We introduce mvSuSiE, a multi-trait fine-mapping method for identifying putative causal variants from genetic association data . mvSuSiE learns patterns of shared genetic effects from data, and exploits these patterns to improve power to identify causal SNPs. Comparisons on simulated data show that mvSuSiE is competitive in speed, power and precision with existing multi-trait methods, and uniformly improves on single-trait fine-mapping (SuSiE) in each trait separately. We applied mvSuSiE to jointly fine-map 16 blood cell traits using data from the UK Biobank. By jointly analyzing the traits and modeling heterogeneous effect sharing patterns, we discovered a much larger number of causal SNPs  compared with single-trait fine-mapping, and with narrower credible sets. mvSuSiE also more comprehensively characterized the ways in which the genetic variants affect one or more blood cell traits; 68% of causal SNPs showed significant effects in more than one blood cell type. However, integration of results is not straightforward; for example, it is difficult to say whether signals identified in different single-trait analyses likely correspond to the same underlying causal SNP. Further, analyzing each trait independently is inefficient in that it cannot exploit the potential for increased power of a multivariate analysis [multi-trait fine-mapping.Genome-wide association analyses (GWAS) have been performed for thousands of traits and have identified many genomic regions associated with diseases and complex traits ,71,85,91analysis . TherefoAlthough several methods have been developed for multi-trait fine-mapping , these mHere we introduce mvSuSiE, a fast and flexible method for multi-trait fine-mapping. The name “mvSuSiE” evokes its origins as an extension of the “Sum of Single Effects” (SuSiE) model  to the mConsider fine-mapping problem” , 63: mosSum of Single Effects (SuSiE) model [Our new mvSuSiE method achieves this goal by extending the E) model  to the mE) model , it can Among existing approaches to fine-mapping, mvSuSiE is most closely related to CAFEH , which aelection , which imvSuSiE uses a flexible prior distribution—a mixture of multivariate normal distributions, as in —to modelmvSuSiE allows for correlations in measurements among traits, with these correlations again being estimated from the data. In contrast, CAFEH assumes measurements are independent across traits, which is often not the case because association studies often involve correlated traits.For (a), estimating the prior distribution from the data involves combining information across many causal SNPs from many regions, which is an additional step compared with standard single-trait fine-mapping analyses. This additional step can be avoided by using a simpler fixed prior  indicates how precisely one can pinpoint the causal SNP underlying this signal. For multi-trait analyses, it may seem natural to report PIPs and CSs separately for each trait. However, this raises tricky issues; for example, if the reported CSs for two traits overlap, do these represent the “same” signal, with a single underlying causal SNP, or different signals with multiple causal SNPs? To avoid this problem, we separate inference into two questions.We also introduce novel ways to summarize the inferences from multi-trait fine-mapping. Again, this builds on SuSiE, which summarizes single-trait results by reporting, for each SNP, a “posterior inclusion probability” (PIP) quantifying the probability that the SNP is causal, and by reporting “credible sets” (CSs) ,96 that at least one trait? This question is answered by cross-trait PIPs and CSs that summarize the inferences across all traits.Which SNPs are causal for i.e., CS) identified, which traits does it affect? This is answered by computing a trait-specific measure of significance, the local false sign rate (sign of the effect). Because SNPs in a CS are typically in high LD, their trait-specific average , as a trait-specific measure of significance of each CS. If the average  for trait For each causal SNP (e (lfsr) , 89, forcross-trait PIPs and CSs together with trait-specific measures of significance ;“Complex Shared Effects,” in which the SNP effects on 16 correlated traits were generated from a variety of sharing patterns derived from the UK Biobank blood cell traits.To compare with PAINTOR and flashfm we also simulated a third smaller set of data with 2 independent traits and shared effects.We simulated traits under two scenarios:We compared methods in their detection of cross-trait causal SNPs—in which we define a cross-trait causal SNP as one that affects at least one trait—and trait-specific causal SNPs. We assessed the performance of both SNP-wise measures  and Credible Sets (CSs) for these tasks. Since PIPs and CSs are typically used in combination in a fine-mapping analysis—CSs identify the independent causal signals, then PIPs identify the strongest causal SNP candidates within each CS—this experiment evaluates the two main aspects of a typical fine-mapping analysis.In all our comparisons, mvSuSiE improved power, coverage and resolution (purity and proportion of 1-SNP CSs) over the SuSiE single-trait analyses . Even though the two traits were simulated independently to conform with PAINTOR’s modeling assumptions, PAINTOR still had much lower power to detect causal SNPs than both SuSiE and mvSuSiE . Both flIn summary, these simulations demonstrate the benefits of mvSuSiE as an efficient and flexible multi-trait fine-mapping method. In particular, mvSuSiE consistently increased power to detect causal SNPs, and improved precision (reduced CS size) compared with fine-mapping each trait separately.To illustrate mvSuSiE in a substantive application, we fine-mapped blood cell traits using data from the UK Biobank ,84. Prevtestvalue < 5 × 10−8) belonged to exactly one of the candidate regions . We then applied the mvSuSiE analysis pipeline to these 975 candidate regions . The median size of a CS was 7 SNPs. Among these CSs, 726 contained just one SNP (“1-SNP CS”), therefore mvSuSiE identified 726 high-probability (95%) candidate causal SNPs. The number of CSs significant in each trait (8 to 335 . (Note t3.5-fold .A key way in which mvSuSiE increases discovery and resolution is by learning about patterns of shared (and non-shared) genetic effects from the data. In these data, the most prominent learned patterns involved strong sharing of effects amongst traits for the same blood cell type . HoweverTo illustrate the potential for mvSuSiE to help dissect complex genetic association signals, we examine four example regions in more detail .−8). Similarly, single-trait fine-mapping with SuSiE identified a single CS for basophil percentage containing 10 candidate SNPs, and no CSs in other traits. From these results one might conclude that the causal SNP is specific to basophil percentage. However, the mvSuSiE fine-mapping results assess the CS as significant in most traits, suggesting that in fact the causal SNP has broad effects across many traits. . Instead of inducing trait-specific sparsity on the effects of causal SNPs, we focussed on bly well , and so bly well . That behttps://github.com/stephenslab/susieR; mvSuSiE R package, https://github.com/stephenslab/mvsusieR; mashr R package, https://github.com/stephenslab/mashr; flashr R package, https://github.com/stephenslab/flashr; CAFEH Python package, https://github.com/karltayeb/cafeh; PAINTOR software, https://github.com/gkichaev/PAINTOR_V3.0; BayesSUR R package, https://cran.r-project.org/package=BayesSUR; flashfm R package, https://github.com/jennasimit/flashfm; FINEMAP software, http://www.christianbenner.com; msCAVIAR software, https://github.com/nlapier2/MsCAVIAR; HyPrColoc R package, https://github.com/cnfoley/hyprcoloc; moloc R package, https://bogdan.dgsom.ucla.edu/pages/MOLOC; PLINK, https://www.cog-genomics.org/plink2; LDStore, http://christianbenner.com; R, https://cran.r-project.org; Python, https://www.python.org/; DSC software, https://github.com/stephenslab/dsc; UK Biobank, https://www.ukbiobank.ac.uk; code for processing of UK Biobank data, https://github.com/stephenslab/finemap-uk-biobank; PLINK association test statistics for UK Biobank blood traits, https://doi.org/10.5281/zenodo.8088040; code and data resources for fine-mapping simulations and fine-mapping analyses of UK Biobank blood cell traits, https://doi.org/10.5281/zenodo.8094982; simulation results, https://doi.org/10.5281/zenodo.8087907.SuSiE R package, mvSuSiE is based on a basic multivariate multiple regression model for ribution ,36 with We do not explicitly include an intercept in . Insteadgiven in . See themvSuSiE generalizes the “Sum of Single Effects” (SuSiE) model  to the mSimilar to SuSiE, we introduce priors for the indicator variables Ps e.g., .The prior distribution duced in ,(7)glIn summary, mvSuSiE is a multivariate regression model with a flexible mixture-of-normals prior on the “single effects,” Here we outline our approach to estimating the posterior distribution for the unknowns of primary interest, the single effect matrices duced in . A more In this section, we assume that the model parameters The posterior distribution of lo e.g., , 105 leslo e.g., . The alglo e.g.,  leads toThe number of effects, he prior  as zero ination” , 86, andination” .sufficient statistics,” we describe an algorithm that uses sufficient statistics, and produces the same result as running the mvSuSiE IBSS algorithm on the individual-level data; in “mvSuSiE with summary data: mvSuSiE-RSS”, we consider summary data that approximate the sufficient statistics, and therefore yield results that do not exactly reproduce mvSuSiE with individual-level data; and since many genetic association studies provide The strategy used in  to extensufficient statistics for The data enter the mvSuSiE model only through the likelihood, which from  is(8)We use IBSS lgorithm  to the ilgorithm  to the sas PLINK  or LDStoas PLINK .We define mvSuSiE-RSS as the application the IBSS-ss algorithm to the sufficient statistics or approximations to these statistics . Conceptually, this approach combines the mixture prior  with an ℓss is a standard quantity reported by most fine-mapping methods, so PIPs are convenient for comparing performance of different fine-mapping methods. PIPs are also useful for visualizing the fine-mapping signal within a candidate fine-mapping region. For mvSuSiE, we define the PIP for SNP fined in .which traits are affected by the SNP. To quantify this, we calculate a minimum , which we define as the smallest The PIP tells us whether or not a SNP has an effect on at least one trait, but it does not tell us (l) from . In otheA cross-trait credible set fect SNP . The calfect SNP .which traits are affected by the SNPs. To assess significance of a CS for a specific trait average , defined as a weighted average of the conditional average  for trait significant for traitA CS does not indicate In order to run mvSuSiE or mvSuSiE-RSS, we