Clustering genetic variants based on their associations with different traits can provide insight into their underlying biological mechanisms. Existing clustering approaches typically group variants based on the similarity of their association estimates for various traits. We present a new procedure for clustering variants based on their proportional associations with different traits, which is more reflective of the underlying mechanisms to which they relate. The method is based on a mixture model approach for directional clustering and includes a noise cluster that provides robustness to outliers. The procedure performs well across a range of simulation scenarios. In an applied setting, clustering genetic variants associated with body mass index generates groups reflective of distinct biological pathways. Mendelian randomization analyses support that the clusters vary in their effect on coronary heart disease, including one cluster that represents elevated body mass index with a favourable metabolic profile and reduced coronary heart disease risk. Analysis of the biological pathways underlying this cluster identifies inflammation as potentially explaining differences in the effects of increased body mass index on coronary heart disease. Genome-wide association studies have found many genetic variants that are correlated with traits, particularly complex traits such as body mass index (BMI). However, genetic association data cannot tell us how these variants influence the trait, or whether they influence the trait in the same way. Insight into these questions may be gained by analysing the associations between the variants and other related traits. Variants with similar patterns of associations across a set of traits may be thought to act via similar biological mechanisms. Here we present a new statistical method for grouping genetic variants according to their associations with chosen traits, so that each group represents variants acting on these traits in a distinct way. We apply the method to genetic variants associated with BMI and then study the effects of each of the identified groups of variants on coronary heart disease. We find a group of genetic variants associated with higher BMI and decreased risk of heart disease, which is in contrast to the established overall harmful effect of BMI on heart disease. In recent years, the number of genome-wide association studies (GWAS) has grown enormously . Such stA number of techniques have been implemented to cluster genetic variants based on their associations with traits that are believed to be relevant in informing biological pathways. The traits often include separate risk factors or potential mediators of some disease outcome(s) of interest. A common approach is to use hierarchical clustering, which groups observations based on their distance from each other –7. The nA key characteristic of previously implemented approaches is that they cluster based on the Euclidean distance between vectors of the genetic variant-trait association estimates, defined as the length of the line between the association estimates plotted as points on a graph. However, when trying to determine shared biological mechanisms, a more relevant clustering target is the proportional associations of each genetic variant with the set of traits. If two variants influence a set of related traits via a common mechanism, the genetic associations may differ considerably in magnitude due to one variant having a stronger effect than the other. However, their proportional associations across the traits will be similar for both variants. Equivalent to looking at proportional associations is to consider the direction of the association vector from the origin. That is, in order to distinguish between variants which act via different mechanisms, it is the direction of the association vector rather than its location in space which is of most importance. This is illustrated graphically in In this paper we introduce a novel procedure for clustering genetic variants based on their associations with a given set of traits to identify groups with common biological mechanisms. We develop the NAvMix (Noise-Augmented von Mises–Fisher Mixture model) clustering method, which extends a directional clustering approach to include a noise cluster as well as a data-driven method for choosing the number of clusters. The method is shown in a simulation study to perform well in identifying true clusters and to outperform alternative approaches across a range of scenarios. We further apply the procedure to cluster genetic variants associated with body mass index (BMI). We study the downstream effects of the different components of BMI on coronary heart disease (CHD) using Mendelian randomization, which uses genetic variants as instrumental variables to study potential causal effects of a risk factor on an outcome , 11. We We use a mixture model approach to clustering, which supposes that each observation is a realisation from one of a fixed number of probability distributions. Since we are interested in clustering based on direction of association, we fit a mixture of von Mises–Fisher (vMF) distributions, which is a distribution characterised by the mean direction of the observations from the origin and a dispersion parameter. A mixture model of vMF distributions has previously been described by Banerjee et al. . We augmThe NAvMix algorithm outputs a probability for each observation belonging to each cluster based on the given data. Each observation can then be assigned according to which cluster it has the highest probability of membership (referred to as hard clustering). The approach also provides the ability for soft clustering, which is where an observation is assigned to any cluster for which it has a probability of membership over a certain level, so that observations may belong to more than one cluster. Although the algorithm requires a fixed number of clusters to be specified, we repeat the procedure for varying numbers of clusters then chose the final number using the Bayesian Information Criterion (BIC). Full details of the procedure are given in the Methods section.j with the set of traits under consideration, and let jth variant. The standardisation means that each element of the input vector is independent and has the same standard error. It thus is able to account for correlation between association estimates. Assuming all genetic associations are estimated with the same sample size for a given trait, this will not distort the direction vector. If there are significant differences between sample sizes used to estimate genetic associations for the same trait, and associations with different traits are on similar scales, the unstandardised association estimates may also be used, possibly as a sensitivity analysis. The first step in the algorithm is to transform each input vector to have a magnitude of one. This is done by dividing each vector by its Euclidean distance from the origin. We shall refer to this as normalisation. The normalised vectors represent the proportional association estimates.Let The diagonal elements of the covariance matrices represent the variances of the genetic variant-trait association estimates. The off-diagonal elements represent the covariances between these estimates. If the genetic associations are estimated in separate samples for each trait, these covariances will be theoretically equal to zero. If the association estimates are taken from the same sample, the covariances will still be approximately zero if the traits are independent. If the traits are correlated, an estimate of this correlation is required to estimate the full covariance matrix in the one sample setting. This is easily computed using individual level data . If publWe performed a simulation study in order to evaluate the performance of the proposed method and to compare it with alternative clustering approaches. We chose two methods for comparison. The first was to fit Gaussian mixture models to the standardised association estimates using the mclust algorithm in R . The metm) was either 2 or 9 and the number of clusters (K) was either 1, 2 or 4. In each scenario, each of 80 genetic variants were associated with one of K latent factors, representing the different clusters. Each trait was a function of these latent factors, 20 additional noise genetic variants, and random variation of which a proportion, determined by the parameter γ, came from a shared unmeasured confounding variable. The γ = 0 case represents uncorrelated traits, however it also proxies the scenario where the traits may be correlated but measured in separate, non-overlapping samples. Increasing values of γ therefore demonstrate the effect of increased trait correlation and/or sample overlap. We applied NAvMix in two ways. In the first, the off-diagonal entries of the covariance matrices were set to zero. In the second, the estimated trait correlation from individual level data was incorporated into the procedure, so the full estimated covariance matrices were used. In the primary simulation study presented here, the genetic variant-trait associations were estimated in a single sample of 20 000 individuals. We simulated data for genetic variants across six scenarios, where the number of traits . The exception was when the traits were highly correlated (with γ = 0.8), where NAvMix tended to select too many clusters. However, incorporating the trait correlation estimates in NAvMix improved the performance in these cases. Note that when K = 4, one of the clusters had only 10 genetic variants. Nonetheless, NAvMix still selected close to 4 clusters, on average, and had higher median adjusted Rand indices and silhouette coefficients than the mclust approaches. Other than in the scenarios with both a higher number of traits (m = 9) and high trait correlation (γ = 0.8), there was not a big difference in the results between using NAvMix with and without trait correlation estimates. This suggests that, unless there is substantial trait correlation or sample overlap, the procedure is robust to missing these estimates. Incorporating trait correlation becomes more important as the number of traits increases and the number of true clusters decreases. Finally, mclust tended to allocate fewer observations to the noise cluster than NAvMix, particularly in the lower dimensional (m = 2) settings.NAvMix performed very well in terms of allocating the observations to the correct clusters, with a median adjusted Rand index above the mclust approaches in nearly all scenarios. It similarly outperformed with respect to the silhouette coefficient, and selected, on average, a number of clusters closer to the true number. The mclust algorithm tended to overestimate the number of clusters, particularly when there were no truly distinct clusters ; triglycerides; high-density lipoprotein cholesterol (HDL); educational attainment; physical activity; lifetime smoking score; waist-to-hip ratio (WHR); and type 2 diabetes. These are lifestyle or cardiometabolic traits which have previously been shown to be related to BMI and which may offer insight into the pathways to downstream effects of BMI such as CHD . We . We 23].We conducted gene set analysis on the BMI associated variants using the Functional Mapping and Annotation Platform  in orderThe role of Cluster 5 variants in inflammation is of particular interest given its proposed relation to favourable adiposity. In order to confirm the role of these variants in inflammation, we conducted a Mendelian randomization analysis to examine the association of genetically predicted BMI, using all variants and each cluster separately, with C-reactive protein (CRP), a measure of systemic inflammation . The resTo further explore the pathways by which the various clusters affect inflammation, we performed separate Mendelian randomization analyses with the 41 cytokines and growth factors studied by Ahola-Olli et al.  and KalaIn this paper we have presented a procedure for clustering genetic variants based on their associations with a given set of traits using the NAvMix method. The method uses a directional clustering algorithm to distinguish between genetic variants based on their proportional associations with the traits. Since it is a model-based clustering approach, it has many advantages over current methods that are employed for clustering genetic variants based on trait associations, such as a data-driven method for choosing the number of clusters and the ability to use soft clustering. The inclusion of a noise cluster provides robustness to outliers, offering greater confidence in the identified clusters. A simulation study showed the method performs well in a range of settings, and that it outperformed alternative clustering approaches in assigning observations based on proportional associations. Importantly, the method did not identify false positive clusters in the simulation setting when no true clusters existed in the data, in contrast to the other methods considered.The application to clustering BMI associated genetic variants identified five clusters, suggesting that genetic predictors of BMI can be broken down into five separate mechanisms based on their associations with the traits considered. Interestingly, variants in Clusters 1 and 2 were similar in their average associations across each of the traits considered with the exception of smoking, where Cluster 2 had close to zero association. One possible explanation for this is that these variants differ according to some addictive behaviour related mechanism. However, no such pathways were identified in the gene set analysis for Cluster 1. This suggests that some other mechanism may be driving this change, although further analysis is required to identify what this may be.Mendelian randomization analyses provided evidence that the different pathways affecting BMI have different downstream effects on CHD risk. When using as instruments the set of genetic variants in Clusters 1 and 2, the Mendelian randomization estimate of BMI on CHD risk was positive, in line with the established overall effect of increased BMI. When using as instruments the set of variants in Cluster 3, the estimate was still positive but attenuated to the null. The main difference between this cluster and Clusters 1 and 2 is that the variants do not, on average, associate with increased SBP. Previous evidence suggests that increased SBP is a downstream consequence of increased BMI , and hasWhen using as instruments the set of genetic variants in Cluster 4, which have average associations with increased HDL and decreased triglycerides, Mendelian randomization suggested there was no association with CHD risk. Furthermore, the Mendelian randomization estimate of the component of BMI predicted by the variants in Cluster 5 was negative. That is, in Cluster 5, we have identified genetic variants related to a BMI increasing pathway that is protective of CHD. Orientating to the BMI-increasing alleles, these genetic variants are associated with a favourable metabolic profile, namely increased HDL and decreased SBP, triglycerides, WHR and type 2 diabetes liability.By analysing the biological pathways underpinning the different clusters, we found evidence supporting that the heterogeneity between the effects of the different components of BMI on cardiovascular risk may be related to inflammation. Furthermore, our findings identify possible inflammatory pathways related to elevated BMI that represent therapeutic targets for preventing CHD. Specifically, the estimated effects of Cluster 5 variants, in contrast to the BMI increasing variants more generally, are consistent with lower levels of key inflammatory cytokines implicated in CHD pathogenesis, including HGF , MCP1 3 and TRAIA number of studies have previously sought to identify genetic variants associated with metabolically favourable adiposity. Huang et al.  conducteThe proposed approach has some limitations. It uses as input the full covariance matrix of the genetic variant-trait associations. If it assumed that the traits are uncorrelated or that the genetic variant-trait associations are estimated in separate samples, then these matrices can be easily constructed from the standard errors of the genetic association estimates which are typically available from published GWAS results. In practice, it is unlikely that the entire set of traits will be uncorrelated, since they would typically be related at least via common association with the primary trait of interest. We have shown how the full covariance matrices can be estimated using estimates of the trait correlations, either from individual level data or from a reference dataset. Furthermore, the simulation study suggested that, unless the traits are highly correlated with each other, the method is robust to ignoring the genetic variant-trait association correlations. This also suggests that the approach is robust to some participant overlap in the samples. If the traits are highly correlated, there is significant sample overlap, and individual level data are not available, there exist methods to estimate the correlation between genetic associations using summary level data. One approach is to use the intercept term from cross-trait LD score regression . AnotherAnother limitation is that the results are dependent on the choice of traits used to cluster on. Domain knowledge should be used to select a set of traits which are believed to be informative of potential mechanisms of the genetic variants under consideration. Future research will look to extend the method to include feature selection , so thatIn the applied example, the genetic variants used for clustering were chosen according to them being associated with a primary trait of interest, in this case BMI. This resulted in a fairly large number of variants to cluster, in part because of the very large sample size of the GWAS in which these associations were estimated. Other traits of interest may not have so many independent variants associated with them at genome-wide significance. A low number of variants may make it more difficult to find true clusters if the cluster sizes are small. Nonetheless, there are many traits for which, say, 100 or more variants have been found to associate, and this will only grow as GWAS sample sizes increase. Furthermore, the simulation results showed that our clustering approach is still generally able to detect relatively small clusters, with clusters as small as 10 variants out of 100 in total in some settings. In the case where there are only a very small number of variants associated with the primary trait of interest, we would recommend lowering the threshold for inclusion below genome-wide significance rather than include correlated variants. Genetic variants which are not independent would be expected to associate similarly with the given traits, and so it would not be informative to include these.In conclusion, we have presented a procedure for clustering genetic variants based on their direction of association with relevant traits, in order to gain insight into their underlying biological mechanisms and pathways. We have demonstrated the utility of clustering genetic variants in this way by applying the method to BMI associated genetic variants and performing Mendelian randomization analyses to infer the differential effects of distinct BMI increasing pathways on CHD risk.m-dimensional von Mises–Fisher (vMF) distribution has probability density functionx‖ = ‖μ‖ = 1 and Cm(κ) is a normalising constant given byIν(x) is the modified Bessel function of the first kind and order ν We are sorry that we cannot be more positive about your manuscript at this stage. Please do not hesitate to contact us if you have any concerns or questions.Yours sincerely,Michael P. EpsteinAssociate EditorPLOS GeneticsDavid BaldingSection Editor: MethodsPLOS GeneticsReviewer's Responses to QuestionsComments to the Authors:Reviewer #1: The manuscript by Grant and colleagues proposed a novel method for clustering genetics variants based on their associations with multiple related traits. The advantage of cross-trait analysis, compared with single-trait analysis, is that it can potentially partition variants underlying a trait of interest into multiple clusters/patterns, each associated with a distinct mechanism. The manuscript proposed a novel approach to variant clustering, based on directions of variant effects on multiple traits. This is an interesting and well-motivated idea and is a timely contribution to this field. Applying this method, NAvMix, the authors reported some interesting findings in BMI and related traits.Major comments(1) One major issue of cross-trait analysis is overlapping samples between different studies. This is potentially a serious problem, as it would induce correlations of variant effects across traits, a pattern potentially mis-identified as true clusters. The proposed strategy to deal with this seems inadequate. Most often, individual level data is not available, and according to the authors, NAvMix, will simply set the off-diagonal terms in the covariance matrix 0, i.e. ignoring the possible correlations. The justification is that this is not a problem in simulations. However, it's possible that in the simulation setting, the correlations induced by shared samples are too weak, compared with the correlation of true effect sizes. As a result, ignoring induced correlations does not change the results much. This may not be the case, however, in the real data.My suggestion is: better justification using more extensive simulations. In particular, it would be helpful to vary the relative importance of true effect size correlations vs. correlation induced by shared samples. It would be helpful, for example, to vary how much phenotypic variations are explained by genetic variants vs. by the shared underlying factors . Related to this point: it would be helpful to better explain some of the parameter settings in simulations. Ex. effect sizes are drawn from certain distributions. Are the parameters of these distributions realistic?Another suggestion: it is possible to estimate correlation of effect sizes between traits, due to shared samples, using cross-trait LD score regression [PMID: 26414676]. That paper uses full GWAS summary statistics to estimate genetic correlation, while accounting for shared samples. It shows that the "residual" correlation due to shared samples is a simple function of phenotypic correlations, the sample sizes of the two studies, and the number of shared samples. In fact, it can directly estimate this residual correlation. It may be possible to directly use these estimates  in NAvMix.