Associations between exposures and outcomes reported in epidemiological studies are typically unadjusted for genetic confounding. We propose a two-stage approach for estimating the degree to which such observed associations can be explained by genetic confounding. First, we assess attenuation of exposure effects in regressions controlling for increasingly powerful polygenic scores. Second, we use structural equation models to estimate genetic confounding using heritability estimates derived from both SNP-based and twin-based studies. We examine associations between maternal education and three developmental outcomes – child educational achievement, Body Mass Index, and Attention Deficit Hyperactivity Disorder. Polygenic scores explain between 14.3% and 23.0% of the original associations, while analyses under SNP- and twin-based heritability scenarios indicate that observed associations could be almost entirely explained by genetic confounding. Thus, caution is needed when interpreting associations from non-genetically informed epidemiology studies. Our approach, akin to a genetically informed sensitivity analysis can be applied widely. An objective shared across the life, behavioural, and social sciences is to identify factors that increase risk for a particular disease or trait. However, identifying true risk factors is challenging. Often, a risk factor is statistically associated with a disease even if it is not really relevant, meaning that even successfully improving the risk factor will not impact the disease. One reason for the existence of such misleading associations stems from genetic confounding. This is when genetic factors influence directly both the risk factor and the disease, which generates a statistical association even in the absence of a true effect of the risk factor. Here, we propose a method to estimate genetic confounding and quantify its effect on observed associations. We show that a large part of the associations between maternal education and three child outcomes—educational achievement, body mass index and Attention-Deficit Hyperactivity Disorder—is explained by genetic confounding. Our findings can be applied to better understand the role of genetics in explaining associations of key risk factors with diseases and traits. Gsens, to assess to what extent genetic confounding can account for observed associations.Associations between exposures and outcomes are commonly reported in epidemiological research, but often without estimating or accounting for the contribution from genetics. However, most exposures and outcomes are substantially heritable, and genetics can confound these associations. Here, we propose a new genetic sensitivity analysis, which we call sensitivity analysis, which consists of estimating how strong an unknown confounder needs to be in order to explain away an observed association, providing insights into the robustness of that association  [Identifying exposures that can be targeted in effective interventions is a fundamental objective shared across the life, behavioural and social sciences. To this end, identifying causal exposures is essential as interventions that target non-causal exposures will likely fail. To establish causation, it is necessary to account for confounding, which happens when a third variable causally influences both the exposure and the outcome, thereby generating a non-causal association between them. Genetic confounding is a special case when genetic factors play the role of the third variable. The concept of genetic confounding was introduced during the controversy regarding the effect of cigarette smoking on lung cancer. In a letter entitled ’alleged dangers of cigarette-smoking’, Ronald Fisher qualified ‘the mild and soothing weed’ as ‘possibly an entirely imaginary cause’ for lung cancer . He argu or not) . Since t or not)  proposed or not) ). Howeve or not) . Gsens aTo illustrate our approach, we focus on maternal educational attainment  as the exposure of interest. Greater maternal education is associated with child developmental outcomes in several key domains: social development , physical health , and mental health (e.g. lower levels of Attention-Deficit Hyperactivity Disorder (ADHD) symptoms) –10. HoweGsens to estimate the role of genetic confounding in explaining the associations between maternal educational and three developmental outcomes in the child: educational achievement operationalized by the General Certificate of Secondary Education (GCSE), BMI, and ADHD. Importantly, Gsens has a wide scope of applications as it only requires genome-wide data on large samples and a focus on outcomes for which polygenic scores are available. Its applicability will further expand with the steady increase in the number and the accuracy of available polygenic scores [Here, we illustrate the use of c scores .observed scenarios. However, even the best-fitting polygenic scores only captured a fraction of the