Mycobacterium avium subsp. paratuberculosis (MAP) causes Johne's disease or paratuberculosis (PTB), with important animal health and economic implications. There are no therapeutic strategies to control this disease, and vaccination with inactivated vaccines is limited in many countries because it can interfere with the intradermal test used for bovine tuberculosis detection. Thus, infected animals either get culled after a positive ELISA or fecal PCR result or die due to clinical disease. In this study, we review recent studies aimed to discover genetic markers which could help to identify and select cattle less susceptible and more resilient to PTB. In recent years, the genotyping and subsequent imputation to whole-genome sequence (WGS) has allowed the identification of single-nucleotide polymorphisms (SNPs), quantitative trait loci (QTL), and candidate genes in the Bos taurus genome associated with susceptibility to MAP infection. In most of these genome-wide association studies (GWAS), phenotypes were based on ante-mortem test results including serum ELISA, milk ELISA, and detection of MAP by fecal PCR and bacteriological culture. Cattle infected with MAP display lesions with distinct severity but the associations between host genetics and PTB-associated pathology had not been explored until very recently. On the contrary, the understanding of the mechanisms and genetic loci influencing pathogen resistance, and disease tolerance in asymptomatic individuals is currently very limited. The identification of long-time asymptomatic cattle that is able to resist the infection and/or tolerate the disease without having their health and milk production compromised is important for disease control and breeding purposes. Mycobacterium avium subsp. paratuberculosis (MAP) infections affecting domestic and wild ruminants represent a global major issue on animal health, recognized by the World Organization for Animal Health (OIE) (th (OIE) , which rth (OIE) . Paratubth (OIE) –5. More th (OIE) , 7. In Cth (OIE) . In Irelth (OIE) . The ecoth (OIE) . The ecoth (OIE) . There ith (OIE) . It has th (OIE) –15. MAP th (OIE) –19.Mycobacterium bovis detection tests  estimates of susceptibility to MAP in Friesian cattle ranges from 0.03 to 0.27 (Bos taurus genome associated with susceptibility to MAP infection. N = 983) using WGS data .The application of animal genetics in breeding programs is currently an important motor for efficient livestock production, not only to increase performance and productivity but also to ensure the resilience and health of livestock while improving their longevity. A widely accepted strategy to reduce or eliminate animal diseases is through the selective breeding of animals with reduced susceptibility and/or enhanced resilience against specific pathogens. Over the last decade, specific candidate genes provided evidence for the existence of single nucleotide polymorphisms (SNPs) associated with differences in susceptibility to bovine PTB . The ide to 0.27 , 32. TheWGS data . We obseh2 estimates (P ≤ 5 × 10−7) with the multifocal (h2 = 0.075) and the diffuse (h2 = 0.189) lesions, respectively. No overlap was seen in the SNPs associated with each type of lesion which suggested that distinct genetic variants might control the multifocal and diffuse lesions and that these lesions represent divergent disease outcomes. Pathway analysis with the candidate genes overlapping the identified QTLs revealed a significant enrichment of the keratinization pathway and cholesterol metabolism in the animals with multifocal and diffuse lesions, respectively. The keratin family (KRT), the major subgroup among the intermediate filament family of cytoskeletal proteins, is responsible for maintaining the integrity of the gastrointestinal epithelium, providing resilience against many agents, and regulating various cellular functions such as cellular proliferation, and inflammatory and immune responses. In recent years, it has been demonstrated that the presence of epithelioid granulomas with multifocal distribution in leprosy controls M. leprae replication and its dissemination  with PTB susceptibility using ante-mortem and post-mortem definitions in a common set of Spanish Holstein cattle (N = 983) (P < 10−6), and the multiple positive correction was limited only to 50,000 independent tests.Although we identified a total of 380 SNPs associated  , 47, no N = 983)  genotypeN = 983)  carried h2 = 0.55) and that this variation is indicative of an immunogenic profile in the PTB tolerant animals designed to control bacterial growth, modulate inflammation, and limit tissue damage . So. Soh2 = Since it is well recognized that not all asymptomatic animals will progress into clinical cases during their productive life, the identification of genetic markers associated with PTB tolerance might help farmers or animal health managers to select which infected cows should not be culled which in turn should increase the benefit/cost of their control program. In addition, the introduction of novel genetic variants associated with PTB susceptibility and tolerance into marker-assisted breeding programs would help producers to select less susceptible cattle, and more tolerant to PTB and likely to other bovine diseases as well, ultimately preventing economic losses and reducing antimicrobial use. Preventing endemic and chronic diseases such as PTB by selecting resilient cattle is important for sustainable and efficient dairy farming and the maintenance of the rural economy. Although this is a long-term control strategy, the benefits of breeding resilient animals could be permanent and transferred to subsequent generations.MAH conceived and coordinated the project and wrote the manuscript. All authors contributed to the article and approved the submitted version.Financial support for this study was provided by a grant (RTI2018-094192-R-C21) funded by MCIN/AEI/10.13039/501100011033 and by FEDER, Una manera de hacer Europa. MC and GBB have been awarded fellowships from MCIN/AEI/10.13039/501100011033 and FSE Invierte en tu futuro; grants FPI2016-00041 and PRE2019-090562, respectively.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


The primary objective of this study was to determine the genetic parameters for reproductive traits among Large White pigs, including the following traits: total number born (TNB), number born alive (NBA), litter birth weight (LBW), average birth weight (ABW), gestation length (GL), age at first service (AFS) and age at first farrowing (AFF).The dataset consisted of 19,036 reproductive records from 4,986 sows, and a multi-trait animal model was used to estimate genetic variance components of seven reproductive traits.The heritability estimates for these reproductive traits ranged from 0.09 to 0.26, with the highest heritability for GL and AFF, and the lowest heritability for NBA. The repeatabilities for TNB, NBA, LWB, ABW, and GL were ranged from 0.16 to 0.34. Genetic and phenotypic correlations ranged from −0.41 to 0.99, and −0.34 to 0.98, respectively. In particular, the correlations between TNB, NBA and LBW, between AFS and AFF, exhibited a strong positive correlation. Furthermore, for TNB, NBA, LBW, ABW, and GL, genetic correlations of the same trait between different parities were moderately to strongly correlated (0.32 to 0.97), and the correlations of adjacent parities were higher than those of nonadjacent parities.All the results in the present study can be used as a basis for the genetic assessment of the target population. In the formulation of dam line selection index, AFS or AFF can be considered to combine with TNB in a multiple trait swine breeding value estimation system. Moreover, breeders are encouraged to increase the proportion of sows at parity 3–5 and reinforce the management of sows at parity 1 and parity ≥8. In the pig industry, female reproductive traits are the most functional traits affecting the economic benefit of pig production. According to previous studies, reproductive problems cause approximately 30% of culling in pig production systems . Thus, iTo date, many studies have been performed to estimate the genetic parameters of economic traits in pigs, such as growth trait , semen tBased on the above studies, the purpose of this study was to estimate the genetic parameters of female reproductive traits in Large White pigs, including total number born (TNB), number born alive (NBA), litter birth weight (LBW), average birth weight (ABW), gestation length (GL), age at first service (AFS), and age at first farrowing (AFF). The results of this study will facilitate the development of a genetic evaluation system for female reproductive traits, and improve the reproduction efficiency of pigs.All experiments involved in this study followed the “Guidelines for Experimental Animals” of the Ministry of Science and Technology . Operations and animal care were sustained by the experimental animal ethics committee of China Agricultural University .The population used for this study is from the nucleus pig breeding farm of Beijing Shunxin Agriculture Co., Ltd., Beijing, China. The core group of this farm is comprised approximately 600 sows and 50 boars. These individuals are fed and managed in a consistent manner. The sows were selected based on the dam line selection index, which was composed of the traits with