Sex differences in complex traits are suspected to be in part due to widespread gene-by-sex interactions (GxSex), but empirical evidence has been elusive. Here, we infer the mixture of ways in which polygenic effects on physiological traits covary between males and females. We find that GxSex is pervasive but acts primarily through systematic sex differences in the magnitude of many genetic effects (“amplification”) rather than in the identity of causal variants. Amplification patterns account for sex differences in trait variance. In some cases, testosterone may mediate amplification. Finally, we develop a population-genetic test linking GxSex to contemporary natural selection and find evidence of sexually antagonistic selection on variants affecting testosterone levels. Our results suggest that amplification of polygenic effects is a common mode of GxSex that may contribute to sex differences and fuel their evolution.  •Genetic effects on physiology often depend on sex in an underappreciated way•Amplification: differences in magnitude shared by many genetic effects•Amplification may act jointly on co-moderated environmental and genetic effects•Polygenic scores that incorporate amplification improve phenotypic prediction Zhu et al. estimate the ways in which genetic effects on anthropometric measurements and biomarkers depend on sex. They find pervasive sex contingency acting not through differences in genetic basis but largely through “amplification”—systematic differences in the magnitude of numerous genetic effects. They show that amplification explains trait variance differences between the sexes and that it may be consequential for sex-specific natural selection. If the distribution of contexts differs between groups of people, as it does for males and females, so should the average genetic effects on traits.,,,,,,,Here, we set out to study governing principles of GxSex in complex human traits and explain why current approaches for characterizing GxSex may be lacking for this goal. We then suggest a mode of GxSex that may have gone largely underappreciated: a shared difference in the magnitude of effect of many variants between the sexes, which we refer to as “amplification.”We developed a new approach for flexibly estimating male-female genetic covariance relationships and applied it to 27 complex physiological traits in the UK Biobank. We found that amplification is pervasive across traits. The inferred polygenic covariance structure explains sex differences in trait variance remarkably well and, in most cases, helps improve phenotypic prediction. Finally, we consider an implication of polygenic GxSex for sexually antagonistic selection. We develop a model that demonstrates how variants that affect traits may be subject to sexually antagonistic selection when male and female trait optima are very different or, surprisingly, even when the trait optima are very similar. We developed a novel test for sexually antagonistic polygenic selection that connects GxSex to signals of contemporary viability selection. Using this test, we find subtle evidence of sexually antagonistic selection on variants affecting testosterone levels.,,We conducted GWASs stratified by sex chromosome karyotype for 27 continuous physiological traits in the UK Biobank (UKB) using a sample of ∼150,000 individuals with two X chromosomes, another sample of ∼150,000 individuals with XY, and a combined sample that included the XX and XY samples. We chose to analyze traits with SNP heritabilities over 7.5% in the combined sample to have higher statistical power. While there is not a strict one-to-one relationship between sex chromosome karyotype and biological sex, we label XX individuals as females and XY individuals as males and view these labels as capturing group differences in distributions of contexts for autosomal effects rather than as a dichotomy.,Among the 27 traits, we observed substantial discordance between males and females in associations with the trait only for testosterone and waist:hip ratio For the majority of traits (18 of 27), male and female heritabilities were greater than the heritability in a sample that included both sexes. For instance, in arm fat-free mass (right), the heritability in the both-sex sample was 0.232 (±0.009), while the heritabilities for male and female were 0.279 (±0.012) and 0.255 (±0.011), respectively. In particular, all body mass-related traits, excluding BMI-adjusted waist:hip ratio, had greater sex-specific heritabilities A and 1B.−10; In addition, we noticed a trend where, as the genetic correlation decreased, the difference between the heritabilities within each sex and in the sample combining both sexes tended to become larger , genetic predictors of a complex trait. Under this hypothesis, regardless of whether the PGS is estimated in a sample of males, females, or a combined sample of both males and females, it should be predictive in both sexes because the causal variants and the direction of their effects are shared, and the magnitude is correlated ,e matrix A. Our coe matrix .Figure 3We first focus on testosterone, for which previous research sets the expectation for polygenic male-female covariance. In terms of magnitude, the vast majority of effects should have much greater effect in males. In terms of correlation, we expect a class of genetic effects acting through largely independent and uncorrelated pathways alongside a class of effects via shared pathways.The only trait of the 27 where a large fraction  of genetic effects and varies in its distribution between the sexes. As an example of such a cue, we considered testosterone. Testosterone may be a plausible instigator because the hormone is present in distinctive pathways and levels between the sexes and is a known contributor to the development of male secondary characteristics and therefore could modulate genetic causes on sex-differentiated traits.To test this idea, we first binned individuals of each sex by their testosterone levels. Then, for each trait and within the bin, we quantified the magnitude of total genetic effect as the linear regression coefficient of trait values to a PGS for the trait A. For alWe performed two additional analyses designed to control for possible caveats to the association of testosterone and the magnitude of polygenic effect. First, a test that controls for possible confounding with age . Second,,Our results thus far suggest that polygenic amplification across sexes is pervasive across traits and that the ratio of phenotypic variance scales with amplification A. An immWe tested the fit of the theoretical prediction under pervasive joint amplification across traits. We used our estimates of sex-specific phenotypic variance and SNP heritabilities to estimate the ratios of genetic and environmental variances. We note that environmental variance is proxied here by all trait variance not due to additive genetic effects, and caution is advised with interpretation of this proxy. Twenty of the 27 traits were consistent with the null model of pervasive joint amplification . Testosterone is among the three strongest signals in the two other samples as well, although none of the traits are statistically significant in these samples.With these conservative criteria considered, we only find evidence of sexually antagonistic polygenic selection on testosterone. In the non-Finnish sample, the largest of the three samples, the null hypothesis Departing from previous studies that sought GxSex through single loci or heritability analyses, we modeled GxSex as a mixture of polygenic relationships across the genome. Our analysis supports pervasive context dependency of genetic effects on complex traits, acting largely through amplification. Surprisingly, even for some traits such as red blood cell count, previously considered non-sex specific because of high genetic correlations between sexes and a concordance in top GWAS hits, we find evidence of substantial GxSex. The strong relationships we find between amplification, environmental variance, and phenotypic variance further point to its potential importance for sex differences.We have shown that considering the polygenic covariance structure, including amplification signals, improves phenotypic prediction for most traits. Its incorporation in PGSs is straightforward. We therefore recommend its broad application and further building on our approach to improve clinical risk stratification and other applications of PGSs.Our findings may seem at odds with previous reports of GxSex primarily consisting of sex-limited effects  or antagonistic effects (differences in sign).Localization of GxSex signals can provide clues regarding the modulators underlying amplification. Here, we proposed one such modulator, testosterone, and found a correlation between testosterone levels and the magnitude of genetic effect on whole body fat mass. The opposite signs of these correlations in females and males may reflect the discrepant relationship between testosterone and these traits at the phenotypic level.,,,,,Our approach for studying GxSex in complex physiological traits can be adopted to study the moderation of polygenic effects by other environments. Starting out with sex as an environmental variable offers a methodological advantage. The study of context dependency in humans is often complicated by study participation biases, leading to a genetic ancestry structure that confounds genotype-phenotype associations,Finally, we developed a model—the first to our knowledge—that considers how GxSex may fuel sexually antagonistic selection on complex traits. Over long evolutionary timescales, the two scenarios depicted in ,,,,We found suggestive signals of sexually antagonistic selection on variation associated with testosterone levels .Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Arbel Harpak  as identified by the UK Biobank in data field 22020. To reduce potential population structure confounding, we further limited our sample to individuals identified by the UK Biobank as “White British” in data field 22006. These are individuals who both self-identified as White and as British and were additionally very tightly clustered in the genetic principal component space.,In this study, we considered 337,111 individuals who passed quality control (QC) checks, which included the removal of samples identified by the UK Biobank with sex chromosome aneuploidy or self-reported sex differing from sex determined from genotyping analysis. We excluded related individuals , givingmash) to examine correlation and differences in magnitude of SNP effects between males and females.mash is an adaptive shrinkage methodWe used multivariate adaptive shrinkage  to be differences in the magnitude of genetic effects, we performed a simulation study. In short, samples of males and females were generated under the model given by mash, and test whether the estimated mixture weights spuriously suggest the presence of GxSex. We performed this simulation on a grid of parameters, including heritabilities in males set to either 5% or 50%, female to male environmental variance ratio of 1, 1.5 or 5; and 100, 1,000 or 10,000 causal SNPs.To ensure that First, we created a sample of 300K individuals with randomly assigned sex. We then sampled genotypes for all individuals consisting of 20K SNPs by sampling from the observed distribution of allele frequencies from UK Biobank’s imputed data,mash.Phenotypes were then set using the following additive model,mash was not grossly mistaking differences in environmental variance as amplification.For nearly all parameters, out of the weights on matrices other than the null matrix, the vast majority was placed on the matrix for perfect correlation, equal magnitude . As the mash accurately captures sex-biased amplification of genetic effects , the equal effect matrix received 78% of the weight, and the difference between male-larger and female-larger magnitude was 1% . For modWe tested a model of testosterone as a modulator of magnitude differences in males and females. We first split individuals by sex and for each sex, created 10 bins of testosterone levels. We adjusted one of the 10 bins to have testosterone levels overlap between males and females. The overlapping testosterone bin was based on fewer individuals (∼800) compared to the other bins (∼2200). For each trait, each of the sexes, and within each bin, we performed a simple linear regression of trait values to the PGS for the trait (using a PGS based on both-sex summary statistics ). We int,To mitigate the possible effects of confounding (of testosterone and magnitude of polygenic effect) or reverse causation  we employed a version of Mendelian RandomizationWe also examined whether participants’ age may have confounded the relationship between testosterone and polygenic effect. In this analysis, instead of using the polygenic effect as the response variable across bins, we used the polygenic effect residualized for mean age in the bin and examined the effect of an individual’s polygenic score on the residual .Here, we suggest a null model in which amplification is shared between genetic and environmental effects. We then suggest a prediction that the model yields and explain how we tested this prediction across traits .c is a constant, If an amplifier is shared, it may be modeled as having the same scalar multiplier effect on genetic and environmental effects. Consider the within-sex additive model of Allele frequencies are once again assumed to be close to equal between males and females, since due to random segregation of alleles during meiosis, genotype frequencies at autosomal sites are independent of sex; and further assuming no substantial interaction between genotype and sex affecting participation in UKB.The model we would like to test is one where the amplification of environmental effects can also be simplified to the same scalar multiplier,Hence, with equal amplification,To test the model of shared amplification between environmental and polygenic effects  we obtaigression .nd-order Taylor approximation for the standard error of a ratio of estimators of Representing male genetic or environmental variance as Plugging in the point estimate In this case, Finally, for each trait, we estimated Z score, i.e., further treating In We developed a model relating sex differences in additive effects on a trait at a biallelic locus  as in the main text. Since individual level data was available in this case, we replaced In the main text, we focus on the results performed this estimation for Ashkenazi Jewish, Finnish, and Non-Finnish European populations as the other ancestry group-stratified subsamples in  females .