heritability of their corresponding phenotypes, thus underestimating the magnitude of genetic confounding. In the second stage, the sensitivity analysis therefore aimed to answer the following question: to what extent is the exposure X associated with the outcome Y after controlling for all genetic confounding? In other words, if βXY is the coefficient of regression of Y on X, to what extent would it attenuate if we were to control for ‘perfect’ polygenic scores capturing all genetic influences on X and Y rather than the small fraction accounted for by available polygenic scores? To this end, we estimated βXY under plausible scenarios combining information on current polygenic scores and heritability estimates. The estimation of βXY is based on the matrix of observed correlations between polygenic scores, exposure and outcomes. We then fit a Structural Equation Model to this matrix of correlations that aims to reflect the true extent of genetic confounding , with sample sizes between 3,663 and 4,693 individuals with data for maternal education and child educational achievement, BMI, and ADHD. Polygenic scores were estimated in the child using PRSice software  at diffeding see . ApproacAs shown in Table A in The sensitivity analysis is represented in k as the ratio of the standardized path from the polygenic score to the exposure divided by the standardized path from the polygenic score to the outcome . Using the best fitting polygenic scores for years of education and BMI, the genetic confounding effect was estimated at -0.021 , corresponding to 23.0% of the total effect. After taking this genetic confounding effect into account, the relationship between maternal education and child BMI was -0.069 . The first scenario used SNP-based heritability estimates for years of education and BMI . Using the best fitting polygenic scores for years of education and ADHD, the genetic confounding effect was estimated to be -0.018 , corresponding to 14.3% of the total effect. After taking genetic confounding as captured by the polygenic scores into account, the relationship between maternal education and child ADHD attenuated to -0.106 . Tables Gsens uses estimates of heritability that provide useful benchmarks to estimate the extent of genetic confounding. It provides estimates of the strength of genetic confounding as well as of the residual association, which comprises the causal effect plus the association through non-genetic confounders. However, these estimates are biased by the association between genetic and non-genetic confounders induced by conditioning on the exposure X, an instance of collider bias . As shown in Gsens estimators recover the causal effect.We conducted four sets of simulations based on the underlying causal model presented in Methods. In the first, we simulated polygenic scores capturing all genetic influences to examine the effect of collider bias independent of measurement error. We compared estimates from the three In the second set, we simulated polygenic scores that captured only a fraction of heritability. We simulated scenarios under which the polygenic score for X captures more of the variance of Y than the polygenic score for Y itself. This may happen with differentially powered GWAS. In our empirical example, the polygenic score for education captures almost as much variance in ADHD as the polygenic score for ADHD itself. Conceivably under such scenarios, using GsensX or GsensXY may better account for genetic confounding than GsensY. In our example, both GsensX and GsensXY using the polygenic score for education found a larger genetic confounding effect than when using the polygenic score for ADHD in GsensY alone. However, our simulations showed that, even under such circumstances, the effect of collider bias under twin heritability scenarios remains larger for GsensX and GsensXY than for GsensY. Numerical results for all simulations are provided in The third and fourth sets were based on simulating individual SNP effects rather than polygenic scores, while replicating parameters in the first and second set respectively . In both the third and fourth sets, the true residual association was also closely estimated by GsensY but not as closely by GsensX and GsensXY due to collider bias. In the third set, results closely match those of the first set, showing that generating true polygenic scores based on a mixture of SNP with different patterns did not substantially affect results compared to directly generating polygenic scores. In the fourth set, a small but consistent downward bias in GsensY estimates was observed compared to the second set. Across all simulation scenarios, the median discrepancy between the true residual association and the GsensY estimate was 0.001 in the second set of simulations but -0.014 in the SNP-based fourth set . This downward bias may be due to overfitting (arising from selecting the best-fitting polygenic score), which overestimates