TNB, backfat at 100 kg live weight, and age at 100 kg live weight. The selection intensity of breeding sows is 12% and the replacement rate is about 56%. Furthermore, culling is usually passive, mainly caused by individuals with genetic defects or disease.A total of 19,306 farrowing records, generated from 570 boars and 4,986 sows, were collected from 2007 to 2016. Seven reproductive traits  were considered in this study. TNB was defined as the total number of piglets born per litter, NBA was defined as the number of piglets born alive, LBW was defined as the total weight of alive piglets, ABW was defined as the average weight of each individual, GL was defined as the interval between insemination and farrowing, AFS was defined as the interval from birth to first insemination and AFF was defined as the interval from birth to first farrowing. According to the data distribution and prior knowledge, TNB, NBA, LBW, ABW, and GL were approximately normally distributed, but for AFS and AFF, we used the rntransfrom function in the GENABEL R package to normalize the phenotype values. Data within the mean plus or minus three standard deviations were retained in the present study.In this study, we first analyzed the effects of herds, years, seasons, and parities on reproductive traits using PROC general linear model in SAS 9.2 . The linear model was used as Model A:ijkl is the phenotypic value of each trait; μ is the overall mean; hi represents the fixed effect of farms, which contains 2 herds; mj represents the fixed effect of farrowing year, which includes 10 levels (from 2007 to 2016) ; sk represents the fixed effect of season, which includes 4 seasons ; pl represents the fixed effect of parity, which includes 8 levels ; eijkl is the random residual corresponding to the trait observation value. Significance was tested using Duncan's multiple comparison test.where YA multi-trait animal model was used to estimate the genetic variance components. The model B was fitted for TNB, NBA, LBW, ABW, and GL, model C was fitted for AFS and AFF:Y is the vector of observation; β is the vector of fixed effects ; a is the vector of additive genetic effects; pe is the vector of permanent environments of individuals for TNB, NBA, LBW, ABW, and GL; e is a vector of residuals, and X, Z, and W are incidence matrices associated with β, a, and pe, respectively. In addition, for TNB, NBA, LBW, ABW, and GL, we calculated the genetic correlation and phenotypic correlation between the same reproductive trait at different parities using Model C.where in Models B and C, In this study, we used a restricted maximum likelihood procedure to estimate the variance components of each trait in ASReml software . Heritabh2 is the heritability; rA is the genetic correlation between trait 1 and trait 2, covis the genetic covariance of two traits; pe2 is the proportion of phenotypic variance caused by permanent environmental effects. In addition, standard errors (SEs) of heritability were calculated using the formula given by Klei and Tsuruta [where  Tsuruta . GeneticDescriptive statistics of the seven reproductive traits are shown in As shown in The estimates of genetic variance components and genetic parameters were shown are As shown in Understanding the genetic parameters of the target population is crucial for making animal breeding programs, which helps to predict the response to selection and monitor genetic progress . Seven eAs we known, both environmental and genetic factors can affect the reproductive performance of sows. We analyzed the effects of herd, year, season, and parity on reproductive traits in this study. Results showed that different factors need to be considered when making mating plans. Among them, breeders paid more attention to the effect of parities. Some researchers found that the sows have better reproductive performance at or beyond third parity ,16; howeA multi-trait animal model was used to estimate the variance components of seven reproductive traits in this population. Among them, the estimates of the additive genetic variances were able to help animal breeders measure the genetic variations and determine the response to selection. The estimate of additive genetic variance for TNB was larger than those reported by Zhang et al , who estIn this study, the estimated heritabilities of seven reproductive traits ranged from 0.09 to 0.26. Heritabilities for TNB and NBA were in the range reported in previous studies, for instance, Wolf et al  estimateIn the present study, genetic correlations between different traits ranged from −0.41 to 0.98. Among them, the estimated genetic correlations between TNB and NBA agreed with the results from Roehe et al , Zhang eGenetic correlations between different parities for all traits were moderately to strongly positive. For TNB and NBA, genetic correlations between different parities ranged from 0.71 to 0.98, which was consistent with Ye et al  and LopeIn this study, we estimated the genetic parameters for seven reproductive traits in a Large White pig population, which can be used as a basis for the genetic assessment of the target population, and improve the efficiency of breeding work. The performance of some traits, such as TNB, NBA, and LBW, showing a high genetic correlation, can be improved by selecting a certain trait. Meanwhile, AFS or AFF can also be considered in the formulation of dam line selection index in the future. In addition, increasing the proportion of sows at parity 3 to 5, and reinforcing the management of sows at parity 1 and parity ≥8 can be an effective method to improve economic efficiency.


G) for two forms of environmentally covarying local adaptation: counter- and cogradient variation. Using a hierarchical Bayesian meta-analysis, we calculated the overall effect size of VG as 1.05 and 2.13 for populations exhibiting countergradient or cogradient variation, respectively. These results indicate that the genetic contribution to phenotypic variation represents a 1.05 to 2.13 s.d. change in trait value between the most disparate populations depending on if populations are expressing counter- or cogradient variation. We also found that while there was substantial variance among abiotic and biotic covariates, the covariates with the largest mean effects were temperature (2.41) and gamete size (2.81). Our results demonstrate the pervasiveness and large genetic effects underlying environmentally covarying local adaptation in wild populations and highlight the importance of accounting for these effects in future studies.Environmentally covarying local adaptation is a form of cryptic local adaptation in which the covariance of the genetic and environmental effects on a phenotype obscures the divergence between locally adapted genotypes. Here, we systematically document the magnitude and drivers of the genetic effect (V EnvironShared patterns of phenotypic variation along ecological gradients spurred notable research on the environmental and genetic determinants of body size and morphology and led to the establishment of eco-geographical ‘rules’ such as Bergmann's, Allen's, and Hesse's rules and subsequent derivations therein –9. Founda, plasticity alone), this is representative of a purely environmentally driven response where distinct genotypes would express the same trait values (or phenotype) along an environmental gradient. Alternatively, populations may be locally adapted, such that the reaction norms—namely, fitness or fitness-related traits—cross when comparing populations in their respective home and away environments, which is indicative of a genotype by environment interaction . Finally, populations may exhibit a form of cryptic local adaptation, where the genetic and environmental effects covary with one another, either negatively or positively [figure 1c), and when those two factors act in the same direction it is termed cogradient variation  [The variance components of phenotypic plasticity are commonly expressed with reaction norm plots, where the trait value of a genotype is plotted as a function of multiple environmental values . In a refigure 1sitively . In thisgure 1d) ,13. Thusc) . CompenRanid frogs—it wasn't until two-and-a-half decades later that interest in environmentally covarying local adaptation grew substantially. Research with an eastern North American fish, Atlantic silverside (Menidia menidia), revealed that populations had similar body sizes along a latitudinal gradient that spanned from the Gulf of Maine to the Floridian Atlantic Coast. Using a common garden approach, the researchers found that the northern populations were consistently larger than southern populations, regardless of the temperature in which they were raised (e.g. c). This finding led to substantial follow-up research investigating the proximate and ultimate factors driving the trend [While Levins  was the sed e.g. c. This fhe trend ,19, namehe trend . The earhe trend , bivalvehe trend , fishes he trend –25 and ihe trend –28, and he trend ,30, salihe trend , carotenhe trend ,33 and uhe trend .G or the total phenotypic variance driven by genetic differences in populations that exhibit environmentally covarying local adaptation .Despite the attention paid to counter- and cogradient variation, there have been few studies that describe the magnitude and extent of these types of local adaptation, nor has