(2) The noise cluster presumably increases the robustness of the method. However, in the real data, only 1 out of >500 BMI variants is assigned to the noise cluster. One possible explanation is that: the mean of the noise cluster is the global mean direction. This may be too similar to the major clusters (clusters 1 and 2 in the BMI results). As a result, not many variants would be assigned to the noise cluster. It seems to make sense to use a broader distribution  for the noise cluster.(3) The simulation procedure largely follows the model of NAvMix. So perhaps unsurprisingly, NAvMix performs well under those simulations. A more realistic, or biologically motivated simulation would give a better idea of the performance of NAvMix. The authors could explicitly simulate a few "latent factors", which act on the observed phenotypes. Then each variant could either act on these latent fators, or act on some traits directly. I think if each trait acts only on one factor a time, then this reduces to the variant clustering problem. The advantage of this simulation regime is that one could easily vary some of the parameters and assess if NAvMix are robust to these changes. For example, is the method robust to direct effects of variants (i.e. variants acting on a trait without affecting any of the factors)?(4) The main difference of clusters 1 and cluster 2 is that cluster 1 variants are associated with smoking, but cluster 2 not. I found this result interesting/puzzling. Given the smoking association, I would imagine that cluster 1 may capture some "behavior" component of BMI. Indeed, it was reported that hertiability of obesity is mostly enriched in brain, and it is not hard to imagine that smoking variants act through some kind of additive behavior. However, the pathway analysis of cluster 1 does not suggest anything related to behavior/brain. One concern is that the results may be driven by sample sharing between BMI and smoking GWAS, though it's not clear to me if this would lead to different clusters. In any case, it would be helpful to check this - could be done using the intercept term of cross-trait LDSC, as mentioned above. In fact, it would be good to check the correlations driven by shared samples for all pairs of traits.Another relevant question is: has BMI GWAS data adjusted smoking, and vice versa? Is it possible that associations of BMI variants with smoking driven by some kind of collider bias? This could happen when one has a causal model like this: SNP -> smoking <- additive behavior -> BMI. Adjusting smoking in GWAS of BMI may lead to false association of SNP and BMI.(5) The authors suggest that cluster 5 variants represent some kind of "favorable adiposity", that reduces inflammatory cytokines and hence the CHD risk. This is an attractive model. However, I would caution against over-interpretation. The data basically says that cluster 5 variants have effects on inflammatory cytokines. It's unclear that this effect is mediated through favorable/protective adiposity. It's possible that these variants have some pleiotropic effects on both BMI and cytokines, without adoposity playing any role in the regulation of these cytokines. To rigorously make this claim, I'd imagine some mediation type of analysis, where one controls BMI or some measures of favorable adiposity, and show that the cluster 5 variants would be no longer associated with the CHD risk. I doubt such data is available for this type of analysis though.Minor comments- Variants in cluster 4 have metabolic functions, and are associated with HDL and TG. However, it is not found to have an effect on CHD risk in MR analysis. This is a bit unexpected, given that LDL is a known risk factor of CHD. It would be good to examine the LDL association of cluster 4 variants.- Typo: line 314, norm of $x_j$ = 1 for all $i$ - I suppose it should be "for all j".- Typo: denoted $X_{ik}$ for individual i and trait l, in line 406.- Table S5: it would be helpful to show the fold enrichment (or expected number of overlapping genes). Also, the authors used KEGG and REACTOME. It would be helpful to add GO analysis as well, which is more commonly used for this type of analysis, and may cover more biological processes.Reviewer #2: The authors have proposed a new procedure NAvMix (and its R implementation) to cluster variants based on their genetic effects on multiple traits. The procedure considers a separate cluster for noise on top of the existing clustering method on the unit hypersphere based on a mixture of von Mises-Fisher distributions. The authors have shown good performance of NAvMix in simulations. The authors have applied NAvMix on genetic variants associated with BMI to unravel distinct biological pathways. However, I have some concerns with the results. The simulation study is somewhat narrow in scope . Takeaways from different real data analyses are not always clear. I have provided detailed comments below.**Major Comments**1. “Assuming all genetic associations are estimated with the same sample size for a given trait, this will not distort the direction vector. Otherwise, the direction vector will be weighted toward traits for which the associations are more precisely estimated.” - Is this a limitation of the method? What would be practical solution to this issue? Are the authors recommending using NAvMix on traits with similar sample size only? When working with summary statistics on different traits, it is often the case that sample sizes differ widely. For e.g. recent meta-analysis [PMID 34059833] of glycemic traits included ~90K samples for 2hr glucose whereas >280K samples for fasting glucose.2. Lines 68-69: Genetic variants for which vector of association estimates are input in the algorithm are assumed to be independent of each other. Do the authors recommend that only the top hit in a locus be included in the set to be clustered? But then, for most traits, only a handful of loci are significant . Can this method be used for maybe 10-20 independent variants or on traits with modest sample sizes? Do the authors recommend a lower limit to these numbers?3. The data generating mechanism (DGM) for the simulations seems somewhat favorable for the “directional statistics” concept that the authors are leveraging in their procedure. In my opinion, it will be useful to consider more realistic and a different DGM. For e.g., instead of using angles between genetic effects to generate different clusters of effects, the authors can consider a structural equation model (as their DGM) reflecting different DAGs capturing the different underlying biological mechanisms among traits 4. Clustering evaluation metrics: The authors considered Rand Index. Isn’t adjusted Rand index a better metric to use since it is adjusted for chance? What about additionally using other popular metrics  that capture other aspects of clustering that Rand index cannot? For evaluation, I think considering metrics that do not require a priori knowledge of clusters is also important.5. Fig 5: I see that different clusters of genetic instruments may or may not give different causal relation result. I don’t see a clear distinction between clusters in terms of their MR results. Can the authors clarify the takeaway from the MR analysis done here?6. The required input/variables/format for their R package is not clear. What parameter choices do users need to make when using NAvMix package? It will be useful for readers if the authors can provide an outline of how readers can implement their procedure from start to finish.**Minor Comments**7. Line 149: Are the authors including SNPs with r^2<0.001? If not, I am not sure why Lines 68-69 say that variants should not be in LD.8. Lines 332-333: specify the contents of parameter vector \\Theta.9. There might be some notational inconsistency here and there. For e.g., what do X_j, X_k stand for in Line 398 and are they related to vector x_j in the previous paragraphs? Is vector x_j =\\hat\\Sigma_j^{-1/2} \\hat\\beta_j? It is worth clarifying these relations for readers.10. What happens to \\pi_k estimate if there are only a few members in a cluster (other than the noise cluster)? Will the estimate be unstable? Can unstable estimates for such a cluster lead to lack of convergence?11. Figs 3-7: It will be helpful to have the number of SNPs in each cluster mentioned in the figures.12. Figs 6 & 7: Only MR-IVW results are presented. MR-IVW is least likely to be robust to violation of assumptions . Is only MR-IVW presented because the results for these MR analyses using different methods/assumptions give the same qualitative results?Reviewer #3: Noise-augmented directional clustering of genetic association data identifies distinct mechanisms underlying obesityThis paper aims to answer the question ‘how do genetic variants influence complex traits?’ and presents a new approach for clustering genetic variants according to the direction of association with complex traits and incorporates a noise model to improve overall clustering results. They perform simulation studies and apply their method to studying variants associated with high BMI and look at the effects on coronary heart disease.The paper introduces a novel model but needs more extensive benchmarking and robustness tests to convince me of its utility.Major Concerns:I’d like to see some justification/evidence that the magnitude of associations to traits is not important, but the direction of association is the key concern. Is there biological rationale for claiming that magnitudes of association do not encode useful information about how variants influence traits?Benchmarking should be done over a wider range of comparison models and over parameter values (Why were the number of traits chosen to just be 2 or 9?) I’d also like to see answers to questions about limitations of the model - Moderate Concerns:I’d like to see a justification for choosing a uniform noise model. Does incorporating this noise model improve performance over simple pre-processing/data cleaning approaches?I’d like a brief explanation for why they believe that the other approaches they benchmark achieve lower Rand index on their simulations. Why were these models selected for benchmarking?Is the assumption of no linkage disequilibrium a fair assumption?Minor Concerns:Figure 4 is a bit confusing - can this be better illustrated? The figure makes it appear that several clusters are actually quite similar - are the differences between them significant?Figure 5,6 - What do the dotted lines represent?