PRS and environment interaction analysis with twelve known CBP risk factors revealed no significant results, suggesting that the magnitude of G × E interactions with studied factors is small. The limited predictive ability of the PRS that we developed is likely explained by the complexity, heterogeneity, and polygenicity of CBP, for which sample sizes of a few hundred thousand are insufficient to estimate small genetic effects robustly.Chronic back pain (CBP) is a complex heritable trait and a major cause of disability worldwide. We developed and validated a genome-wide polygenic risk score (PRS) for CBP using a large-scale GWAS based on UK Biobank participants of European ancestry . The PRS showed poor overall predictive ability , but individuals from the 99th percentile of PRS distribution had a nearly two-fold increased risk of CBP . We validated the PRS on an independent TwinsUK sample, obtaining a similar magnitude of effect. The PRS was significantly associated with various ICD-10 and OPCS-4 diagnostic codes, including chronic ischemic heart disease (OR = 1.1,  Back pain is a major cause of disability worldwide. According to the Global Burden of Disease Study 2015, low back pain together with neck pain were the leading causes of years lived with disability in 1990–2015 . Genome-A polygenic risk score (PRS) is an estimate of genetic liability for a trait or disease, calculated according to an individual’s genotype profile and relevant GWASs. A PRS is a powerful modern tool for studying the genetic epidemiology of a disease with potential clinical utility, for example, for developing prognostic biomarkers or subphenotyping patients . There aIn this work, we have developed a genome-wide PRS for CBP based on a recent large-scale CBP GWAS. We assessed the ability of the resulting PRS to predict CBP in an independent sample; examined associations between the PRS and diagnostic codes from the International Statistical Classification of Diseases and Related Health Problems, tenth revision (ICD-10), and Classification of Interventions and Procedures, the fourth edition (OPCS-4), in UK biobank in a hypothesis-free manner; and evaluated the interactions between the PRS and major epidemiologic and clinical risk factors for CBP. The general scheme of the model creation is presented in To create and evaluate the CBP PRS model, we used the UK Biobank dataset . SociodeCases and controls of CBP were defined based on questionnaire responses. First, participants responded to “Pain type(s) experienced in the last months” followed by questions inquiring as to whether the specific pain had been present for more than three months. Those who reported back pain lasting more than three months were considered to be CBP cases. Participants who reported no pain or pain lasting for less than three months were categorized as controls, including those who reported pain lasting between 1 month and 3 months. Individuals who preferred not to answer were excluded from the study. We excluded from the analysis individuals who reported more than three months of pain all over the body, because this phenotype was negatively correlated with other pain phenotypes. For training the model, we used a CBP GWAS from our previous study based on 265,000 randomly selected individuals of European ancestry  from UK Biobank . A GWAS For testing the model, we used a set of unrelated individuals (as defined by UK Biobank) of European ancestry  who were not included in the training and validation sets. Prior to testing, PRS values were standardized . We then validated the CBP PRS in an independent sample from TwinsUK. TwinsUK is an adult twin registry, predominantly female, which includes over 14,000 participants. It is the most deeply phenotyped and genotyped twin cohort in the world . We usedhttps://biobank.ctsu.ox.ac.uk/crystal/field.cgi?id=41202, accessed on 30 August 2022 and https://biobank.ndph.ox.ac.uk/ukb/field.cgi?id=41272, accessed on 30 August 2022 for more details on code levels). Codes from the ICD-10 chapters XVIII–XXII and from the OPCS-4 chapters X–Z were excluded. Next, we filtered codes with low prevalence (<0.5% and >99.5%). The resulting list of medical codes contained 165 ICD-10 and 132 OPCS-4 designations. Additionally, we analyzed the association of the PRS with six chronic pain phenotypes  defined by questionnaires, as described above. All traits were analyzed utilizing GLMs and linear regression included in the standard R function glm. In general, models considered the trait  as a dependent variable and the standardized PRS as a predictor with information on sex, age, genotyping batch, and the first 10 principal components (PCs) of the kinship matrix included as the covariates (Trait ~ Age + Sex + batch + PC1 + … + PC10 + PRS). We set the Bonferroni-corrected statistical significance threshold for the analysis at p-value < 1.65× 10−4 = 0.05/(165 + 132 + 6), where 165 corresponds to the number of ICD-10 codes analyzed, 132 reflects the number of OPCS-4 codes, and 6 represents the number of chronic pain phenotypes.We used the PRS of CBP to examine associations with other health conditions, defined by the ICD-10 diagnostic codes  and OPCS-4  procedure codes, in the set of unrelated individuals of European ancestry from UK Biobank . We used ICD-10 and OPCS-4 codes combined at the second level . The optimal PRS model for CBP included 1,090,574 HapMap3 well-imputed SNPs. In the out-of-sample test dataset from the UK Biobank, the mean PRS difference between cases and controls was 0.214 of the PRS standard deviation . When we added sex and age into the model using the linear coefficients estimated in UK Biobank (0.216 × PRS + 0.06 × Sex + 0.005 × Age), the AUC increased to 0.58 (95% CI: 0.58–0.59). The effect of the standardized PRS on LBP was comparable with the effect of PRS on CBP in UK Biobank: OR = 1.21, 95% CI: 1.11–1.32.We evaluated the association of the CBP PRS with ICD-10 and OPCS-4 diagnostic codes . The PRSp-value < 0.05).We evaluated the magnitude of PRS-by-environment interactions with twelve risk factors for CBP. The results are presented in Here, we have developed and replicated the first genome-wide polygenic risk score for CBP. The overall predictive ability of the PRS was modest (AUC = 0.56); however, it was highly statistically significant. Moreover, people from the 99th PRS percentile had almost double the risk of CBP . Given the high prevalence of CBP, this translates to an absolute risk of 28%. The PRS had almost the same performance and effect estimates in an independent sample from the TwinsUK cohort, and a model also including age and sex (0.216 × PRS + 0.06 × Sex + 0.005 × Age) produced a slightly higher AUC in TwinsUK (0.58). The current work shows that this model is replicable, and suggests that it can be used further on other samples.https://r7.risteys.finngen.fi/phenocode/M13_DORSALGIA, accessed on 30 August 2022). Thus, the obtained OR could be underestimated.An analysis of the associations of the CBP PRS with ICD-10 and OPCS-4 codes showed that the PRS is associated with a wide variety of different diseases and conditions. As expected in line with Cheverud’s conjecture ,25, the The analysis of PRS-by-environment interaction revealed no statistically significant results. This analysis was designed to approximate the analysis of genotype according to environment interactions ,27. NoneThe study has several limitations. Firstly, the model was developed using populations of European British descent and should not be generalized to non-European samples. Secondly, the observed squared Pearson correlation of the PRS and CBP was much smaller than the estimated SNP-based heritability on the observed scale for the same trait (0.007 and 0.04, respectively [To conclude, we developed and validated a genome-wide PRS for CBP based on a recent large-scale GWAS, revealing associations with various related disorders and traits, highlighting the challenges posed by the complex nature and polygenicity of CBP.