there been much investigation into the broader abiotic and biotic factors that might contribute to their occurrence ,35,36. WE and VG in equation (1.1) (covGE). To directly measure this, covariation studies are limited to reciprocal transplants or common gardens that recreate home environments [GE may be large, little research has explored how the different phenotypic variance components in equation (1.1) are structured along gradients in wild populations [G represents the full effects of genetic change on phenotypic variance (including drift and gene flow), clinally covarying VG of fitness-related traits covary specifically because of selection and the measure of VG in this specific scenario is a suitable representation of the magnitude of local adaptation in these populations. As such, the goals of our analyses were to (i) quantify the genetic variance component of countergradient and cogradient variation as an effect size, (ii) describe these effect sizes within and across taxa, phenotypic traits and different gradient types and (iii) quantify the effect size of compensation—or how similar countergradient populations are in their home environments—to assess if there are clear trends for phenotypic similarity or dissimilarity along gradients.Counter- and cogradient variation as phenomena represent the negatively or positively covarying contributions of Vronments ,38. Addi. 2 (a)et al. [et al. [Overall, we collected 858 studies that investigated counter- and/or cogradient variation. To generate a full list of studies, we first analysed studies indicated as showing counter- or cogradient variation in the qualitative analysis from Conover et al. . We then [et al.  review,  [et al. —682 studc,d)—and genotypes maintained their rank order across environments . Occasionally, studies investigated these distinctions across multiple species in the place of populations and such studies were discarded.To be further included in our analysis, a study had to meet a set of qualifying criteria. Specifically, a study had to be designed to include some form of a common environment—this may have been in a common garden study or a reciprocal transplant using wild populations or populations recently brought into laboratory conditions. We did not include examples from domestic populations or laboratory-induced selection. Additionally, studies must have included two or more common environments to determine the signal of local adaptation , as well as two or more populations to compare the genotypic difference of the phenotypic response between populations. Finally, studies were determined to show counter- or cogradient based on plotted reaction norms to verify that environmental and genetic effects covaried—i.e. populations in their respective home environments minimized (countergradient) or maximized genetic variance (cogradient) ebPlotDigitizer [x- and y-axes based on the figure values and then, with their cursor, adds digital points to the data of interest. The digital points are then translated to numeric data via the imaging algorithm.To calculate effect sizes, we took data from both tables and figures in manuscripts. For data in the form of figures, we used the software Wigitizer  to extrad, which, for this study, was a standardized mean difference with a correction for small sample sizes [The statistic used to calculate effect size was Hedges' le sizes ,41 to avle sizes ,43. We cd was calculated using the metafor package in R (v.3.6.3) [escalcl function [In all, we calculated 422 total effect sizes from 1204 individual data points extracted from 83 studies. Many studies showed counter- or cogradient patterns in multiple traits and/or trials within a given study. We collected all these data and controlled for their non-independence using a robust, Bayesian hierarchical modelling approach (discussed below). Hedges' v.3.6.3)  with thefunction . Additiobrms [(GxE) (equation (1.1)). As such, nested random intercepts effect was used to control for this non-independence. We originally set out to nest traits in experiments in studies in our random effects, but model parameterization necessary to overcome divergent transitions  extended model run time to be computationally intractable. Random effects were instead reduced to traits nested in studies.To estimate overall effect size and the effect of covariates, Bayesian linear mixed models fit with random intercepts were used in the R package brms ,47, whicbrms . Linear taxize package in R [classification function, we extracted the full taxonomy of a given organism in our dataset from the NCBI database. We then used the class2tree function to generate a phylogenetically accurate tree in terms of taxonomic rank . The function not only clusters taxa on their specific taxonomic rank but also within the taxonomic clade, allowing for more accurate distance measures. The tree created using this method was transformed into a matrix and then used as a custom variance–covariance component in our hierarchical model. The mathematical representation of our random effects in all models is shown in our electronic supplementary materials . We used moderately informative priors for our hierarchical models [Similarly, phylogenetic relationships may provide another source of non-independence and were controlled for by using a phylogenetic random intercepts effect for which we created a variance–covariance matrix . To do sage in R . Using tl models —except fThe overall effect size for both co- and countergradient variation was estimated using random effects-only models, which is the convention when assuming study effects may vary in meta-analytical approaches . We incl (c)sensu Conover et al. [d, because the values of different traits are generally measured on different scales [d, these were meant to reflect a broad distribution around 0 for perfect compensation  when cot scales . Becauserections ) that en. 3 (a)τ—the full random effect standard deviation—was modelled with its own prior distribution and resulted in 2.19 (95% CI = 1.79–2.82) for countergradient variation and 9.33 (95% CI = 4.00–22.45) for cogradient variation. We similarly included a random effect for phylogenetic relatedness, which resulted in an estimate of 2.54 s.d. (95% CI = 1.04–5.28) for countergradient variation and 3.71 s.d. (95% CI = 1.03–14.82) for cogradient variation .The result of our random effects models that estimated overall effect size for countergradient variation was 1.05 (95% CI = 0.30–2.49) and for cogradient variation 2.13 (95% CI = 0.35–7.00) ( (b)We also implemented a mixed-effects metaregression with our countergradient dataset to estimate the effect size for trait classification, gradient classification and taxonomic class effect. The mean effect, posterior distribution and 95% credible intervals for each modelled covariate are presented in  (c)sensu Conover et al. [The results of our compensation analysis were plotted to represent the conceptual relationship between home phenotypes of populations exhibiting countergradient variation  generally swamped the covariate-specific effects estimates . Howevesensu [Our compensation analysis for countergradient variation revealed that populations in their home environments were more commonly over- or undercompensasting, as opposed to perfectly compensating . In othesensu ,13), or sensu .Our results are indicative of a response to selection contributing to strong genetic divergence in trait values distributed along environmental clines, and they reinforce the evolutionary importance of counter and co-gradient variation. As such, negatively or positively environmentally covarying selection is a strong candidate as a mechanism for driving parapatric speciation—if the selection pressure is consistent across the gradient—or peripatric speciation—if selection is strongest at the poles. Genetic differentiation may also be expected by further anthropogenic change, where habitat fragmentation breaks up corridors of gene flow within clines , or clim. 5Our findings illustrate that environmentally covarying local adaptation is pervasive across multiple gradients in a diverse set of taxa. With this meta-analysis, we quantitatively characterized the genetic effect on phenotypic divergence for environmentally covarying local adaptation and find that the result is one to two full s.d. from the mean trait value of a population. While the genetic effect of co- and countergradient variation may be large, the variability of response observed across studies is also quite high, as indicated in the values of our random effects, indicating strong G x E influences. Moreover, when analysing the mean trait difference between home phenotypes of populations exhibiting countergradient variation, we find no support for a strong signal of perfect compensation, indicating that selection for optimal phenotypes across a gradient can or does not perfectly minimize variation in mean phenotypic trait values. Much like local adaptation more generally, environmentally covarying local adaptation necessitates close consideration when working with populations distributed across ecological gradients. We conclude that environmentally covarying local adaptation is ubiquitous with a large effect size and argue that this form of cryptic local adaptation deserves continued attention with theoretical, experimental and genomic approaches.


