The world population is expected to be larger and wealthier over the next few decades and will require more animal products, such as milk and beef. Tropical regions have great potential to meet this growing global demand, where pasturelands play a major role in supporting increased animal production. Better forage is required in consonance with improved sustainability as the planted area should not increase and larger areas cultivated with one or a few forage species should be avoided. Although, conventional tropical forage breeding has successfully released well-adapted and high-yielding cultivars over the last few decades, genetic gains from these programs have been low in view of the growing food demand worldwide. To guarantee their future impact on livestock production, breeding programs should leverage genotyping, phenotyping, and envirotyping strategies to increase genetic gains. Genomic selection (GS) and genome-wide association studies play a primary role in this process, with the advantage of increasing genetic gain due to greater selection accuracy, reduced cycle time, and increased number of individuals that can be evaluated. This strategy provides solutions to bottlenecks faced by conventional breeding methods, including long breeding cycles and difficulties to evaluate complex traits. Initial results from implementing GS in tropical forage grasses (TFGs) are promising with notable improvements over phenotypic selection alone. However, the practical impact of GS in TFG breeding programs remains unclear. The development of appropriately sized training populations is essential for the evaluation and validation of selection markers based on estimated breeding values. Large panels of single-nucleotide polymorphism markers in different tropical forage species are required for multiple application targets at a reduced cost. In this context, this review highlights the current challenges, achievements, availability, and development of genomic resources and statistical methods for the implementation of GS in TFGs. Additionally, the prediction accuracies from recent experiments and the potential to harness diversity from genebanks are discussed. Although, GS in TFGs is still incipient, the advances in genomic tools and statistical models will speed up its implementation in the foreseeable future. All TFG breeding programs should be prepared for these changes. The tropics are home to about a third of the world’s population, accounting for 36% of the Earth’s landmass, and where most of the global demographic increase takes place . The troPlant breeding has evolved from a rudimentary process in its early stages to a modern and sophisticated system in the past few decades. The rediscovery of Mendel’s laws of genetics in 1900 is one of the pillars of modern plant breeding , which cPastures are the main food source for animal feeding in the tropics, as in Brazil, where approximately 90% of the livestock are solely grass-fed . An incrGenomic selection (GS) offers the opportunity to increase agricultural production and reduce the breeding interval cycle to at least half of the conventional time . ReductiCenchrus purpureus syn. Pennisetum purpureum), Guinea grass (Megathyrsus maximus syn. Panicum maximum), and brachiaria , which account for most of the pastures in many parts of the world, including Africa, Asia, Australia, and Latin America. Specific features of breeding programs, availability of genomic resources, statistical methods for GS, and gaps in the application of GS in TFG breeding are discussed here. This discussion is essential for the initiation and practical implementation of GS in TFG breeding programs.This article provides an overview of GS in TFGs focusing on the current scenario, recent advances, and prospects for the effective application of tools and strategies to accelerate TFG breeding. We have focused on elephant grass , increasing adaptation based on expected climate changes, and improving nutritional value to enhance animal performance, resulting in more beef and milk per kilogram of pasture. To address these challenges, research priorities have focused on the development of new capabilities such as the availability of genome sequences, high-throughput genotyping, and germplasm characterization of tropical forage grasses; identification of genes associated with important traits; development and use of large-scale phenotyping tools; and implementation of GS .Therefore, the prospects of applying genomic tools in TFG breeding programs are promising, and these tools, coupled with adequate pasture management, can continue to promote substantial advances in livestock productivity. For each forage species, the objectives of the breeding programs should be well-defined, as highlighted in Perennial forages require selection methods that consider the effects of both between families and within family individuals for higher selection gains, mostly in lower magnitudes of narrow-sense heritability (NSH) , 2014. IMegathyrsus and Urochloa, gametophytic apomixis subtype apospory occurs  interspecific hybrids, which ranged from 18% to 82% , which should have their phenotypes assessed for various traits of interest. Equations for predicting genomic values (random multiple regression) are obtained for each trait. These equations associate each marker or interval with its effect (predicted by RR-BLUP) on the trait of interest. The markers that explain the loci regulating the traits are identified in this population, and their effects are estimated. Recently, yŷ) of GS in estimating phenotypes, which is given by the accuracy of the selection itself (h), or When physically separated from the estimation population, this dataset is smaller than the discovery population and includes individuals that are assessed for SNP markers and various traits of interest. The equations for predicting genomic values are tested to verify their accuracy for this independent sample. To calculate the accuracy, genomic values are predicted, using the estimated effects from the estimation population and subjected to correlation analysis with the observed phenotypic values. As the validation sample is not involved in predicting the marker effects, errors from genomic values and phenotypic values are independent. Correlations between these values are predominantly genetic in nature and equivalent to the predictive ability  is a tetraploid and allogamous species in which open pollinated divergent populations are easy to establish. The two main breeding strategies are: (i) recurrent selection  and brachiaria (Urochloa) breeding programs have recently adopted the full-sib reciprocal recurrent selection as a method, in which thousands of hybrids are generated annually  in M. maximus . Thirdly, as a result of the intra or interspecific crosses, F1 progeny segregates for mode of reproduction in which individuals in the progeny may vary from 99% apomictic to 99% sexual. While this procedure is efficient to explore the panmictic heterosis  of interest . Thus, lRecently, molecular genetic markers that consist of SNPs (based on the detection of polymorphisms that arise from a single nucleotide change in the genome) have been widely used in many species . GeneralLD analysis is based on LD between a marker and a QTL in the whole population and not only within a family, as performed in linkage analysis . For thiAssociation analysis is used for fine mapping and is based on population-level LD . LinkageIn recent times, efforts to use molecular markers in genetic improvement research have evolved into two approaches: (1) GWAS for QTL identification and mapping; and (2) genome-wide selection (GWS) or GS . GS was The conceptual development of GS coincides with the technology associated with SNPs, which is accurate and relatively affordable. GS uses the associations between many SNP markers throughout the genome along with phenotypes and takes advantage of LD between markers and QTLs in close linkage . The preWhen LD between markers is incomplete, the joint allele frequencies for the two loci can change markedly across generations, thereby leading to changes in haplotypes. In this case, the marker effects would need to be estimated again to maintain the accuracy of GS for various generations . In the The number of markers used are directly associated to the genome size, extent of LD and population structure . Larger eL) and the distribution of their effects; iii) number of individuals in the discovery population; iv) effective population size (Ne); and v) marker density, which depends on the number and genome size . The first two factors are beyond the breeder’s control, and the latter three factors can be modified by the breeder to increase the accuracy of GS.The accuracy of GS depends on five factors : i) herik is the standardized selection differential (dependent on the selection intensity), g is the genetic standard deviation (genetic variability) of the trait in the population, and T is the time required to complete a selection cycle.An increase in the selection efficiency using GS can be achieved by changing the four components of the expression for genetic progress, given by T. The increase in T is greatly reduced by GS because genomic prediction and selection can be performed at the seedling stage. Thus, even if T.In perennial and vegetatively propagated plant species, the benefit of GS is from an increase in p matrix . This inThe quality of GS is inferred by correlation and regression among the predicted genetic values and phenotypes in the validation population, as well as by the accuracy of the prediction. The correlation and regression coefficients involving observed and predicted values are practical measures of the ability of the methods to make predictions that are accurate and unbiased, respectively. Correlation provides predictive ability, which is equivalent to the product of accuracy and the square root of heritability . The regThe expected value of the regression coefficient is 1, which indicates an unbiased prediction. Thus, the regression coefficient can also be used to estimate the heritability of the markers . VariousUrochloa, for which the GBS-SNP-CROP pipeline .The availability of a large number of high-quality single-nucleotide polymorphisms (SNPs) that can be genotyped at a reasonable cost is a prerequisite for implementing GS in a crop of choice . Gold-stpipeline  was usedpipeline . This leAssembly quality, which is measured by its accuracy, haplotype phasing, and contiguity, is an important factor influencing marker discovery, GWAS, and GS. In tetraploid blueberries, the selection of probes for targeted SNP genotyping, investigation of the genetic architecture of fruit traits, identification of candidate genes, and genomic prediction benefited from a more complete, chromosome-scale, haplotype-phased genome assembly . A huge Urochloa P. Beauv. Grasses, many of which were previously included in Brachiaria (Trin.) Griseb., are the most widely used forage in Latin America. The main species are U. ruziziensis, U. brizantha, U. decumbens, and U. humidicola. The first genome assembly of a forage grass species in the genus Urochloa has recently been reported for U. ruziziensis  and transcriptome assemblies for M. maximus. The alignment rates ranged between 19.05% for P. hallii and 24.24% for M. maximus transcriptomes, showing that a very large proportion of reads were not used for SNP discovery and genotyping. The sets of allele-dosed SNPs containing up to 5% of missing data from each of the reference assemblies ranged between 5,032 for one of the M. maximus transcriptomes and 8,112 for S. viridis. Although, this was the first report on the development and assessment of prediction models, considering the allele dosage, for GS in M. maximus, increased marker density and prediction accuracies may be expected when a high-quality genome assembly for the species is available for SNP discovery and genotyping.The placement of Guinea grass in the phylogeny of Paniceae has changed over the years, however, plant breeders, seed producers, and farmers in Latin America mostly refer to it as C. purpureus Schumach. Morrone, syn. Pennisetum purpureum Schumach.), also called napier grass, merker grass, or Uganda grass, is a tropical grass native to Eastern and Central Africa. It is an allotetraploid species with a chromosome constitution of 2n = 4x = 28 A’A’BB and an average amount of DNA per G1 nucleus of 4.58 pg  that affect the trait under analysis. The main problem with GS is the estimation of a large number of effects from a limited number of observations and the collinearities arising from LD between the markers. Shrinkage estimators deal with this appropriately by treating the effects of markers as random variables and estimating them simultaneously .If the effects of markers are taken as fixed, it is not possible to consider the covariance between the effects of the markers. With a high density of markers, more than one marker will be in LD with a