must first specify the When the traits are measured in the same samples, it is important to account for possible correlations among the measurements of the different traits; failure to do so can result in miscalibrated fine-mapping statistics . The resTo estimate ribed in , in whicTo verify this estimator, in the simulations we compared  with theY . AlthougWe estimated The simple “random effects prior” that assumes the effects are independent across traits. This is a special case of  in whichPrior with a mixture of “canonical” sharing patterns. , and none of the matrices allow for negatively correlated effects .To complete the canonical prior, we assigned uniform weights We also took an approach similar to  to generFirst, we prepared a data set to learn the prior. For each candidate fine-mapping region, we identified the top initial estimates of covariance matrices using a variety of approaches:ces see “” above.The empirical covariance matrix Three rank-1 matrices of the form A rank-3 approximation of flashr [flashr.A sparse, low-rank approximation of e flashr    to refinted from .) The miFinally, to avoid poor estimation of the The data-driven prior obtained by running the above procedure on the UK Biobank data is shown in The UK Biobank is a prospective cohort study with detailed phenotype and genotype data collected from approximately 500,000 participants recruited in the United Kingdom, with ages between 40 and 69 at time of recruitment ,84. For The UK Biobank imputed genotypes feature a high density of available SNPs, so they are well-suited for fine-mapping ,84. We uWe applied quantile normalization to the 16 blood cell traits measured in the 257,605 samples, separately for each trait, to transform each trait to the standard normal distribution. Since ultimately we aimed to jointly model the 16 blood cell traits, we removed outlying phenotypes according to a simple multivariate normal distribution of the phenotypes. Specifically, after quantile normalization, we measured the Mahalanobis distance Base-pair positions of the SNPs in the UK Biobank genotype data are reported using Genome Reference Consortium human genome assembly 37 (hg19).Using the UK Biobank genotype and phenotype data prepared as described above, we computed association statistics for each of the 16 blood cell traits and for all available biallelic SNPs on autosomal chromosomes meeting the following criteria: minor allele frequency of 0.1% or greater; information (“INFO”) score of 0.6 or greater . The same criteria were used in  to filte--glm function in PLINK  [hide-covarno-x-sexomit-ref--vif 100. Following [model.matrix function in R and standardizing quantitative covariates  to have mean 0 and variance 1.Association statistics were computed using the 1, 2009)  with hidollowing , 92, we ollowing . (These ollowing  and storT_STAT and P columns in the plink2 --glm outputs. The association statistics computed using PLINK have been made available in a Zenodo repository [The summary data provided as input to SuSiE and mvSuSiE were the pository .−8), we defined the fine-mapping region as all SNPs within ±250 kb of the significant association. Next, any regions overlapping by one or more SNPs were combined into a larger region. We repeated combining regions until no regions overlapped. This resulted in a set of fine-mapping regions for each of the 16 blood cell traits, similar to [−8) belong to exactly one region; all SNPs within 250 kb of a significant SNP belong to exactly one region. This procedure generated fine-mapping regions that varied considerably in size: their lengths ranged from 411 kb to 8.73 Mb ; and the number of SNPs ranged from 93 SNPs to 36,605 SNPs . A listing of all 975 regions is given in To select regions for fine-mapping, we adapted the approach used in  to the mmilar to . To formNote that we did not fine-map the extended MHC , definedWe evaluated the fine-mapping methods on data sets generated using real genotypes The genotype data were curated following the data preparation steps described above, so We implemented three fine-mapping scenarios in the simulations.The first scenario was by far the simplest: 2 traits in which the traits were independent and the effects of each causal SNP on the two traits were also independent. This simple scenario was intended mainly for comparisons with PAINTOR and flashfm so as to not unfairly disadvantage these methods: flashfm cannot handle a large number of traits; PAINTOR cannot handle a large number of causal SNPs, and assumes independent traits and independent effects .For comparing other fine-mapping methods , we simulated data sets under two more complex scenarios, which we refer to as “Scenario a” and “Scenario b”.In Scenario a, we simulated 20 independent traits in which the SNP effects were either specific to one trait or shared among traits in simple ways . In the results, we call Scenario a the “Trait-specific + Shared Effects” scenario.Scenario b was intended to capture a combination of factors that one might more realistically encounter in fine-mapping studies. It is also more challenging because the traits are correlated and the effects are shared among the traits in complex ways. Specifically, we simulated using a residual covariance matrix Let The procedure we used to simulate an Center and scale the columns of Choose Sample the indices of the For each SNP  normals , in whicmatrices . For Scematrices .For each SNP Choose the residual variance Specify the variates .†Simulate ng model .Center and scale the columns of BETA, SE, T_STAT and P columns from the plink2 --glm output , we simulated 600 data sets for 600 fine-mapping regions selected from the curated set of 975 regions for the UK Biobank blood cell traits . All selIn this section we describe how we ran the methods on the simulated data sets.SuSiE, mvSuSiE and PAINTOR were run using the -mcmc) because the outputted PIPs when using this option were all zero in our tests. (The same issue was reported in https://github.com/gkichaev/PAINTOR_V3.0/issues/5.) All other PAINTOR options were kept at their default settings. Note that PAINTOR does not accept We ran PAINTOR  in only s traits .FLASHFMwithFINEMAP from R package flashfm (version 0.0.0.9000). This function internally calls FINEMAP [--sss --n-configs-top 1000 --n-causal-snps 10, which allows configurations of up to 10 causal SNPs. We ran flashfm with 4 CPUs (NCORES = 4). All other flashfm settings were kept at their defaults. The inputs to FLASHFMwithFINEMAP were the effect estimates, the standard errors of these effect estimates, minor allele frequencies, vector of trait means, and sample size We ran flashfm  in only  FINEMAP , 9 , we called CAFEH outputs credible sets without any filter on the purity of the CSs. Therefore, to make the CAFEH credible sets comparable to SuSiE and mvSuSiE credible sets, we filtered out CSs with purity less than 0.5.fit_cafeh_summary and fit_cafeh_z—produce the same or very similar results when CAFEHSummary with the same LD matrix, but provide different effect estimates and standard errors of the effect estimates. Let fit_cafeh_summary calls CAFEHSummary with inputs fit_cafeh_z calls CAFEHSummary with inputs CAFEHSummary is invariant to rescaling of CAFEHSummary generates the same result with inputs fit_cafeh_summary and fit_cafeh_z also produce the same result when Note that the two CAFEH summary data interfaces—susie_rss from the susieR R package [susie_rss once per trait. The susie_rss interface accepts different types of summary data; we provided estimate_residual_variance = TRUE), which is the recommended setting when the LD is estimated from the “in-sample” data. We set the maximum number of IBSS iterations to 1,000 (max_iter = 1000). The remaining optional arguments were kept at their defaults.We ran SuSiE in all simulations by calling function  package  . While susie_rss accepts a vector of mvsusie_rss accepts a matrix of mvsusie_rss with the following settings: L = 10, max_iter = 1000, estimate_prior_variance = TRUE, estimate_prior_method = “EM”, precompute_covariances = TRUE and n_thread = 4. We set We ran mvSuSiE using the https://github.com/stephenslab/dsc) version 0.4.3.5 to perform the simulations.All analyses of the simulated data sets were run on Linux machines (Scientific Linux 7.4) with 4 Intel Xeon E5-2680v4 (“Broadwell”) processors, and with R 4.1.0  linked tmvsusie_rss from the mvsusieR package with the following settings: L = 10, N = 248980, precompute_covariances = TRUE, estimate_prior_variance = TRUE, estimate_prior_method = “EM”, max_iter = 1000 and n_thread = 1. We ran SuSiE on each data set i.e., column of n = 248980, L = 10, max_iter = 1000, estimate_prior_variance = TRUE, refine = TRUE. Any CSs returned by susie_rss or mvsusie_rss with purity less than 0.5 were removed.We fit a mvSuSiE model to each fine-mapping data set—specifically the prepared Supplement 1Supplement 2Supplement 31


VA) differs among traits within species, we still know little about how they vary among species. Here we make a first attempt at testing for interspecific variation in two complementary measures of VA and the role of phylogeny in shaping this variation. To this end, we performed a phylogenetic comparative analysis using 1822 narrow‐sense heritability (h2) for 68 species of birds and mammals and 378 coefficients of additive genetic variance (CVA) estimates for 23 species. Controlling for within‐species variation attributable to estimation method and trait type, we found some interspecific variation in h2 (~15%) but not CVA. Although suggestive of interspecific variation in the importance of non‐(additive) genetic sources of variance, sample sizes were insufficient to test this hypothesis directly. Additionally, although power was low, no phylogenetic signal was detected for either measure. Hence, while this suggests interspecific variation in VA is probably small, our understanding of interspecific variation in the adaptive potential of wild vertebrate populations is currently hampered by data limitations, a scarcity of CVA estimates and a measure of their uncertainty in particular.Evolutionary adaptation through genetic change requires genetic variation and is a key mechanism enabling species to persist in changing environments. Although a substantial body of work has focused on understanding how and why additive genetic variance ( Evolutionary adaptation through genetic change requires genetic variation, but little is known about how much this varies across species. To this end, we performed a phylogenetic comparative analysis using 1822 narrow‐sense heritability for 68 species of birds and mammals and 378 coefficients of additive genetic variance estimates for 23 species. Although data limitations meant statistical power was low, we found that species varied little in their additive genetic variance and none of this was explained by phylogeny. After controlling for these differences, we then present the level of interspecific VA