Pmean, directly utilized parental phenotypic information without any preprocessing. While approach 2, denoted as BV, replaced the direct use of phenotypic values of both parents with their respective breeding values. While an improvement in prediction performance was observed in both approaches, with a minimum 4.24% reduction in the normalized root mean square error (NRMSE), the direct incorporation of parental phenotypic information in the Pmean approach slightly outperformed the BV approach. We also compared these two approaches using linear and nonlinear kernels, but no relevant gain was observed. Finally, our results increase empirical evidence confirming that the integration of parental phenotypic information helps increase the prediction performance of hybrids.Genomic selection (GS) plays a pivotal role in hybrid prediction. It can enhance the selection of parental lines, accurately predict hybrid performance, and harness hybrid vigor. Likewise, it can optimize breeding strategies by reducing field trial requirements, expediting hybrid development, facilitating targeted trait improvement, and enhancing adaptability to diverse environments. Leveraging genomic information empowers breeders to make informed decisions and significantly improve the efficiency and success rate of hybrid breeding programs. In order to improve the genomic ability performance, we explored the incorporation of parental phenotypic information as covariates under a multi-trait framework. Approach 1, referred to as  Meeting the increasing global demand for food is an imperative challenge, especially in the face of climate change and its subsequent impact on natural resources. Plant breeding plays a crucial role in the human food chain by contributing to high and stable production yields with minimal external inputs and environmental impact. In the last twenty years, plant breeding has been revolutionized by Genomic Selection (GS), a predictive methodology proposed by Meuwissen et al. 2001) [ [1], whiGS is important because it allows breeders to make more accurate and efficient selection decisions in plant and animal breeding programs. It involves the use of genomic data, such as DNA markers, to predict the genetic value of an individual or a population for a given trait of interest. This prediction is based on the association between the genomic data and the phenotype (observable characteristics) of the individuals ,3,4,5. CNonetheless, the successful implementation of GS in plant breeding for predicting the performance of hybrid combinations based on the genetic makeup of their parents poses several challenges, which include: (1) Non-additive effects: Hybrid prediction assumes additive genetic effects of parental lines, but in reality, non-additive effects, such as dominance and epistasis, significantly influence hybrid performance. Accurately modeling non-additive effects requires larger sample sizes for estimation; (2) Genotype-by-environment (G × E) interaction: Hybrid performance varies across different environments due to G × E interaction. This variation makes it challenging to predict hybrid performance accurately across diverse environments; (3) Limited data: The availability of limited data poses difficulties in accurately predicting hybrid performance, especially for new or untested hybrid combinations. Insufficient data hinders accurate predictions of hybrid performance; (4) Heterogeneous parental populations: Genetic diversity among parental lines used in hybrid creation complicates the accurate prediction of hybrid performance. This challenge is particularly prominent when dealing with open-pollinated populations or composite crosses; and (5) Complex trait architecture: The accurate modeling of complex traits, such as yield or disease resistance, is difficult, posing challenges in predicting hybrid performance for these traits. In conclusion, hybrid prediction in plant breeding is a complex and challenging task that requires careful consideration of the underlying genetic and environmental factors influencing hybrid performance .In this regard, a valuable alternative to genomic prediction in plant breeding is multi-trait hybrid prediction, which permits the simultaneous prediction of hybrid performance for multiple traits, reducing both time and cost in breeding programs. Multi-trait hybrid prediction is advantageous for several reasons, including (1) Improved accuracy: By considering trait correlations, multi-trait hybrid prediction enhances the accuracy of performance prediction. Leveraging similarities in the genetic basis of traits, information from one trait improves predictions for another; (2) Reduced bias: Traditional genomic prediction methods may exhibit bias due to an uneven distribution of phenotypic data or low heritability of traits. Multi-trait hybrid prediction mitigates such bias by integrating genetic information from multiple traits to estimate hybrid genetic value; (3) Enhanced hybrid selection: Multi-trait hybrid prediction facilitates the selection of hybrids with desired combinations of traits, leading to more productive and resilient crops. This is especially valuable for complex traits that are difficult to measure or expressed late in the life cycle; and (4) Improved management of G × E interaction: Multi-trait hybrid prediction assists breeders in effectively managing genotype-by-environment (G × E) interaction. It considers trait correlations and their interaction with environmental factors, aiding the identification of hybrids with consistent performance across diverse environments. Overall, multi-trait hybrid prediction shows promise in improving the accuracy and efficiency of plant breeding programs, resulting in the development of highly productive and resilient crops ,11.Montesinos-López et al. (2022) ,13 showeSince the prediction of hybrids in plant breeding is very challenging, many approaches have been studied to increase prediction accuracy. For example, some authors, such as Xu et al. (2021)  and WangFor this reason, to evaluate if incorporating phenotypic parental information as an additional input improves prediction accuracy in the context of multi-trait with kernel methods, we utilized a wheat dataset provided by the International Maize and Wheat Improvement Center (CIMMYT). We hypothesize that incorporating the phenotypic information of the parents as covariates in the multivariate genomic prediction model with kernels will improve the prediction accuracy of the GS methodology. In this sense, we aim to broaden our understanding of the genetics of the studied traits and maximize the efficiency of hybrid prediction by exploring the multivariate kernel approach.NO_Cov, BV, and Pmean) in each of the six kernels, AC_1, AC_2, AC_3 AC_4, GK, and Linear. These comparisons were carried out for each year and across years.The results presented for each trait and for each year are compared with the three strategies of incorporating the parental phenotypic information .The following BV and Pmean). However, small differences are observed between the different kernels, and we can appreciate that in year 1 under the strategy BV, the best prediction performance was observed under a linear kernel that outperformed the remaining kernels by only 1.534%. While under the Pmean strategy, also in year 1, the linear kernel was the best regarding the remaining kernels but only by 0.706%. The same pattern was observed in years 2 and 3 under the BV strategy, where the best linear kernel outperformed the remaining kernels by 2.125% and 2.33%, respectively, while under the Pmean strategy, the linear kernel outperformed the other in years 2 and 3 by 0.062% and 0.106%, respectively  was the Pmean with an NRMSE = 0.626, followed by the BV strategy with an NRMSE = 0.632 and without incorporating parental phenotypic information. The NO_Cov strategy was the worst with an NRMSE = 0.666, meaning that the Pmean and BV strategies were better than the NO_Cov by 6.4% and 5.4%, respectively. See details in Finally, across years , we can appreciate that the linear kernel was also the best under both strategies of incorporating the phenotypic parental information . HoweverBV and Pmean) consistently resulted in the most accurate predictions across different years. Although there were slight differences among various kernels, the linear kernel stood out in year 1, outperforming others by 1.577% using the BV strategy and 0.468% using the Pmean strategy. This trend continued in years 2 and 3 under the BV strategy, with the linear kernel leading by 1.875% and 2.448%, respectively. In year two, under the Pmean strategy, all six kernels performed equally, while in year three, the linear kernel was slightly better, with a 0.142% advantage.BV and Pmean strategies, improving NRMSE by 1.955% and 0.202%, respectively, compared to other kernels. Interestingly, the best approach for integrating phenotypic information, represented by the linear kernel, was the Pmean strategy, resulting in an NRMSE of 0.610. The BV strategy followed closely with an NRMSE of 0.617. In contrast, the strategy of not including parental phenotypic information (NO_Cov strategy) performed the worst, with an NRMSE of 0.651. This means that the Pmean and BV strategies outperformed the NO_Cov strategy by 6.7% and 5.5%, respectively. For more detailed information, please refer to When considering all years together , the linear kernel stood out as the top performer in both the BV and Pmean) consistently led to the best predictive performance across different years. Nevertheless, there were subtle differences among the various kernels. Specifically, in year one, the linear kernel performed slightly worse than the other kernels by only 0.099% when using the BV strategy. Meanwhile, under the Pmean strategy, the linear kernel performed equally as well as the other kernels. This pattern persisted in years 2 and 3 under the BV strategy, where the linear kernel showed slightly lower performance than the other kernels by 0.075% and 0.194%, respectively. Similarly, under the Pmean strategy, the linear kernel exhibited slightly lower performance than the other five kernels, but the difference was minimal, with only 0.013% and 0.071% variations in years two and three, respectively.BV and Pmean strategies, resulting in a decrease in NRMSE of 0.120% and 0.026% relative to the other kernels  showed the poorest performance, with an NRMSE of 0.796 , the linear kernel showed a slight performance disadvantage compared to other kernels in both the  kernels . Interesof 0.796 . This deSince the linear kernel was