segregating QTL, which will result in covariance between the marker effects. Most markers will have no effect on a trait, and the estimated effects of these empty markers will be false. This problem is greater when the markers are considered to have fixed effects, because in that case, these pseudo effects will not shrink toward zero .In the context of marker-assisted selection (MAS) and genomic prediction, the method of least squares (LS) has serious drawbacks. According to a priori QTL distribution, with an infinitely large variance that disagrees with the known total genetic variance.Another difficulty arises when the number of markers is equal to or greater than the number of genotyped individuals. In this case, the collinearity of the predictor variables causes parametric identification problems, and thus, some type of dimensional reduction, such as singular value decomposition, should be used. Another problem is the inadmissibility (unable to provide the minimum mean square error) of LS estimators, a result that collapses estimates by LS and generalized LS (GLS). Thus, the LS method is not recommended for the MAS and GS analyses. In summary, the LS method is inefficient because it is impossible to simultaneously estimate all effects when the number of effects to be estimated is greater than the number of data points; thus, estimating one effect at a time and testing its significance leads to an overestimation of significant effects, and the accuracy of the method becomes low. In addition, only QTLs with large effects will be detected and used, and consequently, not all genetic variations will be captured by the markers. The LS method assumes Because the number of markers in GS is greater than the number of individuals, there is a lack of degrees of freedom to estimate the effects of all markers. A solution to this problem is to use the RR method  or to coThe main problem for GS is estimating a large number of effects from a limited number of observations, in addition to collinearities resulting from LD between markers. The shrinkage estimators adequately address this issue by treating the marker effects as random variables and estimating them simultaneously .The main methods for GS are based on Random Regression and can be divided into three major classes: explicit, implicit, and dimensionally reduced regression. In the first class, the RR-BLUP, Lasso, BayesA, and BayesB methods stand out among others. In the class of implicit regression, the Reproducing Kernel Hilbert Spaces (RKHS) method, which is semiparametric, is the most popular. The Independent Components, Partial Least Squares, and Principal Components stand out among the regression methods with dimensional reduction. Two new non-parametric approaches for GS proposed by The explicit regression methods are divided into two groups: (i) penalized estimation methods  and (ii) Bayesian estimation methods . Among these, the best and most effective in practice are RR-BLUP and BayesB . Each meThe RR-BLUP is a model equivalent to genomic best linear unbiased prediction (G-BLUP), which is the BLUP method at an individual level with the genealogical relationship matrix A changed to a genomic relationship matrix G. The equivalence between these two methods was given by The traditional quantitative genetics rely on random mating populations. Nowadays, with the availability of SNP markers, random mating does not need to be assumed, because breeders can track the transmission of chromosomal segments. Another assumption is linkage equilibrium in the breeding population. Once linkage among markers is accounted for in the G coefficient matrix in RR-BLUP, this circumvents the need to assume linkage equilibrium .A refinement of GS can be achieved by using QTNs instead of SNPs. The evolution of genomic technology is predictable and the causal mutation of a genetic variation at the nucleotide level (QTN) can be accessed soon. Thus, GS can be improved by the direct use of QTNs instead of SNPs. The use of QTNs will bring the following advantages : GS willjth  is defined as yj = 1njμj + Xjβj + εj, where the vector jy represents nj independent centered observations of the response variable in the jth environment; 1nj is a vector of ones of order nj; μj is the overall mean of the jth environment; jX is the matrix for the p centered and standardized molecular markers in the jth environment; vector βj represents the effect of each of the p markers in the jth environment, and εj is the vector of random errors in the jth environment with normal distribution and common variance The parametric regression model for a single environment j and εj are independent, and that uj = Xjβj, then the above model for the jth environment can be written as yj = 1njμj + uj + εj, where ju, and εj are independent random variables with ju (to be estimated), and jK is a symmetric matrix representing the covariance of the genetic values. Thus, for a single-environment where the jK is of the linear form Assuming that the effects of the markers β RR-BLUP .y = Jμ+Xm+e, where y is the vector of phenotypic observations, μ is the vector of the fixed effect of the general mean, m is the vector of random marker effects and e is the vector of random residuals. J and X are the incidence matrices for μ and m, respectively. The incidence matrix X contains functions of the values 0, 1, and 2 for the number of alleles for the marker (or the supposed QTL) in a diploid individual. A similar coding method uses the values of -1, 0, and 1. The genomic mixed-model equations for predicting m using the RR-BLUP method are equivalent to j is given by Xi is equal to 0, 1, or 2 for the genotypes mm, Mm, and MM, respectively, for biallelic and co-dominant markers, such as SNPs.The following linear mixed model can be fitted to estimate the marker effects a priori that all loci explain equal amounts of genetic variation. Thus, the genetic variation explained by each locus is given by Qn is the number of loci (when each locus is perfectly marked by a single marker), which can be given by ip is the frequency of the allele of the type M in locus i. The genetic variation These prediction equations assume X’X present in the equations of the mixed model described above. This procedure is more efficient because it effectively captures the kinship produced for each individual and not an average kinship matrix associated with the pedigree.There is no need to use the kinship matrix with the RR-BLUP method. The pedigree-based kinship matrix used for traditional BLUP was replaced by a kinship matrix estimated by the markers. This kinship matrix is a function of X uses the values 0, 1, and 2 for the number of alleles of a marker (or supposed QTL) in a diploid individual and 2p for individuals with missing marker data. These values should be centered around 0 so that the effects of co-dominant markers are effects of allelic substitution with a mean of 0 in the population. In this case, assuming Hardy-Weinberg equilibrium, the additive genetic variation of the trait in the population is equal to iX should be replaced by 0 – 2p, 1 – 2p, and 2 – 2p, to obtain a variable with a mean of 0. Thus, with centralization, The parameterization of the incidence matrix X can be standardized as follows for each matrix element iX corresponding to locus i:Additionally, the data for markers in matrix Xi = (0 – 2pi)/(Var(Xi))1/2 if the individual is homozygous for the first allele (mm).Xi = (1 – 2pi)/(Var(Xi))1/2 if the individual is hetero- zygous (Mm).Xi = (2 – 2pi)/(Var(Xi))1/2 if the individual is homozygous for the second allele (MM).Xi = 0 if the individual has missing marker data. The quantity pi is the frequency of the second marker allele.MAF = (1/2N)1/2 which comes from the standard deviation of a proportion, given by (pq)1/2/(2N)1/2, where N is the number of genotyped individuals, meaning that the lower the N value, the greater the MAF needs to be for accurate estimation of the marker effect , which is a measure related to the variation of alleles in the population, given by r effect .X contains the values 0, 1, 2, 3, and 4 for the number of alleles for the marker (or the supposed QTL) in a tetraploid individual. Analysis by G-BLUP uses the kinship matrix given by ∗ is the X matrix after centralization.The incidence matrix y = Jμ + Wα + Sδ + e, , the most appropriate parameterization to estimate the effects on the additive-dominance model (According to the marker model ce model  is:Additive effects (W):The values of W must be centered at zero so that the effects of the codominant markers are effects of allelic substitution (α) with a mean of 0 in the population.Dominance effects (S):y = Jμ + Za + Zd + e, where a is the additive genetic vector of the individuals, and d is the dominance genetic vector of the individuals; The individual mixed model is given by ip and iq are the allelic frequencies; The mixed-model equations for the additive-dominance model are equivalent to aG and dG for additive and dominance effects, respectively.Adjusting an individual genomic model is equivalent to adjusting an individual traditional model but with the pedigree-based matrices A and D replaced by the genomic kinship matrices y = Jμ + Za + e can be fitted with one alteration (replacing matrix G with matrix H) to the mixed-model equations, according to Misztal et al. (2009)In a simultaneous analysis of genotyped and non-genotyped individuals via G-BLUP, for a global evaluation of the three classes of individuals in a single step, the same additive model H includes both the relationships, based on pedigree (A) and differences between those and the genomic relationships (Aδ), such that H = A + Aδ. Thus, H is given byMatrix H, which allows simpler calculations, is given by The inverse of d) can also be fitted.From the estimation of genetic values  interactions, can also be fitted if there are related individuals within the same environment and across environments. In this case, the model is equal to y = Wb + Za + Zae + e, where ae is the vector of effects from the interaction between additive genetic effects and environmental effects (random), and Z is the incidence matrix for a and ae. The mixed-model equations for predicting a and ae using the BLUP method are Gae = G for pairs of individuals in the same environment, and Gae = 0 for pairs of individuals in different environments. The variance of the interaction between the additive genetic and environmental effects is denoted by Models at the level of individuals, including genotype × environment  or lack  direct covariable selection. Bayesian methods are more efficient when the distribution of QTL effects is leptokurtic (positive kurtosis) because of the presence of genes with large effects. The RR-BLUP method is equally efficient when the QTL effects are normally distributed.Bayesian methods are associated with systems of nonlinear equations, and non-linear predictions can be more efficient when the QTL effects are not normally distributed owing to the presence of genes with major effects. The linear predictions associated with RR-BLUP assume that all markers with the same allele frequency contribute equally to genetic variation (lack of genes with major effects). In Bayesian estimation, the shrinkage of effect estimates for the model is controlled by the a priori distribution used for the estimation. This approach yielded greater accuracy for this method, although, such accuracy is unattainable in practice if the actual distribution associated with genetic effects differs from the a priori distribution assumed for analysis. In general, there is no method that is best under any circumstances because each method may yield significantly different results depending on the population structure and nature of the trait. However, the results obtained by Comparisons among the methods for predicting genomic breeding values have been performed. The assumed distributions for the genetic effects of markers in the different GS methods are Gaussian normal with common variance for RR-BLUP, Student’s t-distribution given chi-square priori for variances for Bayesian methods, and Double Laplace exponential for Lasso. It is observed that, in relation to RR-BLUP, the prior density used in Bayesian Lasso shows a greater density mass at zero point and more robust tails providing greater shrinkage on regression coefficients close to zero and lower shrinkage on regression coefficients away from zero. The prior density used in BayesA also has a higher density mass at the zero point and more robust tails than the normally used RR-BLUP. Bayesian Lasso has greater shrinkage on regression coefficients close to zero than BayesA. However, the distribution tails are similar between the two methods .The BayesA method implies a large number of markers with small effects or a few markers with moderate to large effects. BLasso implies a large number of markers with effects close to zero or a few markers with moderate to large effects. RR-BLUP implies a large