according to each metric and to what extent it can be explained by phylogenetic relatedness.Here, we present a phylogenetic comparative analysis of univariate estimates of 22.1h2) and coefficients of additive genetic variance (CVA), respectively) for wild populations of birds and mammals previously used in Postma (https://apps.webofknowledge.com) with the following search terms in the ‘Topic’ field:  AND (‘heritabil*’ OR ‘genetic* estimate*’). Additionally, estimates from all studies cited in Merilä et al. , unless the authors explicitly stated that they considered one estimate superior.Whenever possible, we recorded all reported estimates of h2 was not provided, it was calculated from the additive genetic variance (VA) and phenotypic variance (VP) reported by the authors as:If VP is conditioned on variation attributable to one or more fixed effects will vary among studies  following Garcia‐Gonzalez et al.  were recorded as a measure of the precision of estimates used for weighting estimates in the meta‐analytic mixed models outlined below. If only 95% confidence or credible intervals were available, approximate SEs were calculated from these by dividing half the difference between the upper and lower 95% intervals by 1.96. As CVA estimates are rarely accompanied by an estimate of their precision  is the same for both.Estimates of 2.3h2 estimates   Postma, . To contWe classified traits as morphology, life history, fitness, physiology or behaviour traits. We acknowledge that these classifications are, to some degree, arbitrary and that some traits could be classified in multiple ways. In these instances, we followed the classification used in the original publication. In particular, we treat fitness traits as separate from other life histories, as traits more closely related to fitness are predicted to have different levels of genetic variance  (i.e. Bayesian), animal model (REML), grandparent–offspring regression, half‐sib and full‐sib analyses.The publication year was recorded to account for temporal changes in the size of estimates, thought to be largely due to methodological differences Postma, . ConsequEach study was given its own unique ID to allow us to model any non‐independence among estimates for different traits from the same study.2.4h2 and CVA vary among both traits and species using Bayesian generalised linear mixed effects models implemented in the R package MCMCglmm version 2.3.4  and based on Jetz et al. , trait category  and other life‐history traits) and the sample size and study year as covariates. Both studies and species were included as random effects. The species effect controlled for repeated species measures and estimated the level of interspecific variation. Phylogenetic relatedness was accounted for following Hadfield and Nakagawa  for random effects, the Inverse‐Wishart distribution for the residual variance, and non‐informative priors for the fixed effects. We ran each model for 1,505,000 iterations, with a thinning interval of 1500 and a burn‐in of 5000. This ensured effective sample sizes greater than 1000. We evaluated model convergence and mixing based on the visual examination of trace plots  excluding measurement error. Figures were created using the packages ggplot2 version 3.4.0 . Estimates were based on 5 , with fitness (n = 48), life history (n = 335), physiology (n = 65) and behaviour (n = 126) traits being far less numerous : n = 229; Collared flycatcher : n = 191; Darwin's medium ground finch (Geospiza fortis): n = 156; Bighorn sheep (Ovis canadensis): n = 99; Barnacle goose (Branta leucopsis); n = 98).We analysed 1822  Møller,  to 38,02 Møller,  from stuus Table . The numh2 estimates among trait types: conditioned upon other effects; morphology traits were estimated to have the highest h2 , followed by physiology and behaviour traits having moderate h2  had the lowest h2 of 0.29 [95% CI 0.16–0.48] , whereas the Darwin's medium ground finch (Geospiza fortis) had the highest h2 of 0.51 [95% CI 0.38–0.65] , with fewer life histories (n = 56), fitness (n = 22) and physiological traits (n = 14)  Figure . As theyCVA estimates were not affected by study method, year or sample size , with physiology traits having moderate CVA estimates , we found no interspecific variation in CVA . However, the latter variation was not associated with the phylogeny. Based on these findings, we cautiously present the following conclusions, acknowledging the low power of some of these analyses.To better understand the mechanisms shaping additive genetic variances, we performed phylogenetic comparative analyses of h2 and the absence of interspecific variation in CVA agree with previous analyses  would be among the lowest of all species included in this analysis, not due to particularly low levels of additive genetic variance, even if this could be expected based on their unique demographic characterised by bottlenecks and isolation  drives variation in h2 between trait types . However, estimates of CVE are currently rarely published, and often without the estimates of precision that enable a formal meta‐analysis. Overall, it is likely that further comparative studies of these trends in wild populations are limited by the availability of standardised estimates of VA. Not only are estimates extremely biased towards specific species with long‐running field studies, but CVA still remains far less widely reported than h2, despite little difference in the difficulty of reporting the latter. Given the well‐known difficulties of interpreting estimates of h2 without knowledge of the absolute levels of additive genetic and environmental variance, reporting both metrics together, whenever possible, would be an improvement to the literature. Nevertheless, because coefficients of variation are only meaningful for a subset of traits (as discussed below), sample sizes will always be smaller than for estimates of heritability.Although we currently do not have a good understanding of the role of  variation in trait VA among trait types , we were not able to demonstrate a statistically significant difference in the amount of interspecific variation in both measures of VA. There is therefore a need to move beyond this approach if we are to better understand the factors shaping the coefficients of additive genetic variance. First, understanding how estimates vary within a species between populations  could ba et al.  and selea et al. . AlthougEuan A. Young: Conceptualization ; data curation ; formal analysis (lead); investigation ; methodology ; resources ; software ; validation ; visualization ; writing – original draft (lead); writing – review and editing . Erik Postma: Conceptualization ; data curation ; formal analysis (supporting); funding acquisition (lead); investigation ; methodology ; project administration (lead); resources ; software ; supervision (lead); validation ; visualization ; writing – original draft (supporting); writing – review and editing .Swiss National Science Foundation grants 141110 and 159462.The authors declare no conflicts of interest.


Soft winter wheat has been adapted to the north-central, north-western, and south-central United States over hundreds of years for optimal yield, height, heading date, and pathogen and pest resistance. Environmental factors like weather affect abiotic traits such as pre-harvest sprouting resistance. However, pre-harvest sprouting has rarely been a target for breeding. Owing to changing weather patterns from climate change, pre-harvest sprouting resistance is needed to prevent significant crop losses not only in the United States, but worldwide. Twenty-two traits including age of breeding line as well as agronomic, flour quality, and pre-harvest sprouting traits were studied in a population of 188 lines representing genetic diversity over 200 years of soft winter wheat breeding. Some traits were correlated with one another by principal components analysis and Pearson’s correlations. A genome-wide association study using 1,978 markers uncovered a total of 102 regions encompassing 226 quantitative trait nucleotides. Twenty-six regions overlapped multiple traits with common significant markers. Many of these traits were also found to be correlated by Pearson’s correlation and principal components analyses. Most pre-harvest sprouting regions were not co-located with agronomic traits and thus useful for crop improvement against climate change without affecting crop performance. Six different genome-wide association statistical models  were utilized to search for reasonable models to analyze soft winter wheat populations with increased markers and/or breeding lines going forward. Some flour quality and agronomic traits seem to have been selected over time, but not pre-harvest sprouting. It appears possible to select for pre-harvest sprouting resistance without impacting flour quality or the agronomic value of soft winter wheat. HoweverTaPHS1/MOTHER OF FLOWERING TIME (MFT), MAP KINASE KINASE 3 (MKK3), and VIVIPAROUS 1 (VP1); genes involved in abscisic acid synthesis and degradation like 9-cis-epoxycarotenoid dioxygenase (HvNCED1) and ABA 8’-hydroxylase (HvCYP707A1); and the mutant ENHANCED RESPONSE TO ABA8 (ERA8) in white spring wheat , and arabinoxylans, measured by sucrose solvent retention capacity (SucSRC), can lead to brittle products that take longer to bake . Higher Several previous studies have defined PHS resistance or flour quality traits on nearly every chromosome, but most are of small effect and used modern breeding lines . PHS andTo study the effects of many traits, a population encompassing diversity of breeding lines from the early 1800s to the early 2000s was developed based on previous milling and baking performance using a long-flow Allis-Chalmers milling system by the USDA-Agricultural Research Service Soft Wheat Quality Lab. Included varieties represent variation in important crop traits when grown in eastern North America and were available for study . The popThe goal of this research was to find regions of the genome that could provide resistance to PHS, an important abiotic threat to wheat crops. Also, this study sought to determine if resistance to PHS may overlap with other important flour quality or agronomic traits. This would indicate if breeding efforts over the past ~200 years impacted previously unmeasured PHS and flour quality traits in pursuit of other traits such as yield, pests, and disease resistance. With the pressures of an increasing population requiring more food of higher quality at a time when climate change can cause disruptions in the food supply, it has become more important to protect against abiotic stresses such as PHS without impacting agronomic traits or flour quality in wheat.22.1https://www.ars-grin.gov or http://wheatpedigree.net) as listed in Sixty grams of seed per plot for each of the 188 members of the historic diversity population described in www.wintersteiger.com). For the artificial spike wetting test (Art), ~30 