Inflorescence properties such length, spikelet number, and their spatial distribution across the rachis, are fundamental indicators of seed productivity in grasses and have been a target of selection throughout domestication and crop improvement. However, quantifying such complex morphology is laborious, time-consuming, and commonly limited to human-perceived traits. These limitations can be exacerbated by unfavorable trait correlations between inflorescence architecture and seed yield that can be unconsciously selected for. Computer vision offers an alternative to conventional phenotyping, enabling higher throughput and reducing subjectivity. These approaches provide valuable insights into the determinants of seed yield, and thus, aid breeding decisions.Lolium perenne L.) spikes. SpykProps is able to rapidly and accurately identify spikes (RMSE < 1), estimate their length (R2 = 0.96), and number of spikelets (R2 = 0.61). It also quantifies color and shape from hundreds of interacting descriptors that are accurate predictors of architectural and agronomic traits such as seed yield potential (R2 = 0.94), rachis weight (R2 = 0.83), and seed shattering (R2 = 0.85).Here, we described SpykProps, an inexpensive Python-based imaging system to quantify morphological properties in unilateral inflorescences, that was developed and tested on images of perennial grass (SpykProps is an open-source platform to characterize inflorescence architecture in a wide range of grasses. This imaging tool generates conventional and latent traits that can be used to better characterize developmental and agronomic traits associated with inflorescence architecture, and has applications in fields that include breeding, physiology, evolution, and development biology.The online version contains supplementary material available at 10.1186/s13007-023-01104-z. Inflorescences are flower-bearing structures composed of multidimensional traits that are shaped by both natural and artificial selection. These selective pressures and developmental changes over variable climates resulted in plants with highly complex inflorescence architectures . Hidden Spikes, panicles, and seed heads, all refer to grass inflorescences, the morphology of which contributes to seed yield potential in grasses . In grasZea mays [Sorghum bicolor [Triticum [Avena sativa [Because plant phenotypes are infinite over the lifetime of an organism, phenotyping at a single point in time provides the best estimates of their underlying genetic architecture at a given environment and developmental stage , 14. TheZea mays , Sorghum bicolor , TriticuTriticum , 27, anda sativa . While ta sativa  and studa sativa , 32, thea sativa , 14.Lolium perenne L.), a multifunctional crop that due to its recent domestication for seed production suffers from yield reductions from wild spike architectural traits. Nonetheless, SpykProps can be used to study other species with two-ranked unilateral, i.e., flat inflorescences [Here we describe SpykProps, a tool that, unlike other imaging approaches, allows one to derive latent phenotypes from a myriad of interacting descriptors of color and shape that focus on the inflorescence as a multidimensional phenotype. In addition, our tool can accurately measure conventional traits such as spike length, area, and spikelet number, and does not require proprietary software or sophisticated imaging hardware. This system was developed and tested in perennial ryegrass , resulting in fewer pixels and detail to process, reducing computational time. The spike_segm function produces segmented spikes in individual output images with different representations including, RGB, CIELAB (L*a*b*), and hue-saturation-value (HSV). Using multiple spaces provides a broader range of colors which increases the ability to discriminate across spikes with similar color profiles. Selecting a proper method and threshold that accurately segments the spike is essential since the binary mask that results from this step directly affects the quality of the color and shape descriptors.The first step in the automated pipeline is to identify spikes in the image and separate them from background and other debris. This requires a threshold that can either be set on a channel from the red-green-blue (RGB) value representation, or can be estimated automatically using the Otsu algorithm . This alSpikeSeg_Batch.py) within SpykProps to assist users in determining the method and threshold that is most optimized to their image properties.To determine optimal thresholds for accurately segmenting spikes in our images, we evaluated different thresholds on the red channel as well as scaling factors for the Otsu algorithm Fig. . Specifiskeleton, which relies on Zhang and Suen’s [medial_axis, which computes the medial axis transform of the spike   Fig. D. Any orgth Fig. C, D.Fig.2 = 0.96) and skeleton (R2 = 0.95) that can account for the curved nature of some spikes were more accurate in approximating spike length than using the major axis of a fitted ellipse on the binary spike (R2 = 0.92) or on its convex hull (R2 = 0.81)  Fig. . Neverth81) Fig. E. Using spikelet_segm) that returns spikelet count and generates a mask to quantify their morphology. The first steps involve adding a pad around the spike to facilitate morphological operations such as erosion and opening, which are performed using a cross-shaped kernel of 3 × 3 pixels. These convolutions are executed on a 10% rescaled version of the spike's mask to increase performance, before it is rescaled back to its original size to generate a mask of the Euclidean distances from each pixel to the nearest background pixel. The local peaks in the mask are calculated according to the expected minimum distance (in pixels) between spikelets and are used as markers for the watershed algorithm, which approximates the spikelets boundaries by treating the transformed distance as a topographic map flooded with water  with potential for improvement using conditional or variable minimum expected distances between spikelets.To assess the accuracy of our spikelet segmentation method, we visually counted the number of spikelets across 793 spikes and compared them with automated detection. The spikes were segmented using a minimum threshold of 25 in the red channel and a range of minimum distances from 25 to 75 pixels between spikelets. Our results indicated that values between 25 and 40 pixels missed or overestimated less than two spikelets per spike on average , which generates over 20 possible properties; however, we only focused on those that are more relevant to spike architecture . This step relies on the re Table . Neverthn, bn, cn and dn, derived from the elliptic loci i, yi) with n number or harmonics [CalculateEFD function from the spatial-efd package [pyefd module. To do so, we first provide a binary mask of the spike and fill any holes using the binary_fill_holes function from SciPy [findContours function using the RETR_CCOMP mode and the CHAIN_APPROX_SIMPLE method [n, bn, cn, and dn, are normalized to be insensitive to the spike’s rotation and size. The outline representation of the spike depends on the number of harmonics chosen: the more harmonics included, the more accurate the shape representation  and asymmetric (an and dn harmonics) sources of variance [The spike shape can also be quantified by deriving latent features from its contour. This is done by decomposing the outline into waves with a specified number of harmonic series using the Fourier Transform , 26. Thearmonics . The coe package  which isom SciPy , and theE method  to extraion Fig. . It is wFourierPower function to estimate the number of harmonics needed to exceed a 0.9999 threshold Fourier power [When computing the EFD, the pipeline uses the er power  as a unier power .channel_percentiles which considers all non-zero pixel values in each spike and returns the minimum, maximum, mean, standard deviation, coefficient of variation, percentiles 5, 25, 50, 75, 95, and quantile-based coefficient of variation across nine channels . In addition, channel_percentiles estimates the same parameters for negative and positive values in a* and b*. The resulting dataset can be dimensionally reduced with methods such as principal component analysis, where the resulting eigenvectors could be used as latent variables to separate samples with similar color profiles.Color is an important feature in plant inflorescence, the variation of which often provides information on maturity levels at the time of harvest. Color is a quantitative trait commonly described as qualitative because small variations in hue do not necessarily add relevant information to a biological phenomenon. However, maturity and ripening can be highly variable and arguably impossible to properly quantify at the spikelet or even plant level without high-throughput technology and data. The use of mean intensity values in a region of interest for a given color-space can be problematic when the pixel distribution is not normal. Instead of mean values per channel, SpykProps provides different percentiles across several color spaces as well as descriptors of their variation. There are currently 77 color descriptors that are output using the function An example of how latent color phenotypes could help distinguish spikes with near identical color profiles is shown in Fig. 2) of shape and color descriptors on yield-related traits measured in a perennial ryegrass nursery. Multiple machine learning algorithms showed that some spike properties are more important than others depending on the trait. Gradient boosting machine (gbm) models, in particular, consistently showed that shape and color features were good predictors of theoretical yield potential (R2 = 0.94), while elliptical Fourier were better for rachis weight (R2 = 0.83). Other traits, such as visual shattering, were best modeled using all descriptors from SpykProps  but would not currently work on 6-row barley or wheat (Triticum aestivum) that do not have a flat inflorescence architecture. However, researchers can overcome these challenges reconstructing their 3D-shaped samples by imaging and stitching multiple sides [Given that our system is meant as a foundation for the study of inflorescence architecture through latent phenotypes, it currently has some challenges. First, SpykProps is limited to unbranched inflorescences that can be flattened out without compromising their 3D shape. For example, the system would work on perennial ryegrass, which it was developed on, and other species with similar architectures such as two-row barley  and quartile-based coefficients of variation (QCV) for the color data. The shape data comprises elliptical Fourier descriptors (EFD), as well as geometric properties extracted from the spike's binary mask using the regionprops function , both available for Python.When computing the EFD, the pipeline uses the FourierPower function to estimate the number of harmonics needed to exceed a 0.9999 threshold Fourier power [This pipeline was developed using Python to segment spike and spikelets before extracting features describing variation in morphology. The system includes functions to visualize, compare, and extract data for a single spike, but it is meant to be used on a set of images containing multiple spikes. Ideally, such images contain inflorescences of the same plots, replication, or plant. The most complete datasets are obtained by running the er power , unless We developed multiple machine learning models on SpyProps data from a first-year production nursery evaluated for seed shattering and other seed yield traits. The nursery was located in the Turfgrass Research, Outreach and Education Center at the University of Minnesota, and comprised 20 different maternal clones and their half-sib families , ridge (ridge), least absolute shrinkage and selection operator (lasso), and principal component regression (pcr), elastic net (enet), gradient boosting machine (gbm), support vector machine radial  and lineal (svmLinear), and random forest (rf). Tuning parameters were set based on Caret's default values, which included: up to 30 eigenvectors for pls and pcr; C = 1 for svmLinear and svmRadial, with the latter including sigma = 0.1; lambda = 0.1 for ridge and enet; similar to lasso, enet included fraction = 0.1; finally, gbm was evaluated with different values for tree number , interaction depth , but fixed shrinkage (0.1) and n.minobsinnode (10). The model with the highest R2 was kept when multiple parameters were tested.Combinations of shape and color descriptors were derived from the parents and offspring and used to train the models with data from 70% of the families. Because spike shape and particularly curvature was affected by storing bags, we removed spikes with curvature greater than 5.5 standard deviations above the mean). In some plots, this induced the need for sampling from the imaging data to match the number of processed spikes in the agronomic data. We filtered out near-zero-variance predictors as well as those with a Pearson’s correlation coefficient greater than 0.85, and scale and center the remaining variables before training. All models were trained using the Caret package , cross-vAdditional file 1: Figure S1. Example of an RGB image with segmented and numbered spikes. Figure S2. Spikelet detection with different values for minimum distance. When running the program on a batch of spikes, users should consider the proper minimum distance based on the average number of misdetections, and whether they can be easily filtered as outliers, for example, based on size or shape. Figure S3. Pixel distribution across different descriptors of greenness for three spikes with seemingly alike color profiles. Boxes in density plots indicate the corresponding mean pixel intensity and standard deviation for the spikes in Figure 6 across three channels from different color spaces. Hue in the heatmap indicates the standardized value that each spike has for all color descriptors studied in this project. This shows that the similarity between spikes depends on the descriptor and channels that are being considered. Figure S4. Number of observations for agronomic data by type of germplasm across 20 families. Table S1. Top five most important features for predicting yield related traits using SpykProps.Additional file 2: Table S2. Descriptive statistics for modeled agronomic traits.Additional file 3: Table S3. Results of all machine learning models tested.