number of markers with small effects.Machine-learning algorithms  have been successful in recognizing complex patterns and making correct decisions based on data. Machine learning is a science of creating and studying algorithms that improve their own behavior in an iterative manner by design . Recent Gene discovery or GWAS, which can be accomplished by the BayesCπ and BayesDπ methods , thus producing the BayesCπ and BayesDπ methods. The modeling of π is interesting in the association analysis. The majority of the markers are not in LD with the genes; therefore, a set of markers associated with a trait must be identified. In contrast, the BayesB method determines π subjectively. Using the indicator variable δi, the BayesCπ and BayesDπ methods model the additive genetic effect of individual j as i = . The distribution of δ= is binomial with a probability of π. This mixed model is more parsimonious than the BayesB method. According to the model hierarchy, a distribution must be postulated for π, and there must be a beta distribution, which when appropriately specified, becomes a uniform distribution   .xij are elements of the codominant marker genotype vector and are generally coded as 0, 1 or 2, depending on the number of copies of one of the alleles at the marker locus i, and βi is defined as the element of the vector of the regression coefficients, which includes the marker effects on a phenotypic trait y by means of the LD with the genes that control the trait  of the species, em is the number of independent chromosomal segments, Ne is the effective population size, and F is the inbreeding coefficient of the population. For a desired h2, and nQTL, N can be determined.Genomic data are especially useful for GS, which allows selection at the seedling stage to increase genetic gain in the adult stage. With a high density of markers, the expected squared accuracy of GS is given by Grattapaglia and Resende (2011)rgg equals GS accuracy, N is the number of individuals in the population, NQTL is the number of QTLs that control each trait, and h2 is the individual heritability. The estimate of the number of individuals that must be evaluated to obtain the desired accuracy can be obtained by the following expression, derived from the previous one, The reliability of GS is given by the expression gg2)h2 .2, NQTL, and rgg). Based on these graphs and the genetic information of the traits, breeders can adequately size their studies on inheritance and maximize genetic gain with the improvement made by selection.Various kinds of information can be obtained from NQTL can be estimated for several traits.From the first equation, the estimate of the number of QTLs that control each trait can be calculated based on the expression QTL, given the N and the estimated h2 while varying 2 equal to 0.30, and N equal to 1,500, the NQTL values can be inferred according to 2 equal to 0.20, and N equal to 1,500.A possible exercise is the theoretical determination of N2 = 0.30) and from 32 to 312 , when the accuracy varies from 0.95 to 0.70, respectively.Based on –5 according to the Z1–β are the values of the cumulative distribution function of the standard normal distribution, associated with the probabilities of error type I (α) and error type II (β) for bilateral hypothesis tests.The sample size (N), with power of detection at a significance level of 10The quantity (1−β) is the probability that the experiment will exhibit a statistically significant difference between the treatment averages. Values of 0.80 and 0.90 are common and appropriate in practice.2 <0.50). The power of 0.90 is more appropriate because it leads to an 81% = 0.902 probability that two independent studies will detect the same QTL.Urochloa spp.), Guinea grass (M. maximus) and elephant grass (C. purpureus) are very important and extensively used as pastures in tropical America, Asia, and sub-Saharan Africa.In TFG breeding, combining conventional breeding efforts and GS has not been a simple task. As opposed to advances in animal breeding and crop commodities, they have been slow and challenging in tropical forages. The number of candidate TFG species is high, and decisions about investments need to be made considering the effective benefits of GS, the potential profit that can be achieved by the new cultivars, and the real impact of new forage on livestock production. The three tropical genus/species brachiaria  reference  in GS for agronomic traits. Similar results were obtained by M. maximus in which >32k SNPs were classified as unique and used in GS, although, the maximum value of predictive ability using tetraploid dosage of 0.3955 was achieved for the trait organic matter that displayed secondary importance in forage breeding.Marker number and density are important factors influencing the efficient use of GS in TFG breeding. One of the reasons for the low accuracy of GS is the exceptionally low number of effective markers, which may result from a non-adequate reference genome. Before the 000 SNPs  and M. m322 SNPs . For C. eference . CompareBeadChip  and the BeadChip  are avaiUrochloa and M. maximus hybrid development programs.Current TFG breeding programs lack the important information that could improve and allow the efficient use of GS. Firstly, a major impact will be obtained by increasing the number of markers per genome size by sequencing and generating reference genomes for the target species or more closely related species. Secondly, we need to improve our knowledge about the inheritance of target traits in tropical forages including the genetic effects of biallelism in (auto) tetraploids. Thirdly, we need to work with training populations connected with validation and breeding populations and testing environments that must be correlated with the environment of the target population . FinallyM. maximus and Urochloa breeding programs generate thousands of hybrids annually, and those hybrids must pass through several steps of selection until they finally achieve the status for evaluation under animal feeding pressure to prove their value in animal production and be released as new cultivars. However, it is mandatory for hybrids to show apomixis and resistance/tolerance to spittlebugs (mostly in Urochloa) and diseases (mostly in M. maximus and C. purpureus). These traits are a great bottleneck slowing the subsequent evaluation steps in the breeding program since phenotyping of individuals demands significant labor, time (two or more years), and the dedication of trained technicians. As a result, only a small number of individuals can be evaluated annually reducing the rate of genetic gain. Methods such as GWAS and MAS may help to speed up the identification of individuals showing these important traits and increased rates of genetic gain. Recently published data on mapping genomic regions associated with apospory emphasize the routine application of markers for selection in Urochloa and Megathyrsus  using high-throughput phenotyping methods less expensive than genotyping by sequencing is an opportunity for tropical forage breeding.  maximus  as well Urochloa . Deep leUrochloa . NeverthUrochloa . AlthougUrochloa , high-thUrochloa .The availability of genome-wide, high-throughput, and cost-effective flexible markers, across the genome, suitable for large populations with or without a reference genome sequence, is the most important factor for the effective and efficient implementation of GS. Recent advances in long read quality and sequence throughput, in addition to other technologies such as Hi-C or optical maps, make it possible for virtually any research group with reasonable funding to obtain reference-grade genome assemblies for their crop of choice. While not necessarily easy, the generation of high-quality genome assemblies should be considered as a starting point for any orphan species that would benefit from the use of genomic tools for crop improvement. These assemblies could be extremely useful for resequencing and variant discovery, which can lead to genotyping platforms for association studies and GS. When coupled with well-designed and thoroughly phenotyped training populations, these genomic resources could serve as the basis for implementing GS steps in the breeding of TFGs.As discussed by Urochloa spp. and M. maximus. Performing inter- and intraspecific crosses with sexual plants in these genera increases the variability available for selection and allows the generation of genetic combinations not found in apomictic accessions. The spectrum of possibilities for GS expands considerably for these species; however, the identification of markers is narrowed to large-scale phenotyping and genotyping. The conformation of the discovery population should be carefully considered in terms of the number of hybrid families to be evaluated, the number of individuals per half-sib and full-sib families, and the distribution of markers on the chromosomes of the paternal and maternal genomes. The mother plants to be used in crosses should be exclusively sexual, so that they do not generate, in addition to hybrids, their own clones (by apomixis) in the progeny, which would cause an incorrect bias in the determination of GEBV and the identification of markers and their effects.Furthermore, the considerations stated by Finally, designing forage breeding programs, mainly for polyploid and apomictic grasses, and proposing breeding schemes that make optimum use of GS is a significant task for plant breeders. Although, this is a challenge, it is also a great opportunity to accelerate genetic gain in TFG breeding.All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.The authors declare that this review was written in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Uncovering the genetic architecture of economic traits in pigs is important for agricultural breeding. However, high-density haplotype reference panels are unavailable in most agricultural species, limiting accurate genotype imputation in large populations. Moreover, the infinitesimal model of quantitative traits implies that weak association signals tend to be spread across most of the genome, further complicating the genetic analysis. Hence, there is a need to develop new methods for sequencing large cohorts without large reference panels.ABCD4 for total teat number and HMGA1 for back fat thickness, and provided a starting point for further investigation. The inheritance models of the different traits varied greatly. Most follow the minor-polygene model, but this can be attributed to different reasons, such as the shaping of genetic architecture by artificial selection for this population and sufficiently interconnected minor gene regulatory networks.We describe a Tn5-based highly accurate, cost- and time-efficient, low-coverage sequencing method to obtain 11.3 million whole-genome single-nucleotide polymorphisms in 2,869 Duroc boars at a mean depth of 0.73×. On the basis of these single-nucleotide polymorphisms, a genome-wide association study was performed, resulting in 14 quantitative trait loci (QTLs) for 7 of 21 important agricultural traits in pigs. These QTLs harbour genes, such as Genome-wide association study results for 21 important agricultural traits identified 14 QTLs/genes and showed their genetic architectures, providing guidance for genetic improvement harnessing genomic features. The Tn5-based low-coverage sequencing method can be applied to large-scale genome studies for any species without a good reference panel and can be used for agricultural breeding. Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with complex traits in humans and agricultural species , 2. The Low-coverage sequencing (LCS) of a large cohort has been proposed to be more informative than sequencing fewer individuals at a higher coverage rate . Sample Several large-scale WGS projects have been completed . These pIn this study, we developed a new highly accurate, cost- and time-efficient LCS method to obtain high-density single-nucleotide polymorphism (SNP) markers for a large Duroc pig population . By asseA Tn5-based protocol was used to prepare sequencing libraries of each pig at a low cost (reagent cost: $2.60/library) as described in the Methods section. The libraries were sequenced on the Illumina  and the BGI platform  . The resde novo assembly) , the 948 Program of the Ministry of Agriculture of China (2012-G1(4)), the Science and Technology Innovation Strategy Projects of Guangdong Province [2019B020203002], and the Guangdong Academician Workstation [2011A090700016].X.H., N.L.: conceptualization. X.H., N.L., Y.W., and Z.W.: project administration and supervision. X.H., Y.W., D.Z., X.G., J.R., Z.H., C.B., and R.Y.: methodology, investigation, and formal analysis. R.Y., D.Z., X.G., and Y.W.: data curation and validation. Z.W., G.C., D.L., and C.T.: resources. X.H. and Z.W.: funding acquisition. Y.W. and R.Y.: visualization and original draft preparation. Y.W., X.H., Y.Z., G.C., and D.L.: review and editing.