spikes were hand harvested from the non-irrigated plot at maturity (no green on the spikes) in brown paper bags. Spikes were dried in the bag at ~29˚C for 5 days, and then placed upright ~2.5 cm apart in Styrofoam blocks by their stems and subjected to 95% humidity in a growth chamber with half sodium/half metal halide lights at 200–300 μmol m−2 s−1 and 20˚C for 16 h and no lights and 15˚C for eight h. Spikes were soaked with water from a spray bottle every 12 h. After 3 days, spikes were dried in the greenhouse for 1–2 days, hand threshed, placed in heavy manila envelopes, and stored at −20˚C. All collected seeds were cleaned of debris by blowing air to remove the lighter chaff. All PHS treatments were performed for 3–4 years .For irrigated PHS tests, plots were treated in the field with overhead sprinklers simulating 2.5–5.0 cm of rain for 2 days (Irr). A second set of plots was left in the field until a natural rain event (Nat) occurred . Each wh2.2Grain and flour quality tests for FlProt, test weight (TstWt), WatSRC, NaSRC, SucSRC, LASRC, LAAdSRC, SftEqv, FlYld, CkDia, and CkTpGr were performed on sound grain (not exposed to PHS) and calculated as described previously . BrieflyHD was recorded visually walking the field daily and recording the first day 50% of wheat spikes had fully emerged from the boot jack. Values were calculated by assigning the first date a variety emerged as day 1 and adding the appropriate number of days for each variety that emerged afterward. Hght was recorded in centimeters at maturity, except the first year collected in inches and converted to centimeters.Soft winter wheat has been primarily bred for improvement of traits such as yield, height, heading days, or pathogen and pest resistance over ~200 years. Other traits may have been altered because they were located near genes for selected traits. To observe if PHS or flour quality traits may have been impacted, a comparative measure for how long ago the variety was released by breeders was developed. If this measure co-located with PHS or flour quality traits, it would indicate their inadvertent selection, especially if they also co-locate with agronomic traits. Age of breeding line (Age) was calculated by subtracting the release year of the line from 2020. Awnless or bearded (Awns) and red or white seed color (SdClr) was determined by visual observation and accession reports.www.udyone.com). FN was measured using a Perten Falling Number machine 100 or 1000 (www.perkinelmer.com) in 20 ml of water with grams of ground seeds based on moisture content per manufacturer’s manual Table III (www.perkinelmer.com) for 15 s before placing in the Falling Number machine following AACC method 56-81.03 (www.megazyme.com) with the following modification. Instead of 7 g of ground seeds in 40 ml of extraction solution in 50-ml tubes, 0.3 g of ground seeds was extracted in 2 ml of extraction solution in a 48-well format . Absorbance was determined colorimetrically in a 96-well plate format  using a BioTek plate reader (www.biotek.com) at 405 nm. Activity was calculated using the manufacturer’s standard method for wheat (www.megazyme.com).PHS treatments were tested for grain soundness by Falling Number (FN) and AA tests. Threshed and cleaned seeds were ground in a UDY Mill model 3010-014 with a 1-mm screen (able III . Moisturable III . The pas56-81.03 . Alpha a56-81.03  with an 2.3trait) , irrigated Falling Number (IrrFN), natural alpha amylase activity (NatAA), natural Falling Number (NatFN), TstWt, CkDia, and CkTpGr, and four for artificial alpha amylase activity (ArtAA), artificial Falling Number (ArtFN), FlProt, FlYld, HD, Hght, LAAdSRC, LASRC, NaSRC, SftEqv, SucSRC, and WatSRC were combined into Best Linear Unbiased Predictors (BLUP) using R version 4.0.4 and metafor package version 2.4-0 for samples using means and standard deviations calculated in Microsoft Excel . Histogrtrait) .p-values were calculated using the rcorr command from the Hmisc library in R version 3.63, copied into comma delimited files using the write.csv command and merged into one table in Microsoft Excel.Principal components analysis (PCA) was performed using pcaMethods version 1.78.0 from Bioconducter version 3.10.1 and factoextra version 1.0.7 in R version 3.6.3 necessary to run the combination of tools . Microsowww.zzlab.net) under R version 4.0.4 running in RStudio version 4.2.1 using six models: general linear model (GLM), mixed linear model (MLM), multiple loci mixed model (MLMM), fixed and random model circulating probability unification (FarmCPU), Bayesian-information and linkage-disequilibrium iteratively nested keyway (BLINK), and settlement of MLM under progressively exclusive relationship (SUPER) to discover any differences model type might play in locating significant markers for different phenotypes in a soft winter wheat population  was positively correlated with Hght, FlProt, and HD, and negatively correlated with CkDia, CkTpGr, and SftEqv. SdClr was positively correlated with TstWt and most SRC and negatively correlated with HD, Hght, CkTpGr, and CkDia. Awns were uncorrelated with other traits. Flour protein was positively correlated with Hght and most SRCs and negatively correlated with other flour quality traits while most SRCs were positively correlated with each other and negatively correlated with other flour quality traits with significant correlations  of −0.24 to 0.94 . Means, standard deviations, and number of samples for each trait are in The first three PCs of all traits represented 31%, 18%, and 12% of variation, respectively, and were considered significant based on a plot of Eigenvalues and cumulative variance  was performed in GAPIT3 to test for model performance over diverse traits in a moderate-sized soft winter wheat population. See the R script in p-values of 2 × 10−5 to 2 × 10−6. Quantitative trait nucleotide 5A-5, 99-109 estimated cM region with Age and FlProt had p-values of 5 × 10−5 to 3 × 10−9. Quantitative trait nucleotide 6B-4, 82 estimated cM region with Age and HD had p-values of 1 × 10−6 to 8 × 10−8. Quantitative trait nucleotide 6B-8, 150-151 estimated cM region with Age, CkDia, WatSRC, FlProt, Hght, and CkTpGr had p-values of 2 × 10−5 to 9 × 10−9. Quantitative trait nucleotide 6D-2, 10 estimated cM region with Age and Awns had p-values of 6 × 10−4 to 4 × 10−5. These regions indicated where potential trait changes over time observed by Pearson’s correlation and PCA may have occurred. For identical markers, the FlProt effect was in the same direction as Age three times, while HD and WatSRC, once. Conversely, Awns and CkDia effects were the opposite of Age where increased Age indicated older breeding lines  had an overlap between ArtAA and irrigated PHS measures while irrigated and natural PHS measures were more often co-located. Multiple flour quality traits co-located on chromosomes 1A, 1B, 1D, 2A, 2D, 3A, 5A, 6A, and 6B. Quantitative trait nucleotide 1A-5 was described above. Quantitative trait nucleotide 1A-8 is at an estimated 117 cM including WatSRC and NaSRC with p-values from 3 × 10−4 to 4 × 10−5. Quantitative trait nucleotide 1B-1 is at an estimated 24–27 cM including LASRC and LAAdSRC with p-values from 2 × 10−4 to 7 × 10−12. Quantitative trait nucleotide 1B-2 is at an estimated 30 cM including CkTpGr, FlYld, and SucSRC with p-values of 1 × 10−4 to 7 × 10−7. Quantitative trait nucleotide 1D-1 is at an estimated 14-21 cM including LASRC, LAAdSRC, and SucSRC with p-values of 1 × 10−4 to 8 × 10−5. Quantitative trait nucleotide 1D-2 is at an estimated 89 cM and includes LASRC and LAdSRC with p-values of 1 × 10−6 to 5 × 10−11. Quantitative trait nucleotide 2A-3 is at an estimated 170 cM and includes NaSRC and SucSRC with p-values of 8 × 10−5 to 6 × 10−6. Quantitative trait nucleotide 2D-1 is at an estimated 12 cM and includes FlYld and WatSRC with p-values of 1 × 10−3. Quantitative trait nucleotide 3A-2 is at an estimated 63–64 cM and includes CkTpGr, CkDia, and FlProt with p-values of 2 × 10−4 to 8 × 10−6. Quantitative trait nucleotide 3A-6 is at an estimated 123 cM including LAAdSRC, LASRC, and SdClr with p-values of 1 × 10−4 to 5 × 10−9. Quantitative trait nucleotide 5A-3 is at an estimated 150 cM and includes LAAdSRC and SftEqv with p-values of 1 × 10−5 to 5 × 10−6. Quantitative trait nucleotide 5A-6 is at an estimated 80 cM and includes CkDia, NaSRC, SucSRC, and WatSRC with p-values of 2 × 10−6 to 8 × 10−8. Quantitative trait nucleotide 6A-3 is at an estimated 89–90 cM and includes CkDia, CkTpGr, FlProt, and Hght with p-values of 1 × 10−4 to 6 × 10−8. Quantitative trait nucleotide 6A-5 is at an estimated 114 cM and includes CkDia, FlProt, Hght, and SucSRC with p-values of 1 × 10−5 to 9 × 10−6. Quantitative trait nucleotide 6B-6 is at an estimated 95–97 cM and includes NaSRC, WatSRC, CkTpGr, CkDia, and FlYld with p-values of 1 × 10−4 to 1 × 10−10. Quantitative trait nucleotide 6B-8 is described above with overlap in Age  with the lowest W statistic and fewer white varieties, would have been the most susceptible to false positives. The detection of Age-related QTN across all models with the exception of MLM was also robust regardless of it being skewed more towards more recent breeding lines (less than 60 years since release) as fewer very old breeding lines are available. Single-locus tests such GLM, a naïve model without population correction, and MLM using VanRaden kinship were tested along with more recently released models. The GLM can be particularly prone to false positives as illustrated by the QQ plot for Age but false positives appear less likely with the QQ plot for IrrAA. The MLMM performs multiple locus tests and is an extension of MLM with the most significant marker fitted stepwise as a co-variate (GAPIT3 allowed testing of multiple GWAS models. Nine traits were normally distributed by the Shapiro–Wilk test; however, the majority had near-normal-appearing bell curves by histogram and -variate . The Far-variate . The BLI-variate . The SUP-variate . The GLM-variate . The SUP-variate .5Breeding over time appeared to be a factor in some traits, most notably flour protein content, Hght, and HD. Since PHS-related traits had little overlap with others, several new regions were uncovered to increase resistance in wheat under adverse weather conditions brought about by climate change without impacting agronomic performance or flour quality. Flour quality traits showed much greater overlap both among themselves and with agronomic traits making improvement more challenging. Future research to increase marker density should better resolve QTN and improve detection in areas lacking sufficient coverage utilizing a smaller set of GWAS models.All data used to generate results during this study are available as NP performed some of the experiments, wrote and edited some text. BP designed and supervised the experiments, analyzed the data, wrote and edited text. All authors contributed to the article and approved the submitted version.