the best in two out of three of the traits under study, in this section, we present the results across traits only for this linear kernel.BV) estimated from the parents, and by 5.59% when the parental phenotypic information is incorporated directly as the blues of the parents. In other words, these results point out that incorporating the phenotypic information helps to increase the prediction accuracy of hybrid predictions by at least 4.24% under a multi-trait framework.Across traits and years, we can appreciate in Hybrid prediction is of utmost importance in plant breeding as it harnesses the benefits of hybrid vigor, improves yield potential, enhances genetic diversity, facilitates trait selection, optimizes resource utilization, accelerates breeding progress, increases crop productivity, promotes sustainable agriculture, addresses consumer preferences, and provides economic advantages to stakeholders. However, as mentioned in the introduction, many factors affect the efficient development of highly productive hybrids.For these reasons, the GS methodology is crucial for hybrid development as it enhances breeding efficiency, improves prediction accuracy, enables early-stage selection, aids in complex trait prediction, manages genetic diversity, facilitates information transferability, complements marker-assisted selection, enables selection for novel traits, supports data-driven breeding decisions and can be integrated with other breeding approaches ,9. By leHowever, for a successful implementation of the GS methodology, high accuracy is key for an efficient selection, increasing genetic gain, saving costs and time, utilizing genetic resources effectively, selecting for complex traits, facilitating precision breeding, building confidence in breeding decisions, adapting to changing years, managing genetic diversity, and promoting industry acceptance and adoption. Achieving high accuracy in genomic selection enhances the effectiveness and efficiency of plant breeding programs, ultimately leading to the development of improved and high-performing hybrids.For this reason, the prediction performance of the GS methodology was explored under a multivariate framework with two strategies for incorporating the parental phenotypic information in the modeling process as covariates. The first approach, denoted as Pmean, directly used the parental phenotypic information without any preprocessing, while the second, denoted as BV, used only the breeding values of the parents  of incorporating the parental phenotypic information, we explored the use of nonlinear inputs using different kernels , which were compared to the conventional linear kernel. We did not find relevant differences in prediction performance between the kernels using the NRMSE as a metric. As such, findings suggest that, in general, for this data set, the linear kernel is sufficient, for when nonlinear kernels were evaluated, no significant gain in prediction performance was observed. However, even though the nonlinear kernels were not better in terms of NRMSE than the conventional linear kernel, it is of paramount importance to remember that in many data sets, the use of these nonlinear kernels still helps to increase prediction performance since they can efficiently capture nonlinear patterns in the input data when they are present.In general, genomic prediction models under a multivariate context with nonlinear kernels have the potential to capture complex relationships, improve prediction accuracy, consider trait correlations, account for genetic pleiotropy and interactions, uncover hidden patterns, offer flexibility and adaptability, allow for cross-species applications, support better breeding decisions, and contribute to advancements in data science. By incorporating these models, breeders can enhance the accuracy and efficiency of genomic prediction, leading to improved plant breeding outcomes and the development of superior hybrids.However, the efficacy of the multivariate model in comparison to the single-trait analysis varies depending on the specific problem at hand. Conventional multivariate models presuppose a uniform covariance of effects throughout the genome. In genomic regions where the alignment of effects correlates closely with the average effect correlation across the genome, leveraging information sharing among traits can enhance statistical power. Conversely, in regions where the correlation of effects significantly deviates from the genome’s average correlation pattern, the multivariate model might diminish statistical power. This reduction can be attributed to the tendency of multivariate models to constrict the magnitude of effects towards a shared covariance pattern .Finally, our findings increase empirical evidence that integrating parental phenotypic information improves prediction performance by integrating this information as covariates. It is also important to point out that we did not find any improvement when adding this information under a multi-trait framework versus a uni-trait framework. For this reason, by incorporating parental phenotypic information, prediction models can make more accurate predictions and support more effective breeding decisions in plant breeding programs. However, we did not find an improvement in integrating this information as BV as opposed to integrating it as Pmean.Field experiments were conducted at CIMMYT’s Campo Experimental Norman E. Borlaug (CENEB) near Ciudad Obregon, Sonora, Mexico, over a period of three years. A total of 1888 hybrids resulting from crosses between 667 females and 18 males were evaluated. Specifically, the number of hybrids assessed during the winter growing seasons of 2014–2015 (Year 1), 2015–2016 (Year 2), and 2016–2017 (Year 3) were 703, 655, and 1197, respectively. Among these, 225 hybrids were common between consecutive years (Years 1 and 2), while 383 hybrids were common between Years 2 and 3. The selection of elite female and male parents was based on their performance for desired traits, ability to produce hybrids, and ancestral diversity, which was determined using a coefficient of parentage.In order to produce the hybrids, a chemical hybridizing agent provided by Syngenta Inc.  was utilized in alternate male and female strip plots measuring 6.4 m. The parents and hybrids were evaluated in α-lattice trials, with two replications conducted over a span of two years. Each 4.8 m yield trial plot consisted of 1000 seeds to ensure uniform plant density. Standard agronomic practices, including four supplementary irrigations, were employed in a high-yield-potential environment. All male parents involved in the hybrids and the set of two advanced checks tested each year were planted in all trials. The hybrids and female parents were planted side by side in all the trials. For each entry, data on days to flowering (DTF), days to heading (DTH), days to maturity (DTM), grain yield (GY), and plant height (PHT) per plot were recorded. Phenotypic data were analyzed using a mixed linear model implemented in META-R software (V5.0). Best linear unbiased estimates (BLUEs) were estimated by fitting the model with trial (as a random effect), genotype (as a fixed effect), replication nested within trials (as a random effect), and sub-blocks nested within trials and replications (as random effects). The obtained BLUEs for each hybrid and parent were utilized for subsequent analyses. This paper focuses on the analysis of three traits: grain yield (GY), days to flowering (DTF), and days to heading (DTH).In the first year, 18 male and 667 female parents underwent genotyping using the Illumina iSelect 90K Infinitum SNP genotyping array. In the second and third years, genotyping was performed using the Illumina Infinium 15K wheat SNP array . After combining the data from all three years, a total of 13,005 single-nucleotide polymorphisms (SNPs) remained. SNPs with less than 15% missing values were retained, and any remaining missing markers were imputed using the naive method based on observed allele frequencies. Following imputation, markers with a minor allele frequency below 0.05 were excluded from the analysis. A total of 10,250 markers were ultimately utilized for further analysis. Although a larger set of hybrids and parents were assessed in the field experiments, only hybrids derived from parents that had undergone SNP genotyping were considered for genomic predictions. The number of hybrids included varied in each year of evaluation.This model is given byThe relationship matrices m=WmWmTp ,19 whereIn each of the three methods evaluated , we employed a type of cross-validation that emulates real breeding strategies, referred to as untested lines in tested years, using a seven-fold cross-validation . In thisKernel functions (kernel methods or kernel tricks) are mathematical functions used in various machine learning algorithms. These functions enable the algorithms to operate in a high-dimensional feature space without explicitly computing the coordinates of the data points in that space . Kernel The kernel functions efficiently represent data and perform the kernel trick where the kernel functions take pairs of data points in the original space and calculate the inner product (similarity) between them in a higher-dimensional space. A popular kernel function is the linear one that, in genomic prediction, is basically represented by the Genomic Best Linear Unbiased Predictor (GBLUP). The nonlinear Gaussian kernel (GK) function, also known as the radial basis function kernel, depends on the Euclidean distance between the original attribute value vectors rather than on their dot product, The Arc-cosine (AC) kernel function uses the idea of forming artificial neural networks with more than one hidden layer and Saul  proposedIn this paper, the integration of parental phenotypic information under a multi-trait framework with different kernels was explored. We evaluated two approaches for the integration of parental phenotypic information. We found an increase in prediction performance in the normalized mean square error of at least 4.24% by integrating the parental phenotypic information, but no relevant differences were observed between the two approaches for integrating the parental phenotypic information. Furthermore, we did not find a significant increase in prediction performance using nonlinear kernels regarding linear kernels. Finally, our findings increase empirical evidence that integrating parental phenotypic information as covariates helps to increase the prediction performance of hybrids prediction.