Monilinia spp., is the disease that causes the greatest losses in stone fruit worldwide. Currently, M. fructicola has become the dominant species in the main peach production area in Spain. The fruit cuticle is the first barrier of protection against external aggressions and may have a key role in the susceptibility to brown rot. However, information on the role of skin fruit on the resistance to brown rot in peach is scarce. Previous genetic analyses in peach have demonstrated that brown rot resistance is a complex and quantitative trait in which different fruit parts and resistance mechanisms are involved. To search for genomic areas involved in the control of the cultivar susceptibility to brown rot and to elucidate the role of fruit skin against this infection, we have studied, for two consecutive seasons (2019 and 2020), the fruit susceptibility to M. fructicola, together with fruit cuticle thickness (CT) and density (CD), in a collection of 80 Spanish and 5 foreign peach cultivars from the National Peach Collection at CITA . Brown rot incidence, lesion diameter, and severity index were calculated after 5 days of inoculation on non-wounded fruit. The peach collection has also been genotyped using the new peach SNP chip (9 + 9K). Genotypic and phenotypic data have been used to perform a genome-wide association analysis (GWAS). Phenotyping has shown a wide variability on the brown rot susceptibility within the Spanish germplasm as well as on CD and CT. The GWAS results have identified several significant SNPs associated with disease severity index (DSI), CD, and CT, five of which were considered as reliable SNP-trait associations. A wide protein network analysis, using 127 genes within the regions of the reliable SNPs and previously identified candidate genes (169) associated with Monilinia spp. resistance, highlighted several genes involved in classical hypersensitive response (HR), genes related to wax layers as ceramidases and lignin precursors catalyzers, and a possible role of autophagy during brown rot infection. This work adds relevant information on the complexity resistance mechanisms to brown rot infection in peach fruits and the genetics behind them.Brown rot, caused by the  Due to the growing social and political concern about health and environmental sustainability and the more restricted use of fungicides, host tolerance or reduced susceptibility appears as the most efficient and safe strategy to reduce incidence of brown rot in peach growing. Some degree of tolerance to Bolinha’  and someBolinha’ . HoweverThe Spanish peach germplasm has been genetically characterized in previous works using SSRs and SNPs . The strBrown rot susceptibility in peach has been previously evaluated with different approaches, revealing its polygenic and quantitative inheritance . InitialA relationship between infection susceptibility and cuticle thickness and structure has been suggested for different fruit species such as apple , cranberM. fructicola recognition and plant immunity response in peach like receptor-like protein kinases and mitogen-activated protein kinases  and effector-triggered immunity (ETI)) . Candida kinases , leucine kinases . LRR is  kinases , partici kinases . A rapid kinases . The R p kinases ; however kinases .Here, we study the susceptibility to brown rot infection within a collection of Spanish peach germplasms for the first time, including new related traits such as the cuticle density and thickness, in order to shed some light on the role of fruit skin in the resistance to infection. The peach collection was phenotyped for fruit response to brown rot using non-wounded protocols and then genotyped with the high-density Illumina peach 18K SNP v2 array . Then, w22.1P. persica (L.) Batsch) germplasm from the National Peach Collection at CITA has been described recently, using the high-density Illumina peach 18K SNP v2 array (The genetic diversity in the peach (v2 array . Accordi2.2M. fructicola infections were performed during two consecutive seasons (2019 and 2020). From each tree, 40 fruits were harvested at commercial maturity and immediately transported to the lab for the assays. The harvest date for each tree was recorded for each season.Phenotypic evaluations for fruit response to 2.2.1M. fructicola (Winter) Honey infection was evaluated by controlled inoculation. The strain of M. fructicola used in this study (CPMC3) was provided by the Postharvest Pathology group of IRTA  and was isolated from a latent infection of a peach fruit from a commercial orchard. Out of 40 fruits harvested from each tree, 20 unblemished fruits of similar maturity (0.6–0.8) determined by Index of Absorbance Difference (IAD) (5 conidia per mL of M. fructicola isolate CPMC3. Perpendicular brown rot lesion diameters (mm) (BRD) were recorded 5 days after inoculation and incubation of the peaches in the dark humidified containers at 20°C ( ± 1°C). When the lesion diameter was bigger than 70 mm, a maximum BRD of 70 mm was assigned. The disease severity index (DSI) for each cultivar was calculated as the product of the average lesion diameter × proportion of fruit with lesions greater than 10 mm (disease incidence), following protocol described in Fruit susceptibility to ce (IAD)  were usece (IAD) . There w2.2.2For fruit cuticle assays, three unblemished fruits per tree (and two trees per cultivar) were selected and five epidermal disks (13 mm in diameter) were cut with a cork borer from the equatorial part of each fruit. Maximum amount of flesh was manually removed from each disk, and then cuticles were isolated enzymatically by incubation in pectinase and cellulase buffer, following the protocols of 2.2.3®). Frequency histograms were generated with SigmaPlot® v.15 to observe phenotypic data distributions. Normality of the datasets was tested by the Shapiro–Wilk test with a p-value threshold of 0.05. Correlation analysis among the datasets was performed using Spearman’s rank correlation coefficients at p < 0.05.Statistical analyses were carried out by SPSS Statistics v. 29 , and cuticle thickness (CT). Single-locus and multi-locus models were used by GAPIT v.3.1. R Package  GLM, ML mrMLM, . Peach rINK v1.9 . FunctioINK v1.9 . FinallyINK v1.9 . The STRINK v1.9 . The seq33.13.1.1p = 0.106), whereas in 2020 data did not pass the normality test.A total of 80 peach cultivars with Spanish origin and five foreign ones were evaluated for susceptibility to brown rot respecting the integrity of the fruit skin (unwounded fruit) in order to keep the natural resistance to infection associated with fruit skin Figure 1p = 0.097), whereas data in 2020 showed a non-normal distribution.Regarding BRD, all cultivars showed rot diameters between 4 and 70 mm at both seasons, although extreme values (very high and very low) were more abundant in 2020. Only 10 cultivars showed rot diameters higher than 40 mm in 2019, whereas in 2020 there were 18 mm. Similarly to what was observed for the DSI, the Shapiro–Wilk test showed BRD data in 2019 as normally distributed , suggesting that susceptibility to BR infection could be controlled by a low but significant genetic component.As observed, although some variation for DSI and BRD was observed between years, most cultivars showed both years a similar trend regarding susceptibility/tolerance to ve years Table 2AThe red-skin yellow-fleshed non-melting peach ‘Rojo de Tudela’ was the least susceptible cultivar, together with ‘La Escola’ and ‘Gallur’ (both red-skin yellow-fleshed non-melting peaches), whereas the yellow-fleshed non-melting cultivar ‘Borracho de Jarque’ showed the highest susceptibility, closely followed by two types of white-fleshed melting flat peaches (‘Paraguayo Almudí’ and ‘Paraguayo T. Robert’).3.1.22 in 2019 and between 12.44 and 48.39 µg/mm2 in 2020 , suggesting that this trait could have little but significant genetic control.Fruit cuticle density (CD) of the 85 peach cultivars ranged between 12.01 and 63.40 µg/mmCuticle thickness (CT) also showed considerable variability among the peach cultivars studied Figure 23.1.3Regarding relations between traits Table 2B3.2A total of 16,038 SNPs was analyzed in GenomeStudio . ASSIsT determined 1,257 SNPs (7.8%) as failed and 2,798 (17.4%) as monomorphic, and both groups were removed for subsequent analysis  in the infection protocol.y points  at any dy points . The imp studies . Also, m studies , which d studies . That is studies . HoweverOn the other hand, significant although low seasonal correlation was observed in this work for DSI, whereas brown rot diameter (BRD) showed non-significant correlation between years. These low correlation values between years for BR infection traits have been already previously reported by other authors  when usi2, respectively, similar to the range obtained here. However, in our study, some cultivars showed twofold higher densities such as ‘Maruja Tejar’, ‘Montaced’, ‘Montamar’, and ‘Sudanell’. CD showed a low but significant correlation between years, whereas CT was not significantly correlated between years, which may indicate that CT is more environmentally dependent than CD. As far as we know, no previous data of cuticle thickness analysis in a group of peach cultivars have been previously reported.Regarding the peach cuticle density, although previous works are scarce, M. laxa infection. As far as we know, there are no other studies in peach were the direct influence of fruit cuticle properties to the brown rot susceptibility is studied. Our results introduce one more variable to have into account when selecting for resistant peach cultivars to brown rot.Significant correlations between CD and CT with BRD and DSI found in this study, indicate the importance of cuticle, specially the cuticle thickness, on the fruit defense to brown rot infection. The relationship between susceptibility to different fungus and cuticle thickness and structure has been already reported by previous studies in apple , cranberThe high-density Illumina peach 18K SNP v2 array  used herAs has been commented above, although an extensive number of association studies for brown rot resistance have been completed in peach , few genRegarding the other two SNPs identified here [Peach_AO_0309124  and Peach_AO_0648505 ], no significant association has been identified in these regions in previous studies, which may suggest the existence of specific favorable alleles in the genetic background of the Spanish germplasm. In addition, two new regions in Chromosome 2  and Chromosome 7  were associated with cuticle density and thickness traits for the first time in peach. Indeed, this is the first time that these two traits are included in a GWAS for brown rot susceptibility. The different genetic backgrounds, sources of resistance, and environmental effects together with the polygenic nature may be the causes of the low consistency among studies, even in different datasets in the same study .Prupe.6G161700 gene is annotated as a probable leucine-rich repeat (LRR) receptor-like protein kinase by STRING. LRRs have been previously found in enrichment analysis in peach brown rot resistance association studies  leads to their proteasomal degradation, commonly by the 26S proteasome (Prupe.6G052000) showed annotations of LRR and ubiquitin-like domain protein and protein interactions with LRR-related proteins of other candidate genes . Peach has only two genes from this gene family, in chromosome 2 (Prupe.2G322400) and chromosome 6 (Prupe.6G164000). In this sense, the functional annotation, after the evaluation of the genome architecture of several isolates of Monilinia spp., indicated that Monilinia spp. infection activated multiple pathways involved in carbohydrate catabolism or autophagy for effective colonization  seems to be subject to ubiquitylation and proteasomal degradation in different conditions (nutrient starvation or during recovery)  caused a modifier effect in the intergenic region of the gene nization . The autecovery) . In 2005sicicola . In anotsicicola . The rolsicicola , but at sicicola . In our Monilinia spp. infection. Membrane (KW-0472) was one of the highest significant terms in the enrichment of protein network analysis including 85 proteins, which may reflect the overall importance of the barriers in peach brown rot resistance. Firstly, a