SNP heritability ( The ability to estimate (narrow-sense) heritability   made theividuals -5. This ped SNPs . Indeed,WAS SNPs , approacare used . This haDespite the utility and simple intuition of e mating -12. But variants -11, 13. variants -16 for avariants -23. The Our goal in this paper is to study the behavior of  (GREML) , 5 can bWe begin by describing a generative model for the phenotype. Let e random .We denote the mean, variance, and covariance with Here the first term represents the contribution of individual loci (genic variance) and the second term is the contribution of linkage disequilibrium (LD contribution). We make the assumption that loci are unlinked and therefore, the LD contribution is entirely due to population structure. We describe the behavior of estry as :(1.1)et al. (2001) [et al. (2017) using a parameter From dmixture . In the dmixture . For bre. (2001) . V(θ) isopulation.Under these conditions, the behavior of eviously , 26  . This isWe illustrate this by tracking the genetic variance in admixed populations for two traits, both with the same mean ls model . We drewectively . We simum=1,000, . The obsIn the HI model, t change  so terms + (1.2) . This eq(E(Vg∣θ)  and the , at t=0 . In the ene flow . This miene flow . But thiene flow . After aet al. (2010) defined In their original paper, Yang tability . This isre known . Our goaWe used GREML, implemented in GCTA , 5, to eing GCTA , 4.GCTA under- and over-estimates the genetic variance in admixed populations for traits under divergent (Trait 1) and stabilizing selection (Trait 2), respectively, when there is population structure, i.e., when V(θ)>1 . One rearm (1.4) . But σ^uectively . Alternarm (1.3) . Thus, wThe overall bias in ulations  and ther(1.2)≠Vg .In principle, we can recover the missing components of 2fiV(xi)  (Appendi2fiV(xi) . We can 2fiV(xi) . In matr., Σ=LL′ . GREML rh traits .In practice, however, the LD contribution may not be fully recoverable for two reasons. One, the LD-scaled GRM requires computing the inverse of 2)−(1.3) . Indeed,et al. (2014) [A related quantity of interest in admixed populations is local ancestry heritability (. (2014)  showed tvariants . Here, wWe define local ancestry ancestry . Then, tancestry :Vγ=V(∑to (1.2) . AdditioGREML estimation of enotypes . The folWe show that, in the presence of population structure, i.e., when on of LD . But thehe model , 10. Scael [σ^v2 -H. But atry axis -H.Based on the above, In a previous paper, we suggested that local ancestry heritability could potentially be used to estimate the genetic variance between populations . Our rese (2023) .In the previous sections, we showed theoretically that  Genomes  ASW , is positive and accounts for ≈ 40 — 50% of the total variance explained. This is because of large allele frequency differences between Africans and Europeans that are correlated across skin pigmentation loci, consistent with strong polygenic selection favoring alleles for darker pigmentation in regions with high UV exposure and vice versa , 39-42. et al. (2010) introduced the concept of SNP heritability  , 49 shouWe show that uggested , 33. ButOne limitation of this research is that it focuses on the GREML estimator of  effects . Fixed e effects . This is effects -52. FurtDoes the LD contribution to the genetic variance have practical implications? The answer to this depends on the context in which SNP heritability is used. a priori). We show that for most traits, the contribution of population structure to the variance explained by GWAS SNPs is modest among African Americans. Thus, if we assume that the genetic architecture of GWAS SNPs represents that of all causal variants, then despite incorrect assumptions, the discrepancy between Ultimately, the discrepancy between  studies . While tWe first drew the allele frequency  [We simulated the genotypes, local ancestry, and phenotype for 10,000 admixed individuals per generation under the hybrid isolation (HI) and continuous gene flow (CGF) models by adapting the code from Zaitlen . (2017) . We denois small . To overssion in . At timet−1)1+P2 .We sampled the local ancestry at each reml and --reml-no-constrain flags in GCTA [We used the -- in GCTA  to estimunstandardized matrix of genotypes and For the standard GRM, the genotypes at the 1(X−2P)′ . Similarqcovar flag.We estimated To decompose the variance explained by GWAS SNPs in African Americans, we needed four quantities: (i) effect sizes of GWAS SNPs, (ii) their allele frequencies in Africans and Europeans, and (iii) the mean and variance of global ancestry in African Americans .http://www.nealelab.is/uk-biobank) and processed by Ju and Mathieson [et al. (2019) where effect sizes were meta-analyzed across four admixed cohorts [et al. provide summary statistics separately with and without conditioning on rs1426654 and rs35397 – two large effect variants in SCL24A5 and SLC45A2. We used the ‘conditioned’ effect sizes and added in the effects of rs1426654 and rs35397 to estimate genetic variance.We retrieved the summary statistics of 26 traits from GWAS catalog . Full liathieson  to repre cohorts . Lona-Duet al. (2020) [clump-p1 5e-8) with a pairwise LD cutoff of 0.05 (--clump-r2 0.05) and a physical distance threshold of 250Kb (--clump-kb 250) for clumping. Second, we applied a second round of clumping (--clump-kb 100) to remove SNPs within 100kb.We selected independent hits for each trait by pruning and thresholding with PLINK v1.90b6.21  in two s. (2020) . We used. (2020)  as the L−8) in at least one cohort. This allowed us to maximize the discovery of variants such as the Duffy null allele that are absent among individuals of European ancestry but polymorphic in other populations [When GWAS was carried out separately in different ancestry cohorts in the same study, we used inverse-variance weighting to meta-analyze effect sizes for variants that were genome-wide significant  with CEU and YRI individuals from 1000 genome (phase 3) using ADMIXTURE 1.3.0  with k=2Initially, the multi-ancestry summary statistics for a few traits  yielded values > 1 for the proportion of variance explained. This is likely because, despite LD pruning, some of the variants in the model are not independent and tag large effect variants under divergent selection such as the Duffy null allele, leading to an inflated contribution of LD. We checked this by calculating the pairwise contribution , i.e., l allele -C. A siml allele . For BASscore flag in PLINK, [As a sanity check, we independently estimated the genetic variance as the variance in polygenic scores, calculated using --n PLINK,  in ASW iSupplement 1


Prunus armeniaca L.) is an economically important fruit tree species in arid areas owing to its hardiness and cold and drought tolerance. However, little is known about its genetic background and trait inheritances. In the present study, we first evaluated the population structure of 339 apricot accessions and the genetic diversity of kernel-using apricots using whole genome re-sequencing. Second, the phenotypic data of 222 accessions were investigated for two consecutive seasons (2019 and 2020) for 19 traits, including kernel and stone shell traits and the pistil abortion rate of flowers. Heritability and correlation coefficient of traits were also estimated. The stone shell length (94.46%) showed the highest heritability, followed by the length/width ratio (92.01%) and length/thickness ratio (92.00%) of the stone shell, whereas breaking force of the nut (17.08%) exhibited a very low heritability. A genome-wide association study (GWAS) using general linear model and generalized linear mixed model revealed 122 quantitative trait loci (QTLs). The QTLs of the kernel and stone shell traits were unevenly assigned on the eight chromosomes. Out of the 1,614 candidate genes identified in the 13 consistently reliable QTLs found using the two GWAS methods and/or in the two seasons, 1,021 were annotated. The sweet kernel trait was assigned to chromosome 5 of the genome, similar to the almond, and a new locus was also mapped at 17.34–17.51 Mb on chromosome 3, including 20 candidate genes. The loci and genes identified here will be of significant use in molecular breeding efforts, and the candidate genes could play essential roles in exploring the mechanisms of genetic regulation.Kernel-using apricot ( Because of their hardiness and cold and drought tolerance , kernel-Prunus armeniaca L.). Despite an undocumented history, the kernel-using apricot is known to have been grown for a long time in north Hebei Province (Zhuolu County) and has an overlapping area with wild populations of Prunus sibirica L. Its botanical features appear to be similar to those of Prunus armeniaca L. and P. sibirica; however, it has some particular traits that can be distinguished from P. armeniaca and P. sibirica  transcription  based on next-generation high-throughput sequencing techniques. G WAS are widely used to dissect complex genetic traits . In the 22.1Prunus mume (“Yanmei”). In addition, accessions of 27 individuals of wild apricots including 16 P. armeniaca L., seven P. sibirica L., and four P. mandshurica (Maxim.) Koehne (PsPma) were used. Of these, 180 accessions had been used in a previous study  with inquiry number PRJNA705053 . Genomic DNA from 159 accessions was extracted