Findings from genome-wide association studies have facilitated the generation of genetic predictors for many common human phenotypes. Stratifying individuals misaligned to a genetic predictor based on common variants may be important for follow-up studies that aim to identify alternative causal factors. Using genome-wide imputed genetic data, we aimed to classify 158,951 unrelated individuals from the UK Biobank as either concordant or deviating from two well-measured phenotypes. We first applied our methods to standing height: our primary analysis classified 244 individuals (0.15%) as misaligned to their genetically predicted height. We show that these individuals are enriched for self-reporting being shorter or taller than average at age 10, diagnosed congenital malformations, and rare loss-of-function variants in genes previously catalogued as causal for growth disorders. Secondly, we apply our methods to LDL cholesterol (LDL-C). We classified 156 (0.12%) individuals as misaligned to their genetically predicted LDL-C and show that these individuals were enriched for both clinically actionable cardiovascular risk factors and rare genetic variants in genes previously shown to be involved in metabolic processes. Individuals whose LDL-C was higher than expected based on the genetic predictor were also at higher risk of developing coronary artery disease and type-two diabetes, even after adjustment for measured LDL-C, BMI and age, suggesting upward deviation from genetically predicted LDL-C is indicative of generally poor health. Our results remained broadly consistent when performing sensitivity analysis based on a variety of parametric and non-parametric methods to define individuals deviating from polygenic expectation. Our analyses demonstrate the potential importance of quantitatively identifying individuals for further follow-up based on deviation from genetic predictions. Human genetics is becoming increasingly useful to help predict human traits across a population owing to findings from large-scale genetic association studies and advances in the power of genetic predictors. This provides an opportunity to potentially identify individuals that deviate from genetic predictions for a common phenotype under investigation. For example, an individual may be genetically predicted to be tall, but be shorter than expected. It is potentially important to identify individuals who deviate from genetic predictions as this can facilitate further follow-up to assess likely causes. Using 158,951 unrelated individuals from the UK Biobank, with height and LDL cholesterol as exemplar traits, we demonstrate that approximately 0.15% and 0.12% of individuals deviate from their genetically predicted phenotypes, respectively. We observed these individuals to be enriched for a range of rare clinical diagnoses, as well as rare genetic factors that may be causal. Our analyses also demonstrate several methods for detecting individuals who deviate from genetic predictions that can be applied to a range of continuous human phenotypes. Since 2007 , genome-It may be important to identify individuals who deviate from their predicted phenotype based on an assumed polygenic model of association because they may be more likely to carry rarer and more penetrant pathogenic mutations or have some other cause to their phenotype. Specific alternative causes of an extreme phenotype may require targeted clinical investigations for an individual.Using height and LDL cholesterol (LDL-C) as exemplar traits, chosen for their high heritability and clinical relevance respectively, we aimed to classify individuals who deviate from their genetically predicted phenotype, using 158,951 unrelated individuals from the UK Biobank with whole exome-sequencing data. We subsequently aimed to determine if individuals classified as misaligned to their genetically predicted height were enriched for recall of being relatively short or tall in childhood, disproportionate body stature, clinical diagnoses of syndromes associated with extreme stature, carriers for rare genetic variation relevant to height, or environmental factors that may have influenced growth. Secondly, we aimed to determine if individuals classified as misaligned to their genetically predicted LDL-C were at higher risk of heart disease, more or less likely to have type 2 diabetes, or were carriers for rare genetic variation relevant to LDL-C. Finally, we assessed the sensitivity of our results based on four methods, each with two thresholds, that have the potential to be used to identify individuals whose phenotype deviates from the expectation based on their polygenic score.P < 5 × 10−8 obtained from a meta-analysis of 1.2M individuals from European-based studies (excluding the UK Biobank) contributing to the Genetic Investigation of ANthropometric Traits (GIANT) consortium. The polygenic score explained 31.6% of the variance in height among 158,951 unrelated individuals of European genetic ancestry with exome sequencing in the UK Biobank (P < 1 × 10−128), equivalent to 5.19cm. Effects were similar in males and females .We derived a polygenic score using conditional effect estimates of 3,198 SNPs reaching  Biobank . A 1SD iUsing a simulated dataset of 158,951 individuals and 3,198 SNPs explaining 31.6% of the variance under an additive model see , we clasIndividuals misaligned to their genetically predicted height are more likely to recall being shorter or taller than average at age 10. As a validation of our polygenic deviation classification for height, we hypothesised that individuals deviating from polygenic expectation were likely to self-report being shorter or taller than average during childhood. We tested for enrichment of self-reporting being shorter or taller than average at age 10 among individuals who were shorter or taller than genetically predicted, respectively. We observed evidence of enrichment in both the short and tall deviator groups relative to the group aligned to their genetic score with OR = 10.1 , P = 2 × 10−42 and OR = 10.4 , P = 4 × 10−27, respectively.Individuals who deviate from their genetically predicted height are enriched for having a disproportionate body stature. As individuals at the extremes of the polygenic score distribution for height are enriched for recalling being shorter or taller at age 10, we next hypothesised that individuals classified as deviating from their genetically predicted phenotype are also more likely to have disproportionate body sizes that affect standing height and have more extreme sitting-to-standing height ratios. We observed individuals who were shorter or taller than genetically predicted were enriched for extreme values of sitting-to-standing height ratio (greater than 1SD) with OR = 2.99 , P = 1.22 × 10−10, OR = 6.39 , P = 7.85 × 10−4, respectively.Individuals with shorter stature than genetically predicted are enriched for congenital malformations and deformations of the musculoskeletal system. To identify potential reasons why individuals deviate from polygenic prediction, we first tested for enrichment of clinical diagnoses of congenital malformations and deformations of the musculoskeletal system as captured by ICD9 (754–756) and ICD10 (Q75-Q69) codes from Hospital Episode Statistics and primary care data where an ICD9 or ICD10 code could be extracted. We observed an enrichment within the group of individuals with shorter stature misaligned to the genetic predictor with an odds ratio of 3.45 , P = 2 × 10−5 of having a diagnosis of congenital malformations and deformations of the musculoskeletal system but observed a lack of enrichment among the taller group .Individuals who are shorter relative to their genetically predicted height are enriched for loss-of-function variants in genes most commonly associated with monogenic forms of short stature. We next hypothesised that individuals classified as having relatively short or tall stature given their polygenic score for height would be enriched for rare variants in dominantly inherited genes previously associated with growth disorders, including overgrowth.< 0.1%) loss-of-function (LoF) variants in those genes. We did not observe evidence (at P < 0.05) for enrichment of rare LoF variants present in people defined as relatively short for their polygenic prediction . However, we did observe a stronger enrichment for LoF carriers when limiting the analysis to a subset of 6 genes  in which variants are known to be relatively common Mendelian causes of short stature   see .P = 0.63). These results were nominally significant (P < 0.05) when limiting our analysis to 3 genes in which variants have previously been described as causal for some of the most prevalent syndromes associated with tall stature, specifically Marfan syndrome (FBN1)  and 0.424 SD  change in LDL-C in the males and females, respectively.A 1SD increase in the polygenic score increased rank-inverse normalised residualised LDL-C  by 0.408 SDs , and 92,897 individuals as aligned to their polygenic score .We used the Mahalanobis metric to classify individuals who deviated from their polygenic score. Based on 134,979 individuals and 1,239,184 variants that explained 16.7% of the variance of a normally distributed outcome, we classified 159 individuals from the UK Biobank as deviating from the polygenic expectation  of which had a higher LDL-C than expected. The absolute number of males classified as misaligned to their polygenic score did not change in the sex-stratified analysis, but the relative number of individuals who had a polygenic score higher than expected increased by 12.1%. Due to these differences, we used the sex-stratified analysis as our primary results. We provide scatter plots in Individuals who deviate from their genetically predicted LDL-cholesterol had differing levels of common cardiovascular risk factors. Our primary hypothesis for the LDL-C phenotype was that individuals whose LDL-C was not aligned with their polygenic prediction would have differing levels of common cardiovascular risk factors. Compared to individuals classified as not deviating from their genetically predicted LDL-C levels, males with high LDL-C relative to their polygenic score had higher triglyceride levels  and nominally higher HDL levels . All effect sizes are in sex-specific SD units. Based on the same comparison in females, individuals with a high LDL-C for their polygenic score had higher triglyceride levels , higher BMI  and higher cigarette use .