, suggest that selecting for different SNA traits separately would have different effects on skin lesions at different body parts immediately after mixing and in stable groups. Selection for an index that combines the eigenvector centrality and clustering coefficient could potentially decrease skin lesions after mixing and in the stable group environment at different parts of the body. Incorporating the SNA and other behaviour traits, along with the economically important traits is recommended for establishing a future strategy for simultaneously improving the performance and welfare of pigs.


Worldwide, most beef breeding herds are naturally mated. As such, the ability to identify and select fertile bulls is critically important for both productivity and genetic improvement. Here, we collected ten fertility-related phenotypes for 6,063 bulls from six tropically adapted breeds. Phenotypes were comprised of four bull conformation traits and six traits directly related to the quality of the bull’s semen. We also generated high-density DNA genotypes for all the animals. In total, 680,758 single nucleotide polymorphism (SNP) genotypes were analyzed. The genomic correlation of the same trait observed in different breeds was positive for scrotal circumference and sheath score on most breed comparisons, but close to zero for the percentage of normal sperm, suggesting a divergent genetic background for this trait. We confirmed the importance of a breed being present in the reference population to the generation of accurate genomic estimated breeding values (GEBV) in an across-breed validation scenario. Average GEBV accuracies varied from 0.19 to 0.44 when the breed was not included in the reference population. The range improved to 0.28 to 0.59 when the breed was in the reference population. Variants associated with the gene HDAC4, six genes from the spermatogenesis-associated (SPATA) family of proteins, and 29 transcription factors were identified as candidate genes. Collectively these results enable very early in-life selection for bull fertility traits, supporting genetic improvement strategies currently taking place within tropical beef production systems. This study also improves our understanding of the molecular basis of male fertility in mammals. Under a sustainable intensification framework for livestock production, factors that affect the health of humans and animals, and the environment are considered . Bull feAn understanding of male physiology is available –7, some The multiplicity of breeds used in tropical beef production systems limits the prospect to assemble the large reference populations needed for accurate genomic estimated breeding values (GEBV) for bull fertility. To address this limitation, strategies combining reference populations across breeds using imputed high-density SNP (single nucleotide polymorphisms) genotypes to produce accurate multi-breed GEBV are currently being investigated , 20, 21.This rich dataset was also used to dissect the genomics of bull fertility. Using a 3-way combination of gene network connectivity, pleiotropy, and gene expression in sperm, we identified several candidate functional variants associated with bull fertility traits. Future work could test if these variants aid across breed predictions for bull fertility traits.Our approach was to assemble a large reference population of tropically adapted bulls with fertility-related phenotypes and genotyped at high-density to be used to generate multi-breed GEBVs with useful accuracies. A further aim was to explore the factors affecting the accuracy and bias of GEBVs and the identification of functional variants. Our analysis had 4 major steps :In the Reference step , a multi2) and genetic correlations, as well as to obtain GEBV. The GREML analyses were performed using a multivariate model using the whole dataset, allowing the estimation of GEBVWhole  model, we explored the strength of the statistical association of h2, breed and phenotype on the accuracy, bias, and dispersion of GEBVs.In the Validation step , we compethod LR  approachIn the Functionality step , the seaThe number of records per breed varied from 660 (BTC) to 1,819 (TRC)  and Tropical Composite (TRC) bulls, Porto-Neto et al.  reportedThis study expanded previous analyses by including cattle breeds not evaluated before, further validating the genetic relationship between semen traits. The positive correlations  between weight, condition score and scrotal circumference have been reported in the past , as it wUsing bivariate models, we estimated the genomic correlation of the same trait observed in different breeds . Except We did not observe breed differences for the average GEBV within a trait as they were all non-significantly different from zero. However, there were some differences in the GEBV variation across breeds and these differences could reflect different accuracies with higher variations associated with higher