Fisher’s partitioning of genotypic values and genetic variance is highly relevant in the current era of genome-wide association studies (GWASs). However, despite being more than a century old, a number of persistent misconceptions related to nonadditive genetic effects remain. We developed a user-friendly web tool, the Falconer ShinyApp, to show how the combination of gene action and allele frequencies at causal loci translate to genetic variance and genetic variance components for a complex trait. The app can be used to demonstrate the relationship between a SNP effect size estimated from GWAS and the variation the SNP generates in the population, i.e., how locus-specific effects lead to individual differences in traits. In addition, it can also be used to demonstrate how within and between locus interactions  usually do not lead to a large amount of nonadditive variance relative to additive variance, and therefore, that these interactions usually do not explain individual differences in a population. It is generally agreed that the theoretical foundation of quantitative (complex) trait genetics was the 1918 paper from RA Fisher . FalconeAlthough Fisher’s variance decomposition is more than a century old, it is highly relevant today because we now have the genomic tools to identify individual trait loci, in particular through the experimental design of the genome-wide association study (GWAS). GWAS essentially uses Fisher’s  method oHowever, we and others have found that the concepts that link gene–gene interactions (dominance within a locus and epistasis between loci) with genetic variation and thereby individual differences in a population remain confusing and misunderstood. Here, we present an R ShinyApp for use as a tool for teaching and learning quantitative genetics. We named it the Falconer ShinyApp in memory of Douglas Falconer and his tremendous contribution to the field of quantitative genetics .In the Falconer ShinyApp, we illustrate Chapters 7 and 8 of Falconer and Mackay  as well 1 and A2 at frequency p and 1-p, respectively. Under panmixia  and Hardy–Weinberg equilibrium, the expected genotype frequencies are (1−p)2,2p(1−p) and p2, for A2A2, A1A2 and A1A1, respectively. We arbitrarily assign trait values -a, d, and a to the 3 genotypes, d representing the dominance effect  and 2a the difference between the 2 homozygotes. Under this model, the population mean is M = (2p−1)a+2p(1−p)d , where there is a perfect linear relationship between genotypic value and allelic dosage, the relationship between genotypic values and allelic dosage is nonlinear. Fisher used a linear model to derive the least squares linear relationship between genotypic value and allelic dosage and thereby partition of genotypic values of traits in terms of expected values under pure additivity  and deviations from this model due to the within locus interaction (dominance). The slope of the linear regression of the trait genotype means, weighted by their frequency, on A1 allelic dosage  is the average effect of allelic substitution at a locus :We first consider a single locus model with alleles Aa) and the dominance value d, as does the additive variance (see below). The residuals of the linear regression are the deviations due to the within locus interaction (dominance). Fisher [VG) of this model asVA as the variance of the additive (breeding) values, which is known as the additive variance, and VD as the dominance variance. VA is the variance due to the regression of genotype means onto allele dosage and is given as VA = 2p(1−p)α2 = Hα2, with H being the heterozygosity under Hardy–Weinberg equilibrium of the genotype frequencies. Notably, VA includes contributions from dominance effects  when p≠0.5. Similarly, the dominance variance due to within locus interaction is the variance of the residuals of the linear regression, VD = (2p(1−p)d)2 = H2d2. Therefore, the dominance variance disproportionally depends on the locus heterozygosity compared to the additive variance (H2 versus H) and reaches its maximum at p = 0.5 where dominance deviations are not captured by the linear regression and do not contribute to α (Eq 1). In summary, the additive genetic variance VA is the regression variance, and VD is the residual variance from a regression of genotypic mean trait value on allelic dosage.The average effect depends both on half of the difference between the genotypic values of the 2 homozygotes  of reference alleles at a given locus, i.e., the allelic “dosage,” where the reference allele for this dosage count is arbitrarily the major or minor allele (but this arbitrary choice is reflected in the sign of the regression coefficient β): y = μ+βx+e, where the residuals e include both the nonadditive genetic effects at the locus, the genetic effects (additive and nonadditive) at other loci, and an environmental and/or chance (nongenetic) effect. The quantity of interest is the slope β of the model (the effect size of the locus), which is the average effect of allele substitution, hence β = α, because the expected phenotypic value of a genotype is its expected genotypic value, under the assumption of independence between genetic and environmental effects. Hence, performing a regression of phenotype on allelic dosage at, for example, a SNP marker, as routinely done in GWAS, is equivalent to estimating the average effect size, and the regression variance is the additive genetic variance due to the locus.When performing a GWAS, individual phenotypes y = 0 or y = 1), GWAS analysis is often performed using logistic regression, so that β and the regression variance are on an underlying logistic scale. Note that a nonlinear transformation between the observed (0 and 1) and underlying continuous scale implies that absence of dominance variance on one scale  does not imply absence on the other scale.For noncontinuous trait and GWAS, the same model as above can be used on either the actual scale of the trait measurement or on a transformed scale. For example, for binary disease traits  and dominance (VD) genetic variance as well as the proportion of total genetic variance explained by the additive variance (VA/VG) as a function of the arbitrarily assigned genotypic values a and d.In the Falconer ShinyApp, we let the user choose the arbitrarily assigned genotypic values by specifying 1 allele dominant over the recessive allele A2. We arbitrarily assign genotypic values a = 4 and d = 4. In this example, the distributions of the additive, dominance, and total genotypic variance, as well as the ratio VA/VG, are shown in Fig 1. It shows that the contribution of additive variance to the total genotypic variance (VA/VG) increases when the frequency p of the dominant allele decreases, with VA/VG→1 for p→0. It also shows that VA (and VG) is much higher when the dominant allele is at low frequency  than VD (and VG) when the dominant allele is at higher frequency .In a simple numerical example, we consider a locus with complete dominance and the Ad = 0 at both loci). We introduce a second (unlinked) locus with alleles B1 and B2 and frequencies q and 1-q, respectively. The genotypic values and frequencies of the 9 genotypes are described in Table 1, where aAB is the additive-by-additive interaction effect.We extend the 1-locus to a 2-locus model with additive and additive-by-additive epistatic interaction only, assuming no within loci dominance effects  as well as the additive-by-additive effect and the allele frequency of the interacting locus. In this model, the total genotypic variance (VG) is partitioned in additive (VA) and additive-by-additive variance Hi is the frequency of heterozygote genotype at locus i , αi the average effect at locus i, and the additive-by-additive varianceTherefore, the average effect at each locus depends on half of the difference between the genotypic values of the homozygotes . Hence, it illustrates the departure from the additive model (aAB = 0) when additive-by-additive interactions are present . We use a graphical representation[VA), additive-by-additive (VAA), and proportion of genotypic variance explained by additive variance (VA/VG) as a function of the allele frequencies p and q given the genotypic values.In the Falconer ShinyApp, the user chooses the allele frequencies p and q). The genotypic values as well as the linear regressions are plotted as a function of the A1 allelic dosage for the different genotypes at locus B, and so does the linear regression of the genotypic values, weighted by their frequency on the A1 allele dosage. The total genotypic variance (VG) of this model is then partitioned in 5 components:VAD is the additive-by-dominance variance  and VDD the dominance-by-dominance variance (due to the interaction between the dominance deviations at the 2 loci). Definitions and derivations of these and higher-order interaction components were given by Cockerham [In the previous models, we illustrated the effect of within and between loci interaction on the average effect and additive variance. Lastly, we propose a generalized 2-locus model where the user can provide all the genotypic values in an interactive table and choose the allele frequencies at the 2 (unlinked) loci . Shull [Table 2) where genotypic values are c except for the double recessive homozygote which has value 0. In this highly epistatic model and as described by Hill and colleagues [VA/VG→1 when allele frequencies p,q→0. Choosing c = 4 and p = q = 0.5 , the total genotypic variance is then partitioned asAs numerical examples, we will consider 2 classical epistatic models that involve all nonadditive components. The first example is the 2-locus duplicate factor model, such as described by Shull  when he ). Shull  found thlleagues , we expeVA/VG = 0.27, in accordance with theoretical expectation [Leading to ectation .Lathyrus odoratus) studied by Bateson and colleagues [Table 3), we chose c = 4 and p = q = 0.5 , resulting in a partitioning of the total genotypic varianceA second classical example of epistasis is the complementary model of flower color in sweet pea , hence where all genetic variation is nonadditive. In such cases, an additive model  will fail to capture any genetic variation. That said, very little evidence for nonadditive genetic variation have been found in human traits when analyzing a broad range of phenotypes [There are special cases (at least in theory) where there is no additive variance (enotypes –17.Eqs 2).Despite the theory being more than a century old, persistent misconceptions related to gene interactions effects remain. One common misunderstanding is that models that estimate additive effects of alleles or estimate additive variance assume that there are no gene interactions, which is not correct. Indeed, an additive model does not fit nonadditive effects explicitly; however, the average effect that is estimated is a function of nonadditive effects .The Falconer ShinyApp is accessible using web browsers at