β = −0.885 , P = 2.00 × 10−12), lower HDL levels  and nominally lower diastolic blood pressure . In females, individuals with a low LDL-C for their polygenic score had lower triglyceride levels  and were nominally older —see Compared to individuals labelled as aligned to the genetically predicted LDL-C, males whose LDL-C was low for their polygenic score had lower triglyceride levels , even after adjusting for the effects of measured LDL-C, age and BMI. We did not observe an association with higher risk of T2D in males labelled as deviating from genetically predicted LDL-C.P = 8.87 × 10−7) and nominally higher risk of type-two diabetes . In females, individuals with a low LDL-C for their polygenic score showed no evidence of enrichment for T2D or CAD. Refer to Among males classified as misaligned to their LDL-C genetic predictor and whose LDL-C was lower than expected, we observed an enrichment for coronary artery disease  loss-of-function variants in the LDLR gene .APOB , and for males in PCSK9 .Males and females whose LDL-C was low for their LDL-C polygenic score showed evidence of enrichment for rare loss-of-function variants in Refer to P = 2.09 × 10−6). We present all GRS-ranking method results in Tables G and H in We additionally classified individuals who were misaligned to their polygenic score for LDL-C using the GRS ranking method, interquartile ranges, and residuals derived from regressing LDL-C on the polygenic score. The results of classifying deviators from a polygenic score for each of the four methods can be found in Tables G and H in We have established novel, robust methods for identifying individuals whose phenotype is misaligned to their polygenic prediction, which we referred to as deviating from a polygenic score, applied to two well-known phenotypes: height, chosen for its high heritability and strongly predictive polygenic score, and LDL-C, chosen for being clinically actionable into adulthood, with a range of associated co-morbidities.Our results were broadly consistent across the methods tested and are thus likely to be applicable to a range of phenotypes. With ever-increasing sample sizes, we suspect more traits will have highly powered polygenic risk scores that increase the efficacy of this method.ACAN and SHOX for height and LDLR and PCSK9 for LDL-C. These results are similar to that of Lu et. al . However, we did not apply methods to determine this because 1) some methods rely on phenotypic mismatch with polygenic expectation, and 2) we have used samples that have not been flagged by UK Biobank <h>as having sex-mismatches."2. In relation to the previous point, the question "whether the reported polygenic deviations consequence of sample swaps or not?", is not fully answered. While cross-sex sample swaps may have been identified, same-sex swaps will run undetected and the numbers (0.15% for height and 0.12% for LDL-C) seem consistent with those few who may have escaped the QC control. Rather, specify in the discussion that the deviants in the height analysis are NOT the same individuals of the LDL-C analysis; just as Idefix works by identifying those individuals that behave as deviants across multiple PRS's.3) The table provided for my raised point 3 with subject characteristics across LDL-C quintiles (in women with lower measued LDL-C) lacks the sample size (n) of deviators per quintile. I could predict, Q4 is where the largest amount of deviant is given that it holds the biggest contrast in age is observed, correct?. Strikingly, all deviants (independent of quintile) show rather consistently lower BMI, alcohol use and smoking. This is somewhere marginally stated by the authors along the manuscript. Yet, this also means a healthy lifestyle "overrides" the genetic predisposition... don't you want to emphasise more that message? In the conclusion, authors focus only on one perspective: "These individuals are more likely to carry rare genetic variation, or be at greater risk of co-morbidities, and should be considered in future discovery studies." You can also emphasise such positive perspective that has great potential to catch media attention. ;)</h></what?>Reviewer #3: All of my comments have been nicely addressed by the authors. I have no further suggestions to make.**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: YesReviewer #2: YesReviewer #3: Yes**********what does this mean?). 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If you experience any difficulties in submitting your data, please contact help@datadryad.org for support.More information about depositing data in Dryad is available at data availability policy requires that all numerical data underlying display items are included with the submission, and you will need to provide this before we can formally accept your manuscript, if not already present.Additionally, please be aware that our ----------------------------------------------------Press Queriesplosgenetics@plos.org.If you or your institution will be preparing press materials for this manuscript, or if you need to know your paper's publication date for media purposes, please inform the journal staff as soon as possible so that your submission can be scheduled accordingly. Your manuscript will remain under a strict press embargo until the publication date and time. This means an early version of your manuscript will not be published ahead of your final version. PLOS Genetics may also choose to issue a press release for your article. If there's anything the journal should know or you'd like more information, please get in touch via  18 Sep 2023PGENETICS-D-23-00163R2 Identification and analysis of individuals who deviate from their genetically-predicted phenotype Dear Dr Wood, We are pleased to inform you that your manuscript entitled "Identification and analysis of individuals who deviate from their genetically-predicted phenotype" has been formally accepted for publication in PLOS Genetics! Your manuscript is now with our production department and you will be notified of the publication date in due course.The corresponding author will soon be receiving a typeset proof for review, to ensure errors have not been introduced during production. Please review the PDF proof of your manuscript carefully, as this is the last chance to correct any errors. 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Single‐step genomic predictions using SNP (H‐BLUP) or haplotypes (HAP‐BLUP) from blocks with different linkage disequilibrium (LD) thresholds  were evaluated. We also considered different blending parameters when constructing the genomic relationship matrix used to predict the genomic‐enhanced estimated breeding values (GEBV), with alpha equal to 0.95 or 0.50. The GEBV were compared to the estimated breeding values (EBV) obtained from traditional pedigree‐based evaluations (A‐BLUP). The mean theoretical accuracy ranged from 0.499 (A‐BLUP for PWT) to 0.795 . The prediction accuracies ranged from 0.143 (A‐BLUP for PWT) to 0.330 (A‐BLUP for YGFW) while the prediction bias ranged from −0.104 (H‐BLUP for PWT) to 0.087 . The GEBV dispersion ranged from 0.428 (A‐BLUP for PWT) to 1.035 (A‐BLUP for YGFW). Similar results were observed for H‐BLUP or HAP‐BLUP, independently of the LD threshold to create the haplotypes, alpha value, or trait analysed. Using genomic information  provided similar or higher prediction and theoretical accuracies and reduced the dispersion of the GEBV for body weight, wool, and reproductive traits in Rambouillet sheep. However, there were no clear improvements in the prediction bias when compared to pedigree‐based predictions. The next step will be to enlarge the training populations for this breed to increase the benefits of genomic predictions.Rambouillet sheep are commonly raised in extensive grazing systems in the US, mainly for wool and meat production. Genomic evaluations in US sheep breeds, including Rambouillet, are still incipient. Therefore, we aimed to evaluate the feasibility of performing genomic prediction of breeding values for various traits in Rambouillet sheep based on single nucleotide polymorphisms (SNP) or haplotypes (fitted as pseudo‐SNP) under a single‐step GBLUP approach. A total of 28,834 records for birth weight (BWT), 23,306 for postweaning weight (PWT), 5,832 for yearling weight (YWT), 9,880 for yearling fibre diameter (YFD), 11,872 for yearling greasy fleece weight (YGFW), and 15,984 for number of lambs born (NLB) were used in this study. Seven hundred forty‐one individuals were genotyped using a moderate (50 K;  Further scientific innovation, with its greater application through increased education and training, is needed to meet this demand , originally used to obtain EBV from Best Linear Unbiased Predictions (BLUP), can be replaced or combined with the genomic relationship matrix (G) to predict genomic‐enhanced breeding values , are commonly used to include a proportion of A in the G that is used in the genomic evaluation  has been the standard method used in genomic analyses. However, haplotypes can also be used for both genomic prediction . Furthermore, in these studies, the factors that might contribute to better haplotype‐based predictions  were not fully explored. Second, the method used to create the haplotypes can influence the results , postweaning weight (PWT), and yearling weight (YWT)], two wool traits [yearling fibre diameter (YFD) and yearling greasy fleece weight (YGFW)] and one reproductive trait [number of lambs born (NLB)] as described in Table http://nsip.org/wp‐content/uploads/2015/04/Lambplan‐TC‐Report‐Notter.pdf). Briefly, the preadjustment considered birth and rearing type (fixed levels as a multiplicative adjustment), and age of dam (measured in days) at recording (quadratic and linear regressions). No preadjustments were done for NLB. The data underwent quality control (QC) with observations deviating more than three standard deviations from the mean removed from further analyses.The phenotypic datasets used for the genetic and genomic prediction analyses for the body weight and wool traits were processed previously by the NSIP, which provided preadjusted phenotypes (Contemporary groups (CG) were created by concatenating flock, year, season, management group, sex, recording date, and 70‐day age groups to split lambing (birth) dates into 70‐day consecutive periods for PWT, YWT, YFD, and YGFW. For BWT, the CG included all the effects previously mentioned for body weight and wool traits, excluding recording date; 35‐ rather than 70‐day age group were also used. The CG for the NLB were created considering ewe's flock, birth year, season, management group, and parturition number . The preadjusted phenotypes for body weight and wool traits and the NLB phenotypes were then adjusted for the CG effect, so that the phenotypes analysed—henceforth referred to as corrected phenotypes—accounted for all systematic environmental effects considered in the NSIP genetic evaluations. The CG for all analysed traits were treated as fixed effects and, as a final QC step, CG with less than three animals and with no phenotypic variability within CG were removed.2.2Neogen . These individuals were chosen to be genotyped based on pedigree‐based relatedness (genetic connectedness) aiming to capture as much genetic diversity as possible in animals with DNA samples, coming from nine representative NSIP Rambouillet flocks. Connectedness values were derived from prediction error co‐variances among EBV   and BovineHD BeadChips (Illumina Inc.)  