genetic confounding and thus underestimates the true residual association. However, this downward bias remained small. In the SNP-based simulation, the SE accurately estimates the empirical SD and by extension we can infer that confidence intervals have appropriate coverage. Type-1 error was close to 0.05 for GsensY, sometimes a bit conservative when polygenic scores captured only 1% of the variance. Numerical results for all simulations are provided in In simulations, constraints imposed on the model to avoid impossible or implausible results often removed part or all bias. However, we caution against systematically applying constraints as they do not necessarily remove bias and may artificially reduce standard errors. Results of constrained models, as well as standard errors for all models, are reported in These results suggest that GsensY should be preferred in all situations and that Gsens is best adapted when the outcome of interest is strongly predicted by its polygenic score. When the polygenic score for the exposure is more predictive, GsensXY can be used, particularly to estimate genetic confounding with observed polygenic scores, but should be interpreted with caution under heritability scenarios.In addition, although GsensY closely recovered the expected estimates, the range of estimates across simulations was wider with polygenic scores capturing 1% of the variance, in particular for the smaller sample size of 3000. This means that estimates in a particular sample can be more unstable. In practice, when applying the method, users should be able to detect some of this instability by examining standard errors.Gsens–aiming to gauge to what extent genetic confounding can account for observed epidemiological associations. The genetic sensitivity analysis we propose adds a new tool to probe the robustness of associations between exposures and outcomes. This approach requires a genotyped cohort with relevant phenotypic measurements, which is increasingly the rule for epidemiological cohorts rather than the exception. It is therefore possible to envisage Gsens analysis becoming routine. Below, we first discuss our empirical findings regarding the associations between maternal education and child educational attainment, BMI, and ADHD. We then discuss the interpretation and applicability of Gsens.In the present study, we combined polygenic scores with heritability estimates in a genetic sensitivity analysis–Our findings show that the association between maternal education and child developmental outcomes were still present under a SNP-heritability scenario but were null under a twin-heritability scenario. Overall, the observed association between maternal education and these three developmental outcomes may largely be due to genetic confounding.k parameter, consistent with previous findings. In addition, scenarios based on lower heritability estimates also yielded small but significant effects, raising the possibility that null findings resulted from overestimated twin heritability estimates, a possibility further discussed below. Taken together, this set of findings represents a clear call for caution when interpreting non-genetically informed epidemiological studies on the role of maternal education.Relevant to our findings is previous research using causal inference designs to investigate the effect of parental educational attainment on child educational attainment. In particular, a systematic review on the topic has summarized evidence from twin and adoption designs, as well as non-genetic instrumental variable estimations . The sysGsens findings must be highlighted. First, the reliability of findings depends on the accuracy of heritability estimates. Overestimating heritability would lead to overestimating genetic confounding and thus underestimating the residual association between exposure and outcome. For example, a recent study of 193,518 twins across 16 countries showed that educational attainment is 43% heritable [Gsens in the following ways: (i) by increasing the predictive power of polygenic scores and therefore the accuracy of observed scenarios; (ii) by improving the accuracy of parameter estimates for the sensitivity analysis.Two key points regarding the interpretation of eritable . As can Gsens aims to estimate genetic confounding and the residual association net of genetic confounding. This is distinct from genetic overlap, as estimated by bivariate twin or mixed-model methods, which decomposes the phenotypic association into genetic and environmental components . This is because a genetic correlation can arise from genetic effects on the outcome mediated via the exposure and the causal path (i.e. mediated pleiotropy) or by direct genetic effects on the outcome (i.e. unmediated pleiotropy). In twin-based methods, the corresponding residual association is an environmental association in that it excludes all genetic components from the observed association, including