from fresh young leaves using the modified cetyl trimethylammonium bromide method. Approximately 1 μg of genomic DNA for each accession was fragmented by sonication to a size of 300–500 bp with a Covaris S2 Focused Ultrasonicator , and then end-polished, A-tailed, ligated with the full-length adapters, and polymerase chain reaction (PCR) amplified. A whole-genome shotgun paired-end library was prepared and sequenced on an Illumina HiSeq X Ten platform at BMK  using the PE150  strategy according to the manufacturer’s recommendations. Raw reads were filtered prior to genome mapping. The adaptor sequences in the raw reads were removed, and ambiguous and low-quality bases from the start or end of the raw reads were trimmed using SOAPnuke . Of the NA705053 . The raw2.3The remaining high-quality paired-end reads were mapped to the apricot reference genome (Yinxiangbai v1.0) using BWA (version 0.7.15-r1140) with the command “mem –t 4 –k 32 -M” . To reduW), gene diversity/heterozygosity (He), STF, and Tajima’s D for apricot populations were estimated using VCFtools (v0.1.14) (https://github.com/BGI-shenzhen/VCF2Dis), and a phylogenetic neighbor-joining tree was constructed based on the distance matrix using the software PHYLIP v3.68 (http://evolution.genetics.washington.edu/phylip.html), and presented using MEGA7  error was tested for K values between 2 and 10; K = 6 was chosen because the lowest CV error was observed at K = 6. For each sample, if the component for a sample within the major group was ≥ 0.60, the sample was classified as this major group, and the remaining samples were deemed admixed. Linkage disequilibrium (LD) was calculated using PopLDdecay v3.31 (r2) values between the two SNPs and the physical distance between the two SNPs.The nucleotide diversity (π), Watterson’s estimator (θv0.1.14) . For theng MEGA7 . Principng MEGA7 . Populatng MEGA7 , which iay v3.31  with par2.4Phenotypic measurements were conducted during fruit ripening in 2019 and 2020. One hundred representative fruits were randomly collected from the outer canopy of the tree, and whole mature nuts were removed from the fully mature fruits, washed and dried for investigation. The shapes of the nuts and seed kernels were measured using Vernier calipers, including stone shell or kernel length (SL or KL), width (SW or KW), thickness (ST or KT), length/width ratio (SL/SW or KL/KW), and length/thickness ratio (SL/ST or KL/KT). Samples were randomly selected to obtain 30 records. The average values of dry shell weight with kernel (SDW) and dry kernel weight (KDW) of the samples were recorded using an electronic balance, and the kernel/shell ratio (KR) was calculated as (KDW × 100)/SDW. All samples were analyzed out with an average of 100 seeds.-1, tested speed 1.0 mm s-1, upstream speed 2.0 mm s-1, compression deformation of the sample as 30%, and the trigger force as 1.0 N. Twenty nuts were randomly selected for each accession. The nut shell thickness (STH) was measured using a Vernier caliper at the thinnest point in the middle of the cracked shell. The average STH per sample was recorded for the 20 nuts.The shell breaking force (SBF) and hardness (SH) of the nuts were measured using the TPA module of the TMS-PRO physical property analyzer , and 2500 N sensors (diameter 35 mm) was selected. The parameters were set as follows: downstream speed 2.0 mm sAll the dry nuts of each sample were broken open and the seed kernel were removed and, then, the shell was crushed into a fine powder with a grinder. After filtering although a 60-mesh screen, the powder was stored in a plastic Ziplock bag to determine the acid insoluble lignin content. The acid insoluble lignin content (SLC) was determined using the Klason method , and eacKernel bitterness (SK) was evaluated in 2020. The nuts of mature fruit were cracked, and each sample was tested by two people, who classified its flavor as bitter (0) or non-bitter . The value of pistil abortion (AR) is usually determined as the ration between the number of abnormal flowers  and the total number of flowers from the entire tree. More than 300 flowers from short shoots were randomly sampled around the canopy at the full-blooming stage.2H) of these traits was calculated based on the components of variance between and within cultivars using one-way ANOVA as follows:The broad-sense heritability . Correlation analysis of different traits was performed using the corrplot R package.where Ve sample . Correla2.510(P) ≥ 8.0 at P = 0.05 level [–log10(0.1/3.47 × 10-6) = 7.8], and the significance threshold in the GLMM method was set to 6.5. To reduce false positives and increase the statistical accuracy, the Bonferroni-corrected (FDR) P-value threshold was set at P< 0.01. We considered a QTL reliable when a QTL was consistently detected in two seasons or methods. These QTLs were named as “qtn” + trait name abbreviation + scaffold + detected QTL order on chromosome, such as qtnSTH_4.1.A total of 3,472,166 SNPs were used in the GWAS. General linear models (GLMs) and generalized linear mixed model (GLMM) were generated using the Genomic Association and Prediction Integrated Tool (GAPIT 6.0 Version)  and fast2.6Prunus armeniaca “Yinxiangbai” genome . Borkh was used as an outgroup based on these high-quality SNPs indentified (P. mume). The other accessions formed at the second clade, which included five main groups. The group I included most wild common apricots and all of accessions from XJ; group II contained majority accessions from NW and three kernel-using accessions (KU), and group III contained the majority KU cultivars, NE accessions and the close species (P. sibirica and P. mandshurica) of wild apricot; and group IV included cultivated apricots in the EU group; and group V consisted of all cultivars from NC, some NW cultivars, and mixed with several native wild common apricots. The result showed that most kernel-using accessions clustered with the NE accessions, P. sibirica, and P. mandshurica.To investigate the population structures of these apricot accessions, we first constructed a rooted neighbor-joining (NJ) tree with P. sibirica. However, groups could not clearly distinguish landraces between NW and NC based on their geographical distribution, which may be owing to frequent genetic exchanges generated by selection or introduction, reflecting the complex domestication and breeding history of cultivated apricots.Next, we performed PCA of these samples , gene diversity/heterozygosity (He), and Tajima’s D. Across the genome, π, θW, and HE for the KU population were estimated to be 6.19 × 10−3, 6.03 × 10−3, and 6.04 × 10−3, respectively, indicating that the level of diversity and heterozygosity of kernel-using apricot are high; however, there were a large number of medium frequency alleles in the population, which may be caused by the bottleneck effect of the population. The Siberian apricot (Ps) had the highest level of genetic diversity (π = 7.05 × 10−3 and θW = 7.46 × 10−3), whereas the cultivated group NC had the lowest level with π = 5.68 × 10−3 and θW = 5.80 × 10−3 , Watterson’s estimator (θ0 × 10−3 Table 1.3.32H) was estimated for 13 traits (2H (> 85%) were observed for SL (94.46%), SW (88.96%), ST (86.84%), SL/SW (92.00%), and SL/ST (92.01%).Two hundred and twenty-two accessions were evaluated for 19 different traits, including 10 kernel traits, seven seed traits, KR, and AR. The normal distribution and maximum, minimum, and mean values of these traits for different accessions are presented in 2H values of other shell-opening traits were lower in SH (61.10%) and SBF (17.08%).Because the hardness of the stone of the kernel-using apricot increases the cost of opening the shell and using the kernel, STH, SBF, SH, and SLC were also used for germplasm evaluation in this study. The variability in SH was very high in different years, and the CV was 24.89% in 2019 and 22.60% in 2020. Values for SH varied from 305.31 N in Lve to 1573.37 N in Taohexing, whereas STH ranged from 2.95 mm in Momoxing to 0.80 mm in Luren with a CV of 20.47%. Mean SH and STH values were 889.25 N and 1.90 mm, respectively. In this study, a total of 18 genotypes had STH< 600 N or STH< 1.40 g. The lowest SLC was recorded for Weixuan NO1 16.54%, whereas the highest SLC of 38.02%, was found in Wantianxing with a CV of 13.08%. The mean SLC was recorded as 28.23 ± 4.68%. Compared with STH (80.43%), the 2H of KL, KW, KT, KL/KW, and KL/KT were 89.92, 88.08, 69.31, 86.37, and 76.32%, respectively. The SK trait is an important quality index in kernel-using apricots. The kernel taste of 123 accessions was sweet and that of the remaining 99 was bitter.The seed kernel is the main edible portion of kernel-using apricots and a higher KR ratio is an important agronomic attribute. The KR value ranged from 13.78% in Gaxing to 51.8%, in Luren with an average of 27.20% and CV of 21.83. A total of 11 accessions had KR > 35%. The KDW ranged from 0.17 g, in Tangwangchuan Dajiexing to 1.19 g in 80D05, with mean of 0.67 g and CV of 26.54. Thirteen genotypes had a KDW > 0.90 g. The distribution of KL ranged from 12.68 mm (in Caopixing) to 24.16 mm (in Tianhuangkouwai) with an average of 18.17 mm, whereas the distribution of KW ranged from 7.57 mm (Zaojinmi) to 18.58 mm (80D05) with an average of 13.28 mm. The CV of KL and KW were 12.32 