SNP panels by plink 1.9 software , located on non‐autosomal chromosomes, or a duplicate on the array removed. Samples with call rate < 0.90 were also removed. A total of 32,584 SNP and 722 samples remained for further analyses. The average distance between adjacent markers was 75.433 kb, with standard deviation, minimum, median, and maximum equal to 67.275 kb, 0.002 kb, 59.492 kb, and 2307.471 kb, respectively, in the 32 K panel used for the analyses.Approximately 35 K  autosomal SNP were in common between the two panels. The QC for the genotypic data was done using the 2.3fimpute v.3.0 software  is a repeatability model, in which p is the random permanent environment effect, y2 contains the repeated corrected phenotypic records, and the other vectors are the same as in model (1). The model (3) also includes the random maternal additive genetic and maternal permanent environment effects, m and q, respectively. The 1′ is a vector of ones used to calculate the overall mean and Z, W, Z2, and S are the incidence matrices that relates the corrected phenotypic records to the random direct additive, permanent environment, maternal additive, and maternal permanent environment effects, respectively. The random effects for the above models were assumed to be normally distributed with (co)variance structures as follows:σu2, σp2, σm2, σq2, andσe2 are the additive genetic, permanent environment, maternal genetic, maternal permanent environment, and residual variances, respectively, and model (1) was used to make the EBV prediction for the YFD, model (2) for NLB, and model (3) for BWT, PWT, YWT, and YGFW.Three linear mixed models for the pedigree‐based BLUP (A‐BLUP) were used in this study, which are defined as follow:blupf90 software  and is centred based on twice of the allelic frequencies . The pregsf90 software . Different values of α and β were used to evaluate the impact of increasing the proportion of A22 on G, with α = 0.95 and 0.50, and thereby β = 0.05 and 0.50, respectively, in which the former is the default value in the pregsf90 software and the later was suggested as the choice in Terminal Sire sheep populations  approach were similar to the ones used in A‐BLUP, except for the inclusion of genomic relationships from the genotyped individuals. In the assumptions of the H‐BLUP, the Vanraden :(8)G=M2.4.3G used in the αG+βA22−1 component was constructed using non‐LD‐clustered SNP (NCSNP) and ps‐SNP. A ps‐SNP corresponds to one of the unique haplotype alleles present within a haploblock, coded as 0, 1, or 2 to account for the number of copies of the reference haplotype allele, similar to Teissier et al.  approach were similar to those described for H‐BLUP. However, the r et al.  and Araur et al. . As a har et al. . All the2.5The whole (complete) and partial datasets used to compare the genetic and genomic predictions  to evaluate the connectedness between the genotyped samples considered as training and validation  in the whole and partial datasets. The VED is based on the variance of unit effects, which approximates the mean prediction error variance (PEV) over unities  and partial (GEBVP) datasets, F¯ is the average inbreeding, ave represent the arithmetic average function, uGEBVW^ and uGEBVP^ are the predicted GEBV or EBV in the whole and partial datasets, respectively, and varGEBVP is the variance of the GEBV or EBV. The other components were previously described.The performance of genetic and genomic predictions was evaluated using the linear regression (LR) method as described by Legarra and Reverter . The LR sei2 is the square of the GEBV or EBV standard error for the individual i, fi is the inbreeding coefficient for the individual i, and the other variables were previously described. The TA was calculated for both whole and partial datasets but presented only for the whole dataset to highlight the overall increase in the TA comparing GEBV and EBV considering all phenotypes available.In addition to the LR statistics, the individual theoretical accuracies (TA) were calculated for the focal individuals according to Van Vleck :(12)TA2.6α = 0.95 and 0.50 to construct G, and (3) HAP‐BLUP using ps‐SNP from different LD thresholds  also with α = 0.95 and 0.50 to construct G. In total, 13 scenarios were evaluated for each of the six traits, resulting in 78 analyses.The scenarios consisted of combinations of (1) A‐BLUP, (2) H‐BLUP with 33.1α value and trait evaluated. We, therefore, only presented the results for the HAP‐BLUP considering the LD threshold of 0.50 (HAP‐BLUP‐LD_0.50) to compare the predictions between pedigree, SNP, and haplotype‐based methods for all traits , ~62% (~0.12), ~8% (~0.02), and ~37% (~0.05) in the GEBV prediction accuracies was observed for the PWT, YWT, YFD, and NLB, respectively, when using 3.2α of 0.95 for YGFW; Appendix The prediction bias ranged between −0.104 .Incorporating genomic information in the analyses resulted in similar or more bias when compared to the pedigree‐based prediction. Alpha equal to 0.95 tended to reduce the bias for BWT and YWT, while the opposite was observed for the other traits , showing reduced dispersion for genomic‐based models. Pedigree‐based models presented similar or lower dispersion for BWT and wool traits. The dispersion with H‐BLUP and HAP‐BLUP‐LD_0.50 showed similar results regardless of the α values. Alpha equal to 0.95 tended to present better dispersion for PWT, YWT, and NLB compared to 0.50, while the opposite was observed for the other traits.A dispersion of −0.29, −0.16, and − 0.35 was observed for PWT, YWT, and NLB, respectively, using H‐BLUP and HAP‐BLUP‐LD_0.50 with 3.4The mean TA ranged from 0.499  was observed in the increase of the mean TA between H‐BLUP and HAP‐BLUP‐LD_0.50 with α of 0.95. Using αequal to 0.50 resulted in the smallest increase in the mean TA (less than 2%) with both SNP‐ and haplotype‐based methods for all traits. At the individual level, the TA using H‐BLUP with α of 0.95 were higher compared to A‐BLUP for the younger individuals and those with no phenotypic information (sires and dams with genotyped progeny) in the partial datasets for all traits , ~9% ~0.05), ~4% (~0.03), ~3% (~0.02), ~5% (~0.03), and ~6% (~0.04) for BWT, PWT, YWT, YFD, YGFW, and NLB, respectively, using H‐BLUP and HAP‐BLUP‐LD_0.50 with , ~4% (~0Increase in the TA for ungenotyped close relatives (progeny or parents) of the genotyped individuals when using genomic information was also observed Appendix , althoug4Genomic selection is the state‐of‐the‐art in modern sheep breeding programs. Here we present the first results of genomic predictions for body weight, wool, and reproductive traits in North American Rambouillet sheep. We performed single‐step genomic predictions fitting SNP or haplotypes to create the genomic relationship matrices used to compute GEBV. Despite the small dataset, promising results were obtained, which can be used as a starting point for the implementation of genomic selection in Rambouillet sheep as well as in other sheep populations.4.1The accuracy of genomic predictions relies mainly on the trait heritability, LD between SNP and QTL  phenotypes or EBV on the GEBV is usually used to measure the “bias” of GEBV  when increasing α, accuracies increased until reaching an asymptote at around 0.50, which was not the case in the current study; (2) the GEBV using α between 0.50 and 0.95 were highly correlated; and (3) less variation was observed in the GEBV of genotyped individuals without phenotypes with α equal to 0.50; and (4) with higher α values, GEBV bias (over‐prediction) increased.In general, appropriate α of 0.50 showed only half of the increase in the accuracies compared to 0.95. No clear advantage in GEBV bias, dispersion, or TA was observed with one α value compared to the other. Therefore, we recommend α of 0.95 for single‐step genomic evaluations in U.S. Rambouillet sheep. However, it is important to highlight that our study included a smaller number of genotyped individuals compared to McMillan and Swan . Haplotype‐based genomic predictions could outperform SNP‐based models in sheep datasets because the former can capture epistasis and these populations could have more complex interactions within haplotype blocks due to higher effective population size. Liang et al. (n = 722) as well as the density of the SNP panel used (~32 K SNP) could have affected both SNP and haplotype genomic predictions.The HAP‐BLUP‐LD_0.50 scenario was chosen to represent the haplotype‐based methods because the LD of 0.50 was the level most likely to estimate the recombination hotspots properly, which are the specific points in the genome with higher probability of recombination . In general, GEBV prediction results for haplotype‐based methods are scarce in small ruminants and additional studies are needed.The haplotypes can be multiallelic markers  relationship matrix for both genomic prediction and variance component estimation using haplotypes or SNP  than the one used in this research (35 K), genotype imputation prior to haplotype blocking and prediction can also be hampered by the number of reference individuals , generally predictions using the imputed 50 K were more biased and the GEBV were more dispersed for all traits. Legarra and Reverter  emphasiz5Using genomic information (SNP or haplotypes as pseudo‐SNP) provided similar or higher GEBV prediction and theoretical accuracies, and reduced the dispersion of the GEBV, for body weight, wool, and reproductive traits in Rambouillet sheep. However, there were no clear improvements in prediction bias compared to pedigree‐based predictions. Alpha value equal to 0.95 is recommended to weight the genomic relationships when modelling the covariances between individuals. The use of haplotypes showed no advantage compared to SNP at the current reference population size and SNP panel density used, regardless of the LD threshold used to create the haploblocks. SNP‐based genomic predictions are therefore recommended since they are easier to implement than those based on haplotypes. Efforts to increase the number of genotyped individuals are paramount to take full advantage of genomic information to accelerate genetic progress in the U.S. Rambouillet sheep breeding program.ACA, PLSC, RML, and LFB: conception of the work; RML and LFB: data acquisition; ACA: SNP and haplotype‐based single‐step genomic prediction analyses; ACA, RML, and LFB: results interpretation; ACA: drafting the manuscript; ACA, PLSC, HRO, RML, and LFB: critical revision of the manuscript; and, ACA, PLSC, HRO, RML, and LFB: final approval of the version to be published. All authors contributed to the article and approved the submitted version. All authors have read and agreed to the published version of the manuscript.This research was funded by the National Sheep Industry Improvement Center (NSIIC‐USDA), the American Rambouillet Sheep Breeders Association, and the American Sheep Industry Association Let us Grow program. The State University of Southwest Bahia and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior , Financial Code 001, provided the scholarship of the first author.The authors declare no conflict of interest.Appendix S1.Click here for additional data file.Appendix S2.Click here for additional data file.Appendix S3.Click here for additional data file.Appendix S4.Click here for additional data file.


Eleven genotypes were selected in each moisture condition through MGIDI by assuming 15% selection intensity where two hybrids, viz., ZH161289 and ZH161303, were found to be common across all the moisture regimes, indicating their moisture stress resilience, a unique potential for broader adaptation in rainfed stress-vulnerable ecologies. The selected hybrids showed desired genetic gains such as positive gains for grain yield  and negative gains in flowering traits. The view on strengths and weaknesses as depicted by the MGIDI assists the breeders to develop maize hybrids with desired traits, such as grain yield and other yield contributors under specific stress conditions. The MGIDI would be a robust and easy-to-handle multi-trait selection process under various test environments with minimal multicollinearity issues. It was found to be a powerful tool in developing better selection strategies and optimizing the breeding scheme, thus contributing to the development of climate-resilient maize hybrids.Unpredictable weather vagaries in the Asian tropics often increase the risk of a series of abiotic stresses in maize-growing areas, hindering the efforts to reach the projected demands. Breeding climate-resilient maize hybrids with a cross-tolerance to drought and waterlogging is necessary yet challenging because of the presence of genotype-by-environment interaction (GEI) and the lack of an efficient multi-trait-based selection technique. The present study aimed at estimating the variance components, genetic parameters, inter-trait relations, and expected selection gains (SGs) across the soil moisture regimes through genotype selection obtained based on the novel multi-trait genotype–ideotype distance index (MGIDI) for a set of 75 tropical pre-released maize hybrids. Twelve traits including