Introduction: Fine wool production is an important source of revenue, accounting for up to 13% of total revenue in extensively managed wool sheep production systems of the United States. The Rambouillet are a predominant breed that excels in wool quality characteristics. Understanding the genetic basis of wool quality characteristics would aid in the development of genomic breeding strategies to facilitate genetic improvement.Methods: Wool characteristics and DNA were collected for rams enrolled in the North Dakota State University and University of Wyoming annual central performance ram tests over a three-year period . The relationships of wool quality characteristics including grease fleece weight adjusted 365 days (wt. 365 adj.), clean fleece wt. 365 adj., staple length 365 adj., average fiber diameter, face wool cover, amount of skin wrinkles and belly wool were evaluated through genome-wide association studies (GWAS), Pearson correlation and ANOVA.Results: The GWAS identified four genome-wide significant genetic markers  and five chromosome-wide significant markers  on chromosomes 1, 2, 4, 15, and 19. Significant markers were associated with genes notable for relevant wool biological functions, including the gene ABCC8 which codes for SUR1, an ATP-sensitive potassium channel known to affect hair growth and 60S ribosomal protein L17-like, previously found to be expressed during follicle formation. The strongest Pearson correlation coefficients were identified between clean fleece wt. 365 adj. and grease fleece wt. 365 adj. (r = 0.83) and between clean fleece wt. 365 adj. and staple length 365 adj. (r = 0.53). Additionally, clean fleece wt. 365 adj. was correlated with final body weight (r = 0.35) and scrotal circumference (r = 0.16). Staple length 365 adj. , average fiber diameter  and clean fleece wt. 365 adj.  were significantly associated with belly wool score.Discussion: The results of this study provide important insight into the relationships between wool quality characteristics and report specific markers that Rambouillet sheep producers may use to help inform selection and breeding decisions for improved wool quality. Rambouillet are a predominant United States breed in extensive and semi-extensive production systems. This breed is commonly used in arid and semi-arid rangeland systems as a dual-purpose breed excelling in both fine wool and meat products . Wool prWool quality is driven by clean fleece weight and fiber diameter  but manyMuch progress has been made in sheep production through the identification and utilization of genetic markers for disease susceptibility risk or carrier identification , reproduThe aim of this study was to utilize data collected during NDSU and UWY central performance ram tests over a three-year period to characterize relationships between traits and with genomic single nucleotide polymorphism (SNP) markers. Pearson correlation and analysis of variance (ANOVA) testing were conducted with wool characteristics grease fleece weight adjusted to 365 days (wt. 365 adj.), clean fleece wt. 365 adj., staple length 365 adj., average fiber diameter, face wool score, skin wrinkle and belly wool scores and production traits including initial and final weights, 140-day average daily gain (ADG) and scrotal circumference. Wool traits were evaluated in individual GWAS with 50 k genotype data to identify markers for use in genomic breeding strategies.ad libitum textured diets  for 140 days in a dry-lot management system.Ram lambs 7 ± 3 months of age from regional  seedstock producers were brought to the University of Wyoming—Laramie Research and Extension Center  or North Dakota State University—Hettinger Research and Extension Center . Initial body weights were measured and animals were managed as one cohort. Rams were provided Rams were shorn after a 7–10-day acclimation period and once again at the conclusion of the 140-day feeding period. Upon conclusion of the performance test, scrotal circumference was obtained and wool staple length was measured on shoulder, side and britch, the three measurements averaged, and adjusted from 140-day to 365-day lengths in accordance with the standard practice of the National Sheep Improvement Program (NSIP) for this trait . This waThe presence of belly-type wool (belly wool) was scored from 1 to 4. In brief, belly wool is that which grows on the ventral region of the sheep and is characterized as uneven, tender in tensile strength, and compressed in staple length. Phenotypic selection pressure against this “belly wool” fiber type extending beyond the ventral portions of the sheep has been employed to avoid the resultant reduction in overall wool quality . Thus, aSimilarly, a subjective 1 to 4 scoring system was assigned for face cover where: 1 = no wool cover over top of the head and on the side of muzzle, nor between eyes and ears, 2 = minimal wool cover over top of the head and on side of muzzle, and between eyes and ears, 3 = moderate wool cover over top of the head and on side of muzzle, and between eyes and ears, 4 = heavy wool cover over top of the head and on side of muzzle, and between eyes and ears. A skin wrinkle score was assessed once wool was shorn, where: 1 = no observable wrinkles on body surface 2 = minimal observable wrinkles on body surface 3 = moderate observable wrinkles on body and 4 = heavy wrinkles on body surface.At shearing, whole fleeces were weighed and then individually cored in a custom-built apparatus  consisting of 16 coring tubes (2.2 cm in diameter) that were plunged into and retracted from compacted fleeces by hydraulic cylinders. Cores were split into duplicate 25-g sub-samples for each animal to determine average laboratory scoured yield  from whin = 273), rams with belly wool on less than one-third of the side comprising category two (n = 25) and rams with belly wool from one-third of the side to over one-half of the side comprising category three (n = 15). Wool characteristics were analyzed against other production traits including initial body weight and final body weight (pounds), 140-day average daily gain (140 days ADG) and scrotal circumference (centimeters).Wool characteristics analyzed included grease fleece weight adjusted to 365 days (wt. 365 adj.) and clean fleece wt. 365 adj. (pounds), average fiber diameter (micron), staple length 365 adj. (inches), face wool score and skin wrinkle score as continuous variables and belly wool score as a categorical variable. All traits were tested for normality using the Shapiro Wilks test in R version 4.2.1 ; face anpost hoc Tukey HSD testing to compare p-values between categories  was tested by ANOVA to determine significance for potential GWAS fixed effects  testing was utilized to compare production trait and continuous wool quality trait means between belly wool categories. All ANOVA tests were further analyzed with tegories . Ram tes effects . Pearson effects . ANOVA a effects .https://pngu.mgh.harvard.edu/purcell/plink/). Markers were filtered for quality control in the following order: non-autosomal markers , markers with a call rate (CR) <90% (87 SNPs), markers with a minor allele frequency (MAF) <0.01  and markers with Hardy-Weinberg Equilibrium p-values <1e-50 (30 SNPs) were excluded, for a total of 41,888 high-quality autosomal SNPs retained for final analyses. All rams had a CR of 95% or greater.Ram DNA samples were extracted from either whole blood samples or ear tissue samples stored in tissue sampling units (TSU) collected by University of Wyoming or North Dakota State University personnel. DNA was isolated from blood at the University of Idaho using the phenol-chloroform method described previously  and TSU https://pngu.mgh.harvard.edu/purcell/plink/; versus PC2 (y-axis). Separate plots were generated for each continuous wool characteristic and rams were color-coded on a gradient scale to indicate their position within the trait distribution.Principal component analysis (PCA) was carried out to investigate population structure. Analysis was conducted with plinkv1.9 and visualized with the package ggplot2 in R (www.goldenhelix.com). The EMMAX models estimated the proportion of variance explained (PVE) for each marker as previously described  and a chromosome-wide significance threshold was determined by Bonferroni-adjustment of the number of markers on the largest chromosome . The trait distributions of significant markers were visualized using boxplot figures and significance was further evaluated through analysis of covariance (ANCOVA) and Tukey HSD testing in R with the rstatix, ggplot2, ggpubr, multcomp and patchwork packages  