accuracies.Two schemes were used to estimate GEBV accuracies : #1) rem2) was highest for the accuracy estimated using the method LR (ACCLR) than for traditional accuracy (ACCR), being 85.1% and 71.9% for validation schemes #1 and #2, respectively. The bias was not affected by any effect included in the ANOVA model indicating the random nature of its variation. Trait and breed were significant sources of variation for both measures of accuracy  approach exploits patterns of SNP co-association across multiple traits to form connections between the genes harbouring those SNP. The resultant network can be subject to topological analysis that is thought to provide biological insights over and above what can be inferred using traditional approaches such as GWAS. The AWM captured 3,479 SNP-Genes scattered genome-wide, of which 161 genes were annotated as transcription factors (TF). When the AWM was subjected to the PCIT network inference algorithm, 914,955 significant connections between genes were identified. Gene HDAC4  was found to have the highest degree  with 1,200 connections, making it a key causal candidate. The class II histone deacetylase HDAC4 regulates endocrine functions including male fertility and appetite , 29.With undisputed importance in male fertility, the spermatogenesis-associated (SPATA) family consists of 25 genes . Six SPATA genes were captured by the AWM, representing a significant enrichment . The captured genes were: SPATA16 chr1:94,583,401), SPATA18 , SPATA6L , SPATA2 , SPATA17  and SPATA5 . Of these, we highlight SPATA6L with 1,139 network connections and its strongest association with the trait PNS, and SPATA16 with 1,058 connections and strongest association with the trait MASS. In fact, a missense variant (p.Ile193Met) in SPATA16 has been recently associated with male fertility of dairy cattle  SAS Institute Inc. SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc., Cary, NC, USA. The model for adjustment was as follows: y = Xβ + εn Qxpak5 . To estin Qxpak5 , the genWhole   and MethThe following four metrics were employed:Correlation-based Accuracy (ACCR): In the context of cross-validation, the accuracy of a GEBV is traditionally computed from the Pearson correlation between a GEBV and the adjusted phenotype  for individuals in the validation population, and divided by the square root of heritability (h2):Method LR Accuracy (ACCLR): For individuals in the validation population, Method LR accuracy was computed as follows:Method LR Bias (BiasLR): Difference between the average GEBV of individuals in the validation population using the partial data minus that using the whole data:LR is zero.In the absence of bias, the expected value of BiasMethod LR Dispersion (DispLR): For individuals in the validation population, dispersion was measured from the slope of the regression of LR is 0. Values less than 0 indicate under-dispersion (or deflation) of In the absence of bias, the expected value of DispWe used the AWM methodology , 57 to iFirst, for each trait, SNP effects were estimated using derivations from , 60 as fλ is the ratio of SNP variance to genetic variance and assumed 0.85 throughout, M is the matrix of genotypes centred for observed allele frequencies with dimension equal to the number of animals  by number of SNP , G is the GRM computing using Method 1 of [2  =  0.45) than their indicine (r2  =  0.25) and composite (r2  =  0.32) counterparts. Therefore, we selected SNP located in the coding region or within 10 kb of an annotated gene based on the ARS_UCD1.2 bovine genome assembly [NPNS, and selected the remaining SNP-Genes associated  to more than NPNS phenotypes. To further characterize the pleiotropic potential of SNP we computed the multi-trait χ2 statistic for the i-th SNP following derivations from [In which hod 1 of  across aribution –S3 Data.assembly . Third, ons from :χiT=s^i-th SNP and V−1 is the inverse of a 10 × 10 correlation matrix calculated overall estimated SNP effects. The χ2 value of each SNP was assessed for significance based on a χ2 distribution with 10 degrees of freedom to test against the null hypothesis that the SNP had no significant effect on any of the 10 traits. The final AWM contained as many rows as SNP (assigned to genes) and as many columns as traits, in this case ten traits.Where To build the co-association network, we used the AWM as input, and identified significant gene-gene interactions using the PCIT algorithm  which caBos taurus genes annotated as transcription factors and the Cattle Gene Atlas [To flag functional variants a 3-way search for key genes was performed by ranking transcription factors based on network connectivity, pleiotropy score and sperm-specific expression. To do that, we accessed the Animal Transcription Factor Database Click here for additional data file.S1 Data(GZ)Click here for additional data file.S2 Data(GZ)Click here for additional data file.S3 Data(GZ)Click here for additional data file.