grain yield and other secondary characteristics for experimental maize hybrids were studied at two locations. Positive and negative SGs were estimated across moisture regimes, including drought, waterlogging, and optimal moisture conditions. Hybrid, moisture condition, and hybrid-by-moisture condition interaction effects were significant ( The pot–Asia maize program largely focused on the development of breeding strategies to reach attainable yields across a range of environments by incorporating reasonable levels of cross-tolerance against a combination of major abiotic stresses without compromising grain yields under favorable/optimal growing conditions. It implies the maximum yield potential under optimal conditions along with a guarantee of average yields under stress-prone areas by improving the stress-resilient breeding pipelines through precision phenotyping, index-based selection for secondary traits, and stage-wise gateway screening  showing the highest increase in demand, followed by Sub-Saharan Africa (79%), Southeast Asia (70%), and South Asia (36%) . The devcreening . Under tcreening . Comprehcreening . Variouscreening .Although grain yield is the most important characteristic of genotypes, other secondary traits are also common, such as days to flowering, plant height, ear height, ear length, and number of kernel rows . The yieIn that perspective, a novel multi-trait genotype–ideotype distance index (MGIDI) was proposed to select genotypes with desirable mean performances of multiple traits that overcome the fragility of classical linear indices . A few p22.1The experimental material consists of 75 medium-duration maize hybrids including five commercial checks  were conducted at two locations, viz., Banaras Hindu University (BHU), Varanasi, India (Location 1) and CIMMYT, Hyderabad, ICRISAT Campus, India (Location 2), during winter 2017 and its subsequent summer–rainy season 2018. Location 1 is situated in the middle of the Indo-Gangetic plains of northern India, which experiences alternating floods and high temperatures in a year, while Location 2 is represented by the arid region of the Deccan Plateau with evident frequent occurrence of water scarcity followed by scattered rainfalls. The soil type of the experiment site at Location 1 was sandy loam, whereas it was shallow black soils at Location 2. The detailed information of seven test environments (E1 to E7) including three moisture conditions with season and location combinations is shown in 2.3−1 was maintained by thinning in over-sown plots. All the recommended agronomic and cultural operations including irrigation were taken care of for optimal soil moisture (well-watered) trials. Drought and waterlogging phenotyping protocols by CIMMYT were strictly followed in both locations during managed stress trials  design  with twos trials . Field s2.3.1Rabi season, and irrigation schedule was modified to impose drought stress at the reproductive stage of the crop. Cumulative growing degree days (GDD) were calculated from the day of life irrigation to ensure accurate stress intensity at the target stage of the crop at all the test environments. Withdrawal of irrigation at 550 cumulative GDD and release of stress by providing “rescue irrigation” at 1,000 cumulative GDD were followed to expose flowering to severe moisture stress .where Progress in imposing stress was tracked by measuring moisture depletion at different soil depths up to 100 cm at 10-cm intervals with the “Delta-T PR2 soil moisture profile probe”. The probe was pre-installed in the fields where drought trials were conducted and weekly data were recorded from the first week after withdrawal of irrigation (a few days before anthesis), until the stress is relieved. Rescue irrigation was confirmed by the soil moisture content reaching the “permanent wilting point” (PWP), i.e., 16.8% v/v at the soil depth of 30–40 cm. Cumulative vapor–pressure deficit or ∑VPD values were also recorded as complementary to GDDs to endorse pausing and to resume the irrigation at 120 VPD and at 220 kPa VPD values, respectively.2.3.25–V6 leaf stage or “knee-high” stage. Considering evaporation and seepage losses, additional need-based irrigation was provided to maintain the depth of water during the stress period. The crop was relieved from the stress by draining out the excess water in the experimental plots from the seventh day and a normal irrigation schedule was recommenced 2.5The combined data from all the test environments were checked using the Shapiro–Wilk test  for ANOV2.5.1gamem_met from the metan package , β is a vector of fixed effects, u is a vector of random effects; X is a design matrix of 0s and 1s relating y to β, Z is a design matrix of 0s and 1s relating y to u, and ε is a vector of random errors.where The estimates of variance components were obtained by REstricted Maximum Likelihood (REML) using the expectation-maximum algorithm . A likele and b are the number of environments and blocks per environments, respectively.Where 2.5.2To better understand the inheritable relationships among traits and to see if these relationships are changed across moisture regimes, a genetic correlation was performed in each moisture condition. The correlation matrix was represented as network plots.2.5.3rXij) of the jth trait (column) of the ith genotype (row) was calculated using the following formula:The estimation of MGIDI values for test hybrids in each moisture condition was based on two-way Best Linear Unbiased Predictions (BLUPs) for each genotype (row) and trait (column) and was carried out in four steps, i.e., rescaling of the studied traits, exploratory factor analysis (EFA) to reduce the dimensionality, planning for ideotype with maximum rescaled value, and calculation of Euclidean distance between the genotypes and ideotype planned as the MGIDI index . Rescaling the traits was performed so that all have a similar range, i.e., 0–100. The rescaled value  was maintained by the rescaled trait values (rXij) in a two-way table in which each column with a range of 0–100 made a selection, i.e., increase or decrease.where rXij) to group correlated traits into “factors”. By assuming p and f are the number of traits included and common factors retained through EFA, respectively, the scores were calculated as follows:In the second step, the factorial scores of each test hybrid/genotype was estimated by performing EFA with rescaled values ; A is a p × f matrix of canonical loadings; and R is a p × p correlation matrix between the traits. g, f, and p denote the number of test hybrids/genotypes (rows), factors retained (FA), and traits analyzed, respectively.where p vector ID such that ID = . The final scores for ID were also obtained according to the above formula. Finally, the MGIDI values were computed with the function mgidi from the metan package. If g and f are the number of genotypes/rows and factors retained, respectively, the MGIDI for the ith genotype (MGIDIi) is calculated as follows:The ideotype (ID) was designed by assuming that it has the highest rescaled value, i.e., 100 for all the traits analyzed. Thus, the ID can be defined by 1 × γij  is the score of the ith genotype (row) in the jth factor  and γj  is the jth score of the ideotype. The genotypes with the lowest MGIDI values, i.e., genotypes closer to the ID, exhibited the desired values for all the traits studied. The strengths and weaknesses of a genotype were represented by the proportion of the MGIDI index of the ith row/genotype explained by the jth factor (ij) estimated as follows:where ijD is the distance between the ith genotype (row) and the ID for the jth factor. Low contributions of a factor specify that the traits within that factor are similar to the ideotype designed.where 2.5.4ΔS% ) was then computed for each trait as follows:The hybrids were selected under different soil moisture regimes through MGIDI values by assuming a selection intensity of ~15% and the selection differential in the percentage of population mean  mean, respectively.where 2.6gamem_met for genotype analysis in multi-environments using mixed-effect or random-effect models, gmd for extracting variance components, and mgidi for the computation of MGIDI values were supplied. The network plots of the pairwise correlation data frame were constructed by using “corrr” package version 0.4.4  for most of the studied traits except for ASI, SPAD, and KNR under optimal moisture conditions, D50S and EG under drought, and D50 and ASI under waterlogging according to LRT (p ≤ 0.001 and p ≤ 0.01) on all the studied traits except PH across three moisture conditions, D50S under drought, and EH under waterlogging. Similarly, the environment effect was highly significant (p ≤ 0.001 and p ≤ 0.01) for all the evaluated traits except for KRE under optimal and drought environment and D50S, ASI, and EL under waterlogging stress conditions. The proportions of total variation explained by genotype, environment, and their interactions (GEI) under individual moisture regimes are shown in The genotype had a highly significant effect  contributing 68.7% of total variability were retained under optimal conditions whereas four factors with 69.6% and four factors with 76.4% towards total variability were retained under drought and waterlogging conditions, respectively Table 3.3.4r-values) for studied traits were estimated under each moisture regime. The network plots (r = 0.63) under optimal conditions and had a weak correlation under drought (r = 0.27) and waterlogging (r = 0.17) conditions  for the mean performance of all the studied traits, i.e., positive SGs for GY, PH, EH, EG, EL, KNR, KRE, and SPAD, and negative gains for the flowering traits such as D50A, D50S, and ASI Table 5.3.6The radar plot (4p ≤ 0.001 or p ≤ 0.01). This shows that hybrid mean performances varied across the soil moisture conditions, which can be attributed more towards the diversification of genotypes and provides ample amount of variation for easy selection  under three soil moisture regimes including optimal, drought, and waterlogging at two locations. In general, the grain yield potential and the performance of other yield-contributing characteristics of the available germplasm are a very crucial step in identifying genotypes with ideal trait combinations suitable across target environments, which can be used in future breeding programs . The maielection . The reselection .Rabi/winter maize crop , 42 (ZH161054), and 55 (ZH15449) were placed at the cutting points under optimal, drought, and waterlogging conditions, respectively Figure 45Our experimental findings recommended that MGIDI can be used for the effective selection of superior hybrids/genotypes by considering multiple traits and helping plant breeders make better strategic decisions. The results showed that the hybrids ZH161053, ZH161289, ZH161063, ZH161398, and ZH161047 were found to be common across all the three moisture regimes solely on the basis of grain yield, while two genotypes, ZH161289 and ZH161303, were found to be common in terms of all the studied traits. Also, the study helps improve a certain trait or a group of traits (either yield contributors or stress-responsive ones) in particular moisture stress environments.The original contributions presented in the study are included in the article/AS, PZ, and KSe contributed to the conceptualization and design of the study, field experimentation, and preparation of the manuscript. KSe, MV, and AM revised and edited the original manuscript. AS and TV contributed to formal analysis of data and visualization. AS, KM, MK and KSh contributed to field experiments and data recording. All authors have read and approved the final manuscript.