**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: YesReviewer #2: YesReviewer #3: Yes**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  Provide a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript.archive. 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EpsteinAssociate EditorPLOS GeneticsDavid BaldingSection Editor: MethodsPLOS GeneticsReviewer's Responses to QuestionsReviewer #1: The authors have done a thorough job in addressing all my comments. I do not have any more concerns.Reviewer #2: The authors have reasonably addressed my previous concerns. Some minor comments below.1. Table 1: In the caption or somewhere appropriate, it will be useful to provide the actual number of noise variants in the simulated data to better appreciate the estimated “Number of noise variants” from each method.2. Lines 153-154: The authors say “This suggests that, unless there is substantial trait correlation or sample overlap, the procedure is robust to missing these estimates.” Since the difference in adjusted Rand index between NAvMix and NAvMix (cor) increases quite a bit with increasing number of traits, decreasing number of clusters, and increasing strength of correlation , the authors need to include these other conditions in the above statement.3. Regarding this correlation: Authors discuss limitations of NAvMix, which includes “It uses as input the full covariance matrix of the genetic variant-trait associations.” However, I am not sure why this is a limitation. Under reasonable assumptions, the authors approximate \\Sigma_j as in lines 450-451. While individual-level data readily gives Corr, one can also estimate this correlation easily and quickly using summary statistics only. The field of cross-phenotype association tests using summary statistics uses such an estimate all the time (see for e.g. PMID 29226385). I believe the authors can use such an estimate instead of making the sub-optimal assumption that off-diagonal elements of \\Sigma_j are 0.4. I may have missed but did not find details about sample sizes, the number of significant variants in all, and the number of significant variants after pruning for each of the traits considered from Pulit et al, UK Biobank, etc. I think readers will find these details useful in interpreting results from NAvMix. In particular, I think NAvMix requires large sample sizes and highly polygenic traits.5. With respect to Fig 5, the authors mention “The components of BMI predicted by Clusters 1, 2, and 3 show a similar effect size and direction to the overall result.” Does this mean the clusters 1, 2 and 3 are not quite different and could have been just one cluster?Reviewer #3: The revision adequately addressed all our concerns**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: YesReviewer #2: NoneReviewer #3: Yes**********what does this mean?). 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Ne), and linkage disequilibrium (LD) patterns. Thus, the assessment of this information has become essential to the implementation of genomic selection on purebred and crossbred cattle breeding programs. In this way, we assessed the genotype of 19 cattle breeds raised in Brazil belonging to taurine, indicine, synthetic crossbreds, and Iberian-derived locally adapted ancestries to evaluate the overall LD decay patterns, Ne, ROH, and breed composition. We were able to obtain a general overview of the genomic architecture of cattle breeds currently raised in Brazil and other tropical countries. We found that, among the evaluated breeds, different marker densities should be used to improve the genomic prediction accuracy and power of genome-wide association studies. Breeds showing low Ne values indicate a recent inbreeding, also reflected by the occurrence of longer ROH, which demand special attention in the matting schemes to avoid extensive inbreeding. Candidate genes  located in the identified ROH islands were evaluated, highlighting biological processes involved with milk production, behavior, rusticity, and fertility. Furthermore, we were successful in obtaining the breed composition regarding the taurine and indicine composition using single-nucleotide polymorphism (SNP) data. Our results were able to observe in detail the genomic backgrounds that are present in each breed and allowed to better understand the various contributions of ancestor breeds to the modern breed composition to the Brazilian cattle.Cattle population history, breeding systems, and geographic subdivision may be reflected in runs of homozygosity (ROH), effective population size ( Cattle domestication has generated many differentiated phenotypes that evolved into distinct breeds scattered across the globe. Evidence based on mitochondrial DNA (mtDNA) data indicates that divergence between taurine and indicine subspecies occurred approximately 10,000 years ago, long before domestication . It is eIn Brazil, the first taurine animals were introduced by the European conquerors between the sixteenth and seventeenth centuries to be used for food, leather, and animal traction. After several generations of random crossings in distinct and variable ecosystems throughout the country, these animals became adapted to a wide range of environments and showed different levels of improved fitness to local conditions. They become recognized as Iberian-derived locally adapted breeds , such asIn addition to the taurine breeds, indicine cattle were brought to Brazil in the nineteenth century . Since tPopulation history, breeding systems, and geographic subdivisions of the Brazilian cattle may be accessed through runs of homozygosity (ROH) and linkage disequilibrium (LD) patterns throughout the genome. Runs of homozygosity are continuous homozygous segments of DNA , while LNe) across generations, (iii) evaluate ROH across populations, and (iv) evaluate the breed composition across all populations.In this way, we assessed genomic information of 19 cattle breeds representative of four groups: (1) taurine ; (2) indicine ; (3) synthetic crossbreds (Canchim and Girolando); and (4) Iberian-derived locally adapted breeds . The genomic data was used to (i) compare the overall LD decay patterns of different populations, (ii) estimate the effective population size , and GeneSeek GGP BosIndicus HD chip . A standardized set of single-nucleotide polymorphisms (SNPs) based on the overlapping of the SNPs among the chips was used as the data set to analyze each breed. SNP genotypes were excluded from the analysis when the call rate <0.95 and minor allele frequency <0.01. In addition, samples showing overall call rates <0.85 were excluded from further analysis. A total of 432 taurine, 366 indicine, 281 locally adapted, and 241 crossbred animals were analyzed after quality control . MoreoveTo evaluate the extent of LD, we used the r2 statistics, since this approach is robust and not sensitive to gene frequency and effective population size . PLINK vParametric nonlinear regression models have been used to study the physical distance between markers (LD decay) as reported by LDijk was the observed i and j in breed k; dij was the distance in kb (kilobase pair) between SNPs i and j; ßk was the coefficient that describes the LD decay with distance for breed k; and eijk was a random residual defined as eijkN. In summary, according to k estimates indicate a higher extent of LD. Additionally, this model is useful under situations involving individual’s relationship through infinitely long pathways from remote ancestors and also by descent from recent ancestors, such as bottlenecks at some point in history followed by admixture with modern breeds mainly derived from semen importation.where k estimates to compare the nonlinear curves in all breeds. This test allowed a statistical comparison of the LD decay parameter (β) and the visualization of clusters among breeds. Clustering was performed based on NbClust package v. 3.0  in the corresponding generation (T) was estimated from the associated estimated average of r2. Thus, Ne was estimated across generation according to the following formula:The effective population size  and used to determine the Ne in 50, 16.6, 10, and 5 generations, respectively.where T = 1/2c . From thTo date, studies have used different methodologies for predicting ROH. In addition, to identify ROH islands throughout the genome of each breed, homozygous segments shared by more than 50% of the individuals were chosen as an indication of homozygosity. The “–homozyg-group” function implemented in PLINK was used to assess ROH islands shared among individuals. The GenBank annotation based on the ARS-UCD1.2 assembly of the bovine genome was used to identify genes in ROH regions. Gene networks highlighting biological processes among the gene sets identified for each breed group  were generated using the ClueGO plugin for Cytoscape . ClueGO The ADMIXTURE package , which p2 values over genomic distances (bp) from each population using a nonlinear regression model (The LD decay parameter (β) was estimated from the curves of ron model . Statiston model . Since sstimates . Based oNe was estimated across four generations classes  according to markers distances in the genome, in which the shorter is the marker distance, the higher is the estimated generation  at generation 5.neration . To obselculated . BRA shoThe pattern of ROH differed across breeds . ConsideK = 2, we observed that each group showed distinct genomic compositions representative of taurine (red) and indicine breeds (blue). Locally adapted breeds display a taurine genome content ≥65%. In addition, it was consistently shown that synthetic crossbreds shared taurine and indicine genome content. At K = 3, two taurine ancestries were discriminated (light green and red), whereas at K = 4, a third taurine ancestry was predominant in the locally adapted breeds (purple), and the light green taurine ancestry was predominant in the JER breed. At K = 5, ANG breed showed a distinct taurine ancestry (yellow), whereas CAN displayed four uniform taurine composition . At this K, we could notice four taurine breeds showing three well-defined taurine ancestry . GIO breed showed the red taurine ancestry of 52%, while in CAN breed, the taurine ancestry was shared by the red (17%), green (13%), yellow (16%), and purple (21%) components. Among