Background: Observational studies have implied an association between polycystic ovary syndrome (PCOS) and psychiatric disorders. Here we examined whether PCOS might contribute causally to such disorders, focusing on anxiety disorder (AD), bipolar disorder (BIP), major depression disorder (MDD), obsessive compulsive disorder (OCD), and schizophrenia (SCZ).Methods: Causality was explored using two-sample Mendelian randomization (MR) with genetic variants as instrumental variables. The genetic variants were from summary data of genome-wide association studies in European populations. First, potential causal effects of PCOS on each psychiatric disorder were evaluated, and then potential reverse causality was also assessed once PCOS was found to be causally associated with any psychiatric disorder. Causal effects were explored using inverse variance weighting, MR-Egger analysis, simulation extrapolation, and weighted median analysis.Results: Genetically predicted PCOS was positively associated with OCD based on inverse variance weighting , simulation extrapolation  and weighted median analysis . However, genetically predicted OCD was not associated with PCOS. Genetically predicted PCOS did not exert causal effects on AD, BIP, MDD, or SCZ.Conclusions: In European populations, PCOS may be a causal factor in OCD, but not AD, BIP, MDD, or SCZ. Polycystic ovary syndrome (PCOS) affects 5–15% of women of reproductive age, making it one of the most common endocrine disorders in that group. It is characterized mainly by hirsutism, elevated serum testosterone, oligo-/amenorrhea, and polycystic ovaries , bipolar disorder (BIP), major depression disorder (MDD), obsessive compulsive disorder (OCD), and schizophrenia (SCZ) , which relies on genetic variants as instrumental variables (IVs) to evaluate causality between an exposure and an outcome  in order to examine potential causal associations of PCOS with five common psychiatric disorders: AD, BIP, MDD, OCD, and SCZ.https://doi.org/10.17863/CAM.27720), while GWAS data for AD, BIP, MDD, OCD, and SCZ were taken from the Psychiatric Genomics Consortium (https://www.med.unc.edu/pgc/results-and-downloads) (GWAS data for PCOS were taken from Apollo (wnloads) . All subThe original articles that published GWAS exposure and outcome data were obtained to retrieve detailed information about study design and sample collection. Participants recruited from the same consortium or hospital in the exposure and outcome studies were regarded as duplicates. The maximized overlap was calculated as n/N, where n referred to the number of potentially repetitive recruiters, and N to the total sample number in the larger dataset  was performed to exclude linkage disequilibrium (LD) between the SNPs. Among SNP-shaving LD, only those with the lowest p-values were retained. Third, SNPs related to a confounder-associated phenotype were removed. The potentially related phenotypes were detected using the online database “PhenoScanner” (www.phenoscanner.medschl.cam.ac.uk/phenoscanner), by filtration of r2 > 0.8 and p < 5 × 10−8.Several quality control steps were conducted to select eligible SNPs as IVs from the exposure data. First, SNPs had to meet genome-wide significance, defined as r2 > 0.8, MAF for palindromes <0.3) with the requested one. Second, the exposure and outcome data were harmonized to ensure that the effect of the SNP was on the same allele. Otherwise, the SNP was deleted.Before statistical analysis of causal relationships, we ensured that GWAS exposure and outcome data matched well. First, information about exposure-associated SNPs was extracted from each outcome dataset. Any exposure-associated SNP absent from the outcome dataset was substituted with a proxy SNP; that is, if it existed, and it was in LD  correction was performed  analysis assumed no or balanced pleiotropy. We used the random-effects model to avoid heterogeneity bias, which was measured using Cochran's Q test. The MR-Egger method not only allowed for, but also detected, horizontal pleiotropy based on its intercept with a y-axis. When the intercept was not zero, there was horizontal pleiotropy. The MR-Egger method was based on the “instrument strength independent of the direct effects” (INSIDE) and “no measurement error in the SNP exposure effects” (NOME) assumptions, and it also used the random-effects model. In addition, when the regression dilution Fourth, SNP pleiotropy and sensitivity were assessed using pleiotropy tests, forest plots, funnel plots, and leave-one-out plots. The forest plot estimated the causal effect of each SNP on the outcome by using Wald ratio analysis. The Funnel plot was used to assess heterogeneity by depicting the reciprocal of the se of the SNP against SNP effects on the outcome. The leave-one-out plot ascertained whether an association was disproportionately influenced by a single SNP. In such a plot, each black point represented the IVW analysis after exclusion of that particular SNP.We investigated whether PCOS-SNPs could induce major mental illness , so the direction of MR analysis was defined as forward when PCOS was the exposure and psychiatric disorders were the outcomes. When PCOS was found to be causally associated with any outcome, reverse MR analysis was performed, in which the precise psychiatric disorder was the exposure and PCOS was the outcome. This allowed us to eliminate bias due to reverse causation.p < 0.05. In the case of multiple testing, the threshold for statistical significance was adjusted by the conservative Bonferroni correction according to the formula p < 0.05/n, where n referred to the number of MR tests. Since the present study included five forward and one reverse two-sample MR analyses, the adjusted p-values for the forward and reverse MR tests were, respectively, 0.01 (0.05/5) and 0.05 (0.05/1). When a p-value for an association was below the adjusted cut-off value, the association was considered statistically significant as a causal association. When a p-value was below 0.05 but equal to or greater than the adjusted cut-off value, the association was considered one of potential causality needing further confirmation. When a p-value was equal to or >0.05, it was considered not to be causal.Analyses were conducted using the “sqldf,” “biomaRt,” “TwoSampleMR,” “MendelianRandomization,” or “simex” modules in the R package (version 4.0.3). In general, statistical significance was defined as Ethics approval was not required since the data were published GWAS summary statistics from public databases.Two-sample MR analysis requires that the exposure and outcome studies be conducted in two independent, non-overlapping cohorts from the same population. High participant overlap can increase type I error, biasing the MR results  and eliminating SNPs in LD , SIMEX  and WM . The causal estimates from the three methods were consistent in direction and magnitude, which is unlikely to be a coincidence. In addition, no significant heterogeneity was detected by Cochran's Q statistic in the IVW analysis  or MR-Egger analysis , and no significant horizontal pleiotropy was detected based on the SIMEX intercept . The funnel plot showed symmetric distribution, further validating the absence of heterogeneity. The leave-one-out plot showed that excluding any single SNP from the IVs did not substantially alter the results. This suggests that the association between PCOS and OCD was not driven by any single SNP and is therefore likely to be reliable.Genetically predicted PCOS was positively associated with OCD according to models based on random-effect IVW , so we relaxed the threshold to p < 5 × 10−6, leading to a set of 15 independent SNPs as IVs (I2 of the MR-Egger method was 98.8% (>90%), so the results were not corrected using SIMEX.To eliminate the bias of reverse causation, the causal effect from OCD to PCOS was assessed , 2. No Ss as IVs . The SNPp = 0.929), MR-Egger  or WM . We found no evidence of significant heterogeneity or horizontal pleiotropy that might bias the results, and no single SNP strongly drove the overall effect. We conclude that the relationship between PCOS and OCD is not likely to be biased by reverse causation.Genetically predicted OCD showed no association with PCOS based on models involving random-effect IVW  and their OCD symptoms were more severe , highlights the neuroendocrinal role in PCOS etiology , compulsions (repetitive behaviors), or both. OCD appears to involve the cortico-striato-thalamo-cortical (CSTC) circuit, as well as the fronto-limbic, fronto-parietal, and cerebellar networks , which is expressed in GABAergic interneurons but also in midbrain dopaminergic neurons, where it regulates dopamine levels by binding to neuregulin 1 (NRG1)  of 0.22 with BIP, 0.21 with MDD, and 0.35 with SCZ  , BIP , MDD , and SCZ  reported in observational studies  can be found in the article/Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent for participation was not required for this study in accordance with the national legislation and the institutional requirements.LJ designed the study. LJ, JY, YC, and HP acquired and analyzed the data. LJ and JY drafted the manuscript. JS and HH obtained funding and revised the manuscript. All authors reviewed, contributed to, 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.