D/D′, https://github.com/Rong-Zh/GWLD/tree/master/GWLD-R) and the standalone C++ software (https://github.com/Rong-Zh/GWLD/tree/master/GWLD-C%2B%2B), are freely available on GitHub.Linkage disequilibrium (LD) analysis is fundamental to the investigation of the genetic architecture of complex traits  and population structure and evolution dynamics. However, until now, studies primarily focus on LD status between genetic variants located on the same chromosome. Moreover, genome (re)sequencing produces unprecedented numbers of genetic variants, and fast LD computation becomes a challenge. Here, we have developed GWLD, a parallelized and generalized tool designed for the rapid genome-wide calculation of LD values, including conventional  et al. present GWLD: a parallelized and generalized tool for rapid, genome-wide calculation and visualization of LD values. The authors compare the accuracy and speed of LD calculation between GWLD and other software packages and find that interchromosomal LD patterns from different species potentially reflect the level of selection intensity.Until now, LD analysis has focused on genetic variants on the same chromosome. Additionally, the large number of variants produced by current sequencing technologies challenges LD computing speed. Zhang  Linkage disequilibrium (LD) refers to the nonrandom association of alleles between 2 genetic loci. LD analysis is an important tool for population genetics and evolution and has been widely applied in dissecting the genetic architecture of complex traits, such as human disease and animal and plant breeding . A numbeD/D′ and With the advancement and application of next-generation sequencing, genetic variants can now be produced at an unprecedented level. Efficient genome-wide LD calculation is crucial to save time and resources, so the development of new methods or software packages is needed. Compared with traditional LD measures  across 29 chromosomes for 542 Pekin ducks  or Plink file format were used as inputs for calculating LD measures (The R package (GWLD-R) was developed in the R environment with the Rcpp package, which was fast in speed and capable of handling huge volumes of data inputs. Additionally, a standalone software version, GWLD-C++, was implemented in C++. Moreover, the parallel computing option was added.GWLD was executed according to the following 3 steps: file format conversion and input, LD calculation, and visualization of LD results , Box 1. Box 1.##install the GWLD packagesdevtools::install_github(‘Rong-Zh/GWLD/GWLD-R’)##using packageslibrary(GWLD)#0) Loading example data with base-type genotypedata(duck)data <- duck$SNPSNP <- data$genotypeInfo <- data$info## Read data from vcf or plink format file# Recode the genotypes in vcf file as 0, 1, 2, NA, or recode to another typevcf_data <- read.vcfplink_data <- read.plink(“plink format file’s prefix”)#1) recode the genotype with 0,1,2,NASNP <- codegeno#2) calculate with different methods result <- GWLD##or use the following code `r2 <- LDrmi <- RMImi <- MI#2.1) LD heatmap plotp <- HeatMap#3) decay from result(step 2)rmi_decay <- decay#or calculate circos from datarmi_decay <- calc_decay#4) circos from result(step 2)rmi_circos <- circos#or calculate circos from datarmi_circos <- calc_circos#4.1) circos plotcircosdata <- duck$Circoscircos.ideogram(circosdata$chr)circos.linksnp)The input file for GWLD can be prepared in either VCF or Plink format . Genotype data can be arranged as raw nucleotides or recoded as 0, 1, and 2 .D/D′, Once the input files are read into the software and transformed into a genotype matrix, GWLD allows for the calculation of LD measures such as D/D′, The calculated LD results can be visualized either as LD heatmap and LD decay plots  existed among MI, RMI, and 2 values . Furthersome 26)  and genosome 26) . Perfectsome 26) .After interchromosomal LD analysis (RMI only), a circos-like genome-wide plot clearly showed that a nonrandom association of alleles between genetic loci on different chromosomes existed . HoweverWe demonstrated and compared the computing speeds required for the calculation of different LD measures using the duck dataset  Xeon(R) CPU E7-4820 v4 @2.00GHz; 1T RAM).First, benchmark analyses and comparisons between GWLD and different software and R packages were shown . The R GNext, we showed that for 1,000 SNPs and 542 ducks, when choosing the single-thread mode, GWLD R-base scripts took 20.3 min for We further evaluated the impact of different numbers of SNPs and samples on computing speed. With the increase of SNP numbers and sample sizes, the amount of time was considerably increased, as required for computing re found . Furtherso found . Though When using the complete duck dataset , we found that for GWLD R-base scripts with the single-thread mode, calculation of ctively) . In contctively) , the whoUntil recently, LD analyses still only consider the relationship of genetic variants on the same chromosome and focus on the incorporation of different formats of input data, the speed of calculation, and better visualization and annotation (jkad154_Supplementary_DataClick here for additional data file.


Proprietary genetic datasets are valuable for boosting the statistical power of genome-wide association studies (GWASs), but their use can restrict investigators from publicly sharing the resulting summary statistics. Although researchers can resort to sharing down-sampled versions that exclude restricted data, down-sampling reduces power and might change the genetic etiology of the phenotype being studied. These problems are further complicated when using multivariate GWAS methods, such as genomic structural equation modeling (Genomic SEM), that model genetic correlations across multiple traits. Here, we propose a systematic approach to assess the comparability of GWAS summary statistics that include versus exclude restricted data. Illustrating this approach with a multivariate GWAS of an externalizing factor, we assessed the impact of down-sampling on (1) the strength of the genetic signal in univariate GWASs, (2) the factor loadings and model fit in multivariate Genomic SEM, (3) the strength of the genetic signal at the factor level, (4) insights from gene-property analyses, (5) the pattern of genetic correlations with other traits, and (6) polygenic score analyses in independent samples. For the externalizing GWAS, although down-sampling resulted in a loss of genetic signal and fewer genome-wide significant loci; the factor loadings and model fit, gene-property analyses, genetic correlations, and polygenic score analyses were found robust. Given the importance of data sharing for the advancement of open science, we recommend that investigators who generate and share down-sampled summary statistics report these analyses as accompanying documentation to support other researchers’ use of the summary statistics.The online version contains supplementary material available at 10.1007/s10519-023-10152-z. The success of genome-wide association studies (GWASs) depends on sample size  factor, reflecting shared genetic liability among seven indicator phenotypes ?How do the factor loadings and factor model fit differ in multivariate Genomic SEM when the indicator phenotypes are down-sampled univariate GWASs?What is the loss of genetic signal at the factor level of multivariate GWAS when the indicator phenotypes are down-sampled univariate GWASs?How similar are gene-property analyses when using down-sampled GWASs?How similar is the pattern of genetic correlations with other traits when using down-sampled GWASs?How much explanatory power is lost when using polygenic scores (PGSs) constructed from down-sampled GWASs?We recommend that investigators who share down-sampled summary statistics generated with multivariate GWAS methods  report all six steps as supporting documentation, while steps 2–3 can be skipped when generating down-sampled univariate GWAS:https://github.com/Camzcamz/EXTminus23andMe, and the GWAS summary statistics on externalizing that excluded restricted data from 23andMe (“EXT-minus-23andMe”) are available here: https://externalizing.rutgers.edu/request-data/.What is the loss of genetic signal in down-sampled univariate GWASs?The code is publicly available here: EffN), (2) heritability, (3) mean χ2, (4) genomic inflation factor, and (5) the LD Score regression attenuation/stratification bias ratio . For a meta-analysis of k cohort-level univariate summary statistics, it is the sum of EffN can be replaced by the total sample size (N). The remaining four key indicators are standard estimates of LD Score regression  effective sample size ( effectivP < 1 × 10–5). The three checks are to (1) test for sign concordance, (2) inspect for outliers, and (3) run a regression of the down-sampled GWAS coefficients on their full-data counterparts .In addition to evaluating the loss of genetic signal, we recommend three checks to examine concordance in GWAS coefficients (R2) is high. These checks are applicable to both univariate and multivariate GWAS . Here, because we did not generate any down-sampled univariate summary statistics to be disseminated, we report these checks only for the down-sampled multivariate GWAS on externalizing.Sign concordance can be evaluated by reporting the proportion of SNPs that have concordant direction of effect or by performing a binomial test. The binomial test requires an assumed null hypothesis of the true probability of success, which we set to 99% to make the test sensitive enough to detect minor deviations from near-perfect concordance (100% is too sensitive as a single discordant observation will reject the null). Power calculations show that 150 independent SNPs provide ≥ 80% power to reject this null even if the true, imperfect concordance is as high as 95%. To detect outliers, we suggest evaluating whether the down-sampled GWAS coefficients fall outside the 95% confidence intervals of their full-data counterparts. If outliers are detected, then we recommend adding an extra indicator column to the down-sampled summary statistics to allow its users to filter out SNPs with deviating down-sampled GWAS coefficients. The regression analysis of the down-sampled coefficients on the full-data coefficients should investigate whether (a) the intercept is zero, (b) whether the regression coefficient is unity , and (c) whether the adjusted coefficient of determination .2.How do the factor loadings and factor model fit differ in Genomic SEM when the indicator phenotypes are down-sampled univariate GWASs?Stable heritability estimates and attenuation ratios across the original and down-sampled indicators should yield comparable factor loadings in the down-sampled Genomic SEM factor analysis (Step 2), whereas loss of genetic signal, indicated by a decrease in mean Genomic SEM is a flexible modeling approach that (1) estimates an empirical genetic covariance matrix and sampling covariance matrix from input GWAS summary statistics, and (2) evaluates a set of conventional parameters for structural equation modeling, such as factor loadings and residual variances, to minimize the discrepancy between the model-implied and empirical genetic covariance matrices  onto the empirical genetic covariance matrix of the down-sampled summary statistics, and then evaluating the stability of the factor loadings and factor model fit indicators . We do not suggest searching for a better factor solution with the down-sampled indicators because the aim is to evaluate whether down-sampled analyses are representative of their corresponding versions with restricted data.3.What is the loss of genetic signal at the factor level of down-sampled multivariate GWAS when the indicator phenotypes are down-sampled univariate GWASs?Thus, we ran the best-fitting Genomic SEM factor model of the original study  examining the genetic correlation between the respective latent factors of the full and down-sampled summary statistics using bivariate LD Score regression  in the down-sampled GWAS. Given that statistical power