the indicine breeds, we observed a well-defined indicine ancestry in blue (>92%), whereas NEL and GIR breeds showed the highest ancestries . The locally adapted breeds showed mostly the purple taurine ancestry (>43%), and CCD was the most homogeneous (95%).Breed composition for each population was obtained using the admixture analysis . With K In addition, the neighbor-joining analysis also clearly discriminated the history of development and the ancestry of each group of breeds . As expe2 and showed the same pattern of LD decrease  highlighting the similarity of LD extent, although they have different genetic backgrounds. Thus, the set of SNPs that provides the best prediction accuracy at a given marker density should be different between HOL and NEL. We also observed different extents of LD between clusters 1 and 4, with higher LD observed in cluster 4 and lower in cluster 1. This information implies that different marker densities may be used for GS and GWAS for these breeds, which could also influence the accuracy of GS. However, in a practical way, a minimal marker density of 60 kb would be useful for all breeds besides removing monomorphic SNPs.Ne to better understand the relationship between ROH and Ne. The CUR breed showed the lowest Ne value in the estimated generation 5, suggesting a recent inbreeding that is supported by the occurrence of the longest ROH found in this study. Using microsatellite markers, A run of homozygosity is the probability that all consecutive markers on a pair of homologous chromosome segments, in the same or different individual(s), display identical alleles . The extNe and prevalence of small ROH. As expected, synthetic crossbreds (GIO and CAN) showed high occurrence of small ROH and Ne, since these breeds were recently originated from a systematic crossing breeding up to the establishment of each breed. The BRA breed showed the largest differences in Ne values across generations, 123.53 at generation 50 to 14.3 at generation 5, suggesting strong inbreeding events along generations that could be explained by the breeding programs that presumably minimized the inbreeding occurrence in this breed.On the other hand, further locally adapted breeds such as Caracu (CCB and CCD), CRI, and PAN seem to be successful in relation to matting schemes, since these breeds showed higher ABCA7) and neutrophil-mediated killing of bacteria (AZU1 and ELANE). ABCA7 gene encodes for ATP binding cassette subfamily A member 7 protein, previously reported to be expressed in the mammary gland of lactating cows . It is reported that animals with Brahman genetics may be considered more reactive to humans when compared with taurine breeds, such as Angus and Hereford , which was found to be associated with the prolactin signaling pathway biological process. Likewise, variations in this gene have been associated with milk performance traits . A reasonable explanation for that may be the use of indicine animals for cross breeding or another population founder effects. Indicine breeds were used in the beginning of their production in Brazil aiming to obtain adapted animals for the tropical weather  in addition to the supposed Iberian-derived taurine composition (purple) observed in locally adapted animals. This scenario is in agreement with cattle domestication events that occurred in Europe, in which European breeds would descend from domestication events of aurochs (Bosprimigenius) in the Near East and its further introduction throughout the European continent. Environmental conditions and domestication events could explain the diverse taurine backgrounds found in Europe. In this way, southern European breeds could have been more affected by introductions from northern Africa as well , while in the CAN breed, the taurine composition was shared by red, green, yellow, and purple taurine ancestries. GIO breed was developed for milk production in tropical and subtropical conditions through HOL with GIR breeds crossing followed by mattings schemes to establish the genetic composition of 5/8 HOL and 3/8 GIR  were originated by crossings between breeds brought from Iberian Peninsula to Brazil, including the Portuguese Minhota Breed. Natural selection throughout centuries enabled their adaptation to adverse conditions, contributing to their rusticity and high feed efficiency (3). In addition, these breeds were kept as purebred in regions of São Paulo state for meat production (CCB) and selected in Minas Gerais state for milk production (CCD), originating these two Caracu lineages. In a previous study of genetic diversity with locally adapted and zebu breeds, we also observed that CCD showed a homogeneous population , corroboMoreover, our results of neighbor-joining analysis and PCAs reinforce the admixture results in the genetic discrimination among cattle breeds and their development history. From the neighbor-joining analysis, indicine, and taurine breeds are shown widely apart following the genetic distances. On the other hand, locally adapted breeds showed a closer genetic distance to taurine breeds, as predictable. The GIO breed clustered with taurine breeds and closer to HOL, while CAN clustered with the indicine breeds and closer to BRA breed, as expected. The PCAs also showed the same results overall, and highlighted the genetic proximity of the indicine breeds, as they clustered together in a close and narrowed span group. Thus, it is possible to assume that indicine breeds have kept their majority genetic background from their ancestors in India, although they have been extensively selected and genetically improved for important economical traits in Brazil.Ne value in the estimated generation 5, suggesting a recent inbreeding also reflected by the occurrence of longest ROH islands in our analyses. Thus, a special attention in matting schemes for this breed is needed. Genes located in ROH islands were evaluated and explored throughout their biological processes, which provided genetic insights about the breeds. We were successful in revealing the breed composition of all breeds besides the complex taurine and indicine compositions in all breeds. In addition to the LD clustering results, we suggest that taurine SNP genotyping arrays may also be used in locally adapted breeds, since they seem to share most of their genetic architecture and LD extent.In this study, we adjusted a linear model to analyze the equality of the LD curves across 19 cattle breeds raised in Brazil, which revealed different extents of LD. Our results suggest that different marker densities may be used for a giving accuracy of GS and GWAS in these breeds. We found that CUR breed showed the lowest Ne. Even though BRA breed did not show the smallest Ne in this study, it showed a significant decrease in Ne, ranging from 123.53 at generation 50 to 14.3 at generation 5, and must be carefully examined by the current breeding programs. Candidate genes were found on ROH islands in various breeds, and their association with important traits were highlighted .A general overview of the genetic architecture of 19 cattle breeds raised in Brazil was successfully obtained. Special attention should be given to CUR and JER breeds in order to improve matting schemes regarding the low values of The original contributions presented in the study are included in the article/Ethical review and approval was not required for the animal study because it used genotypes data provided.LV, MSi, FS, MM, and JC conceived, designed, and supervised the experiments. LV and MSi conducted the experiment. LV analyzed the results and prepared the manuscript draft. DL, PO, LA, LS, AE, MSo, MM, and LV edited the manuscript. All authors reviewed and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Since the inception of the theory and conceptual framework of genomic selection (GS), extensive research has been done on evaluating its efficiency for utilization in crop improvement. Though, the marker-assisted selection has proven its potential for improvement of qualitative traits controlled by one to few genes with large effects. Its role in improving quantitative traits controlled by several genes with small effects is limited. In this regard, GS that utilizes genomic-estimated breeding values of individuals obtained from genome-wide markers to choose candidates for the next breeding cycle is a powerful approach to improve quantitative traits. In the last two decades, GS has been widely adopted in animal breeding programs globally because of its potential to improve selection accuracy, minimize phenotyping, reduce cycle time, and increase genetic gains. In addition, given the promising initial evaluation outcomes of GS for the improvement of yield, biotic and abiotic stress tolerance, and quality in cereal crops like wheat, maize, and rice, prospects of integrating it in breeding crops are also being explored. Improved statistical models that leverage the genomic information to increase the prediction accuracies are critical for the effectiveness of GS-enabled breeding programs. Study on genetic architecture under drought and heat stress helps in developing production markers that can significantly accelerate the development of stress-resilient crop varieties through GS. This review focuses on the transition from traditional selection methods to GS, underlying statistical methods and tools used for this purpose, current status of GS studies in crop plants, and perspectives for its successful implementation in the development of climate-resilient crops. The advancement in genomics approaches leads to the availability of huge resources like genome sequence information, transcriptome, and proteome that have paved the way to hasten the identification of target genes mitigating the effects of climate change . MAS is an indirect selection process, where individuals for a particular trait of interest are selected based on the known markers linked to it . This meThe major advantage of using GS is that it allows for a drastic reduction in the duration of the breeding cycle as compared to traditional breeding and also minimizes the cost associated with extensive phenotyping, thereby subsequently accelerating genetic gains and ensuring food and nutritional security . HoweverThe choice of models is an important factor in implementing GS, and several parametric and non-parametric genomic prediction models are available for this purpose. One of the most common and widely used parametric genomic selection model is the best linear unbiased prediction (BLUP). It is a mixed model–based whole-genome regression approach that is used to estimate the marker effects, and the same has been successfully applied to predict complex traits . In geneThe process of selecting the suitable individuals in GS starts with a simple linear model sometimes also called least-squares regression or ordinary least-squares regression (OLS):One