The phenomic predictive ability depends on the genetic architecture of the target trait, being high for complex traits and low for traits with major QTL.Genomic selection is a powerful tool to assist breeding of complex traits, but a limitation is the costs required for genotyping. Recently, phenomic selection has been suggested, which uses spectral data instead of molecular markers as predictors. It was shown to be competitive with genomic prediction, as it achieved predictive abilities as high or even higher than its genomic counterpart. The objective of this study was to evaluate the performance of phenomic prediction for triticale and the dependency of the predictive ability on the genetic architecture of the target trait. We found that for traits with a complex genetic architecture, like grain yield, phenomic prediction with NIRS data as predictors achieved high predictive abilities and performed better than genomic prediction. By contrast, for mono- or oligogenic traits, for example, yellow rust, marker-based approaches achieved high predictive abilities, while those of phenomic prediction were very low. Compared with molecular markers, the predictive ability obtained using NIRS data was more robust to varying degrees of genetic relatedness between the training and prediction set. Moreover, for grain yield, smaller training sets were required to achieve a similar predictive ability for phenomic prediction than for genomic prediction. In addition, our results illustrate the potential of using field-based spectral data for phenomic prediction. Overall, our result confirmed phenomic prediction as an efficient approach to improve the selection gain for complex traits in plant breeding.The online version contains supplementary material available at 10.1007/s00122-021-03997-7. Selection approaches in plant breeding have seen a rapid development with the decreasing costs of molecular marker data  is a man-made cross between wheat and rye, and is extensively used for animal feed and bioenergy  and two doubled haploid populations, DH1 (n = 180) and DH2 (n = 190). Our objectives were to (1) compare the predictive abilities of phenomic prediction and genomic prediction for yield, yield-related traits and disease resistance traits, (2) investigate the phenomic predictive ability using NIRS data from a single environment to predict trait performance at another environment, (3) evaluate the predictive ability across material groups, and (4) assess the effect of the training set size on the predictive ability. Collectively, our results confirmed phenomic prediction as a valuable tool for the selection of complex traits in plant breeding programs.Phenomic prediction is still in its infancy compared to genomic prediction and advantages as well as possible limitations for its utilization in breeding need to be further evaluated. The small-grain cereal triticale  design was used for both trials, with a replication rate of 1.3 in trial 1 and 1.2 in trial 2. As for the observation plots, both trial 1 and trial 2 were grown in 2015 at three locations. Each plot consisted of three rows of length 1.25 m and spacing at 0.17 m between rows. All genotypes in both trials were evaluated in a randomized incomplete block design with two replications. The observation plots were not treated with fungicides to enable disease scorings.For the field trials, we used yield plots and observation plots to evaluate yield and yield-related traits or disease resistance traits, respectively. The total of 1280 triticale genotypes were divided into two trials: trial 1 with 800 lines and trial 2 with 500 lines, with 20 common genotypes as checks (Table S1). The yield plots of trial 1 were evaluated in 2014 and 2015 and trial 2 in 2015 at five locations in southern Germany. The size of the yield plots varied among the locations, ranging from 5 to 10.5 mThe five traits grain yield, thousand-kernel weight, plant height, powdery mildew, and yellow rust were used in this study. The yield plots were harvested and grain yield was calculated at a moisture content of 14%. Thousand-kernel weight was evaluated by a MARVIN seed analyzer (GTA Sensorik GmbH). Plant height was evaluated in the yield plots and the observation plots, by measuring the height after flowering from the ground to the tip of the ears, excluding awns. Powdery mildew and yellow leaf rust infestation was scored in the field on a 1  to 9 (completely infected) scale.n = 129; advanced breeding lines, n = 717; 787 in trial 1 and 79 in trial 2 with 20 common genotypes) and two doubled haploid populations, DH1  and DH2 .In the end, 1216 genotypes were used for further analysis since these genotypes had genotypic data available. These consisted of 846 lines from the diversity panel  was modified by removing the environment term:Some environments only had one trial, e.g., all five locations in 2014, and thus a simpler statistical model without trial factor was used:ith genotype, estimated by a model treating ith genotype, Heritability was estimated by the regression approach described in Schmidt et al. , as \docNear-infrared spectroscopy (NIRS) data were obtained from five locations in both 2014 and 2015, except MSB and FCA for trial 1 in 2015 (Table S1). After harvesting, the grains were dried to a uniform moisture content of approximately 14% and then analyzed using a stationary NIRS instrument . Intensity of reflectance was measured for each wavelength in the spectral range from 1200 to 2400 nm with a step size of 1 nm. Note that in contrast to marker data where we have two genotypic classes (or three if heterozygotes are present) at each marker, for NIRS data, we have a continuous distribution of the reflectance values at each wavelength and thus many different states Fig.  and the Hyperspectral imaging data were collected at some locations in 2014 and 2015 at one to three time points (Table S1). In 2014, hyperspectral data consisted of 250 wavelengths ranging from 976.1 to 1689.4 nm with a width of around 2.9 nm  obtained by the BreedVision platform  at Diversity Arrays Technology Pty. Ltd. Quality checks were performed separately in the diversity panel and the DH1 and DH2 populations. For the diversity panel, markers with a missing rate higher than 0.2 or a minor allele frequency (MAF) lower than 0.03 were discarded. Imputation was performed with LinkImpute  of 4 was chosen and the explained phenotypic variance (R2) was calculated by fitting all significant markers in the order of their strength together in a joint model. Markers with R2 above eight percent were selected as major QTL and used in further analysis.Genome-wide association analysis was performed separately within the diversity panel, DH1, and DH2. Marker data were filtered for MAF of 0.05 for the diversity panel and 0.2 for the DH1 and DH2 populations. The mixed linear model (MLM) approach including a kinship matrix was used for analysis using Tassel 5  was used as implemented in the R package ‘rrBLUP’  with 846, 180, and 190 lines, respectively. All lines were evaluated for grain yield, thousand-kernel weight, plant height, powdery mildew, and yellow rust in multi-environment field trials .The raw NIRS data were obtained from harvested and dried seeds and showed substantial variation Fig. a. The heWe used the NIRS data as predictors for phenomic prediction and compared the predictive abilities of the five traits in each group with those obtained by genomic prediction Fig. a. For grThis prompted us to investigate the genetic architecture of these traits. QTL explaining more than 8% of the phenotypic variance were declared as medium- to major-effect QTL and used to assess their predictive ability Fig. a.In addition, we used these QTL as fixed effects in the prediction model together with either NIRS data or marker data as random effect to construct two weighted models and compared their performance with the fully random models. The model incorporating QTL and marker always achieved the highest predictive ability among all models . Apart from exceptions like yellow rust in DH2, the inclusion of QTL improved the phenomic and genomic predictive abilities only slightly.These findings substantiated the potential of phenomic prediction especially for complex traits like grain yield. We therefore investigated the predictive ability of NIRS data for grain yield in the diversity panel, when the NIRS and the trait values are derived from different environments. As a reference, the phenomic predictive ability obtained by cross-validation within the respective environment can be used, and in addition, the results from genomic prediction are shown for comparison Fig. . For theThe genetic relatedness between the training set and the prediction set is a key factor for the success of genomic prediction in plant breeding Below is the link to the electronic supplementary material.


Genomic prediction in crop breeding is hindered by modeling on limited phenotypic traits. We propose an integrative multi-trait breeding strategy via machine learning algorithm, target-oriented prioritization (TOP). Using a large hybrid maize population, we demonstrate that the accuracy for identifying a candidate that is phenotypically closest to an ideotype, or target variety, achieves up to 91%. The strength of TOP is enhanced when omics level traits are included. We show that TOP enables selection of inbreds or hybrids that outperform existing commercial varieties. It improves multiple traits and accurately identifies improved candidates for new varieties, which will greatly influence breeding.The online version contains supplementary material available at 10.1186/s13059-022-02650-w. The likelihood of reduced yields of major food crops due to the changing climate continues to rise, as does the global population, thus making the development of genetically improved, climate-resilient crops a research priority –3. ConveGenomics, phenomics, and analytics technologies are powerful tools to boost breeding progress , 8. JoinSelecting individuals that are higher yielding, resistant to stress and disease, or otherwise more attractive is of extreme consequence in plant breeding and has been since the first farmers began the process of plant domestication . One sigWe applied omics and machine learning towards the goal of correctly identifying the best breeding candidates. Post-genomics technologies including transcriptomes, proteomics, and metabolomics offer mechanistic links between genotype and phenotype . TogetheHere we present an integrative multi-trait breeding strategy that incorporates agronomic and omics traits (transcriptomes and metabolomes) to predict the best performing candidates to create new varieties through a machine learning algorithm. This algorithm, called target-oriented prioritization (TOP), learns the inherent correlations among traits in a training population, balances the selection of multiple traits simultaneously, and predicts the degree of similarity between an untested genotype and a target, which can be a current commercial variety Fig. A. We exa1 hybrids with 156,269 SNPs (see the “Methods” section). The maize NCII population consists of 194 maternal inbred lines and 30 paternal lines originating from different heterotic groups. Genomic prediction was conducted with a training set composed of hybrids in the leading diagonal line of the NCII mating scheme  but showed a significant loss of ear weight   learning multi-trait similarity between genomic-predicted and field-observed values for obtaining optimal weights, which represent the balanced status of individual traits in maximizing the overall performance and similarity to the ideotype, and (2) predicting the multi-trait similarity