moderate effect caused by the reliable SNP Peach_AO_0100138 produces a change of amino acid (missense variant) over the gene Prupe.1G356500 . Functional annotations of Prupe.1G356500 described it as a ceramidase. Ceramidases are enzymes which hydrolyze ceramide and have been related with the regularity of wax layer and susceptibility to Pseudomonas syringae in Arabidopsis , including nine proteins. Phenylpropanoid metabolism was associated with apple fruit resistance to gray mold disease caused by ect ways . High leect ways . In addibidopsis . Also, tbidopsis . RecentlPenicillium expansum , according to the STRING tool. CAD is a NADP(H)-specific oxidoreductase, which catalyzes the last step in the biosynthesis of monolignols, the monomeric units of the lignin . Peroxidexpansum . Also, anfection . RecentlM. fructicola, and therefore selecting cultivars with thicker and denser cuticles could be one more factor to take into account in the combination of factors needed to select for more resistant cultivars to brown rot infection. We carried out a GWAS using different single- and multi-locus models identifying three reliable SNPs associated with DSI in linkage groups 1, 3, and 6. The low consistency in the DSI-associated genomic regions identified in previous studies in different genetic backgrounds has been discussed here, identifying the current consensus regions among studies. Moreover, SNPs associated with cuticle thickness and density traits, the first barrier against brown rot infection, have been identified in linkages group 7 and 2, respectively, being the first report identifying markers associated with these defense traits. The combination of more than a decade of results to understand the genetic control of brown rot resistance and the new results obtained here highlighted a complex network of genes and proteins, reflecting the expected multilayered innate immune system to prevent brown rot invasion and proliferation. From the primary barriers’ perspective, candidate genes related to wax layers, as ceramidases, and to cell wall components, as lignin precursors catalyzers  have been identified and could be considered as candidate genes for marker-assisted breeding (MAS). In addition, our results suggest that autophagy could contribute in some way (positively or negatively) in the resistance to brown rot, participating in the defense response or in the pathogenicity associated with this disease in peach. This work highlights the importance of preserving traditional germplasm collections, where favorable alleles can be retrieved to improve brown rot resistance in peach, and provides new information for breeding programs in order to advance toward the selection of less susceptible cultivars to brown rot.For the first time, brown rot resistance in peach and the role of skin cuticle on it has been studied in a large Spanish germplasm and its genetic control has been explored. Brown rot resistance is a complex trait, with a considerable environmental effect and tedious phenotyping process. We have demonstrated for the first time that peach skin cuticle is the first barrier against The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/Conceptualization, PM-G and CC; methodology, PM-G, JB, and CC; investigation, JM-G, AP, CC, and PM-G; data curation, PM-G, CC, and JM-G; writing—original draft preparation, JM-G, AP, JB, CC, and PM-G; writing—review and editing, JM-G, PM-G, and CC. All authors contributed to the article and approved the submitted version.


R2 value. One of the key assumptions of linear regression is that the variance of the residual should be constant at each level of the predictor variables, called homoscedasticity. However, some studies show that PRS models exhibit heteroscedasticity between PRS and traits. This study analyzes whether heteroscedasticity exists in PRS models of diverse disease-related traits and, if any, it affects the accuracy of PRS-based prediction in 354,761 Europeans from the UK Biobank. We constructed PRSs for 15 quantitative traits using LDpred2 and estimated the existence of heteroscedasticity between PRSs and 15 traits using three different tests of the Breusch-Pagan (BP) test, score test, and F test. Thirteen out of fifteen traits show significant heteroscedasticity. Further replication using new PRSs from the PGS catalog and independent samples  from the UK Biobank confirmed the heteroscedasticity in ten traits. As a result, ten out of fifteen quantitative traits show statistically significant heteroscedasticity between the PRS and each trait. There was a greater variance of residuals as PRS increased, and the prediction accuracy at each level of PRS tended to decrease as the variance of residuals increased. In conclusion, heteroscedasticity was frequently observed in the PRS-based prediction models of quantitative traits, and the accuracy of the predictive model may differ according to PRS values. Therefore, prediction models using the PRS should be constructed by considering heteroscedasticity.The polygenic risk score (PRS) could be used to stratify individuals with high risk of diseases and predict complex trait of individual in a population. Previous studies developed a PRS-based prediction model using linear regression and evaluated the predictive performance of the model using the  Genome-wide association studies (GWAS) have identified numerous genetic variants associated with various complex traits . This ha2] across deciles of PRS for BMI  for the linear regression model . However, the R2 may not be equally estimated at each level of predictor variables if there is a non-constant variance of residuals (such as heteroscedasticity). The predictive performance for previous PRS models was evaluated without considering whether they are homoscedastic or heteroscedastic  test, score test, and F test. We then investigated whether heteroscedasticity affected the accuracy of the PRS-based prediction models.Homoscedasticity describes a situation in which the error variance is constant across all levels of predictor variable(s) in a linear regression model. In other words, the variability of the errors is the same across all values of the independent variable(s) . In contR2 value of 0.9, 2) HS0 with a R2 value of 0.5, 3) HS0 with a R2 value of 0.1, 4) mildly heteroscedastic data (HS1) with a R2 value of 0.9, 5) HS1 with a R2 value of 0.5, 6) HS1 with a R2 value of 0.1, 7) moderately heteroscedastic data (HS2) with a R2 value of 0.9, 8) HS2 with a R2 value of 0.5, 9) HS2 with a R2 value of 0.1, 10) severely heteroscedastic data (HS3) with a R2 value of 0.9, 11) HS3 with a R2 value of 0.5, 12) HS3 with a R2 value of 0.1.To understand heteroscedasticity and homoscedasticity, we generated twelve sets of simulation data: 1) homoscedastic data (HS0) with a i, ranging from 1 to 2,000; the intercept and slope coefficients of Xi are both 0.5. The residual term, ei, represents the residual of observation i on dependent variables such as Y, and follows a normal distribution with a mean of 0 and variance of σε2. The value of σε2 represents the variance of the random error term (ei) for the ith observation. The variability of the errors is constant for different values of Xi. Consequently, Y is dependent on observation i and is calculated using the equation 0.5 + 0.5Xi + ei. In addition, for HS0, each R2 value of 0.9, 0.5, and 0.1 satisfies the following equation:HS0 is generated using a linear regression formula, which is represented as:i, ranging from 1 to 2,000; the intercept and slope coefficients of Xi are both 0.5. The residual term, ei, represents the residual of observation i on dependent variables such as Y, and follows a normal distribution with a mean of 0 and variance of σεi2. The value of σε2 represents the variance of the random error term (ei) for the ith observation. The variance of the error term (ei) for the ith observation, denoted by σεi2, indicates that the variability of the errors differs for various values of Xi. For HS1, each R2 value of 0.9, 0.5, and 0.1 satisfies the following equation:HS1 is generated using a linear regression formula, which is represented as:i, ranging from 1 to 2,000; the intercept and slope coefficients of Xi are both 0.5. The residual term, ei, represents the residual of observation i on dependent variables such as Y, and follows a normal distribution with a mean of 0 and variance of σεi2. The value of σε2 represents the variance of the random error term (ei) for the ith observation. The variance of the error term (ei) for the ith observation, denoted by σεi2, indicates that the variability of the errors differs for various values of Xi. For HS2, each R2 value of 0.9, 0.5, and 0.1 satisfies the following equation:HS2 is generated using a linear regression formula, which is represented as:i, ranging from 1 to 2,000; the intercept and slope coefficients of Xi are both 0.5. The residual term, ei, represents the residual of observation i on dependent variables such as Y, and follows a normal distribution with a mean of 0 and variance of σεi2. The value of σε2 represents the variance of the random error term (ei) for the ith observation. The variance of the error term (ei) for the ith observation, denoted by σεi2, indicates that the variability of the errors differs for various values of Xi. For HS3, each R2 value of 0.9, 0.5, and 0.1 satisfies the following equation:HS3 is generated using a linear regression formula, which is represented as:www.r-project.org). In addition, linear regression (the LM function in R stats package version 4.0.5) was used to estimate the effect size and R2 between X and Y.All simulation processes were performed using R stats packages version 4.0.5 : principal component (PC) analysis calculation filter for selecting unrelated samples; sex chromosome filter for removing aneuploidy; filtering of PCs for European sample selection to determine British ancestry; and filters for selecting self-reported “white-British,” “Irish,” and “white.” The total number of unrelated white British participants amounted to 364,761.We used the UK Biobank resource, a large-scale population-based dataset that recruited over 487,409 individuals aged 40–69 years during 2006–2010 . QualityN = 177,380) and the PRS set . The GWAS set was used for GWAS and consisted of unrelated white British Europeans  and their phenotypic information was collected during the initial assessment period . The individual PRS for 15 traits was estimated using LDpred2 in the PRS set , whose phenotypic information was also collected during the initial assessment period . Next, we randomly selected 80% of the individuals in the PRS set as the modeling set , in which linear regression models between PRS and traits were generated and evaluated for heteroscedasticity. The remaining 20% of individuals in the PRS set  were designated as the validation set, which was used to investigate the prediction accuracy of the PRS model  matrix. The remaining 354,761 samples were divided into two subsets: the GWAS set  coded as “Yes” in the UK Biobank PRS release testing subgroup (field ID: 26200); 2) coded as “No kinship found” in the “genetic kinship to other participants” field; and 3) identified as having a white British, Irish, or White background (field ID: 21000). Lastly, we excluded the 364,761 samples used in the initial analysis, and the remaining 23,620 unrelated white British samples were used for the replication analysis.http://www.hra.nhs.uk/). This allows applicants to conduct research on UK Biobank data without obtaining separate ethical approvals. Access to the UK Biobank data was granted under application no. 83990: “Genetic and environmental analysis for disease prediction models.”All participants provided signed consent to participate in the UK Biobank . The UK Biobank was granted ethical approval to collect participant data by the North West Multicenter Research Ethics Committee, covering the United Kingdom; the National Information Governance Board for Health and Social Care, covering England and Wales; and the Community Health Index Advisory Group, covering Scotland. The UK Biobank possesses generic Research Tissue Bank approval granted by the National Research Ethics Service (https://biobank.ndph.ox.ac.uk/showcase/). The following 15 quantitative traits were selected: alanine aminotransferase (ALT) (field ID:30620), alkaline phosphatase (ALP) (field ID:30610), aspartate aminotransferase (AST) (field ID:30650), body mass index (BMI) (field ID:21001), cholesterol (field ID:30690), creatinine (field ID:30700), cystatin C (field ID:30720), forced expiratory volume in one second (FEV1), and forced vital capacity (FVC) ratio (FFR) (field ID:20258), height (field ID:50), phosphate (field ID:30810), platelet count (field ID:30080), red blood cell count (RBC) (field ID:30010), total protein (TP) (field ID:30860), triglycerides (TG) (field ID:30870), and waist-to-hip ratio adjusted for BMI (WHRadjBMI) calculated by waist circumference (field ID:48), hip circumference (field ID:49), and BMI (Fifteen quantitative traits were selected based on 1) over 5% heritability of traits , 2) over and BMI . Among tIndividuals known to be on lipid-lowering medications  were excluded from the TG and cholesterol analyses  to minimTo prevent the bias of prediction accuracy from extreme trait outliers, we excluded the samples showing extreme trait outlier satisfaction : Y < Q1 p-value < 1.00 × 10−6, insertion-deletion 780000. Finally, 1,149,057 SNPs were extracted for further analyses after referring to HapMap 3 SNPs and strand-ambiguous SNPs   participants were genotyped using the UKB Axiom Array and the United Kingdom BiLEVE Axiom Array from Affymetrix . Genotyp or C/G) .j, as a weighted sum of SNP allele counts , Score, and F tests in the ordinary least squares (OLS) R package version 0.5.3 to evaluate the heteroscedasticity of a trait across the PRS . The BP,p-value is used to determine whether to reject the null hypothesis of homoscedasticity in favor of the alternative hypothesis of heteroscedasticity.The BP test determines whether the variance of the residuals is constant across all independent variables by assessing the association between the squared residuals and the independent variables. A significant result suggests the presence of heteroscedasticity. The resulting test statistic follows a chi-squared distribution with degrees of freedom equal to the number of independent variables, and the resulting The Score test uses the likelihood ratio test to compare the fit of the original regression model to a modified model that includes an additional term to account for heteroscedasticity. The resulting test statistic follows a chi-squared distribution with degrees of freedom equal to the number of parameters in the additional term, and its significance is interpreted similarly to that of the BP test.Similarly, the F test assesses the overall model fit and can also be used to test for heteroscedasticity. It compares the fit of the original regression model to a modified model that includes an additional term to account for heteroscedasticity, with the resulting test statistic following an F distribution with degrees of freedom equal to the difference in the number of parameters between the two models.The amount of heteroscedasticity was quantified by determining the ratio of the mean of the absolute residuals for the largest 10 percent PRS (G10) and the smallest 10 percent PRS (G1).adjBMI , β2 denotes the effect size of age at recruitment (ranging from 40 to 69), β3 denotes the effect size of sex , β4 denotes the effect size of genotyping array (coded as 0 or 1 for the UKB Axiom Array and the UK BiLEVE Axiom Array)  , β5∼ βR2 of PRS-based prediction model using the Pearson correlation method in R stats packages version 4.1.0. To investigate the relationship between the X and Y variables in the simulation, as well as between each of the 15 PRS and trait values in both the PRS and replication sets, a linear regression model was performed using the R package version 4.1.0.Correlation was tested between heritability and the We depicted the scatter plot, line plot, histogram, and bar plot using ggplot2 version 3.3.6 in R. Heteroscedasticity for linear regression models was detected using the Breusch-Pagan (BP), score, and F test in ordinary least squares (OLS) R packages version 0.5.3 provided in R .N = 141,905), we obtained the effect size (β1) of the PRS on each trait using linear regression model in R package version 4.1.0. Additionally, we estimated the intercept values (β0) of the linear regression model between the PRS and trait values. Next, in the validation set , we estimated the predicted trait values using the following formula:Ŷij represents the predicted value of trait j for in dividual i. β0 is the intercept value that was estimated through linear regression between the PRS and trait j in the modeling set. β1 is the effect size of the PRS that was calculated through linear regression between the PRS and trait j in the modeling set. PRSij refers to the individual PRS on each trait (j).In the modeling set  calculate the individual error of the PRS model, 2) find an error more than ±1 SD error value from the mean of the error value, 3) compute the proportion of errors found in 2) by PRS groups.R2 values of 0.9, 0.5, and 0.1  fitted to the linear regression model . Simulat and 0.1 ; 2) thre and 0.1 ; 3) thre and 0.1 ; and 4)  and 0.1 .p-values < 2.00E-16. The R2 values varied between models and heteroscedasticity levels, ranging from 0.10 to 0.91 (R2 = 0.90), 0.99 (R2 = 0.50), and 0.90 (R2 = 0.10). For HS1, the ratio of the mean absolute residual was 1.99 (R2 = 0.90), 1.83 (R2 = 0.50), and 2.29 (R2 = 0.10). For HS2, the ratio of the mean absolute residual was 3.10 (R2 = 0.90), 3.59 (R2 = 0.51), and 3.19 (R2 = 0.10). For HS3, the ratio of the mean absolute residual was 17.82 (R2 = 0.91), 17.73 (R2 = 0.50), and 20.61 (R2 = 0.10)  was randomly divided into two subsets: modeling set (50%) and validation set (50%) to perform all tests using independent datasets. An association analysis using a linear regression model was performed between X and Y in the modeling set . For eac to 0.91 . Formal  to 0.91  (Breusch to 0.91 . HS0 did to 0.91 . Additio to 0.91 . However to 0.91 . Heteros to 0.91 . For HS0 = 0.10) . The ratYi - Ŷi. Also the error rate was defined as the ratio of samples outside 1 standard deviation (SD) of error values. The A consequence of heteroscedasticity in regression analysis is that coefficient estimates remain unbiased and consistent, but are no longer efficient or less accurate . This isWe applied these analysis schemes from the simulation results to real data from the UK Biobank to test for heteroscedasticity between the PRSs and traits . The bash2) explained by common variants (h2 and intercept representing the genomic inflation using linkage disequilibrium score regression (LDSC) based on GWAS summaries for 15 quantitative traits (h2 was observed in the height (0.43), and the lowest h2 was observed in aspartate aminotransferase (AST) (0.06).We selected 15 quantitative traits based on heritability .Next, we calculated PRSs of individuals included in the PRS set. The effect sizes of each genetic variant were reweighted based on its effect size and statistical significance from 15 GWAS summary statistics using LDpred2 . The PRSand 0.13 . Height 2 value . The R2P-threshold of 3.33E-03 (= 0.05/15 quantitative traits) (adjBMI). The variance of residuals for each decile group of PRS from G1 to G10 showed that the variances of residuals in these 13 PRS models tended to increase as PRS increased  . Howeverncreased . Heterosncreased : 1.53 foncreased .Yij - Ŷij . The error rate was defined as the ratio of samples outside 1 SD of error values. The error was calculated in each decile group of the PRS as an indicator of prediction accuracy. The error rate tended to increase as PRS increased from G1 to G10 for the 13 traits showing statistical significance for heteroscedasticity . We calculated the PRSs of individuals using PGS catalog data base, which resulted in an average R2 increase of 0.06–0.13 across 15 quantitative traits in the modeling of the replication set   .We quantified heteroscedasticity using the ratio of mean absolute residuals between each decile group of the PRS from G1 to G10 and found that the variance tended to increase as the PRS increased for these 10 PRS models: 1.60 for TG, 1.42 for ALT, 1.34 for BMI, 1.32 for cholesterol, 1.23 for platelet count, 1.22 for ALP, 1.20 for AST, 1.16 for cystatin C, 1.09 for creatinine, and 1.07 for RBC .Yij − Ŷij . The error rate was defined as the ratio of samples outside 1 SD of error values. The error was calculated in each decile group of PRS as an indicator of prediction accuracy. We found that the error rate tended to increase as PRS increased from G1 to G10 for the 10 traits showing statistical significance for heteroscedasticity. For example, the error rates of G1 to G10 in TG were 0.14 and 0.44, respectively, indicating that the PRS model for TG was 3.14 times more precise in the low PRS group than in the high PRS group  was different for each level of the PRS in the PRS models with heteroscedasticity. These differences in the prediction performance were caused by the disparity in variance of the residuals according to the PRS  were similar across all levels of the predictor variable X, ranging from 23% to 39%. Meanwhile, the error rates of the heteroscedastic models  differed according to the predictor variable X, and the difference of the error rates among the three heteroscedastic models depended on the severity of heteroscedasticity; ranges of the error rate were 25%–36% in HS1 with an R2 value of 0.10, 1%–48% in HS2 with an R2 value of 0.10, and 0%–53% in HS3 with an R2 value of 0.10. The error rates in the HS3 model with a R2 value of 0.10 indicate that all individuals with G1 group (the lowest PRS decile) were precisely predicted, whereas more than half of the individuals with G10 group (the highest PRS decile) were incorrectly predicted. These results were confirmed in the PRS-based prediction models using the real data from the UK Biobank. The prediction models for phosphate, creatinine and ALT had similar prediction performance (R2) as follows; 0.03 for phosphate, 0.03 for creatinine, and 0.02 for ALT (r = 0.89), suggesting the necessity to consider heteroscedasticity to accurately assess the performance of the PRS-based prediction model.A key public health need is to identify individuals at high risk of the disease to enable enhanced disease screening or preventive therapies . Therefon models . Howeveresiduals . The err for ALT . However for ALT . The ran for ALT  and the  for ALT . As mentBMI were obese and overweight, while the remaining 17% had a normal BMI range or were underweight. ALT and found that the disease risks (or ORs) between the groups of the bottom 10% and the top 10% of PRSALT were 1.88 for cirrhosis, and 1.67 for hepatic steatosis. However, differences in prediction accuracy according to PRS groups may occur if heteroscedasticity occurs in PRS models because of differences in residuals for individuals. Accordingly, our results showed that traits exhibiting heteroscedasticity in the PRS model have a larger variance of residuals in the genetically high-risk group based on PRS; this consequently leads to a higher error value. Therefore, it is necessary to test the heteroscedasticity of PRS models to utilize the PRS for the stratification of high-risk disease groups.Recently, PRSs were used as predictive biomarkers to identify high-risk disease groups . Khera eOur study had several limitations. First, heteroscedasticity was only analyzed using European participants. Therefore, heteroscedasticity should be evaluated across various ethnic groups. Second, we focused on detecting and understanding heteroscedasticity in the PRS-based prediction models, but did not investigate the causes of heteroscedasticity. It is important to find factors causing the heteroscedasticity in order to improve prediction models more precise.In conclusion, we identified 10 quantitative traits out of 15 that showed statistical significance for heteroscedasticity using BP, score, and F-test. In these 10 PRS models, we observed that the variances of residuals differed among the PRS groups, and the error rates tended to increase with increasing PRS. This indicates that the accuracy of the predictive model may differ according to PRS values. Therefore, prediction models using PRS for such quantitative traits should consider heteroscedasticity.