is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true, it can be computed as  χ2 distribution with 1 degree of freedom and the non-centrality parameter EffN of the summary statistics being evaluated. The term P < 5 × 10–8) for a χ2-test with 1 degree of freedom. As a complement, we suggest evaluating the power to detect arbitrary effect-size magnitudes, for which we selected three magnitudes representative of effects reaching genome-wide significance in recent large-scale GWAS , though the original study used a larger restricted-access reference panel that combined the 1000 Genomes Phase 3 reference panel with other reference data.4.How similar are gene-property analyses when using down-sampled GWASs?Because of its accessibility and ease of use, we recommend using FUMA to find near-independent genome-wide significant “lead SNPs”. FUMA conducts conventional linkage-disequilibrium (LD) informed pruning (“clumping”). The default settings are sensible to use in most cases. FUMA computes LD with the publicly available European subsample of the 1000 Genomes Phase 3 reference panel as the default setting . The default settings largely overlap with those of the original study on EXT  gene-property analyses in the 5.How similar is the pattern of genetic correlations with other traits when using down-sampled GWASs?As done in the original paper, we ran gene-property analyses on the EXT-minus-23andMe summary statistics to (1) test 54 tissue-specific gene expression profiles, and (2) test gene expression profiles across 11 brain tissues and developmental stages with reference data from BrainSpan  constructed from down-sampled GWASs?R2/pseudo-R2) and (ii) with the rank correlation of point estimates to evaluate the comparability of the overall pattern of polygenic score associations.Generally, the loss of genetic signal from down-sampling will only exacerbate the problem of measurement error in PGSs constructed with finite-sample estimates as weights  from the variance explained by a model with the covariates and PGS. Confidence intervals were estimated with the percentile bootstrap method (1000 iterations). We then evaluated whether the coefficient estimates of the down-sampled EXT-minus-23andMe PGSs were comparable to the estimates of the PGS of EXT from the original paper.We compared the explanatory power of the EXT-minus-23andMe PGSs with the one reported in the original study from analyses of a phenotypic externalizing factor, followed by a set of outcomes related to, or affected by, externalizing behaviors and disorders  (Table S6). Linear regression was applied to continuous outcomes and logistic regression to dichotomous outcomes. We evaluated the incremental R2/pseudo-R2, but the results of these two alternative approaches are often highly similar . For comparability with the original study, we retained the incremental R2/pseudo-R2 measure.We are aware of recent suggestions to evaluate the squared (semi-)partial correlation in favor of the incremental What is the loss of genetic signal in down-sampled univariate GWASs?In the initial check of genetic overlap between the full and down-sampled summary statistics of the same trait, we found genetic correlations close to, but still significantly less than unity: 0.966 (SE = 0.007) for SMOK and 0.953 SE = 0.012) for CANN, for CANNEffN of the two univariate GWASs on SMOK and CANN by about 47% and 12%, respectively , while the decrease for CANN was less pronounced (– 1.3%). Similar decreases were observed for the genomic inflation factor: – 25.9% and – 1.0% for SMOK and CANN, respectively. The overall stability we observed for the heritability estimates and attenuation ratios suggest that the factor loadings in the down-sampled Genomic SEM factor analysis will resemble those of the original paper (Step 2). The decrease in genetic signal in SMOK and CANN should translate into larger standard errors in the factor analysis and loss of statistical power to detect SNP effects in the multivariate GWAS of EXT-minus-23andMe (Step 3).Nevertheless, there was a noticeable loss of genetic signal as measured by mean2.How do the factor loadings and factor model fit differ in multivariate Genomic SEM when the indicator phenotypes are down-sampled univariate GWASs?SE = 0.03) to 0.56 (SE = 0.03). A similar-sized, non-significant decrease was observed for CANN: from 0.77 (SE = 0.03) to 0.75 (SE = 0.03). Furthermore, the comparative fit index (CFI) and standardized root mean square residual (SRMR) were similar between the down-sampled and original factor models and were within the preregistered thresholds for “good fit”  of the original study. In our example, we obtain close to identical factor loadings and model fit when applying the best-fitting factor solution of the original study to the empirical genetic covariance matrix of the down-sampled summary statistics.The factor loadings, residual variances, and model fit statistics were comparable in the down-sampled single factor solution , which motivated Steps 4–6. The χ2 of the EXT and EXT-minus-23andMe factors were 3.12 and 2.37, respectively, corresponding to a 24% decrease. The reduction in the genomic inflation factor was similar (–18%). Thus, there was an appreciable loss of genetic signal in the down-sampled GWAS of EXT-minus-23andMe.We estimated a multivariate GWAS of the EXT-minus-23andMe factor (see Step 2) . The genetic correlation between the summary statistics from the multivariate GWAS of EXT and EXT-minus-23andMe was strong but significantly less than unity , and about 5–45 pp less power to detect the three assumed effect-size magnitudes (The reduction in mean P = 1). Moreover, there was 100% sign concordance among all 130,176 SNPs with P < 1 × 10–5 (in the full-data GWAS). Second, we identified only 21 lead SNPs  for which the down-sampled coefficient fell outside the 95% confidence interval of the full-data estimate. Among the 130,176 SNPs, we found 2202 such outliers (1.7%). We marked these SNPs in the disseminated summary statistics, but otherwise interpret their small number as unproblematic for the comparability of the down-sampled multivariate GWAS. Third, regression analysis of the down-sampled coefficients on the full-data estimates with the 842 lead SNPs found an intercept close to zero , a regression coefficient statistically different from but still near unity , and high adjusted R2 = 0.86. We found similar results for the 130,176 SNPs . The regression results suggest the down-sampling induced some, but not marked, attenuation of the coefficients. Overall, these results demonstrate satisfactory concordance for the down-sampled multivariate coefficients.Pruning of the summary statistics to find near-independent lead SNPs (using the FUMA default settings), identified 358 lead SNPs for the down-sampled EXT-minus-23andMe, as compared to 842 in the full-sample version.  Thus, down-sampling reduced the number of lead SNPs by 57.5%, which could appear problematic. However, the results of the following three checks of the concordance in coefficients (see Step 1) suggested no strong reason for concern . First, all the 842 lead SNPs identified in the full-data version had a consistent direction of effect, meaning the null hypothesis of near-perfect sign concordance (99%) could not be rejected  . Furthermore, the same 14 tissues, and three developmental stages, remained significant after Bonferroni-correction in the down-sampled analysis (Table S3–4). This evaluation showed that, in the case of EXT-minus-23andMe, the down-sampled gene-property analyses led to similar biological insights as those from the original paper . The Spearman rank correlation of the point estimates from the MAGMA gene expression profiles across 11 brain tissues and developmental stages also suggested great similarity (5.How similar is the pattern of genetic correlations with other traits when using down-sampled GWASs?r ~ 1)  constructed from down-sampled GWASs?The down-sampled PGS for EXT-minus-23andMe explained 8.4% and 8.5% of the variance of a phenotypic externalizing factor in Add Health and COGA, respectively, which is 1.9 pp and 0.5 pp less compared to the same analysis in the original study (Table S6). The overall reduction in explanatory power across other outcomes was less pronounced, on average 0.35 pp in Add Health, and 0.23 pp in COGA. The largest decrease was observed for lifetime smoking initiation with 2.1 pp and 1.7 pp, followed by lifetime cannabis use with 1.1 pp in Add Health (but only 0.55 pp in COGA), which may be explained by these two indicator phenotypes being most affected by the down-sampling. For most other traits, the variance explained by the down-sampled PGS was comparable to the original study.Secondly, the Spearman rank correlation of the regression coefficients was 0.996, suggesting great similarity in point estimates Fig. . All theUnrestricted access to data and results is the cardinal tenet of open science. Here, we propose a systematic approach for researchers disseminating GWAS summary statistics with restricted data removed (i) to evaluate the comparability of down-sampled GWAS summary statistics with their restricted data counterparts, and (ii) to assess the impact of using down-sampled univariate summary statistics in multivariate GWAS with Genomic SEM. We examined the loss of genetic signal in down-sampled univariate GWAS (Step 1), the change in the factor model loadings and fit (Step 2), the loss of genetic signal at the factor-level of down-sampled multivariate GWAS (Step 3); and for potential changes to gene-property analyses (Step 4), the pattern of genetic correlations with other traits (Step 5), and the explanatory power of polygenic score analyses in independent samples (Step 6).We applied these steps to the largest available multivariate GWAS of externalizing to evaluate the quality and predictive performance of the results following restricted data removal. We found nearly identical model fit and parameter estimates, genetic correlations with other phenotypes, and polygenic score analyses of externalizing phenotypes in independent samples. As expected, we observed a decrease in power and genetic signal in the down-sampled univariate and multivariate summary statistics. Although fewer lead SNPs were identified for EXT-minus-23andMe compared to EXT, the genes associated with EXT and EXT-minus-23andMe were similar in terms of region and developmental timing of expression. In the PGS context, EXT and EXT-minus-23andMe performed similarly well. Therefore, while we suggest that the down-sampled summary statistics may be used in analyses related to gene enrichment, genetic correlations, or polygenic scores, the summary statistics with restricted data should be prioritized for gene identification or to follow up on genome-wide significant hits. Prioritizing the restricted data when following up on individual GWAS hits is less of a problem because results for significant SNPs are more likely to be reported in full in the original study.χ2 of SMOK). In the circumstance that more indicators had included 23andMe data, we could have expected greater discrepancies between EXT and EXT-minus-23andMe.In our example, removing restricted data did not change the construct that was identified by genetic factor analysis: The genetic correlation between the factor identified without 23andMe data and the factor identified with 23andMe data was near unity, and the factors had highly similar associations with external variables. But this outcome is not guaranteed. Removing restricted data may be more impactful for univariate GWASs prior to their inclusion in meta-analyses and multivariate GWAS with different indicator phenotypes and model structures. The consistency we observed between EXT and EXT-minus-23andMe is likely explained by the inclusion of restricted data in only a subset of indicators, with just one of seven summary statistics experiencing a substantive reduction in genetic signal Supplementary file2 (XLSX 257 KB)Below is the link to the electronic supplementary material.