between predicted objects (inbreds or hybrids) and a target . Two of the datasets were association panels, including 368 diverse inbred lines from China and 282 diverse inbred lines from the US, called Maize368 and Maize282, respectively. The other was a rice bi-parental population with 210 recombinant inbred lines (Rice210).P=1.35E−25; Fig. P=2.66E−7; Fig. P=3.36E−216; Fig. Maize368 were genotyped with 1.25M SNPs and phenotyped for 17 agronomic traits, 88 transcriptomic traits, and 24 metabolic traits. To validate the ability of the machine learning algorithm to select superior breeding candidates in this dataset, we performed TOP with agronomic traits first, then adding transcriptomic traits, and then further adding metabolic traits. We found that TOP’s identification rate significantly increased after adding transcriptomic traits (r). Indeed, by keeping predictable traits only (r>0.5), the identification rate in Maize368 significantly increased across all pool sizes (P=1.48E−20). In particular, a nearly 2-fold accuracy increase occurred in the largest pool of 80 individuals  that are improved versions of certain traits. We chose Zhengdan958 as the model variety as it is an elite commercial maize hybrid and has been widely grown in the Chinese Corn Belt in the past decades [A segregating maize NCII population with 5251 F decades . Two verTOP was run to identify the 100 hybrids most similar to the Zhengdan958 early version target in the Maize NCII population. Of these, 89 hybrids were found to actually flower earlier than Zhengdan958 , and one with a 5% increase (late and high). As a control, Zhengdan958 was itself again included in the testing set as a target. We found that the hybrids selected by TOP were phenotypically highly similar to the target for multiple traits. More specifically, when hybrids were randomly selected, only 11% of them fell into the domain of early flowering and short plants and 46% into the domain of late flowering and tall plants. In contrast, TOP increased these percentages to 54% and 80%, respectively  as check lines. We accordingly created the 86 hybrids and tested the field performance of three traits compared to check lines. The field data demonstrated over a quarter of predictive F1 had superior ear weight while kept relatively stable or even early flowering time and lower plant height compared to the check lines , while maintaining relatively stable flowering time and plant height (within ±5%). The variety “Jingke968” has the characteristics of high ear weight and tall plant height. We still found four hybrids had superior performance than Jingke968 in simultaneously ear weight, flowering time, and plant height. These hybrid combinations showed the potential for maize yield breeding programs by balancing and simultaneously improving early maturity and logging resistance.Early maturity, short plant height, and high yield are the crucial goal in maize breeding. We tried using our algorithm to assist design hybrid combinations. We previously systematically predicted three traits  of 34,188 potential hybrids with 1221 maternal lines and 28 paternal lines that had not been actually created . Based oGenomic selection is a useful approach to predict trait performance in large populations . This apP<0.01), and the selection of earlier flowering than Zhengdan958 is likely due to the higher frequency of the early allele of the VGT1 gene  to first learn the similarity between genomic-predicted values and measured phenotypic values and then to predict the degree of similarity between inbreds or hybrids and the target with respect to hundreds of traits. This strategy resulted in high identification accuracy in a maize NCII population, two maize association panels, and one rice recombinant inbred line population, suggesting robustness and reliability of this strategy for identifying target candidates. TOP was also used to improve an existing commercial variety for key traits. The resulting hybrids selected by TOP not only retained the favorable characteristics of the commercial variety, but improved on unfavorable aspects. For instance, we found the 100 candidates selected for the early Zhengdan958 target significantly enriched two major haplotypes compared to random selection  population [1 hybrids for analysis. Missing genotypes in the hybrids due to heterozygosity of either parent was imputed using Beagle V4.0 [The maize NCII population includes 5820 Fpulation  and 30 dpulation . We usedpulation  to filtegle V4.0 .1 hybrids were grown in five locations in 2015 for phenotype collection. A total of 18 agronomic traits were measured and include flowering traits , plant architecture traits  and yield traits . The measurements of these traits followed standard procedures described previously [The 5820 Feviously . The besThe Maize368 dataset consists of 368 maize inbred lines from a widely used maize association mapping panel . The 368The Maize282 dataset consists of 282 maize inbred lines from a US maize association mapping panel . All inbThe Rice210 dataset is comprised of 210 recombinant inbred lines created from crossing between two rice varieties Zhenshan 97 and Minghui 63 . A totaly = Xb + Zμ + ε, with y is an n × 1 vector of phenotypic values of a quantitative trait for n individuals; X is an n × p design matrix; b is a p × 1 vector of fixed effects, Z is an n × n design matrix; μ is an n × 1 vector of random effects representing individual genetic values with the variance-covariance matrix K, also known as genomic relationship matrix estimated by the software GEMMA [ε is an n × 1 vector of residual errors; I is an identity matrix; and μ = KV−1(y − Xb), where b = (XTV−1X)−1(XTV−1y), and r) between predicted and observed values was used to measure the prediction accuracy.The genomic best linear unbiased prediction (GBLUP) approach based on a mixed linear model was used for trait predictions. The formula is expressed as: re GEMMA ; ε is an“rrBLUP”  and the For testing the TOP algorithm, the whole population (5820 hybrids) was divided into training and testing set. The algorithm required predicted and measured trait values for the same individuals for learning model and testing performance. First, the training set of 569 hybrids was used train the GBLUP model for predicting the testing set. Second, to obtain the predicted trait values of the training set, we further divided 569 hybrids into 10 parts; for any one part of hybrids, the predicted values can be obtained by training the GBLUP model in the remaining 9 parts; ten rounds of iterations enabled to generate all predictions in the 569 hybrids.Target-oriented prioritization (TOP) is a flexible machine learning algorithm that integrates predictions of multiple traits for identifying a breeding candidate with maximized similarity to a target entry (hybrid maize in this study). TOP was implemented using the following steps: (1) in the training population, a similarity function was used to connect the predicted and measured traits for each individual; (2) through machine learning in the training population, the optimal weights of multiple traits were obtained, indicating the importance of individual traits in maximizing the similarity; and (3) in the testing population, the individuals that were the most similar phenotypically to a target were selected based on the degree of similarity, calculated with genomic-predicted phenotypes, observed phenotypes of the target entry, and optimal weights learned in the training population.N0 individuals, where N0 is from 20 to all individuals in the testing population. From the pool of N0 individuals, a randomly picked individual was defined to be the target (O1), the phenotypes across multiple traits of O1 were compared with a given individual (O2) from N0 individuals. If TOP identified O2 as a candidate based on the highest degree of similarity between genomic-predicted phenotypes with observed phenotypes of the O1 target, and the O2 is exactly the same to the O1, identification was successful. Because the target O1 was picked randomly from the pool of N0 individuals, we ran the identification procedure N0 times by considering each individual from the pool as an O1. The identification rate is the proportion of successful identifications of O2  and was defined as the accuracy of TOP.To validate the reliability of the TOP algorithm, we split the testing population into many pools, each comprised of A similarity function between multi-trait predicted and observed values was defined and learned in the training population. The similarity function was expressed as:i in the individual n, d is trait number, N is the training population size, and wi is the weight for the trait i. For omics data, traits here refer to the principal components that retain most (>80%) of the variation presented in the original transcriptomic or metabolic features.where The optimal weights of multiple traits were obtained by maximizing the likelihood function  problem , with inIn the testing population, the similarity degree was defined by the above similarity function in the training population, denoted by Y is the observed value of a given target; n in the testing population.where Rn is an n-dimensional Euclidean space and f : Rn → R. The iterative formula for the quasi-Newton methods is defined as: xk + 1 = xk + αkdk, αk is the step size, dk is the search direction, gk is the gradient of f at xk, and Bk is an approximation of Hesssian of f at xk. The computation of BFGS algorithm is described as follows:The BFGS method is one of the quasi-Newton methods that are well-known methods in solving unconstrained optimization problems. In general, the unconstrained optimization problems are described as follows: x0 and B0 = In.Step 1. Given a starting point gk‖<10−6.Step 2. Terminate if ‖Step 3. Calculate αk by a line search.Step 4. Calculate sk = xk + 1 − xk and yk = gk + 1 − gk.Step 5. Compute xk + 1 = xk + αkdk, Step 6. Calculate L(w)) be the above function f, then the optimal weight w can be obtained using the BFGS method.In this paper, let − ln vector of desired genetic gains, G∗ is an n × m matrix which is derived from additive genetic variance-covariance matrix G by keeping the m columns for the traits that appeared in Q. Then economic values can be calculated by a = G−1pb.where Q: i) a 5 % reduction in DTT (Days to tassel), a 5 % reduction in PH (Plant height), a 5 % increase in ERN (Ear row number), and a 5 % increase in TL (Tassel length); ii) a 5 % reduction in DTT, a 5 % reduction in PH, a 10 % increase in ERN, and a 5 % increase in TL; iii) a 10 % reduction in DTT, a 15 % reduction in PH, a 20 % increase in ERN, and a 5 % increase in TL. Hence, three scenarios of weights on economic value obtained corresponding to Index1, Index2, and Index3.In this paper, we set three scenarios for Take the ERN trait for example, if the trait value of a select hybrid is 0.5 times the standard deviation larger than the ERN mean value of the testing population, the selection is considered a success for the above two methods. For the TOP method, if the difference between the trait value of a select hybrid and the corresponding trait value of the target less than 0.5 times the standard deviation, the selection is considered a success. The selection performance of the three methods is defined as the number of successes divided by the selection number denoted by NS (NS=100).We previously systematically predicted three traits  of 34,188 potential hybrids with 1221 maternal lines and 28 paternal lines, using the GBLUP model trained in 8632 hybrids . Based oAdditional file 1. Figures S1-S11.Additional file 2. Target-Oriented Prioritization (TOP) tutorial.Additional file 3. Review history.