Penaeus monodon, is the second most economically important aquaculture shrimp species in the world, and in Australia it is one of the most commonly farmed shrimp species. Despite its economic significance, very few studies have reported the genetic evaluation of economically important morphological size and shape traits of shrimp grown in commercial grow-out environments. In this study we obtained genetic parameter estimates and evaluated genotype-by-environment interaction (GxE) for nine body morphological traits of shrimp derived from images. The data set contained image and body weight (BW) records of 5,308 shrimp, from 64 sires and 54 dams, reared in eight grow-out ponds for an average of 133 days. From the images, landmark based morphological distances were computed from which novel morphological traits associated with size and shape were derived for genetic evaluation. These traits included body weight (BW), body length (BL), body size (BS), head size (HS), Abdominal size (AS), abdominal percentage (AP), tail tip (TT), front by back ratio (FBR), condition factor (CF) and condition factor length (CFL). We also evaluated G×E interaction effects of these traits for shrimp reared in different ponds. The heritability estimates for growth related morphological and body weight traits were moderately high  and low for abdominal percentage and body shape traits . G × E interaction were negligible for all traits for shrimp reared in different ponds, suggesting re-ranking is not prevalent for this population. Genetic correlations among growth related morphological traits were high ranging from 0.36 to 0.99, suggesting these traits can be simultaneously improved through indirect genetic selection. However, negative genetic correlations were observed for FBR & CF shape traits with major growth traits (ranged −0.08 to −0.95), suggesting genetic selection for rapid growth will likely result in thick/fatty shrimp over generations. Our study showed image-based landmark data can be successfully employed for genetic evaluation of complex morphological traits of shrimp and is potentially amenable to machine-learning derived parameters in semi-automated high volume phenotyping systems needed under commercial conditions.The black tiger shrimp,  Penaeus monodon), hereafter shrimp, is one of the most commercially important aquaculture species in the world , as it ensures higher yields. However, shape traits  are equally important as candidate traits for genetic improvement . Shrimp An important aspect of all aquaculture production is to understand the underlying biological processes involved in size and shape of the animal, as it is reflected in the final product quality found in the marketplace. A key component of this is the estimation of genetic parameters associated with size and shape traits. Genetic improvement in shrimp aquaculture production can be made by developing selection programs utilizing these genetic parameter estimates. In Australia, genetic parameter estimates for growth traits have been previously studied for the black tiger shrimp in the tank environments . HoweverFurthermore, as with other aquaculture breeding programs, shrimp are often selected in one breeding station and are then distributed across different grow-out ponds or environments. To exploit the full genetic potential in the breeding program of a species, it is important to understand the performance and extent of realized genetic gains across environments. Genotype-by-environment interaction (G × E), which is the variable expression of phenotypes of genetically identical organisms in different environments, can occur if genotypes are not well adapted in their respective rearing environments. G × E reduces the efficiency of selection breeding programs, since the best-performing genotypes in one environment are not necessarily the best in another environment. Meta-analysis studies with both fish and shrimp species have reported the presence of significant G × E for growth traits .The present study was conducted to provide genetic parameter estimates of novel digital image-derived size and shape traits of shrimp from an Australian population of this species. In addition to this, we investigated the extent of G × E interactions in the shrimp population studied, which were raised across different grow-out ponds.P. monodon raised by Seafarms Group Ltd., as described in −2 at 28 ± 0.5°C) and broodstock were fed a commercial maturation diet. For each cohort, broodstock were allowed to mate naturally within the tanks, with any unmated females then artificially inseminated following industry practices. Females were spawned in communal spawning tanks and spawned eggs were transferred hatching tanks, and hatched nauplii were then transferred into 20,000-L larval rearing tanks (LRTs) at a density from 100 to 125 nauplii/L, and reared on a commercial diet  until 30 days of culture (DOC). LTRs were then pooled and stocked into seven 4000-m2 grow-out earthen ponds and reared under commercial conditions at a density of 45 m−2 until harvest. Preharvest ponds were immediately sampled by random cast net. From post-larval stage 15 (PL15) to harvest, the growth periods ranged from 124 to 143 days across ponds. In total 76 full sib and half-sib families were produced across 5,308 progeny and stocked across eight ponds as shown in All progeny in this