using the Efficient Mixed-Model Association eXpedited (EMMAX) in SNP and Variation Suite™ v8.9.1   with all traits tested. Average fiber diameter was found to have significant positive correlations with both clean and grease fleece 365 adj. weights  respectively, and clean fleece wt. 365 adj. had significant positive correlations with staple length 365 adj.  and skin wrinkle score . Skin wrinkle and face wool scores had a significant positive correlation . Clean and grease fleece 365 adj. weights were significantly correlated with initial body weight , final body weight , 140 days ADG  and scrotal circumference .Descriptive statistics of wool characteristics are reported for the 313 rams , by test.22e-80) . Grease p-value ∼0.01) , average fiber diameter  and clean fleece wt. 365 adj. . Post hoc Tukey HSD tests revealed that rams within belly wool category two had significantly longer staple length 365 adj. than category one  and category three  rams. Rams with belly wool scores in category three had significantly finer average fiber diameter than rams in category one , although there was no significant difference between rams in categories three and two or two and one. For clean fleece wt. 365 adj., rams in belly wool category two had significantly greater measurements than rams in category one   . Signifi1.05e-2) . The relPrincipal component analysis (PCA) was used to investigate the population structure as it related to wool quality characteristics. Plots were constructed with principal component 1 (PC1) on the x-axis and principal component 2 (PC2) on the y-axis. PC1 had an eigenvalue of 8.57 and explained 11.17% of the total variance, PC2 had an eigenvalue of 6.91 and explained 9.00% of the total variance . There dp-value <0.05) ANOVA or t-test results. The results of GWAS are displayed in a multi-trait Manhattan plot  and were estimated to explain 8.25% and 7.85% of phenotypic variance. The significant SNP rs420943224 was found to be significant for clean fleece wt. 365 adj. by genome-wide threshold and for grease fleece wt. 365 adj. by chromosome-wide threshold in the corresponding additive inheritance models  with 7.40% and 6.60% proportion of variance explained (PVE), respectively. Two significant SNPs were identified on chromosome 15 for skin wrinkle score  and staple length  and three significant SNPs on chromosomes 2, 4, and 19 were associated with face wool score in a recessive inheritance model . The PVE for significant SNPs ranged from 6.13% to 8.25% and MAF ranged from 5.13% to 48.40%.Genome-wide association studies (GWAS) were conducted for each of the six continuous wool quality characteristics. Ram test location and/or ram test year were included as fixed effects for traits with significant  or homozygous for the minor allele   . Presencectively . BoxplotABCC8) and OAR19_14805437.1 within unc-51 like Kinase 4 (ULK4) were queried for TFBS differences. Score difference between reference and alternate allele sequences of 0.3 or −0.3 or greater are recorded .To investigate the genomic context of GWAS results, the reference genome sequence was evaluated for the presence of known or predicted genes . The funrecorded . Four SOUSP13 and NLGN1 associated with staple length and positioned 1.8 Mb and 3.3 Mb, respectively, from markers identified for average fiber diameter  in the present study. Genetic markers for wool quality in sheep have also been suggested through candidate gene studies, including markers associated with genes MTR (FST (DKK1 (KIF16B (FGF5 (KRT) and keratin-associated protein (KAP) genes have been suggested for genomic selection  which codes for SUR1, an ATP-sensitive potassium channel known to affect fiber growth  has been suggested to be related to sheep growth (ULK4). Overexpression of the gene ULK4 has been shown to inhibit apoptosis  locus of rats (Rattus norvegicus assembly as it was not predicted in a later annotation (NCBI Gene ID: 364797). The Homo sapiens orthologs of 40S ribosomal protein S19-like and 60S ribosomal protein L17-like have known protein interactions, suggesting a potential for similar interaction of these proteins in sheep. The swh locus is known to be associated with follicle hypoplasia, as well as impaired development of the sebaceous glands and mammary glands . The gene similar to ribosomal protein S19 (LOC364797) was identified within the sparse and wavy hair ( of rats , althougy glands . The mary glands . Finallyr growth . The proPADI1 in human keratinocyte cells (in silico analyses suggest functional ramifications of variant alleles associated with wool quality characteristics.Prediction analysis for TFBS suggested binding motifs for SOX2, SOX3, SOX10 and/or SOX17 may have less specific binding abilities between the alternate and reference alleles at rs404487383. SOX2 is expressed in mesenchymal cells during skin development , and botte cells . These iThe trait correlations reported in the current study largely agree with previously published work for Rambouillet sheep. Clean fleece wt. 365 adj. is a component of grease fleece wt. 365 adj., which is reflected in their robust correlation in this study and previous . Clean fSimilar associations as those reported between belly wool category and wool quality characteristics in the present study have been previously noted in Merino sheep . GeneticThe PCA investigated in this study indicated an overall lack of segregation of genetically similar animals with any of the specific wool quality characteristics tested by PC1 or PC2, suggesting an opportunity for genetic progress for wool quality characteristics. Previously reported heritabilities suggest that genetics are a major factor in wool quality phenotypes and genetic improvements should be possible even in the short term . This st


We propose a novel effective framework for the analysis of the shared genetic background for a set of genetically correlated traits using SNP-level GWAS summary statistics. This framework called SHAHER is based on the construction of a linear combination of traits by maximizing the proportion of its genetic variance explained by the shared genetic factors. SHAHER requires only full GWAS summary statistics and matrices of genetic and phenotypic correlations between traits as inputs. Our framework allows both shared and unshared genetic factors to be effectively analyzed. We tested our framework using simulation studies, compared it with previous developments, and assessed its performance using three real datasets: anthropometric traits, psychiatric conditions and lipid concentrations. SHAHER is versatile and applicable to summary statistics from GWASs with arbitrary sample sizes and sample overlaps, allows for the incorporation of different GWAS models , and is computationally fast. There is a growing interest in studying the shared genetic background between genetically correlated traits ,2,3,4,5 The problem of the decomposition of the variance of several traits into the shared/unshared genetic and environment components were first formulated by S. Wright in 1921 . There aThere are several terms for these common and specific genetic impacts. We will call them the “shared genetic impact” (SGI) and “unshared genetic impacts” (UGI). The genetic factors that determine these impacts will be called “shared genetic factors” (SGF) and “unshared genetic factors” (UGF), respectively. The heritability of each trait explained by SGF and UGF will be called “shared heritability” and “unshared heritability”, respectively. Note that the term “unshared” for every trait means the rest other than the “shared”. For any incomplete set of traits, UGFs can be partially overlapping.The application of different methods of multivariate analysis in genome-wide association studies (GWAS) allows the problem of SGF and UGF identification to be partially solved ,11,12,13We had previously developed a method for obtaining genetically independent phenotypes (GIPs) . This meHere, we present a novel general framework for the estimation of shared and unshared heritability and identification of the shared and unshared genetic factors using the summary statistics of original traits. The essence of our approach is to find the optimum linear combination of traits which has the maximum proportion of its genetic variance explained by the SGF. We validated our framework using simulation studies under different scenarios by comparing it with the developed GIP approach, and assessed its performance using three real datasets: anthropometric indices, psychiatric disorders and conditions, and lipid concentrations.N unrelated individuals measured for K traits and