and 11.82%, respectively. The KT ranged from 3.81 mm, in Liaoxing5 to 10.36 mm in Luren with an average of 6.34 mm and a CV of 13.52. The heritability of kernel traits was usually lower than that of stone shell traits. The P< 0.01) between the size of the stone  and kernel . However, the KT correlations showed non-significant values for SL, SW, and KL. Highly significant correlations were also found between stone shape and kernel traits such as KL/KW, KL/KT, SL/SW, and SL/ST. The negative correlation between SH and SL/ST was −0.280, whereas it was 0.365, 0.334, 0.556, and 0.559 between SH and SDW, SH and SW, SH and ST, and SH and SBF, respectively. The correlation between STH and SH (0.493) was extremely significant (P< 0.01), whereas, STH also had a similar correlation with SH and other traits but no correlation between STH and SL/ST. Highly significant positive correlation values were observed between KR and KDW (0.395) and KT (0.400); however, negative correlations were observed between KR and STH (−0.579), and SH (−0.513), and stone sizes . Of note, the correlation coefficient between KR and KL or KW was not significant, but that between KR and KT was significant. There was no reproducible correlation between SLC and other traits in different years, but a positive correlation was found between SLC and SH19 (0.231) in 2019.The Pearson’s correlation coefficient is an important statistical method for quantifying the association or coherence between two variables. The data for all traits were at an extremely significant between 2019 and 2020, with correlation coefficients ranging from 0.475 (AR) to 0.906 (SL/ST). The Pearson correlation coefficient matrix for the 18 quantitative traits is shown in 3.4The SNPs of 222 samples with phenotypic data were selected from 339 samples, and a phylogenetic matrix  and Chr4 25,762,245 bp (PVE 7%), respectively. According to the recently released genome sequence of apricot . The location of SK on Chr5 is similar to that reported in almond, indicating that they were a homologous gene controlling SK trait /glutamyl-tRNA(Gln) amidotransferase subunit A [EC:6.3.5.6 6.3.5.7], and 3 interleukin-1 receptor-associated kinase 4 [EC:2.7.11.1].There were 13 annotated genes on the 17.34–17.51 Mb segment of Chr3  and Siberian apricot (P. sibirica)  was derived from natural hybrid; however, the genetic variation in KU was lower than that of the other groups because of their reproduction from a few genotypes by asexual grafting. Therefore, it is necessary to cross the common or Siberian apricots to expand the genetic background of kernel-using apricot.Owing to an unreliable cultivation history, the origin and taxonomic status of kernel-using apricot have been unclear. In recent years, these uncertainties have been addressed using molecular markers. The results of simple-sequence repeat markers suggested that ibirica) . In the  pathway . Our res4.2Studying trait variation in different cultivars is an important pre-requisite for breeding. The present study revealed a high level of variability in stone shell and kernel traits among apricot cultivars compared with previous study . All traThe physical traits of apricot shells do not affect the organoleptic characteristics of the kernel; nevertheless, they are very important properties in all harvesting and industrial processes and must also be considered during cultivar evaluation . Shell tr2 = 0.36). In almond, the in-shell/kernel ratio was positively correlated with shell weight (−0.82) and shell hardness (−0.84)  . Our res (−0.84) , and an Apricot stone and kernel traits should be considered in kernel-using apricot breeding programs. The continuous variation exhibited by the quantitative traits that plant breeders deal with includes heritable and non-heritable components. The parameters of stone and kernel traits, including size, shape, and thickness, are heritable and must be considered in the design of crosses for breeding programs. Therefore, in the present study, the heritability of stone and kernel traits was determined based on a one-way ANOVA of apricots. The result showed that the heritability of the shell size and shape was higher than that of the kernel, and the heritability of SL was the highest (94.46%). High heritability estimates indicate that the selection of these traits is effective and less influenced by environmental factors . High heAlthough physical traits do not affect the organoleptic characteristics of apricot kernels, they are important in the processing industry. Stone shell traits include shell thinness and hardness and affect nut cracking. The heritability of STH, SH, and SBF was 80.43, 61.10, and 17.08%, respectively, which indicated that SH and SBF were highly affected by the environment during the process of shell opening. These results agree with the findings of the almond study .4.3Owing to differences in recombination rates, selective pressures, and effective population sizes, LD decay may vary across populations; for example, narrow-based germplasm groups have longer LD blocks than broad-based germplasm groups. In the present study, the LD decay in KU (~40 kb) was longer than that in the other studies, perhaps owing to a consistent cultivation environment that resulted in a narrow genetic background and vegetative propagation . The LD The inheritance of kernel taste in almonds is characterized as a monogenic trait  and mappKernel size is an important phenotypic trait that distinguishes kernel-using cultivars from fleshy cultivars. Discovering the major loci underlying the genes that determine stone and kernel size has been a high priority because of the importance of kernel size for growers’ profitability and requirement of breeders. Fruit size is a classic quantitative trait controlled by many loci. In almonds, a total of 14 putative QTLs controlling these traits were detected, including three for KW, three for KT, and four for KL, but the low phenotypic variance explained less than 30% of the variation found for all these traits . In the qtnSL/SW_1.2, qtnSL/ST_4.1, and qtnSL/SW_8.1) were located on Chr1, 4 and 8, respectively. These SL/SW QTL regions were annotated as candidate genes associated with cell division, DNA replication, and endocarp development.In addition, the QTLs for nut shape were located in Chr1, 5, and 7 bases on the linkage map with 56 simple-sequence repeat markers in almond . HoweverqtnSTH_2.2 on Chr2 in the region of 7.59–9.45 Mb, which is related to multiple tandem genes associated with lignin synthesis and regulation, such as phenylalanine ammonia-lyase (Pa02g07108.1 and Pa02g07109.1), tyramine N-feruloyltransferase (Pa02g07115.1 and Pa02g07116.1), three caffeic acid 3-O-methyltransferase genes , and seven 3-hydroxyisobutyryl-CoA hydrolase genes. This result is consistent with the differences in expression at the transcriptional and metabolic levels  and has been considered as a qualitative characteristic determined by a single gene (D/d) located in the middle of Chr2 . Dicentac levels . We stilqtnAR_2.1 in AR19 and qtnAR_2.2 in AR20) were located on the Chr2 at 14.43–17.34 Mb, which was annotated to calcium-binding protein CML (Pa02g08051.1), transcription factor MYC2 (Pa02g08065.1), cell division protease (Pa02g08066.1), and glucuronyl/N-acetylglucosaminyl transferase (Pa02g08067.1) genes. This difference may have been caused by the different evaluation methods or detection accuracies.In apricots, in a perfect flower, the pistil is stronger and longer than the stamens and can successfully bear fruit after pollination. However, flower development in apricots is a complex process that is strongly affected by genetic factors and environmental conditions, which may result in pistil abortion. Pistil-aborted flowers can fail to bear fruit. Based on the linkage map of specific-locus amplified fragment markers, several QTLs of pistil abortion were detected and mapped to the middle regions of LG5  and LG6 , with nine markers closely linked to it . In the There are two frequently QTL mapping methods for complex traits at present: one is genetic linkage analysis based on segregating populations derived from two parental lines, and the other is GWAS using natural variation population. For a specific locus, genetic linkage analysis can only detect polymorphic loci in the segregation population and two alleles segregated from each locus in a diploid species , while GIn the present study, we demonstrated the origin and genetic diversity of kernel-using apricots based on re-sequencing data. Seventeen physical traits of stone shells and kernels were studied for the first time in apricots by observing their quantitative nature, correlations, and heritability. Our results also identified QTLs and candidate genes associated with these physical parameters, kernel taste, and pistil abortion traits to provide a genetic framework for use in breeding program to improve the quality of kernel-using apricots.The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/QZ designed the research, conducted the data analyses, and wrote the manuscript; YPZ, NL, XM and CL collected the phenotyping data; WL made suggestions on methods and design; MX, SL, and YJZ participated in the management of test materials. All authors have read and agreed to the published version of the manuscript.