The percentages of the mediatory effect of LDL cholesterol, apolipoprotein B, and lipoprotein A under psoriasis conditions on MI risk was 7.4%, 10.2%, and 4.1%, respectively. Psoriasis was causally linked to an elevated risk of lipid metabolism levels and MI. This study further demonstrated that LDL cholesterol, apolipoprotein B, and lipoprotein A mediated the effect of psoriasis on MI risk. And timely lipid-lowering treatment should be given to MI patients. Mendelian randomization (MR) analysis was performed to explore the effect of psoriasis on lipid metabolism traits and myocardial infarction (MI) risk and to analyze the proportion of the mediatory effect of lipid metabolism traits. Publicly accessible summary-level data for psoriasis, lipid metabolism traits, and MI were provided by the genome-wide association studies (GWASs) of the FinnGen Biobank, UK Biobank, and CARDIoGRAMplusC4D, respectively. A two-sample MR was carried out to evaluate the association of psoriasis with lipid metabolism traits and MI. Furthermore, the current research focused on determining if the impact of psoriasis on MI is mediated by lipid metabolism traits. The outcomes of the random effect inverse-variance-weighted (IVW) technique indicated a substantial link between genetically predicted psoriasis and a higher risk of low-density lipoprotein (LDL) cholesterol (OR: 1.006, 95% CI: 1.005–1.007,  Psoriasis, a prevalent and chronic papulosquamous skin disease, imposes a significant societal burden . PsoriasThe relationship between psoriasis and myocardial infarction (MI) has been controversial in epidemiologic studies . GelfandFurthermore, the mechanisms underlying the impact of psoriasis on MI risk are not fully comprehended. In a previous report, psoriasis was linked to abnormalities in lipid traits , with ORs ranging from 1.04 to 5.55 . MeanwhiThe current research involved a two-sample MR analysis to assess the association of psoriasis with MI, referred to as the total effect. To further explore if lipid metabolism traits act as mediators of the effects of psoriasis on disease, another two-step MR was conducted. Initially, the link between psoriasis and lipid traits was assessed. Subsequently, the effect of lipid traits on MI risk was analyzed. Finally, multivariable MR was carried out to identify the direct effect of psoriasis on MI, which was subtracted from the total effect to obtain an estimate of the indirect effects. The summary of the current research design is shown in The current research acquired comprehensive data on the correlation between the single nucleotide polymorphism (SNP) and phenotype from various genome-wide association studies (GWASs). Publicly accessible summary-level data for psoriasis were acquired from the GWAS using data from FinnGen Biobank. The FinnGen study is a unique study that integrates genomic data with digital health care records of more than 500,000 Finnish biobank participants .Summary statistic data for lipid traits, including LDL-C, HDL-C, apolipoprotein B, apolipoprotein A-1, and lipoprotein A, were retrieved from a genome-wide association meta-analysis of 35 biomarkers. These data are deposited in the UK Biobank (UKB) and consist of information from 304,818 participants of European descent . The UKBSummary statistic data for MI were obtained from a genome-wide association meta-analysis of 185,000 coronary artery disease (CAD) cases and controls. This analysis assessed 6.7 million common variants with a minor allele frequency (MAF) > 0.05 and 2.7 million low-frequency (0.005 < MAF < 0.05) variants . The spep < 5 × 10−8) and were distinct from the variants for lipid traits [r2 < 0.001 [https://www.ebi.ac.uk/gwas/ (accessed on 1 June 2022)) and PhenoScanner (http://www.phenoscanner.medschl.cam.ac.uk/ (accessed on 1 June 2022)) using MI as an outcome to help eradicate any potential pleiotropic effects [The genetic variants utilized as IVs for psoriasis had a genome-wide significance (d traits . Similar < 0.001 . SNPs li effects . Followi2/(1 − R2)], where R2 indicates the proportion of variance in instruments according to the formula R2 = 2 × (1 − MAF) × MAF × (Beta/stand error)2. The F-statistic value for each instrument-exposure association ranged from 15.996 to 64.356, revealing less likelihood of a weak IV bias in the final results, as detailed in The F-statistic value for each instrument-exposure effect was above 10, suggesting a low risk of weak instrument bias. The F-statistic was computed using the following formula: F = [(N − K − 1)/K] × [RThe total effect of exposure on an outcome can be classified into two components: indirect and direct effects . The immβ1 denotes the MR effect of psoriasis on a mediator, β2 denotes the MR effect of mediator k on MI after adjusting for genetically determined psoriasis, and β3 is the MR effect of psoriasis on MI after adjusting for a genetically determined potential mediator.The potential mediators were determined by estimating the variations in the total effect of the genetically determined psoriasis on the risk of MI. The following formula was applied to estimate the proportion of the mediation effect : E%=∑k=1The primary analysis utilized the inverse-variance-weighted (IVW) technique to pool Wald ratio estimates of the causal impacts of various SNPs . The appQ statistic was utilized to calculate heterogeneity. The final MR results were analyzed utilizing a multiplicative random-effects model of IVW if the p value of Cochran’s Q test was below 0.05; otherwise, a fixed-effects model was employed [Cochran’s employed . The MR-employed . Finallyp < 0.05 denoted the significance level.Analyses were carried out by utilizing R software version 4.0.5 using “Two-Sample-MR” and “MR-RAPS” packages. p = 0.024), apolipoprotein B , and lipoprotein A  and apolipoprotein A1 abnormalities  was determined using the random-effect IVW method , apolipoprotein B , and lipoprotein A  with an increased MI risk, whereas HDL cholesterol  and apolipoprotein A1  exhibited a substantial correlation with a reduced risk of MI , no other recognized psoriasis risk polymorphisms displayed a strong correlation with CAD . Since tLipid metabolism abnormalities, closely related to psoriasis and MI, might be an intermediate factor along the pathway from psoriasis to MI. Two meta-analyses highlighted that LDL cholesterol, lipoprotein A, and apolipoprotein B levels were considerably higher in individuals with psoriasis than in controls ,43. LDL The present study has several notable strengths. First, publicly accessible summary-level data for psoriasis, lipid metabolism traits, and MI were drawn from several large-scale consortium data of European populations, enhancing the statistical power of the data. Second, the current research employed a range of techniques for sensitivity analysis, especially excluding SNPs associated with potential confounding factors, to improve estimation reliability. Third, the genetic variants utilized as the IVs were located on distinct chromosomes, thus minimizing the impact of potential gene–gene interactions on the estimated value. Fourth, using mediation, MR reduced the bias due to confounding among exposure factors, mediators, outcomes, and measurement error. Finally, multivariable MR could accommodate the combined effects of numerous mediators, even when bidirectional relationships were present .Nevertheless, the study also has several limitations. First, exposure-associated SNPs explained a relatively small proportion of the variation, thus restricting the statistical power to identify a weak correlation between the genetically predicted exposures and outcomes. However, the F-statistic value exceeding 10 minimized any bias resulting from the use of a weak instrument in the analysis. Second, although the heterogeneity was presented in this study, a GWAS with different ages, sexes, and health statuses could not be obtained to explore the resources of heterogeneity. Third, the success of mediation analysis crucially depended on the correct pre-established formulation of the causal relationships of the exposures, as the mediatory and confounding effects could not be statistically distinguished . FurtherThis MR study indicated a causal association between genetically determined psoriasis and an elevated risk of lipid metabolism levels and MI, with evidence that the LDL cholesterol, apolipoprotein B, and lipoprotein A mediated the effect of psoriasis on the MI risk. Therefore, more attention should be paid to the lipid metabolism levels of patients with psoriasis for the primary prevention of MI. And timely lipid-lowering treatment should be given to MI patients.