experiment were sampled from commercial cohorts of 3) × 100, where BW = body weight, BL = body length, based partly on PC3. Moreover, additional important morphological traits were obtained from the landmark-derived morphological distance data, e.g. body size (BS), head size (HS) and abdominal size (AS) by summing appropriate triangular areas using Heron’s formula. In addition, abdominal percentage (AP) was calculated as (AS/BS) × 100, tail tip (TT), the dorso-ventral distance across the tail, and condition factor length (CFL) calculated as (BS/BL2) × 100; where BS = body size, BL = body length.For the genetic evaluation, 5,308 shrimp that were weighed and photographed, were included. Twelve landmarks’ data points were manually captured from the photographed images of shrimp as described in Since tracing of broodstock contribution could not be done on farm, all potential broodstock were genotyped and parentage analysis was utilized to determine the contributing parents retrospectively as detailed by pi is the proportion of animals in the pond from family i; maximum diversity occurs when families are represented equally  resulting in Hmax = –logen. The proportional family overlaps between pairs of ponds were calculated by the Morisita-Horn index, employed in the “divo” package in “R”  to 1 .The family diversity of shrimp within each pond, which is a measure of the evenness of the distribution of families within ponds, was estimated by calculating the Shannon-Wiener Index using the “vegan” package in “R” . The inde in “R” . The indh2), and genetic correlations (rg) between traits were estimated by restricted maximum-likelihood (REML) methods in ASReml-R 4.0 (VSNi) , β is the vector of fixed effects ,a is the vector of the random animal additive genetic effects, and e is the vector of random residual effects. Further, X and Z are corresponding incidence matrices for β and a, respectively.Initial exploratory analysis of the data was carried out by inspecting the distribution and homogeneity of variance assessed by performing Shapiro-Wilk and Levene’s tests. An ANOVA was performed to evaluate the significance of fixed effect of ponds. Quantitative genetic analysis such as (co)variance components, heritabilities (0 (VSNi)  by fittirg) phenotypic (rp) and environmental (re) correlations. Bivariate animal models were also used to estimate genotype by environment interaction (G×E). Here, G×E was estimated by calculation of covariance components of the same trait of shrimp in different ponds (rg) were calculated from the following equation: Heritability was estimated from the following equation: nt ponds . Geneticy with 1 SD selection differential in trait x from the following equation:SDy is the SD of trait y.Indirect genetic selection was calculated as a correlated response in trait y as a percentage of gain possible from direct selection for trait x is calculated as %IS, the relative efficiency of correlated response in trait y when selection is applied on trait x as a percentage of gain possible from direct selection for trait y, i.e.,The correlated response in trait 1 shrimp produced from 64 sires and 54 dams. These individual shrimp were raised in seven commercial ponds. The analysis of Shannon-Wiener diversity index revealed that families were not evenly distributed across ponds (H = 2.25) and dam families (H = 2.15), with similar low diversity in Pond 160. In contrast, Pond 155 had the most even distribution of families . Family distributions across ponds were also assessed by calculating the Morisita-Horn index (MH = 0.97), the same ponds with low family diversity, but low overlap with all other ponds suggesting unequal family representation across ponds. The population studied was comprised of 5,308 individual Fss ponds . For exarn index . It measMean, standard deviation (SD) and coefficient of variation (CV) of the traits studied are shown in h2) estimates were moderate for BW (0.32 ± 0.05), BL (0.36 ± 0.06), BS (0.32 ± 0.05), HS (0.31 ± 0.05) and AS (0.32 ± 0.05) and were low for AP (0.09 ± 0.02), FBR (0.08 ± 0.02), CF (0.08 ± 0.02) and CFL (0.003 ± 0.004). With the exception of CFL, all estimates were significantly greater than zero based on their small standard errors (SE) (0.004–0.06). However, for CFL the h2 estimate was near zero, indicating presence of minimal additive genetic variability in this trait for selection. To evaluate the extent of family performance across ponds, estimated breeding values (EBVs) of sires and dams were obtained for each pond, and an illustration of this is shown for body length in Heritability (rg) among BW, BL, BS, HS, AS and TT were high (range: rg = 0.96–0.99) (rg was medium with AP trait with the abovementioned traits (range: rg = 0.36–0.40), but highly negative with FBR (rg = -0.96). The phenotypic and environmental correlations were in similar alignment in both direction and magnitude as the genetic correlations for relationships between traits (Genetic correlations (96–0.99) . The rn traits .The genetic correlation between phenotypic expressions of the same traits in different ponds indicated lack of any G × E effect for all the traits studied . AlthougPenaeus vannamei, Penaeus monodon is the next most important cultivated shrimp species in the world. However, compared to its aquaculture importance, genetic improvement of this species has been quite limited. Although