those mediated by the causal effect. In contrast, Gsens aims to remove only the genetic confounding or unmediated pleiotropy. In the absence of nongenetic confounding, the Gsens residual association would correspond to the causal effect, while the environmental association would be lower than the causal effect. Further clarifications regarding these conceptual differences can be found in Annex A in Second, A number of key assumptions of Gsens should be noted. Gsens assumes that the polygenic score reflects the true genetic value plus classical measurement error. This assumption would hold under an additive model but not necessarily under interactions (epistasis or gene-environment interactions). Note that SNP-heritability estimates and narrow-sense twin-heritability estimates used in Gsens also assume additivity. SNP-heritability estimates the variance explained by common SNPs and is thus the ceiling for polygenic scores estimated from the same common SNPs. Extrapolation to the twin-heritability estimates therefore assumes that additive genetic effects captured in twin heritability have the same confounding structure . In addition to true genetic effects, polygenic scores may capture the effects of residual population stratification, assortative mating, and dynastic effects. Although not reflecting true genetic effects, these effects do represent additional sources of confounding of the association between X and Y. Gsens thus adjusts for the confounding associated with empirical polygenic scores, which include broader genetically related confounding rather than genetic confounding arising from direct genetic effects alone  and the fourth set  did not result in a substantial change in the estimation of the residual association.Gsens does not directly address the question of reverse causation. As in typical epidemiological studies, reverse causation can be, entirely or partly, ruled out based on the temporal sequence between exposure and outcome .In addition to the limitations addressed above, it is worth noting that large-scale GWAS are still largely restricted to people of European descent, thereby limiting the generalizability of polygenic score analyses and derived applications such as Gsens. We note that polygenic scores derived from European samples can still be associated  with non-European populations, and so Gsens can, in principle, still be applied as long as realistic heritability estimates are available for those populations. Current efforts towards more inclusive GWAS should also help in progressively overcoming this limitation. Furthermore, providing the sampling populations are exchangeable, it is not necessary for the genetic and observational associations, nor the heritabilities, to be estimated in the same datasets.Gsens may be extended in future to explicitly consider measured confounders, which may further reduce residual confounding as well as the effect of collider bias due to nongenetic confounding.We note that a conceptually similar approach to ours is taken in the latent causal variable (LCV) model , which aWe propose a genetic sensitivity analysis aiming to adjust for genetic confounding in epidemiological associations. Gsens implements structural equation models to adjust for genetic confounding based on polygenic scores and heritability estimates. Gsens can be applied as long as a suitable GWAS for the outcome is available, even when a GWAS for the exposure is not available or does not provide adequate instruments for MR analyses. For example, Gsens can be applied to test whether the association between urbanicity and schizophrenia is susceptible to genetic confounding based on the polygenic score and heritability estimates for schizophrenia. We therefore propose that Gsens can be conceived as a complementary method, suited for complex environmental exposures that are of interest for health, behavioural and social sciences.Ethical approval for TEDS has been provided by the King’s College London Ethics Committee (reference: PNM/09/10–104). Written parental consent was obtained before data collection.Participants were drawn from the Twins Early Development Study (TEDS), a longitudinal study of twin pairs born in England and Wales, between 1994 and 1996. Detail regarding TEDS, the recruitment process, and representativeness can be found elsewhere . A totalMaternal educational attainment was reported by mothers at first contact, when children were on average 18 months old, with 8 levels: 1 = no qualifications; 2 = CSE grade 2–5 or O-level/GCSE grade D-G; 3 = CSE grade 1 or O-level/GCSE grade A-C; 4 = A-level or S-level; 5 = HNC; 6 = HND; 7 = undergraduate degree; 8 = postgraduate qualification.Child educational achievement was operationalized as performance on the standardized UK-wide examination, the General Certificate of Secondary Education (GCSE), at 16 years. We computed a mean of the three compulsory core subjects, mathematics, English, and