Ongoing increases in the size of human genotype and phenotype collections offer the promise of improved understanding of the genetics of complex diseases. In addition to the biological insights that can be gained from the nature of the variants that contribute to the genetic component of complex trait variability, these data bring forward the prospect of predicting complex traits and the risk of complex genetic diseases from genotype data. Here we show that advances in phenotype prediction can be applied to improve the power of genome-wide association studies. We demonstrate a simple and efficient method to model genetic background effects using polygenic scores derived from SNPs that are not on the same chromosome as the target SNP. Using simulated and real data we found that this can result in a substantial increase in the number of variants passing genome-wide significance thresholds. This increase in power to detect trait-associated variants also translates into an increase in the accuracy with which the resulting polygenic score predicts the phenotype from genotype data. Our results suggest that advances in methods for phenotype prediction can be exploited to improve the control of background genetic effects, leading to more accurate GWAS results and further improvements in phenotype prediction. Compared to fixed effects models for GWAS10, LMMs can be designed that have the advantage of being applicable to samples that include related individuals12. LMMs for this purpose typically include a random effect with covariance proportional to the kinship matrix that indicates the degree of relatedness between pairs of individuals in the sample12. The relatedness of individuals in the sample may be known a priori or may be derived from the genotype data by constructing a genetic relationship matrix (GRM), with entries corresponding to the genotypic covariance between pairs of individuals. When the entries of the GRM below a specified threshold are set to zero, the GRM is approximately equivalent to a family kinship matrix, with the degree of relatedness that the matrix captures controlled by this threshold. Thresholding the matrix to capture close family relationships (or cryptic relatedness13) allows specialized computational methods for sparse matrices to be applied so that model fitting remains tractable for studies that include large numbers of individuals9. This is the approach taken by fastGWA9, a recently developed tool that has been shown to generate correctly calibrated statistical results efficiently for biobank-scale GWAS.Linear mixed effects models (LMMs) are routinely applied to detect associations between SNPs and phenotypes in genome-wide association studies (GWAS) and many methods have been developed that enable these models to be applied efficiently to the large scale datasets that are typically now encountered in studies of complex traits14. When a statistical model is used to test for a relationship between a given SNP (the test SNP) and a phenotype, genetic variants in the genome that are not in linkage disequilibrium with the test SNP may also make a substantial contribution to the phenotypic variation. If this contribution to phenotypic variation is not accounted for it contributes to the error term in the model. If the trait of interest is both highly polygenic and highly heritable this noise may be substantial. Failure to account for sources of variance in the response in a statistical model can reduce the power to detect a relationship of interest16. A LMM with a full GRM  is equivalent to a model in which all variants are assumed to have a causal effect on the phenotype, with effect sizes consisting of independent samples from a Gaussian distribution8. This is typically not a good fit to the true effect size distribution, and instead, the software package BOLT-LMM8 uses a spike-and-slab Gaussian mixture for the effect size distribution, with a component (the spike) close to zero corresponding to weak genome-wide effects and accounting for family relationships, and component with larger variance (the slab) corresponding to variants with large effects8. Fitting this more sophisticated model requires specialist numeric methods, that are relatively computationally intensive. Consequently BOLT-LMM is much more computationally intensive than fastGWA9.In addition to enabling application to samples containing related individuals, LMMs can also account for genetic background effectsN is the number of individuals in the study. The memory requirement of BOLT-LMM is kept tractable by not explicitly evaluating the GRM but rather BOLT-LMM solves the mixed model equations by computing the product of the inverse GRM and the phenotype vectors. Nonetheless, the overall compute time and memory requirements of BOLT-LMM are a function of both N and the number of model SNPs, M, that contribute to the GRM  SNPs that are not in LD with the target SNP, e.g. using a Leave One Chromosome Out (LOCO) approach, can result in dilution of the extent to which the relevant part of the genetic background is captured by the GRM. In the latter case, SNPs that are not relevant, in that they do not capture direct genetic effects or tag relevant population structure effects, effectively add noise to the GRM14. Alternatively, the GRM can be built from only the SNPs that are found using a linear model to be associated with the phenotype. Although this results in an increase in statistical power18, it does not fully control for population structure and is not recommended if population structure is of substantial concern11. Methods have been developed that incorporate principal components into the GRM calculation built from significant SNPs; however, most of these methods are not suited to large biobank-scale data, without access to cloud computing or large compute farms21. Background genetic effects can also be included in the statistical model as fixed effects and this is the recommended approach when there are SNPs with large effect sizes11. A model fitting approach to determine the SNPs to include as fixed effects has been developed, and this also results in increased power in GWAS14.The full GRM is an 23. PGS are constructed from weighted sums of allele dosages, with the weights corresponding to the effects size of the variants. Risk variants (variants associated with the phenotype) are typically inferred from the largest available GWAS, generally a meta-analysis. The clinical potential of PGS has already been shown in complex diseases such as coronary artery disease (CAD), diabetes and cancer25. In CAD, the identification of individuals with similar risk to those with rare high-risk monogenic variants has been reported24. Similarly, in breast cancer, pathogenic variants in BRCA1/2 account for 25% of familial risk of the disease with genome wide variants accounting for a further 18% of the risk27. It is likely that in the future specialist machine learning methods will be developed to predict phenotype from genotype23, potentially achieving higher accuracy by incorporating the possibility of non-additive effects.As the genomic architecture of complex diseases is uncovered with the help of large biobanks, there is an advancing prospect of predicting quantitative phenotypes and the risk of complex diseases from genotype data. Recent years have seen substantial success and emerging clinical utility in phenotype prediction from polygenic scores (PGS)Here, we set out an approach to GWAS that seeks to separate the model fitting at the test locus and estimation of the genetic background effect. After carrying out an initial round of GWAS using an existing method, we derive a PGS for each chromosome, using the summary statistics for SNPs on the remaining chromosomes. We refer to this as the Leave One Chromosome Out Poly Genic Score (LOCO PGS). We then perform a second round of GWAS, including the relevant LOCO PGS as a fixed effect to account for the contribution to the variation in the phenotype of SNPs that are not on the same chromosome as the test locus. We tested this approach in two ways. Firstly, using simulated data we tested for an improvement in power on the task of recovering known causal variants as a function of study size, number of causal variants and trait heritability. In addition, we applied the method to three phenotypes from the UK Biobank and determined the number and characteristics of additional variants that were detected. For an objective assessment of performance on real data, where the true associations are unknown, we divided the data into test and training sets and predicted the phenotype in the test set. The improvement in performance on the critical task of complex phenotype prediction illustrates the utility of the PGS as a means of accounting for off target genetic effects. This straightforward, modular approach to accounting for genetic background effects in GWAS has the advantage of leveraging advances in phenotype prediction as they become available. It also offers significant improvements in speed relative to existing methods that correct for genetic background.28. We refer to the methods that result from including the LOCO PGS fixed effect by appending PGS and the name of the method used to calculate the PGS to the name of the original tool. For example, fastGWA with a LOCO PGS fixed effect, calculated using the pruning and thresholding (P&T29) or LDpred230 methods are referred to as fastGWA-PGS-PT and fastGWA-PGS-LDpred2, respectively. We simulated data to evaluate the impact of including the LOCO PGS as a fixed effect in GWAS. The simulations consisted initially of a normally-distributed continuous trait in 100,000 individuals. The trait had a narrow-sense heritability  Fig. , S5.MN/4 bytes, where N is the number of individuals in the dataset and M is the number of SNPs included in the GRM8. When we ran BOLT-LMM with a subset of 165,683 SNPs  curves to investigate whether the increased number of causal variants recovered when we included the LOCO PGS as a fixed effect reflected a reduction in P-values across the board for the phenotype-associated variants or also an improvement in the ordering of the variants, when the variants are ordered by the evidence of an association with the phenotype. Over 100 simulations we found that the area under the ROC curve (AUC) was always higher for fastGWA-PGS-LDpred2 than for fastGWA without the LOCO PGS fixed effect Fig.  showed tIn addition to increasing the statistical power to detect causal variants, including the PGS fixed effect also resulted in an improvement in effect size estimates Fig. . We foun31.We simulated data over a range of values of sample size, mentclass2pt{minim0.2 Fig. . The impl Tables , S11. ThThe improvement in power resulting from the inclusion of the PGS fixed effect increased consistently with increasing numbers of causal variants in the case of the larger sample size. This was not the case for the smaller sample size, for which the improvement decreased or was lost altogether when the number of causal variants was large Fig. . This isoci Fig. .We assessed the impact of including the LOCO PGS fixed effect on the performance of fastGWA on real data using standing height, BMI, and heel bone mineral density (HBMD) in individuals of British ancestry , the power exceeded that of REGENIE28, a recent, computationally efficient tool for GWAS that uses ridge regression to control for genetic background effects. When BOLT-LMM8 was used with a GRM derived from all of the simulated variants, the LOCO PGS fixed effect did not provide any boost in power  and body mass index (BMI) in individuals of British ancestry in the UK Biobank). Consistent with the simulation results, we found more independent trait-associated loci using fastGWA-PGS-LDpred2 than with fastGWA alone for all three traits  approval from the NHS North West Research Ethics Committee, UK. The simulated genotype data was based on autosomal genotyped data from the UK Biobank. To limit the effects of population stratification only individuals reporting white British ancestry  was used to calculate the LOCO PGS-LDpred2 fixed effects. To reduce computation time, 22 LOCO genotype objects containing the SNP correlations were precomputed.Association testing was performed using fastGWA, REGENIE and BOLT-LMM. To account for known sources of covariation  10 PCs, sex, age, genotype batch and assessment centre were included as fixed-effect covariates in statistical models. For the PGS method we first performed GWAS  and calculated PGS scores on a Leave One Chromosome Out (LOCO) basis. This resulted in 22 sets of PGS values . Two PGS strategies were used in this study, pruning and thresholding (P+T), denoted with the suffix PGS-PT and LDpred2, denoted by the suffix PGS-LDpred2. The LOCO PGS-PT were calculated using PRSice2 (version 2.2.12 (2020-02-20))9. The genetic relationship matrix used with fastGWA and BOLT-LMM was calculated for all European individuals  and the polygenic score predictions were tested on the remaining independent European samples. Summary statistics were generated using fastGWA, fastGWA-PGS-PT, fastGWA-PGS-LDpred2 and BOLT-LMM. We used LDpred2 and PRSice2 to predict the phenotypic values in the test set. LDpred2 requires LD correlation data and we used a pre-computed set built on the 1.1 million HAPMAP3 variants for this purpose. The model fit was assessed for each method by fitting a linear model to the values of the phenotype in the test set as a function of their predicted values, accounting for known sources of phenotypic variation, i.e. sex, age, PC’s. We report both the proportion of variation explained collectively by the PGS, sex, age, the first 4 principal components and assessment centre as well as the Supplementary Information.