major problem in linear models using several thousands of genome-wide markers is that the number of markers (p) exceeds the number of observations (n), i.e., genotype/individuals/lines, and this creates the problem of over-parameterization ). Using a subset of significant markers can be an alternative for dealing with the large “p” and small “n” problem. Meuwissen et al. (2001) used a modification of the least-squares regression for GS. They performed least-squares regression analysis on each marker separately with the following model:Markers with significant effects are selected using the log likelihood of this model, and those are further used for estimation of breeding values. However, it has to be noted that some key information may be lost by selection based on the subset of markers.1 penalized least-squares criterion to obtain a sparse solution. However, sometimes LASSO may not work well with highly correlated predictors  , which is a penalized regression–based approach . It also (LASSO)  is anothlibrium) . The elalibrium) , and it librium) .The RR model considers that each marker contributes to equal variance, which is not the case for all traits. Therefore, the variance of the markers based on the trait’s genetic architecture has to be modeled. For this purpose, several Bayesian models have been proposed where it is assumed that there is some prior distribution of marker effects. Furthermore, inferences about model parameters are obtained on the basis of posterior distributions of marker effects. There are several variants of Bayesian models for genomic prediction such as Bayes A, Bayes B, Bayes Cπ, and Bayes Dπ  and otheThe genomic prediction models discussed so far perform well for traits with additive genetic architecture, but their performance becomes very poor in case of epistatic genetic architectures. Hence, Methods discussed earlier in this section are based on genomic information where information is available for a single trait, i.e., single-trait genomic selection (STGS). As the performance of STGS-based methods may be affected significantly in case of pleiotropy, i.e., one gene linked to multiple traits, a mutation in a pleiotropic gene may have an effect on several traits simultaneously. It was observed that low heritability traits can borrow information from correlated traits and consequently achieve higher prediction accuracy. However, STGS-based methods consider the information of each trait independently. Hence, we may lose crucial information which may ultimately result in poor genomic prediction accuracy. Nowadays, as we are receiving data on multiple traits, so multi-trait genomic selection (MTGS)-based methods may provide more accurate GEBV and subsequently a higher prediction accuracy. Several MTGS-based methods have been studied in relation to GS, e.g., multivariate mixed model approach , BayesiaCereals are an important part of our daily diet as they contribute about 50% of the total dietary energy supply . Wheat, Grain yield is a major trait which is affected directly or indirectly by other traits including thousand grain weight, number of tillers bearing panicle, number of grains per panicle, number of filled grains per panicle etc. Genomic prediction for these traits utilizing different types of training populations and models have been evaluated. The variations in the accuracies of genomic prediction have been attributed to the heritability of the trait, training population, and models used. The genomic prediction accuracy for a very complex and physiological trait–like distribution of weight to the individual grain in the panicle in rice  ranged fFusarium head blight, septoria tritici blotch, powdery mildew, tan spot, and Stagonospora nodorum blotch. The genomic prediction accuracies for these diseases ranged from 0.14 to 0.85  followed by oil content (0.64) using GBLUP. They also evaluated genomic prediction for compositional fatty acid estimated under rainfed and irrigated conditions and concluded that the prediction accuracies for these traits were lower under non-irrigated conditions. B. napus and reported the two-stage method OLS post-LASSO to be the most accurate  with the provision of incorporating GxE interactions. For oil content in sunflower which is highly heritable and additive in nature, Oilseeds are a source of livelihood to the smallholder farmers in developing countries of Asia and Africa. The yield potential is still to be realized by bridging the yield gap  quality . Differe quality . Hence, G. max X G. sojae), From a cross between cultivated and wild progenitors of soybean  in Phaseolus and proposed it to be promising for improving quantitative tolerance.Under the circumstance of less connectedness in the training and prediction populations, markers generated using the whole genome re-sequencing (WGRS) platform increase the prediction accuracy; however, Fruit and vegetables are indispensable in achieving nutritional security. However, the problem associated with their breeding, especially of fruits, has its own limitations, viz., long juvenile phase and highly heterozygous nature. Therefore, genetic gain is not much as per the Lush equation. In such crops, GS can be a perfect tool where prediction of performance for quality- and yield-related traits which are under a complex genetic system can be utilized to improve selection accuracy and efficiency in developing varieties. The success of GS in annual crops has led the horticultural crop breeder to utilize its potential in perennial fruit as well as annual fruit and vegetable crops. As fruits are perishable produce and the post-harvest attribute of the fruits plays an important role in storability, attempts have been made to employ GS for such traits. In apricot, Several tools and packages have been developed for the evaluation of genomic prediction and implementation of GS, some of which are discussed below.p-values  in the GWAS and then chooses the relevant markers set to be included in the final prediction model. GMStool is R-based and freely available through the GitHub repository at https://github.com/JaeYoonKim72/GMStool. The whole process or its algorithm is basically divided into three steps: data preparation, marker selection, and final prediction model. The detailed procedure of GMStool is discussed below.It is a genome-wide association study (GWAS)-based tool for genomic prediction using genome-wide marker data. It searches for the optimum number of markers for prediction using appropriate statistical and machine learning/deep learning–based models and chooses the best prediction model . FurtherStep 1: Input data are divided into training and test sets (user defined)Step 2: The training set is further divided into small datasets for performing cross validation  followed by marker selection in each group or fold. The process of marker selection is performed in each fold/group simultaneously.Step 3: The selected marker from each fold is integrated into the final marker set for updating the model. Appropriate statistical and machine learning–based models are then used for genomic prediction.http://nextgencassava.org) and implemented at the Cassavabase website (http://cassavabase.org/solgs).It is an open-source tool based on the Linux operating system. The workflow of the tool is broadly divided into two steps, i.e., training of the prediction model and obtaining GEBV. However, there are three approaches available for training the prediction model, i.e., trait-based approach, trial approach, and custom lists approach. Here, model input and output could be visualized graphically and can be interactively explored or downloaded. It is designed to store a large amount of genotypic, phenotypic, and experimental data. In the background, it basically uses two R-based packages, i.e., nlme  for datamixed.solve function, a linear mixed model equation which estimates marker effects and GEBV, is one of the most commonly used functions of this package. An additive relationship matrix of individuals can be calculated using genotypic data for the estimation of GEBV using GBLUP. rrBLUP is an open-source package and can be accessed at https://CRAN.R-project.org/package=rrBLUP.It is an R package based on BLUP, which is a mixed linear model framework . It is ohttps://CRAN.R-project.org/package=BWGS. The BWGS  pipeline  project . It is uhttps://CRAN.R-project.org/package=GSelection. The package comprises of a set of functions to select the important markers and estimates the GEBV of selection candidates using an integrated model framework , where convergence in terms of MCMC  iteration is required . Sometime is the effective population size and L is the genome size in Morgan) and the number of markers as 10*Ne*L to achieve a prediction accuracy of 0.9 and reducing the size of the training population to 1*Ne*L results in a prediction accuracy of 0.7, provided that training population and breeding population are unrelated or both separated by many generations   . Numerou2 < 0.4) , and at Genomic selection has shown its potential in plant and animal breeding research by increasing genetic gains in the last two decades. Revolution in terms of cheaper NGS technologies has made it possible to sequence the crop and animal genomes at a relatively low cost. It resulted in a number of completely sequenced crop and animal genomes with high-density SNP genotyping chips and their availability in the public domain, which may further boost the predictive ability of a GS model. Even after more than a decade in the field of genomic selection studies, still there is a lot of scope for improvement in this area. Methodological refinements  will be definitely helpful for a successful implementation of GS in plant and animal breeding programs. Consistent updation of the training set for GS is highly desirable by including the new markers in each generation. Evaluation of the training populations should be done in controlled and well-managed conditions as it significantly affects the performance of prediction models. There is a need for a structured program in the field of genomic selection including human resource development, advanced data recording methodologies, and trait phenotyping in order to come out with fruitful outcomes.