science (further details in [tails in ). A totaBody Mass Index (BMI) was derived from parent reported (ages 11 and 14 years) and self-reported weight and height (age 16 years). Extreme BMI values (<1% and >99% quantiles) were winsorized and resulting values were averaged across ages 11 to 16 years. A total of 3,663 genotyped individuals had data on maternal education and the resulting BMI score.The DSM-IV ADHD symptom subscale, taken from the Conners’ Parent Rating Scales–Revised  was comp−5. Non-autosomal markers and indels were removed.Genotyping, quality control procedures and principal component analysis are detailed in Section A in 2 > 0.10). PRSice allowed us to select the best-fitting polygenic score for each trait, e.g. maximizing the amount of variance explained by the polygenic score for BMI in TEDS participants’ BMI. To this end, we computed a series of polygenic scores including an increasing number of SNPs corresponding to increasing p-value thresholds  as illustrated in Figs A, B and C in We computed genome-wide polygenic scores based on summary statistics from the following genome-wide association studies (GWAS): (i) years of education ; (ii) ADβXGβGY. We also calculated the proportion of the observed effect of X on Y that is accounted for by genetic confounding, i.e. We assume a linear structural equation model framework . Akin toWhen the polygenic score for the predictor (G1) is different from the polygenic score for the outcome (G2), the confounding effect is estimated in a similar fashion as the sum of all the indirect effects from X to Y through G1 and/or G2 .Genetic confounding effects were calculated for all three developmental outcomes:Maternal education to child educational achievement using the best-fitting polygenic score for years of education as in ;Maternal education to child BMI using best-fitting polygenic scores for years of education (G1) and BMI (G2) as in ;Maternal education to child ADHD symptoms using best-fitting polygenic scores for years of education (G1) and ADHD symptoms (G2) as in .In these analyses, the effect size of X on Y decreases as a function of the strength of genetic confounding. However, this approach does not account for all genetic confounding. This is because polygenic scores based on current GWAS capture a relatively small amount of all genetic influences. For example, the current polygenic score for BMI explains around 6% of the variance in BMI in TEDS, far less than SNP-based and twin-based estimates of BMI heritability. The sensitivity analysis we propose aims to address this issue.βXY decrease if we were to control for ‘perfect’ polygenic scores capturing all genetic influences on X and Y rather than a small fraction. This is done by estimating βXY under plausible scenarios that combine information on existing polygenic scores and heritability estimates.The sensitivity analysis aims to answer the following question: is X associated with Y after we control for all genetic confounding? In other words, to what extent would For maternal education and child educational achievement, we used a polygenic score for the child, derived from the GWAS of years of education, which predicts a substantial amount of variance both in child GCSE but also in maternal education. The effect of maternal education on child educational attainment can be first adjusted for the observed best-fitting polygenic score. However, this polygenic score does not capture all the heritability of the outcome and therefore incompletely adjusts for genetic confounding. The sensitivity analysis consists in re-examining the effect of maternal education under scenarios where the polygenic score could capture additional variance in child GCSE up to SNP-based and twin-based estimates of heritability.βXY is the adjusted effect and r denotes observed standardized associations. Details are presented in Section B in βXY corresponds to the standardized association between X and Y minus genetic confounding, i.e. the residual association between X and Y net of genetic confounding. In other words, Gsens removes only genetic confounding and not all genetic effects shared between X and Y, which comprise both genetic confounding and genetic effects on Y mediated by X via a causal pathway. When subtracting all shared genetic effects, including those arising from the causal effect, the residual association becomes the ’environmental association’. This is similar to what happens in bivariate decomposition of the phenotypic correlation in twin and mixed model designs and is distinct from Gsens estimates. This distinction is further clarified in Annex A in βXY can be estimated using standardized associations between the observed polygenic score, X and Y, as in expression (1). In the sensitivity analysis, a structural equation model is fitted with a latent variable G* representing heritability, as presented in When using the best-fitting polygenic score, βXY = 0. We can then