genotyped for M SNPs. For a standardized normal trait, y (N × 1), the traditional polygenic (null) model takes the form: y = Gβ + ε, where G is an (N × M) matrix of standardized genotypes; β (M × 1) and ε (N × 1) are genetic and non-genetic random effects, respectively; β ~ N and ε ~ NNI), where 0 is a null mean vector, h2 is the trait heritability, and I is an identity matrix of the given dimension. For unrelated individuals, we expect y ~ N. We adopted a commonly used multivariate pathway model  in termsM SNPs into two non-overlapping SNP sets with sizes M0 and M1 (M0 + M1 = M). The set of M0 SNPs called “SGF” includes only those SNPs whose effects on all traits are collinear. The set of M1 SNPs consists of the other SNPs which do not have shared joint influence on all traits at once, this set being called “UGF”. In accordance with M, G is divided into two matrices, G0 (N × M0) and G1 (N × M1). To decompose every trait into components explained by SGF and UGF, we rewrote the traditional polygenic model in terms of G0 and G1We propose to divide M0 × 1) vector of non-zero SGF effects, which can be presented as β0 is an (M0 × 1) non-zero vector that is the same for all traits, i-th trait explained by SGF. Here iw is a non-zero trait-specific multiplier: iw2 denotes the proportion of ih2 explained by SGF; and the value of iw can be positive and negative, indicating the direction of the SGF effect on the i-th trait. M1 × 1) vector of UGF effects, which can be presented as β0, Here, the first and second terms are genetic components explained by SGF and UGF, respectively, which are assumed to be independent. In the first term, For analyses of SGI and UGI on a set of correlated traits, we propose an effective multi-stage framework named SHAHER see . The conphenU) between the original traits, the matrices of genetic correlations (genU) between the original traits, the heritabilities of the original traits, and GWAS summary statistics of the original traits as inputs. It is worth noting that phenU, genU and heritabilities could be estimated using GWAS summary statistics of the original traits, for example, by the LD score regression method [Our framework requires matrices of phenotypic correlations  vector of units. Using this model, MaxSH solves several tasks. Here genU, we estimate the proportion of heritability of every trait explained by SGF (W). To do this, we minimize the difference between genU and the auxiliary matrix V. This matrix is built using Formula (2), with the identity matrix used instead of unshU. The second task is to determine the α-coefficients, which is solved by maximizing the shared heritability of SGIT. This task is analytically solved asFirst of all, using only the genetic correlation matrix, phenU, H2 and W as input data. It requires α-coefficients and building SGIT, we build a UGIT for every trait using the residual regression equation iUGIT = iy − SGIT*ic, where ic is the impact of SGIT on the i-th original trait, defined asAfter determining the gencov denotes a genetic covariance. Note that we should use genetic rather than phenotypic covariances, as our goal is to adjust only the genetic components of the original traits.Here γ-coefficients form the matrix of the γ-coefficients i-th column of Γ corresponds to the linear combination coefficients for building the i-th UGIT. Since SGIT is the linear combination of the original traits, UGITs are linear combinations of the original traits, as well. The coefficients of these linear combinations called the The sumCOT stage. This stage is aimed at obtaining GWAS summary statistics for SGIT and UGITs using the previously determined α and γ coefficients, GWAS summary statistics  for the original traits and the matrix of phenotypic correlations. The method can use Z scores obtained from any regression model and allows for varying sample sizes and sample overlap between traits. This sample overlap is incorporated into the estimation of the matrix of phenotypic correlations. In short, the SNP effects for combined traits are calculated by summing effect estimates from the individual trait GWASs, each multiplied by their corresponding linear coefficient (α or γ), and standardized by the expected variance. The standard errors of the SNP effect are calculated using variance-covariance arithmetic, taking into account the phenotypic covariance between GWAS results to adjust for the sample overlap. Effective sample sizes are then estimated based on the median Z statistic and allele frequencies by solving Equation (1) in [n (1) in . At the final stage, SHAHER checks for the correctness of the output. In particular, we anticipate that UGITs do not have a shared genetic basis. This is verified by applying MaxSH to the matrix of correlations between UGITs. To summarize, our framework estimates shared and unshared heritabilities for each of the studied original traits and produces GWAS summary statistics for SGIT and UGITs as outputs. The full details and mathematical formulae of SHAHER are in w estimates, (2) assessed the proportion of SGIT heritability explained by SGF to the total heritability of SGIT , and (3) compared the analytically predicted total and shared heritabilities of SGIT and GIP1 with respect to the loss function. The design of our simulation experiment is shown in K is the number of traits; W02 is a (K × K) diagonal matrix, where the i-th diagonal element is iw2 (the proportion of heritability explained by SGF); s is the proportion of zeros in the matrix unshU; d1 is the amplitude of the uniform distribution for non-zero values of unshU and d2 is the amplitude of the uniform distribution for envU; H2 is the diagonal matrix with diagonal elements equal to the trait heritabilities. The parameter values used are given in Under different scenarios, we designed simulations to assess the performance of MaxSH. We (1) assessed the accuracy of K, of the original traits and fixed heritability, ih2 , of each trait, we simulated genU. To do this, we separately modelled two of its components caused by SGF and UGF as 1 is a (K × 1) vector of units, and unshU is a (K × K) matrix randomly generated using the parameters s and d1 . We revealed a dependence of ΔW on the loss function (Loss). The Loss value characterizes the difference between genU and the auxiliary matrix V.Using simulation data W0, (2) using MaxSH and estW, and (3) using the GIP method [We then estimated  and W0,  using MaThe simulated experiments were repeated 10,000 times for each set of parameters. The model parameters and formulas for all calculated values are shown in We used three publicly available real data sets: anthropometric traits, psychiatric conditions and lipid concentrations, which contain five, four and three traits, respectively. http://www.nealelab.is/blog/2017/7/19/rapid-gwas-of-thousands-of-phenotypes-for-337000-samples-in-the-uk-biobank, accessed on 1 September 2020) for people of European ancestry: BMI , weight , hip , waist circumference  and whole body fat mass .The group of anthropometric traits consisted of UK Biobank GWAS summary statistics obtained from the Neale lab  for bipolar disorder, BIP  [N = 110,935)–were derived from UK Biobank data from the Neale lab. All psychometric trait GWASs were conducted using samples from white Europeans.The second dataset reflecting psychometric traits was constructed from GWAS results provided by the Psychiatric Genomics Consortium  , major d 31,358)  and schihttp://csg.sph.umich.edu/willer/public/lipids2013/, accessed on 1 September 2020) for LDL cholesterol , triglycerides , and total cholesterol .The last dataset corresponding to lipid traits was formed using GWAS data for European participants from the Global Lipid Genetics Consortium .Pairwise phenotypic correlations between traits were computed using the GWAS-MAP platform described above. The used method is based on correlations between insignificant ribed in . SNP-basribed in  embeddedThe SHAHER analysis included checking if there was an SGI or not, the application of MaxSH, and conducting SGIT and UGIT GWASs. The threshold for confirming the existence of an SGI at the first stage was empirically set to 0.2.corrplot function from the corrplot R package (v.0.84) [For each dataset, we visualized the full genetic correlation matrices using the (v.0.84) . We alsoFinally, we compared the GWAS results obtained for SGIT by MaxSH and GIP  . p-value < 5 × 10−8) from summary statistics before the genomic control and applied the DEPICT software with default parameters . The MHC region was excluded from analysis. We performed a gene set enrichment analysis and a