With the cost-effectiveness technology in whole-genome sequencing, more sophisticated statistical methods for testing genetic association with both rare and common variants are being investigated to identify the genetic variation between individuals. Several methods which group variants, also called gene-based approaches, are developed. For instance, advanced extensions of the sequence kernel association test, which is a widely used variant-set test, have been proposed for unrelated samples and extended for family data. Family data have been shown to be powerful when analyzing rare variants. However, most of such methods capture familial relatedness using a random effect component within the generalized linear mixed model framework. Therefore, there is a need to develop unified and flexible methods to study the association between a set of genetic variants and a trait, especially for a binary outcome. Copulas are multivariate distribution functions with uniform margins on the  In a genome-wide association studies (GWAS) framework, researchers generally focus on common causal variants with a minor allele frequency (MAF) 3 sequence kernel association test (SKAT), and their various combinations have been proposed.5 Sequence kernel machine-based association methods test for association between a set of rare/common variants and quantitative or binary phenotypes, and most of them are based on generalized linear mixed models.The identification of the association between single nucleotide variants (SNVs) with complex diseases is the main goal of genetic studies. It has the advantage of enriching data sets for familial rare disease variants because of the segregation of alleles within pedigrees, and it may protect data analysis against population stratification issues. Moreover, sequencing data are subject to read (or sequence) errors, and the Mendelian pedigree information available when related individuals are sequenced can help to identify technological artefacts in the data and improve the protection against sequencing errors.10 For such reasons, several whole-genome sequencing (WGS) projects have been conducted for family-based cohorts to identify rare variants’ effects. For example, the National Heart, Lung, and Blood Institute’s Trans-Omics for Precision Medicine (TOPMed) program and the National Human Genome Research Institute’s Genome Sequencing Project, have performed WGS from more than  The Type 2 Diabetes (T2D-GENES) Consortium has been conducted in WGS from 20 large Mexican-American families containing multiple cases of Type 2 diabetes, which aims to detect rare coding variants associated with that disease.12In this study, we focus on family-based designs. Sampling relatives in sequencing studies may sometimes be more advantageous than sampling unrelated subjects.14 GEE methods do not need to impose assumptions on the trait joint distribution within each family. Thus they are more robust to distribution misspecification and might be suitable for large-scale studies with complicated data design. However, the test from GEE can suffer from low power if the working covariance is not well calibrated, that is, if the family size is not uniform. The methods of the second category rely on conditional models, which capture the clustered structure by adding a random effect in the generalized linear mixed model (GLMM) framework.6 Most existing methods in this category are designed for continuous outcomes. To face this situation, a computationally efficient logistic linear mixed model association test (GMMAT) has been proposed by Chen et al. As GMMAT was originally developed for single-variant analysis, the authors, later extended the method to variant-set mixed model association tests (SMMAT) for binary traits.Several region-based sequence kernel association methods have been developed in the literature to analyse familial data. The methods can be broadly divided into two categories to handle the cluster dependencies induced by related subjects: The first category relies on marginal models linking the outcome to genetic predictors, and use the working-correlation trick to control for the within-family dependence structure through generalized estimating equations (GEE). The method is termed allele frequency comparison (AFC) tests. Note that these tests were proposed firstly for single-variant analysis by Bourgain et al. and Choi et al. AFC tests are based on the difference in single nucleotide polymorphism (SNP) allele frequencies in the cases (affected) and controls (unaffected). They use multivariate random-effects with a covariance matrix implying the kinship matrix to account for family relationships between individuals. Unlike the linear mixed models, these tests do not need the kinship matrix to be positive semidefinite, which makes them interesting as they can allow the use of an estimated genetic relationship matrix (GRM) from genotype data, which might not be positive semidefinite. Although the AFC tests are useful, they cannot adjust for covariates. Moreover, they may suffer from type 1 error rate inflation when the correlation between SNPs is not estimated accurately .Other testing approaches that are computationally feasible regarding the family-based designs for binary traits in a region-based framework have been proposed by Saad and Wijsman.2224 That is, the proposed model, termed novel rare variant association test (NRVAT), uses  generalized link functions to relate the binary phenotype to both the covariates and genetic variants and models the dependence between relatives through a Gaussian copula with correlation matrix corresponding to the familial kinship matrix to describe the polygenic relationship between subjects of a same family. The proposed joint modelling approach has several advantages over current GLMM-based methods, such as GMMAT and SMMAT. For instance, the dependence structure can be captured using a different copula model , we show thatUnder such a framework, one hasThe variability of the second term of the right-hand side of  is negliIn Appendix B, we show that the variance–covariance matrix of 2.2., chapter 4) without any loss of generality. The robustness of the derived test to the specification of the underlying copula is well-investigated in the simulation studies section. The Kernel matrix  However, several other choices such as the quadratic and Gaussian kernels can be incorporated in the derived test, without loss of generality. In the simulations, their impact is investigated on both the type I error and the power of the proposed test.In this work, the dependence between the outcomes equation  is known3.; gSKAT and AFC tests. As mentioned previously, SMMAT is a GLMM method which captures family relationships via a random effect; gSKAT is a GEE-based association test which controls for familial relationships via the working-correlation trick; AFC test is a score-type association test based on the difference of SNP allele frequencies in the cases (affected) versus controls (unaffected) and uses a multivariate random effect to account for family relationships between individuals. The methods comparison is based on empirical type I error rate and power.Simulations were carried out to validate and compare the performance of the proposed method, NRVAT, with three existing set-based rare-variant association methods dealing with binary phenotype in presence of families, namely SMMAT3.1.This section outlines the detailed steps pursued to generate simulated data for the methods’ evaluation.Genotypes: we used SIMULATE3 computer program, which allows simulation of genotypes of a set of linked SNPs in family members. In all simulations, we set the number of families to be Covariates: in all simulations, we considered two covariates associated with the binary response: a continuous covariate, Binary phenotype: we considered three settings to generate la model . In SettSetting 1 (data generation from our model): For each family la model . The dat1. generate 2. set the first column of 3. calculate the 4. generate 5. generate Setting 2 (data generation from a GLMM model): We generated the response variable based on the GLMM model for family Setting 3 (copula miss-specification): To investigate the robustness of the derived test to the miss-specification of the underlying/true copula, we conducted two scenarios in which the simulated data were generated from either the student In all three settings, we considered Under the null model, the parameter of interest is To evaluate the methods’ performance in terms of power, five SNPs were randomly chosen among the 20 studied SNPs as causal variants  selection bias, (b) missing at random, and (c) missing completely at random.Of note, the proposed method, like its competitors, might be sensitive to selection bias and it does not handle missing values; that is, subjects with missing values are removed from the data analysis. Although this is beyond the scope of this work, because real familial data are subject to selection bias and/or missing genotypes/phenotypes, we have conducted a sensitivity analysis to emphasize the impact of selection bias and missing data on our method. In Supplemental materials, we also show the conducted additional simulations under the null hypothesis for Setting 1 where the simulated data were generated under two scenarios: (1) To emphasize the impact of linkage disequilibrium between SNPs  and 376 non-affected relatives (NAR) for SZ, 83 AF versus 350 NAR for BP, and 153 AF against 280 NAR for CL. Finally, The data in this analysis consists of 640 subjects belonging to 17 extended families from Eastern Quebec, with some family members known to have schizophrenia (SZ) or bipolar disorder (BP).4.2.L traits  and 12, SMYD3 by our method with the quadratic kernel matrix (NRVAT-Quadratic) and the SMMAT model with the hybrid test (O) method  .5.SMYD3, and with the BP binary trait for two genes, C1ORF77 and CGI-96.In this work, we have developed NRVAT, a flexible set-based association test for rare and common variants and binary phenotypes, in family-based designs. NRVAT uses marginal generalized linear mixed models to relate the outcome to both the covariates and a set of SNPs and uses copulas to account for possible dependence between subjects of the same family/pedigree through the kinship matrix. An advantage of NRVAT joint modelling is that the regression parameters linking both covariates and genotypes to the phenotype are marginally meaningful. Moreover, trait polygenic heritability is ‘margin-free’, in the sense that it is characterized by the copula alone. The NRVAT framework includes five different kernel matrices to capture genotype–phenotype relationships, namely, the linear (L), quadratic (Q), identity-by-state (IBS), Gaussian (G), and polynomial (P) kernel matrices. Through simulations, we have shown that NRVAT has a valid type I error rate and allows for more power than existing models in family-based designs, even when the true copula was not well specified. We have also evaluated the performance of the NRVAT model using schizophrenia and bipolar disorder data and we have found an association signal with the SZ binary trait for one gene  marginal models instead of the latent logistic model in (One of the main advantages of NRVAT is that it models the dependence structure between subjects regardless of their marginal distributions, which allows the use of different margins to link the binary response to the covariates and the genotypes. For instance, one can use latent Probit or Robitmodel in . Our met33 Such matrices, by construction, are not block diagonals and thus their use within NRVAT might not be suitable. This means that NRVAT might not handle a population structure other than the well-defined familial structure. Also, people should be aware that the NRVAT model could give incorrect results when the number of families is small. Several extensions to our methodological proposal could also be investigated. Our approach could be extended to develop a functional association test for dichotomous traits in the presence of family data. To parallel what is done in Jiang et al., genotype–phenotype functional relationship can be modelled in the marginal distributions based on generalized functional linear mixed models while, again, a copula model can be used to characterize the trait dependence between subjects of the same family. So far, our approach only handles a single binary trait for each subject, but an extension to a mixture of binary-continuous trait cases for familial data could be possible. In fact, an additional source of dependency, stemming from within-subject correlated phenotypic values, could be accounted for by choosing an appropriate copula model.It is necessary to note that the NRVAT model has some limitations. In fact, the derivation of  In the case where there is a priori knowledge of the existence of more complex relationships, the Gaussian and IBS kernels may be the better choice.NRVAT integrates five kernel matrices within the association test to better capture the phenotype–genotype relationship. Although the optimal choice of the kernel matrix for real data analysis is a daunting question, here are some guidelines on how to choose a kernel matrix in NRVAT: when the underlying genotype–phenotype relationship is unknown, one may choose a linear kernel if there is a priori knowledge that relationships are linear and there are no interactions. In the presence of interactions, the quadratic kernel can be a good alternative as it implicitly assumes that the underlying relationship depends on the main and second-order effects.https://github.com/houssoudossa/NRVATGFLMM.The NRVAT method is implemented in a software R package PedGFLMM, which is freely available at https://github.com/houssoudossa/NRVAT-simulation-code.Codes are also publicly available in Github for reproducibility of the simulation scenarios of Setting 1 at Click here for additional data file.Supplemental material, sj-pdf-1-smm-10.1177_09622802231197977 for A novel rare variants association test for binary traits in family-based designs via copulas by Houssou R. G. Dossa, Alexandre Bureau, Michel Maziade, Lajmi Lakhal-Chaieb and Karim Oualkacha in Statistical Methods in Medical Research