express the observed standardized association as a function of the heritabilities of X and Y under complete genetic confounding as:In Eq , the assrXY is equal to genetic effects through G. In the special case where X and Y are the same trait in parent and child and assuming constant heritability across generations, we thus obtain:When the adjusted effect of X on Y is null, then This means that the adjusted effect of X on Y is likely to be null whenever the observed association does not exceed half of the trait heritability. As such, a given association between parental and child traits can be assessed against βXY becomes more complex than for the single case polygenic score. We thus generalize the structural equation model to two latent variables and polygenic scores as in When predictor and outcome are different variables–for example maternal education and child BMI–two polygenic scores can be used in the sensitivity analysis, as shown in Latent models represented in Figs Gsens under its own assumptions, and study the impact of collider bias, we conducted simulations based on the underlying causal model presented in In order to verify the performance of G1 and G2 were fixed to unity (thereby simulating polygenic scores capturing the whole heritability) in order to examine collider bias independently of the latent structure of the model. We chose parameters based on reasonable values, with the following combinations: X and Y were 30% or 70% heritable, and influenced by respective non-genetic influences of 55% or 15% (leaving 15% of unexplained variance); genetic and non-genetic correlations between direct effects of 0 or 0.40; a causal effect of 0 or 0.2.In the first set of simulations, loadings from G1 and G2 would capture 1% or 10% of the variance of X and Y, respectively. This resulted in either (i) polygenic scores with equal explanatory power or (ii) asymmetric situations where, e.g. one polygenic score explained 10% of the variance in X and the other polygenic score explained only 1% of the variance in Y. In this case, the resulting association between the first polygenic score and Y may actually be greater than the association between the second and Y, which can result in non-null cross-paths. Such a situation can stem from the differential accuracy of GWAS for X and Y.In the second set of simulations, we fixed the causal effect to 0.20 and heritabilities to 70% but values of the loadings were set so that the resulting polygenic scores 2 was calculated using AVENGEME[training = 2,070 for 1% and 19,306 for 10%. For each scenario, 1,000 replicates were simulated. Genotype data and polygenic scores were generated using PLINK 1.9 [In the third and fourth sets of simulations, we simulated 100,000 independent SNPs with Minor Allele Frequency drawn from a uniform distribution from 1% to 50%. Of all SNPs, 5% were simulated to have effects on exposure and outcome, 5% to have effects on exposure only, and 5% on outcome only. The effects of standardised genotypes were drawn from normal distributions. Estimated SNP effects from the training sample were obtained by adding Gaussian error to the true effects with variance proportional to 1/(size of training sample). Genotypes in the target sample were drawn from a binomial distribution under Hardy Weinberg Equilibrium. In the third set, a polygenic score was computed to reflect the true genetic effects. In the fourth set, the best-fitting polygenic score was identified from the following p-value thresholds: 1e-3, 1e-2, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 1, which include thresholds close to those found in our empirical example. To facilitate comparisons, simulation scenarios were set to match the first and second sets (i.e. third set matching first set and fourth set matching second set), with the following parameters: causal effect of 0 or 0.20, genetic and nongenetic correlations between direct effects of 0 and 0.4, heritability of X and Y of either 0.30 or 0.70, and target sample size of 3,000 or 10,000. In addition, in the fourth set, polygenic scores were set to explain 1% or 10% of the variance of their respective traits. The training sample size to obtain the desired R AVENGEME and was LINK 1.9 .S1 TextSection A. Genotyping protocol and quality control. Fig A. Predictive accuracy of the polygenic score for years of education predicting child GCSE in TEDS for different P-value thresholds. Fig B. Predictive accuracy of the polygenic score for BMI predicting child BMI in TEDS for different P-value thresholds. Fig C. Predictive accuracy of the polygenic score for binary ADHD predicting ADHD symptoms in TEDS for different P-value thresholds. Table A. Correlations between study variables. Section B. Estimating the effect of X on Y in the single polygenic score case, based on observed associations. Section C. Complete genetic confounding in the single polygenic score case. Section D. Estimating the effect of X on Y in the two polygenic scores case. Annex A. Genetic overlap versus genetic confounding. Annex B. Residual confounding by ancestry, assortative mating and dynastic effects.(DOCX)Click here for additional data file.S1 Data(XLSX)Click here for additional data file.