Puccinia arachidis Speg. is a major cause of yield and quality losses in groundnut (Arachis hypogaea L.) in the warm-humid tropics including Tanzania. Breeding and deployment of rust resistant cultivars with farmer-preferred attributes will bolster groundnut production and productivity. The objective of this study was to determine the combining ability effects and gene action controlling rust resistance in groundnut genotypes for breeding. Twelve selected and complementary parental lines were crossed in a diallel design, to develop F1 progenies, which were advanced to the F2 for individual plant selection. Thirty-three successful partial crosses and the 12 parents were field evaluated using a 5 × 9 alpha lattice designs with two replications over two seasons in Tanzania. The tested genotypes exhibited significant (P < 0.05) variation for rust resistance, yield and yield-related traits. There existed significant (P < 0.05) difference on the general combining ability (GCA) effect of parents and the specific combining ability (SCA) effect of progeny for the assessed traits indicating that both additive and non-additive gene effects conditioned trait inheritance. The Bakers’ ratios indicated that the non-additive gene effects predominantly controlling rust resistance and yield components. This suggested that transgressive segregants could be selected for improved rust resistance and yield gains in the advanced pure line generations. Genotypes ICGV-SM 05570 and ICGV-SM 15567 were the best general combiners for rust resistance and grain yield. The crosses ICGV-SM 16589 × Narinut and ICGV-SM 15557 × ICGV-SM 15559 were identified as the best specific combiners for rust resistance with moderate yield levels and medium maturity. Genotypes with desirable GCA or SCA effects were selected for further breeding.Groundnut rust caused by  Arachis hypogaea Speg., AABB, 2n = 4x = 40) is cultivated in more than 100 countries in tropical, subtropical and warm temperate regions globally1. World groundnut production is estimated at approximately 45.95 million tons of shelled grain per year which is mainly used for oil2. Groundnut production in Tanzania is estimated at 0.9 million tonnes per year with an average productivity of less than one tonne per hectare2. Despite its importance, groundnut production and productivity are challenged by a number of biotic and abiotic stress factors. Among biotic stresses, groundnut rust disease caused by Puccinia arachidis Speg. is a major constraint to groundnut production in the hot humid tropics causing yield losses reaching up to 57%3. Reportedly, about 48.3% of groundnut farmers in the hot and humid production environments in Tanzania indicated groundnut rust as the major constraint to high yield and quality4.Groundnut  of parents and the specific combining ability (SCA) of progeny. The GCA and SCA effects are associated with additive and non-additive gene action, respectively15. Both GCA and SCA effects have been reported in foliar disease resistance breeding programs including groundnut using various mating designs17.Knowledge on the gene action conditioning economic traits is a prerequisite for breeding resistant groundnut cultivars18. It is a more appropriate design for self-pollinated species where the success rate for generating crosses is often low such as in groundnut and soybean19. It has been used in genetic analysis of traits of various legume crop species such as cowpea22, soyabean24 and chickpea27. To initiate groundnut pre-breeding for rust resistance and farmer-preferred agronomic traits, genetically diverse collections were characterised using agronomic traits and polymorphic simple sequence repeat (SSR) markers. This enabled selection of potential and complementary parents for strategic breeding28. The combining ability effects of the selected parents and their progenies should be assessed to develop new breeding populations adapted to Tanzania. Therefore, the objectives of this study were to determine the combining ability effects and gene action controlling rust resistance in selected groundnut genotypes to develop breeding populations.The diallel mating design is the most commonly used method to estimate GCA and SCA effectsThe study was conducted at Tanzania Agriculture Research Institute (TARI), Naliendele Agricultural Research Centre. TARI-Naliendele  is situated at an altitude of 135 m above sea level. The mean monthly temperatures range between 24.3 °C in July and 27 °C in December while the mean annual total rainfall is between 820 and 1245 mm with a unimodal rainfall distribution. A dry spell of one to two weeks often occurs at the end of January or at the beginning of February. The soils at TARI-Naliendele are described as sandy loam with pH of 4.5. The prevailing temperatures and rainfall conditions of the test sites during the experiments are summarised in Table 28. The lines consisted of accessions, a landrace and two released varieties  for genetic analysis. The F1 seed of all successful crosses was planted after three weeks for seed bulking and genetic analysis in the F2.Crosses were performed using a full diallel mating design involving the 12 lines according to the scheme shown in Table 2. The recommended practices for fertilizer application and weeding for groundnut were followed33. This site is a hotspot for rust and late leaf spot diseases. Hence genotypes were evaluated under natural rust and late leaf spot infection and disease development.Thirty-three successful progenies and their parents were evaluated in the field using a 5 × 9 alpha lattice designs with two replications at TARI-Naliendele in two seasons (2019 and 2020). The genotypes were evaluated for rust resistance, agronomic performance and yield potential during the off-season in 2019 and the rainy season in 2020. The off-season trial was conducted under irrigation, while the main season trial was done under rainfed condition. Each genotype was planted on two rows of 4 m length, with a spacing of 50 cm between the rows and 10 cm between plants in a row. The plot size for each genotype was 2.0 m−1) was estimated as the weight of kernels harvested from a plot.Data on yield and yield components were recorded during plant growth and at harvest maturity. Days to flowering (DTF) were recorded by counting the number of days from sowing to the time when 75% of the plants in a plot had emerging flowers. Days to maturity (DTM) were recorded by counting the number of days from planting to maturity. Plant height  was measured from ten randomly sampled plants in each plot from the soil surface to the tip of main stem. The number of pods per plant (NPP) was recorded as the average number of pods from ten randomly sampled and tagged plants per plot. Pod yield (PDY) was measured by weighing the dried pods from each plot and was recorded in grams per plot. Shelling percentage (SP) for each genotype was calculated from a random sample of pods weighing 200 g, as the proportion of shelled seed weight to the total weight of the unshelled pods. Additionally, 100 seed weight  for each genotype was recorded as an average weight of two samples of 100 well-developed whole air-dried kernel per plot. Kernel yield  while leaves with 1–5% infection were assigned a score of 2, 6–10% infection (score 3), 11–20% infection (score 4), 21–30% (score 5), 31–40% infection (score 6), 41–60% infection (score 7), 61–80% infection (score 8) and 81–100% infection (score 9)35. Plants with a disease score of between 1 and 3, 4 and 6, and 7 and 9 were considered as resistant, moderately resistant and susceptible, respectively36. In addition, late leaf spot reaction was assessed as a secondary trait due to the simultaneous occurrence with rust disease. Late leaf spot severity was assessed at 85 days after planting (%LLSI85) and 100 days after planting (%LLSI100) as in rust severity. For data analysis, the score data were converted into percentage severity using37.Rust severity was scored at 85 days after planting (%RI85) and 100 days after planting (%RI100). The severity was scored using a scale of 1 (least affected) to 9 (most affected) following38 and means were separated by Fischers unprotected least significant difference at 5% probability level. General combining ability (GCA) effects of parents and specific combining (SCA) of crosses were computed based on the partial diallel analysis proposed by39. The general linear model used was as follows:The data were subjected to analysis of variance (ANOVA) using SAS 9.4ij is the reciprocal cross effect between ith and jth parents; bk is the effect of the kth block and where 40 as follows:The relative importance of GCA and SCA effects was estimated using the GCA-SCA prediction ratio proposed bywhere: A trait whose Bakers’ ratio is close to 1.00 indicates that the GCA effects were more important in conditioning the heritability of that trait, whereas a ratio that is close to zero would indicates that SCA effects would be more important in controlling trait heritability.The ANOVA revealed that the genotype × season interaction effects had significant (P < 0.001) impact on DTF and NPP Table . There w−1). The highest HSW was recorded for the cross ICG 12725 × ICGV-SM 06737 (46.35 g/100 seed). The highest pod yield of 4712.82 kg ha−1 was attained by the cross ICGV-SM 15524 × ICGV-SM 05570. The crosses that had better yield response than their mid parents included ICGV-SM 15524 × ICGV-SM 05570 (1548.72 kg ha−1), Narinut × ICGV-SM 05570 (957.23 kg ha−1), Pendo × ICGV-SM 15524 (908.36 kg ha−1), and Pendo × ICGV-SM 16601 (864.37 kg ha−1).Days to flowering varied from 31 days (for cross ICGV-SM06737 × Pendo) to 45 days (cross ICGV-SM16589 × ICGV-SM05570)  variation for yield and yield components, suggesting that the test genotypes were useful genetic resources for groundnut improvement. The groundnut genotypes used in this study included divergent parental lines from Virginia and Spanish botanical groups which invariably contributed to the genetic variation observed in the new breeding population. The parental lines have different genetic constitution, agronomic potential and adaptations providing the F2 progeny with transgressive segregations. This led to wide genetic variation in the observed performance in the F2. The presence of high progeny performance exceeding the parental phenotypic values have been reported in segregating populations43. Transgressive segregation is useful in crop improvement as one of the mechanisms that contribute to genotype discovery with unique genetic composition and novel adaptations compared to the base population44. Crop improvement depends on the availability of genetic variation with stable performance for economic traits45. Genotype × season interaction effects were significant for DTF and NPP suggesting that seasonal variability and change in climatic conditions affects the phenotypic expression of the tested groundnut genotypes. Seasonal variability presents challenges for selection as it reduces correlation between genotype and phenotypic expression. Genotypes such as ICGV-SM 15524 × ICGV-SM 05570 and Kanyomwa × ICGV-SM 15559 that consistently perform across seasons and locations will be ideal for selection. Traits whose expression was not significantly affected by seasonal or genotype × seasonal variability will be easier to select and improve. Mekontchou et al.46 and Bucheyeki et al.47 reported significant genotype, environmental and genotype × environment interaction variations for agronomic traits in groundnuts.The FThe