tissue/cell type enrichment analysis combined with a gene prioritization using the Data-driven Expression Prioritized Integration for Complex Traits (DEPICT) tool v.1.1, release 194 . We seleNext, for the gene set enrichment results, we calculated the number of significant enriched gene sets (FDR < 5%) and constructed an overlapping matrix in which each cell represents the number of overlapping gene sets for each pair of traits. For each pair of traits, we scaled the number of overlapping gene sets by the minimum number of significant gene sets for this pair of traits. The resulting matrix was visualized using the corrplot R-package, as descried above. −8. The associated locus was defined as a genomic region spanning 500 kb in either direction of the lead SNP. Those loci that were significantly associated with SGIT, but not with the original traits, were assumed to be new loci. We performed a clumping procedure to search for loci associated with each of the original traits, SGIT and UGITs at a genome-wide significance level of 5 × 10p-value = 1 × 10−5. For the psychometric traits, it was set at 1 × 10−3. We then analyzed the SGIT p-values for the selected loci and constructed boxplots of −log10 for them with regard to the number of the original traits significantly associated with these loci.We expected that the loci associated with all the original traits used to obtain SGIT were likely to be SGF. To test this expectation, for each dataset we selected all independent loci that were significantly associated with at least one of the original traits and calculated the number of the original traits significantly associated with these loci. For the original anthropometric and lipid traits, we empirically set the significance threshold at w estimates  with respect to the loss function given in Q-value) with respect to the loss function; and (3) compared the analytically predicted total/shared heritabilities of two traits: SGIT and the first component, GIP1, obtained by the GIP method [Q-value can be interpreted as the specificity metrics of SGIT: the closer the Q-value to 1, the lower the share of unshared heritability in the total heritability of SGIT. The simulation scenarios were based on six varying parameters that describe the properties of the genetic and phenotypic correlation matrices. Under each scenario, we considered two situations where all traits have the same w2 and different w2s. To distinguish between these situations, we will hereinafter write either “w2” or “different w2s”. In total, we performed 10,000 iterations of simulations for each of 288 scenarios. To assess the MaxSH performance, we conducted simulation studies. We (1) assessed the accuracy of w values, the higher the accuracy of the w estimates, (2) the accuracy of the w estimates and the Q-value increase with an increasing in the number, K, of traits, (3) for all scenarios with w2 > 0.8, Q-value was more than 90%.The full results are presented in w estimates was generally low: w2 = 0.2 and 0.3, although at w2 equal to or higher than 0.4, Q-value was higher than 60% for almost all scenarios with w2 ≥ 0.4. For all scenarios with three traits, the accuracy of the w estimates was higher: w2 ≥ 0.4 and w2 ≥ 0.5. For the scenarios with w2 ≥ 0.5, the Q-value was more than 70% for four traits and more than 80% for five traits. For the scenarios with four and five traits, the accuracy of s = 0.3 are presented in s = 0.8 were similar to those with s = 0.3. They are presented in h2 = 0.8. For four and five traits, the shared heritabilities of SGIT were higher than the corresponding heritabilities of GIP1 under all scenarios, except for the scenarios with h2 = 0.8. In the scenarios with h2 = 0.8, the shared heritabilities of SGIT were higher than those of the GIP1 at w2 ≥ 0.5. The patterns of the total heritabilities for all scenarios reproduced the corresponding patterns of the shared heritabilities , psychometric (four traits) and lipid traits (three traits). We should note that the performance of SHAHER applied to three traits is limited (see simulation results), yet still passable, although the results should be interpreted with caution. The number of identified loci for each trait for each data set is given in α and γ coefficients and their CI  resulted in 820 genome-wide significantly associated loci  and quality (shared heritability). If obtaining genetically independent phenotypes is not the aim, we suggest using SHAHER, because it is more robust and gives additional metrics like SGI contributions to the heritability of the original traits. The framework is computationally effective. The stage using sumCOT is the most time consuming. However, it only takes several minutes for an average computer to conduct a GWAS of a linear combination of traits with 6M SNPs using a C++ implementation of the sumCOT. MaxSH, based on numerical optimization procedures, and the other parts of the framework take seconds. The proposed sumCOT method can be applied as an independent tool to address additional tasks. One of them is making a summary-level adjustment of traits by other traits using the same scheme as was used for obtaining the UGIT GWAS statistics. This can be helpful, for example, for ridding the studied trait’s genetic component of the genetic component that was caused by the confounding or unaccounted effects of assortative mating or family effects, which is quite a problem in GWAS at the biobank scale ,23. AnotThe main interest in the application of the SHAHER framework lies in the possibility of obtaining novel biological insights into a trait’s heritability composition. This can be achieved by the application of a huge variety of in-silico follow-up techniques to SGIT and UGITs. SGIT is of interest by itself, but we also emphasize the importance of the comparison of shared and unshared effects for each trait. In our real data application, the most remarkable case is BMI in the set of anthropometric traits see C. We fouN = 806,834) to date [N = 500,199) to date [To validate the findings of SHAHER, we have compared the association results for anthropometric and psychometric traits with the biggest publicly available GWAS results for BMI and MDD. The idea is as follows: if the locus was not significant on the original trait but was detected on SGIT or corresponding UGIT, it will be detected on the original trait if the GWAS sample size is increased. For BMI we have used the largest meta-analysis of the UK Biobank and GIANT GWAS ( to date  (see Sup to date  (see SupAlthough SHAHER is effective, it has several limitations. First, when trait-trait genetic correlations are weak, it is expected that the contributions of these traits to the shared heritability will be small as well. In this case, MaxSH may overestimate these contributions. Secondly, the framework is applicable only if the number of traits is no less than three. In the case of three traits, the performance is limited and the SHAHER results should be interpreted with caution. We have shown in simulations and real dataset examples that MaxSH works better at higher numbers of genetically correlated traits being analyzed. However, an increase in the number of weakly correlated traits leads to a decrease in the proportion of SNPs associated with all traits simultaneously and to a decrease in the efficiency of the framework. Thirdly, although the set of SNPs identified by the SGIT GWAS is enriched for the SGF, each SNP should be interpreted with caution for whether it is shared or not, because SHAHER has some level of nonspecificity. Finally, if any confounding effects were included in the GWAS of the original traits, these effects are amplified in the SGIT . The conWe should highlight the distinctive specificity of SHAHER which distinguishes it from existing approaches for multivariate analysis. There are a lot of frameworks that allow for the incorporation of several correlated traits in one analysis to increase the power of mapping ,11,12,13In conclusion, we propose a novel effective framework for analysis of the shared genetic background for a set of genetically correlated traits using GWAS summary statistics. The framework allows us to obtain novel biological insights into the trait’s genetic impact composition. By analyzing shared and unshared genetic impacts separately, we increased the number of identified loci and observed unique gene sets, identified genetic mechanisms that are common for all traits or specific for every trait. Of note, sumCOT can be used as a stand-alone method for obtaining GWAS results of the linear combination of the traits using their summary statistics.