It is long known that inbreeding increases the detrimental effects of recessive sequence variants in “Runs of Homozygosity” (ROHs). However, although the phenotypic association of ROH has been investigated for a variety of traits, the statistical power of the results often remains limited as a sufficiently high number of cases are available for only a restricted number of traits. In the present study, we aim to analyze the association of runs of homozygosity with the trait “in-group ethnic favoritism”. This analysis assumes that if ethnic identity is important for an individual, that individual may tend to marry more frequently within their own group and therefore ROH are expected to increase. We hypothesize that an attitude preferring one’s own ethnic group may be associated with a stronger tendency of inbreeding and, as a result, with more and longer ROHs. Accordingly, we investigated the association between the attitude to someone’s own ethnicity and ROH, using the Wisconsin Longitudinal data  as discovery data set and the Brisbane Twin data as replication data set (N ~ 8000). We find that both the number as well as the total length of homozygous segments are significantly positively associated with “in-group ethnic favoritism”, independent of the method used for ROH calculation.The online version contains supplementary material available at 10.1007/s10519-021-10053-z. The major mechanism leading to large homozygous segments in the genome is inbreeding, i.e. marriage among kin. Although the frequency of consanguineous marriages has become low in Western industrialized societies, in other parts of the world, the proportion of marriages among second or lower order cousins is still rather high  as discovery data set and the Brisbane Twin Study as replication data set.https://www.ssc.wisc.edu/wlsresearch/documentation/GWAS/Herd_QC_report.pdf. Data use agreement from the 30. May 2019; project: “Genome Wide Association Studies and Runs of Homozygosity”.The Wisconsin Longitudinal Study (WLS) is a long-term study of a random sample of men and women who graduated from Wisconsin high schools in 1957 and their siblings. The WLS panel started out with 10,317 members from the class of 1957. A second sample of 8734 randomly selected siblings of the original graduate panel were recruited for the study. Of these combined samples, 9027 individuals contributed saliva for genetic analysis . In total 713,014 SNPs had been genotyped.  and was conducted by the University of Wisconsin). Detailed information on individual recruitment, genotyping, and quality control can be found at (i)Runs of homozygosity according to Howrigan et al. We calculated the runs of homozygosity (ROH) of the WLS genotypic sample using two different methods of ROH estimation:http://zzz.bwh.harvard.edu/plink/). .(ii)Runs of homozygosity according to Clark et al. We calculated ROH on the basis of the recommendations of Howrigan et al.  by firstRuns of homozygosity (ROH) were identified on the basis of SNPs with minor allele frequencies higher than 5%. In line with Clark et al. , we usedTo estimate effects due to the size of the ROH, we additionally estimated ROH according to Clark et al.  with a “Both methods of ROH-calculation produced two measures of ROH each: (i) the total number of homozygotes segments (NSEG), and (ii) the sum of length of homozygotes segments (KB). In the supplement, we show the correlation of NSEG calculated according to Howrigan et al.  vs. ClarHow important is your ethnic group/nationality identity” surveyed in the years 2005–2006 and encoded on a 7 item scale from not important (1) to very important (7) .We analyzed the association of (i) NSEG, and (ii) KB, respectively, and the phenotypic variable “importance of ethnicity” in terms of the answer to the question “Additionally, we included the following variables in our analysis: year of birth, sex , and highest education surveyed in the years 2005–2006 and 2011 .We regressed the ordinal phenotype “importance of ethnicity” using the following four separate mixed ordinal models : “importance of ethnicity” regressing on sex, birth year, highest education and the first 10 principal components of the population structure . Furthermore, to confine effects of ancestry, we only included individuals with > 99% European ancestry determined using ADMIXTURE  only including non-related as well as individuals of only European ancestry in our analyses (results presented in the supplement). Kinship and European ancestry were determined on the basis of genome-wide SNP data: Individuals closer related than third order cousins have been removed by KING  before undergoing Bonferroni correction (α = 0.0125).The association