impact of rust diseases on groundnut production compels breeders to select genotypes that express appreciable levels of rust resistance coupled with high yield potential. Parental lines such as ICGV-SM 15567 and progeny such as ICGV-SM 15524 × ICGV-SM 05570 and Narinut × ICGV-SM 05570 exhibited low rust infection and had high kernel yield response across seasons. Higher mean performance among crosses compared to the parents indicates that there was genetic gain in yield and agronomic performance among the crosses. For groundnut rust resistance breeding, the following families were selected: ICGV-SM 15524 × ICGV-SM 05570, Pendo × ICGV-SM 05570, ICGV-SM 16601 × ICGV-SM 06737 and ICGV-SM 05570 × ICGV-SM 06737. These families exhibited low rust severity than their corresponding parents. This suggests that rust resistance was achieved through gene recombination hence desirable transgressive segregants can be selected in successive generations. For instance, Pendo is known to be susceptible to rust but its progeny, i.e., Pendo × ICGV-SM 05570 was among the crosses with desirable SCA effects for rust resistance.48 and Sukruth et al.49 selected groundnut genotypes that exhibited early flowering for yield improvement under marginal conditions especially drought prone areas. Parental lines and crosses that exhibited desirable mean performance in other desirable traits such as higher shelling percent  and hundred seed weight  should be selected for direct or indirect selection of grain yield. It is, thus, imperative to consider the correlations existing among the target traits to ensure that appropriate selection methods are devised for simultaneous improvement.Incorporating rust resistance, with kernel yield and yield components will enhance groundnut production and productivity. Groundnut breeding should target multiple traits to achieve suitable agronomic performance and high yields. For instance, parental lines Pendo and ICGV-SM 15524 and crosses such as Pendo × ICGV-SM 16589, ICGV-SM 06737 × Pendo and ICGV-SM 15524 × Narinut displayed early flowering and maturity. Hence these genotypes should be selected to improve early maturity for environments with short and erratic rainfall patterns in Tanzania. Chaudhari et al.50. However, other reports indicated that non-additive gene effects were more important for rust resistance and grain yield52. The significant reciprocal effects in the cross ICGV-SM 16589 × ICGV-SM 06737 (for DTF and DTM) and Narinut × ICGV-SM 06737 for HSW suggested the presence of maternal inheritance effect conditioning trait heritability. Maternal effects are contributed by the female parent and thus it is important to purposefully designate the female and male parents during crosses to exploit any favourable maternally inherited trait. Pasupuleti et al.53 and Dwivedi et al.54 reported highly significant reciprocal effects for late leaf spot resistance and kernel yield in groundnut, respectively.Except NPP and SP, all assessed traits exhibited significant GCA and SCA variance except NPP and SP, suggesting that the assessed traits were conditioned by additive and non-additive genes. For NPP, the SCA effect was only significant indicating non-additive genes controlling this trait. In addition, the GCA and SCA variances were consistent across seasons indicating that allele interactions and additive gene effects were less influenced by the environment and were thus highly heritable. The traits that exhibit significant GCA effects may be improved by selection and crossing of parental lines with favourable performance for that trait. Parents will be expected to additively contribute their favourable alleles to develop better performing offspring. In contrast, SCA effects will be exploited through hybrid breeding instead of pure line selection. Dominance genes occur as a result of interaction between alleles governing the inheritance of a trait. Intra-allelic interaction is not easily predictable. For instance, two different parents with favourable mean performance for a trait may produce an off springs with undesirable performance due to poor gene combinations or intra-allelic interaction (dominance) or inter-allelic interaction (epistasis). On the other hand, genes from poor performing parents may combine favourably well to produce high performing offspring due to favourable SCA effects. Traits such as rust and leaf spot resistance and grain yield have been reported to be controlled by additive and non-additive gene effectsI or F2 and later generations55. Developing groundnut cultivars with rust resistance that are adapted to harsh growing conditions is important for sub-Sahara African region where rust and other foliar diseases are endemic. The development of high-yielding cultivar for foliar disease resistance is one of the major objectives of the groundnut improvement programme in Tanzania. Developing suitably adapted cultivars is preceded by identifying parental lines with good combining ability for the suitable traits. Parental genotypes that exhibit good GCA effects often have the ability to transfer their favourable characteristics to the offspring56. Parental genotypes such as ICGV-SM 05570 and ICGV-SM 15567 had negative GCA effects for rust resistance, while genotype Kanyomwa had positive GCA effects for grain yield. These parents are selected for developing breeding populations. The GCA effects of the parental lines is particularly important for traits controlled by additive traits since their inheritance and expression in the offspring are conditioned by the summation of the allelic effects of the different parents. For improving traits such as earliness to flowering and maturity, parental lines ICGV-SM 15524 and ICGV-SM 16601 that exhibited negative GCA effect will be ideal due to their potential to reduce the average DTF and DTM in the offspring. Early flowering and maturity varieties are ideal for marginal environments such as those mostly found in sub-Sahara Africa region, characterised by inadequate rainfall and high temperatures. However, earliness to maturity can lead to yield penalty in environments where soil moisture is adequate, and the rainy season is long57. Groundnut rust disease epidemiology is favored by continuous warm temperatures ranging between 20 and 30 °C and high humidity above 78%58. Under favourable moisture and temperature conditions the following genotypes are recommended for breeding: ICGV-SM 05570, ICGV-SM 15559 and Narinut. These lines had positive GCA effects for DTF and DTM useful for long duration variety development. The parents with positive GCA effects for PH (ICGV-SM 15524 and Pendo), NPP (ICGV-SM 15524 and Pendo), HSW (ICGV-SM 15524 and Pendo) and SP (Kanyomwa) will be useful for trait improvement including grain yield. Groundnut genotypes of the Virginia botanical group have high above ground biomass, high number of pods per plant and large seed types which may likely provide higher grain yield. These group of genotypes exhibited medium to late maturity compared to small-biomass types59. However, there were no parental lines that exhibited good GCA for all assessed traits in the present study. Therefore, different complementary parents should be selected for breeding purposes based on their GCA effects.General combining ability analysis is an effective method in selection of parents based on performance of their progenies, usually at the F37. SCA effects represent the non-additive proportion of variance that is difficult to exploit in trait improvement in self-pollinating crops due to low heritability and unpredictability of reshuffling of genes. The performance of a specific cross depends on the extent of the favourable genes for a trait from the two parents complementing each other55. For instance, crosses such as ICGV-SM 15557 × ICGV-SM 15559, ICGV-SM 16589 × Narinut and ICG 12725 × ICGV-SM 06737 exhibited good SCA effects for rust resistance and reduced number of days to flowering. The families such as ICGV-SM 06737 × ICGV-SM 15524 and Kanyomwa × ICGV-SM 05570 had good SCA effects for kernel yield due to favourable interaction between alleles from the female and male parents. In some cases, `crosses can exhibit good SCA effect even when their parents have poor or unfavourable GCA effects for the trait. This is due to the favourable interaction after recombination showing that there will be potential for selection of transgressive individuals in segregating populations. Crosses such as Narinut × ICGV-SM 05570 had positive SCA effects and high mean values for kernel yield. Conversely, crosses such as ICGV-SM 16589 × Narinut and ICG 12725 × ICGV-SM 06737 had negative SCA effect and lower mean values for rust severity scores compared to their mid parent values. These suggest that the new progeny are transgressive segregants that could be further selected for trait improvement.Specific combining ability effect relates to performance of some crosses relatively better or worse than would be expected based on the average performance of the parents involved51, who reported that rust resistance is controlled by non-additive gene action. The significant differences showed by the reciprocal effects indicate that maternal effects have impact on groundnut rust resistance. Hence, it is important to use appropriate mating design like full diallel that will allow to exploit cytoplasmic inheritance. According to10 rust resistance is controlled by few genes with either monogenic, digenic or trigenic inheritance and hence backcross breeding can facilitate accumulation of major genes in progenies.The ratios of GCA to SCA mean squares for most assessed traits were less than one and had a value close to zero based on Baker’s ratio indicating that non-additive gene action had a more prominent role in the control of groundnut rust resistance and agronomic traits. The relatively lower ratios showed the preponderance of non-additive gene effects for most traits and suggested that trait improvement will only be effective after selection in the advanced generations. The non-additive gene action found in this study were in concurrence withThe assessed groundnut genotypes exhibited wide genetic variation for rust resistance, agronomic traits and kernel yield useful for breeding. The inheritance of rust resistance is conditioned by dominance gene action, while kernel yield was controlled by additive gene action. Parental lines ICGV-SM 05570 and ICGV-SM 15567, which were the best combiners for rust resistance and kernel yield, were selected for breeding population development and pure line maintenance. The individuals ICGV-SM 16589 × Narinut and ICGV-SM 15557 × ICGV-SM 15559 were identified as best specific combiners for rust resistance. The selected families are recommended for genetic advancement and to identify transgressive segregants and develop pure lines for cultivar release and deployment in Tanzania.