Immune traits are considered to serve as potential biomarkers for pig’s health. Medium to high heritabilities have been observed for some of the immune traits suggesting genetic variability of these phenotypes. Consideration of previously established genetic correlations between immune traits can be used to identify pleiotropic genetic markers. Therefore, genome-wide association study (GWAS) approaches are required to explore the joint genetic foundation for health biomarkers. Usually, GWAS explores phenotypes in a univariate (uv), trait-by-trait manner. Besides two uv GWAS methods, four multivariate (mv) GWAS approaches were applied on combinations out of 22 immune traits for Landrace (LR) and Large White (LW) pig lines.In total 433  associations were identified with the uv approach implemented in PLINK and a Bayesian linear regression uv approach (BIMBAM) software. Single Nucleotide Polymorphisms (SNPs) that were identified with both uv approaches (n = 32) were mostly associated with immune traits such as haptoglobin, red blood cell characteristics and cytokines, and were located in protein-coding genes. Mv GWAS approaches detected 647 associations for different mv immune trait combinations which were summarized to 133 Quantitative Trait Loci (QTL). SNPs for different trait combinations (n = 66) were detected with more than one mv method. Most of these SNPs are associated with red blood cell related immune trait combinations. Functional annotation of these QTL revealed 453 immune-relevant protein-coding genes. With uv methods shared markers were not observed between the breeds, whereas mv approaches were able to detect two conjoint SNPs for LR and LW. Due to unmapped positions for these markers, their functional annotation was not clarified.This study evaluated the joint genetic background of immune traits in LR and LW piglets through the application of various uv and mv GWAS approaches. In comparison to uv methods, mv methodologies identified more significant associations, which might reflect the pleiotropic background of the immune system more accurately. In genetic research of complex traits, the SNP effects are generally small. Furthermore, one genetic variant can affect several correlated immune traits at the same time, termed pleiotropy. As mv GWAS methods consider strong dependencies among traits, the power to detect SNPs can be boosted. Both methods revealed immune-relevant potential candidate genes. Our results indicate that one single test is not able to detect all the different types of genetic effects in the most powerful manner and therefore, the methods should be applied complementary.The online version contains supplementary material available at 10.1186/s12864-023-09594-w. In modern swine breeding, the time around birth is one main critical period for piglet survival , 2. Deve2 0.4–0.8) have been estimated for several immune traits suggesting exceeding potential of the genetic impact  in LR, whereas, applying mvBIMBAM, this SNPs was observed for cytokines [IL-4|IL-10:IL-1b:IL-6] in LW. Additionally, this SNP was also identified for the trait basophils in LR within uv GWAS using PLINK.H3GA0016899 (rs80959576) was significantly associated with PC4 Cell in LR. According to the loading value, PLT and HAP mostly contributed to PC4 Cell. Applying CCA allowed to detect this SNP for [PLT|RBC:WBC] in LW. Furthermore, H3GA0016899 was also significantly associated with RBC in LW using an uv GWAS.SSC 5: 79.02 Mbp) was identified for [IL4|EOS:IL10:IL1b:TNF] with CCA in LR, whereas PLINK detected this association for RBC in LW. Currently, the SNP H3GA0016899 is unmapped for Sscrofa 11.1, but was previously mapped on SSC 5.The genetic variant DRGA0006061  gene (12.0 Mbp), the SNP ALGA0113815 (rs81342648) was significantly associated with a PC2 Cyto  by applying the PCA approach in LR, whereas PLINK identified this association for IL-4 in LW  were applied on two maternal pig lines. Results were empirically compared within and across the methods.Comparing the uv approaches, identical significant associations were detected. The investigated data sets were also studied by Dauben et al.  using thOne reason for the different number of significant SNP markers among the studies are caused by the requirement for the multivariate analyses. The number of phenotypes per animals have to be complete. Furthermore, the applied methods to correct for false positives and the determined threshold for genome-wide and chromosome-wide significance differ depending on the applied methodology.SSC 15: 120.35 Mbp). The SNP ASGA0070620 is located near protein-coding genes such as TMBIM1 (transmembrane BAX inhibitor motif containing 1).Among the common associations in LR, 49 SNPs were also identified with mv methods in this study. Common results were mostly associated with immune traits related to RBC, cytokines, and HAP e.g. ASGA0070620   in LR. In the study of Lu et al.  and PC3 Cell , respectively. Luo et al.  in LW with CCA. ALGA0047813 , is located within the intron region of the protein-coding gene TLL1 (tolloid like 1). Studies in mice suggest that TLL1 plays multiple roles in the development of the mammalian heart, and is essential for the formation of the interventricular septum. Allelic variants of this gene are associated with atrial septal defect type 6 [Some of the genetic markers detected in this study have been identified in previous association studies for hematological traits. Wang et al.  detectedo et al.  identifit type 6 . FurtherThis study evaluated the joint genetic background of immune traits in LR and LW piglets through the application of various uv and mv GWAS approaches. In general, mv GWAS approaches outperformed uv methods and detected genome-wide associations for immune traits. It should be considered that the number of significant associations differs between the applied methods and the possibility of chromosome-wide correction for multiple testing was only feasible in two approaches. When associations were compared across the investigated breeds, no overlapping markers were observed with uv methods, indicating genetic breed differences. It was possible to detect two SNPs in both breeds applying mv GWAS. However, further options for pre-selection of the breed-specific mv trait combinations and cross-validation should be considered to enable appropriate breed comparison. Our results support the observation that one single test is not able to detect all the many different types of genetic effects in the most powerful manner. These analyses are initial steps to detect pleiotropic regions in general. Beside the validation of our results with other data sets, it is necessary investigate the identified associations further applying fine-mapping approaches and the analyses of candidate genes.Data sets of purebred LR and LW populations were recorded from 2010 to 2017 and were provided by the German breeding organization BHZP GmbH. Animal care, phenotypic measurements, and consideration of environmental effects were described in Roth et al. . In brieGWAS was performed for complete blood count , HAP, and cytokines  as immune traits of 1144 LR and LW piglets, corrected for environmental impacts within the breeds. A detailed description of all investigated immune traits, their summary statistics, and processing of the data set can be found in Roth et al. .SScrofa 11.1. In total, 38 markers show currently no location under this assembly. Using the assembly SScrofa 10.2 it was possible to report a chromosome number and a base pair position for 15 markers. The remaining 22 markers revealed high linkage disequilibrium to other significantly associated SNP (results not shown). The observed regions correspond to the positional information given in the manifest file of the manufacturer.To study genetic associations between measured phenotypes animals were genotyped with a tissue sample via an Ilumina Porcine SNP60 v2 BeadChip  in an external laboratory . Only autosomal markers were used in the different GWAS approaches. Regardless of the selected association method, quality control of genotype data was performed with PLINK . GeneticThe correction for environmental effects was performed within a breed and included all relevant fixed effects: the class effects parity (1–4) and herd-year-season-sex (1–12). Moreover, age and weight and interaction between age and weight at the time of sample collection were included in the model as covariates. Cytokine detection method requires the quantification of samples distributed among 22 analytical plates. Therefore, plate was included as a random term for cytokine immune traits. The effects of breed (LR or LW) or sex (boar or sow) were not included as main factors in the model because of the hierarchical classification of these effects within herd-year-season-sex classes.After quality control, one frequentist and one Bayesian method were used to analyze immune traits for uv associations with the genotype in a GWAS within each breed data set.The starting point for both approaches is a mixed linear model:where 1 and D2 to model this effects [2 averaging The frequentist association approach in PLINK  tests eat} prior . Assumin effects . Bayesiaterature –59.To condensate the estimated highly correlated immune network PCA was applied to immune observation residuals. PCA proceedings steps and results are already published and described in detail in Roth et al. . Before The realization of all possible mv combinations for all available immune phenotypes is computationally extensive. Networks, paths, and graphs can model interactivity between variables. BN describe conditional in- and dependence relationships among variables . TherefoBriefly, the BN is a graphical representation of a probability distribution over a set of variables –63. The GWAS is generally performed on a uv (trait-by-trait) basis by testing each variant at a time. Association analyses that include multiple phenotypes may be more powerful to identify QTL for complex traits, particularly in the case of causal variants that affect multiple correlated traits . In the In the same way that PCA is applied to one set of possibly correlated traits to extract a number of independent variables (PCs) that explain as much variance in the original data set, CCA is applied to two sets of variables to extract a number of independent pairs of variables that explain as much covariance between the two original sets . Thus, Cocument} . Similarth p-value [Methodology development to increase the statistical power of GWAS is extremely important for study designs with heterogeneous traits and small sample sizes. Meta-analysis was carried out with the software TATES (Trait-based Association Test that uses Extended Simes procedure) . TATES r p-value . Based o p-value , the effU is independent of Z, and YI is conditionally independent of Z given YD. This givesWith the software mvBIMBAM (multivariate Bayesian IMputation-Based Association Mapping)  a BayesiThese scenarios were accessed with the option mph 2 within the mvBIMBAM software. The priors for the genetic effect were set at 0.1 and 0.2 according to the author’s recommendation . Bayes F10 Bayes Factors for each genetic variant evaluated the association between the SNP and the traits averaging over all possible partitions. Log10 Bayes Factors value ≥ 3 was characterized as a spurious association while values ≥ 6 as a solid association between a marker and a trait on genome level.Obtained logGenomic Control  was realTo control the number of false-positive results False Discovery Rate (FDR) was applied  on genomSus scrofa11.1 from Ensembl database [For uv and mv GWAS QTL regions were defined considering significant SNPs that mapped at least ± 1 Mbp from another significant SNP and functional annotation was performed retrieving all annotated genes within a QTL region in database .Below is the link to the electronic supplementary material.Supplementary Material 1Supplementary Material 2Supplementary Material 3Supplementary Material 4