some previous genetic parameter estimates have been reported for this species, they were all derived in tank environments. In commercial breeding programs it is important to simulate commercial conditions during genetic evaluation, so that the animals evaluated and selected for best targeted traits in the breeding nucleus population demonstrate similar yields in commercial settings. In this study, the performance of shrimp was evaluated in standard Australian farming conditions.After P. monodon population studied. All these are growth-related traits and these findings corroborate the previous findings of P. monodon genetic parameter estimates  and 0.47 body weight were reported by P. monodon. There could be various factors that could lead to high level of heterogeneity of heritability estimates of any traits, including common family environmental effects , BL (0.36 ± 0.06) and BS (0.32 ± 0.05), suggesting substantial potential for genetic improvement of these traits in the stimates , althoug effects , charact effects , sex and effects  etc. ForSparus aurata), sea bass (Dicentrarchus labrax) and common carp (Cyprinus carpio) have shown that economically important shape-related traits are associated with unique genomic regions (Carassius auratus), various morphological traits  are modified via selective breeding to increase economic value  and AS (0.32 ± 0.05) were moderately high, and low for AP (0.09 ± 0.02), FBR (0.08 ± 0.02), CF (0.06 ± 0.02) and CFL (0.003 ± 0.004) traits. This suggests that HS and AS traits are suitable for selection to change body shape of shrimp. Shrimp with smaller HS, larger AS and higher AP might be preferable for selection, as it may correspond directly to higher meat yield. Moreover, to attain uniformity of the cultured shrimp body shape, FBR trait can be selected in combination with these other traits by employing multi-trait selection criteria. Until now, no genetic analysis has been conducted on shape traits of shrimp. Quantitative trait loci (QTL) and genome wide association studies (GWAS) with Gilthead seabream . This suggests that key traits for growth and shape of ed shape . Howevered shape . A similrg = 0.74 ± 0.29 and 0.45 ± 0.30) was observed in AP, for pond pairs of 149 and 155 and 149 and 156, respectively. This suggests that G × E interactions were non-existent for these traits and re-ranking of breeding values may be less pronounced across the ponds in this shrimp population, but this may be expected given all the ponds are in the one location. Similar to this finding, a meta-analysis, using data from 29 peer reviewed studies, found that growth-related morphological traits have a high genetic correlation (rg = 0.73 ± 0.05) across various environments and species, indicating low levels of G × E with low re-ranking of breeding values across environments (Genetic correlation estimates (as a measure of G×E) between ponds with high Morisita-Horn index scores (>0.56) were high for BW, BL, BS and HS. Only moderately low G×E , low genetic correlation estimates were recorded for BW, BL, BS and HS. Although this could be an indication of high G × E, the estimates are unreliable due to their large standard error. This suggests the importance of maintaining homogenous family distribution across experimental grow-out environments, to obtain reliable G × E estimates.For efficient improvement of traits under selection, the recording of these traits should be accurate and cost effective. Our study demonstrates that digital images can be used to derive economically-important growth-related morphological traits from landmark data to evaluate genetic merit. While in most breeding programs, body weight is the key trait for selection, it can be predicted from image-derived data as was the case in this study. So, if the breeding goal is to achieve a specific shape of the animal, and taking weight record is not feasible, then body measurements can be an excellent option to examine shrimp production traits. From our image-based analysis of morphological traits, we were able to derive size and shape measurements of the shrimp  which can then be used for selection. For example, meat yield (peeled tail weight) of shrimp may not be feasible to record due to technical difficulties, however abdominal size can be used to infer the meat weight. Similarly, to select shrimp with a thick structure (FBR), body size (BS) trait can be selected. However, future studies are required for 1) phenotyping of morphological traits directly from the images using machine learning approaches without the need to do manual landmarking, and 2) obtaining estimates of economic values of the morphological traits, as these are unknown and need to be studied before incorporating in the breeding programs.Our study shows that landmark-based digital-image analysis is a promising tool of phenotyping of shrimp morphological traits and for genetic evaluation of these traits. Genetic improvement for growth-related morphological and weight traits is feasible, since these traits demonstrated high genetic variation and heritability. Family-level selection breeding is needed for genetic improvement of some shape traits , as the heritability was low. Within the same farm, it is not essential to perform separate genetic evaluations of shrimp across multiple ponds as G × E effects were found to be negligible between ponds.