Oryza sativa L.) genome datasets were analyzed to illustrate the potential applications of the proposed approach. One dataset applied to the parental selection for producing inbred lines with satisfactory performance in primary and secondary traits simultaneously. The other one applied to demonstrate the application of producing inbred lines with high adaptability to different environments. Overall, the results showed that incorporating GEBV and genomic diversity into a selection strategy based on the proposed selection index could assist in selecting superior parents to meet the desired breeding goals and increasing long-term genetic gain. An R package, called IPLGP, was generated to facilitate the widespread application of the approach.A set of superior parental lines is imperative for the development of high-performing inbred lines in any biparental crossing program for crops. The main objectives of this study are to (a) develop a genomic prediction approach to identify superior parental lines for multi-trait selection, and (b) generate a software package for users to execute the proposed approach before conducting field experiments. According to different breeding goals of the target traits, a novel selection index integrating information from genomic-estimated breeding values (GEBVs) of candidate accessions was proposed to evaluate the composite performance of simulated progeny populations. Two rice ( Parental line selection in plant breeding usually has two differing goals: (i) identify suitable parents for commercial hybrid varieties and (ii) identify suitable parents to develop inbred lines for subsequent breeding cycles . The results of this article showed that multi-trait machine- and deep-learning models were able to increase prediction accuracy and should be employed in large-scale breeding programs. To harness the benefits of MTGS for plant breeding, Schulthess et al.  of a crop, most published genomic selection studies have focused on single-trait approaches without exploiting information from multiple correlated agronomic traits  genome dataset presented in Spindel et al. (indica or indica-admixed groups. The phenotypic data include 4 years (from 2009 to 2012), two seasons per year (dry and wet), and YLD, PH, and FT for each season. Unfortunately, PH data for the 2009 wet season were not available. Phenotypic values of 35 of the 363 breeding lines were also missing; hence, adjusted means derived from 328 breeding lines were used in our study. The adjusted means were obtained using the residuals derived separately for each trait by the following model:l et al.  was analyijk is the phenotypic value of the trait at year i, season j and block k; Ai is the fixed effect of year i; Sj is the fixed effect of season j; (AS)ij is the interaction effect between year i and season j; Bk is the fixed effect of block k; and eijk is the residual. One SNP marker was randomly chosen per 0.1-cM interval over each chromosome because Spindel et al. /si, where δ is set to the sample mean of the phenotypic values for both the larger-the-better and the smaller-the-better types, and to the desired target value for the nominal-the-best type; si is the sample standard deviation of those phenotypic values; 1n is the vector of order n with all elements equal to 1; and i = 1, 2, …, t. Here n is the number of individuals in the training population, and t is the number of target traits.The target traits of interest were classified into three types according to their breeding goals. The Leti, gi, and ei, respectively, denote the general mean, the vector of genomic values, and the vector of random errors for trait i. The additive effects multi-trait GBLUP model is given as:where μg and e are mutually independent and separately follow a multivariate normal distribution, as denoted bywhere ⊗ denotes the Kronecker product Searle, . It is aand0 is a zero vector, ΣA is the genetic variance-covariance matrix for additive effects among the t target traits, K is a genomic relationship matrix for additive effects among the n individuals, Σe is the residual variance-covariance matrix among the t target traits, and In is the identity matrix of order n. Here, ΣA and Σe can be represented aswhere i, and σAij and σeij are the corresponding covariances between traits i and j. The genomic relationship matrix was calculated as K = MMT/p, where M is the marker coding matrix regarding the additive effects, and p is the number of markers.where μ, and g, then Let AΣ and eΣ were plugged into Eq. (3) to generate sommer  for hi denote the vector of genomic values for trait i in a simulated progeny population, and Kpt denote the genomic relationship matrix between the simulated progeny population and the training population. From Henderson . The GEBVs for the simulated progeny population are then predicted by i obtained from Eq. (3), for i = 1, 2, …, t.where For a particular individual, the selection index below was used to integrate its normalized GEBVs for the multiple target traits:wi is a pre-specified weight for trait i subject to the constraint that Zi is designated as GEBVi for the larger-the-better case, as −GEBVi for the smaller-the-better case, and as −|GEBVi|  for the nominal-the-best case. The selection index conveys an overall performance score for the individual. Note that the normalized GEBVi are scalars with no measuring units. The larger the selection index, the better the composite performance.where For the tropical rice dataset, the aim was to select a set of parental lines whose progeny populations had high YLD, low PH, and low FT. For the 44k rice dataset, the breeding goal was assumed to identify a set of superior accessions that would produce inbred lines with an FT as close as possible to the nominal value set as 80 days at all three locations . The resulting inbred lines would be anticipated to have high adaptability to the three different locations. The selection procedure can be described as follows.All available phenotypic values in each dataset were normalized as described above. The ensuing normalized data were used to build the multi-trait GBLUP model given by Eq. (2). The trained multi-trait GBLUP model predicted the normalized GEBVs of the target traits for each dataset; then the corresponding selection index values were obtained for all the accessions in the candidate population.The selection index integrating the normalized GEBVs of the three target traits in the tropical rice dataset was defined this way:w1, w2, and w3 are pre-specified index weights. Note the minus signs applied in the equation for PH and FT because smaller values are preferable for these two traits. The index weights w1, w2, and w3 were respectively specified as 0.6, 0.2, and 0.2. For the sake of contrast, another setting of 1, 0, and 0 was used that corresponded to the single-trait selection for YLD. To compare the improvement of the strategy changed from single-trait selection to multi-trait selection, an index was defined as follows:where The selection index for the 44k rice dataset was defined as:w1, w2, and w3 were equally set to be 1/3.where the index weights Sc that is the set composed of those accessions whose selection index values were above average. This resulting optimal subset achieved the maximal D-score, where the D-score is the determinant of the genomic relationship matrix corresponding to the selected accessions, and it was used to measure the genomic diversity of the selected accessions  The GEBV only (GEBV-O) strategy, which selected the top 10 accessions with the highest selection index values. (ii) The GD only (GD-O) strategy, which searched for an optimal subset of 10 accessions from 1 hybrids, and then each F1 hybrid produced 60 individuals by self-pollinating and applying the simulation approach of Chung and Liao .For each subset of 10 parental lines generated from Step 2, any two parental lines were crossed to produce 45 Fand Liao ; hence, 10 individuals presumed to constitute a fixed population of inbred lines.The procedure of generating genotypic data, predicting the GEBVs, and selecting the top 45 individuals was performed repeatedly, to produce 2,700 F10 individuals generated from each subset of 10 parental lines, the best F10 inbred line with the highest index value was identified. The above analysis procedure was repeated 30 times to obtain the best F10 inbred lines from each repetition per strategy. To evaluate improvements in both the larger-the-better and the smaller-the-better target traits attained by each strategy, the genetic gain was calculated this way:For the final 2,700 F10 individuals, and where mean(|GEBVF10 − δ|) is the averaged deviation of the F10 inbred lines from the nominal value δ, and mean(|GEBVp − δ|) is the averaged deviation of the parental lines from δ.where via back-transformation from their normalized GEBVs. Furthermore, pairwise comparisons among the GEBV averages for each trait were carried out using the least significant difference (LSD) test.The GEBVs of the target traits on their original measuring units were obtained Hereafter, GEBVs are reported for the target traits based on their original scales.1 generation. In contrast to YLD, which improved from F1 down through the F10 generation under every strategy tested, the desirability in the GEBV average for both PH and FT improved going from the F1 to F3 or F4 generation, but gradually declined in later generations. A strategy with the index weight of 0.2 provided the best F10 inbred lines, these having a better PH and FT than those generated from the same strategy whose index weight was 0.The GEBV averages of the best individuals from the 30 repetitions per generation are displayed in 10 individuals from the 30 repetitions and the improvement of Eq. (7) are presented in The end-point of the GEBV averages for the best FThe average genetic gain for a given target trait, as calculated by Eq. (9), from the 30 repetitions appears in 10 generations are in The GEBV averages of the best individuals from the 30 repetitions per generation are shown in The genetic gains for these nominal-the-best traits calculated using Eq. (10) are displayed in As suggested in The FT at three different locations in the 44k rice dataset was used to demonstrate that the proposed approach can be applied to select parents for producing inbred lines with high adaptability to different environments. As suggested in Incorporating the multi-trait GBLUP model and the selection index into the framework for single-trait selection presented in our previous article , environment (E), and their G × E interaction. In reality, the local environment can significantly influence the performance of progeny populations during the growth period of each generation until they reach the FThe original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.P-YC: data curation, investigation, software, and validation. C-TL: conceptualization, project administration, supervision, writing the original draft, and review and editing. All authors contributed to the article and approved the submitted version.This research was supported by the Ministry of Science and Technology, Taiwan (grant number MOST 110-2118-M-002-002-MY2).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.