between NSEG and KB, respectively, and in-group ethnic favoritism was assessed by estimating how much of the variance of the phenotype l et al. . This wal et al. . NagelkeWe used the data from Australian twins, one sample of twins born before 1964 and surveyed in 1980, aged between 19 and 87 years Apartheid ii)Multiculturalism ,iii)White Superiority iv)Patriotism v)Asian immigration .As no explicit question on the importance of ethnic identity was included in the BTS, we used the 5 most related questions as phenotypes, each encoded as 0 = No and 1 = Yes for advocating the phenotype:The numbers of cases are drawn from the full data set, actual numbers for each model may vary according to the joint availability of the confounding variables. For further analysis, we recoded the variables “Multiculturalism” and “Asian immigration”, so that for all variables the more right-wing attitude was encoded as 1 and the more left-wing attitude as 0.Genome-wide genotyping was previously performed using a range of genotyping arrays with standard imputation and quality control procedures as previously described . We performed the linear mixed models using the R libraries MASS and MuMIn . As the results from the Brisbane data are a replication of the findings from Wisconsin Longitudinal, we refrained from correction for multiple testing.We calculated separate models for each of the five phenotypes regressing either on NSEG or KB, while controlling for age at the time of the survey, sex , years of education, year of survey, the 10 PCs, and kinship with family ID and Genome-wide regression “and in Mitchell et al. The association between the NSEG and KB scores and the 5 phenotypes characterizing in-group ethnic favoritism (listed above) was assessed by estimating how much of the variance in each phenotype was accounted by the either NSEG or KB scores  NSEG, and ii) KB, respectively, as covariates to estimate the additive genetic heritability using the R umx library. We carried out all analyses in R.3.6.3, PLINK 1.9  in separate models revealed that although NSEG and KB . Approval of Apartheid is marginally significantly positively associated with NSEG P = 0.054) but negatively associated with KB (P = 0.014). The other 3 phenotypes show no significant association with any measure of ROH  or the length of homozygous segments (KB) are used as the indicator for homozygosity. However, estimates calculated on the basis of Clark et al.  are loweBecause Clark et al.  use a fiIn the logistic regression model conducted in GCTA, both NSEG and KB  are significantly or marginally significantly positively associated with one measure of ROH (NSEG or KB) irrespective of whether family ID and zygosity & kin or only family ID are used as random factors. On the contrary, higher ROH is associated with a more left-wing attitude towards multiculturalism and Asian immigration. The results for the attitude towards white superiority are inconsistent as NSEG is significantly negatively but KB is not significantly associated with favouring white superiority.A possible explanation for the partially differing results obtained from the WLS and the Brisbane Twin Study may be found in differences in survey questions and scales. There are seven scales in the WLS data set that allow for more moderate responses compared to a binary scale in the Brisbane data set that covers only extreme positions. These fewer increments correspond with lower “signal” (estimates and significance), which may lead to the observed differences. Furthermore, our sample size may be too small to detect any robust effects . These differences may be caused by the estimation of the genetic relatedness (GRM) matrix by GCTA, which additionally controls for degrees of genetic relatedness and thus more accurately accounts for relatedness than the regressions in R. By including the family ID as a random effect, all family members  are treated equally, whereas the GRM used in GCTA accounts for these specific relationships so that they are modelled differently depending on how much genetic information they share.In contrary to the WLS data, in the Brisbane data, the results from the regression analysis differ in sign and/or significance in part from the results obtained by GCTA (namely for The association between in-group ethnic favoritism and ROH may be caused to some extent by an “underlying association” between ROH and Socio-economic status (SES), as a negative association between ROH, education and general cognitive ability has been already shown , but we found interactions between education, ROH and the measures of in-group ethnic favoritism. Albeit the general results for white superiority are inconsistent, a positive attitude towards white superiority regressed significantly positive on the interaction of education and NSEG—indicating that with increasing education, higher ROH is associated with a more “right wing attitude” towards white superiority (supplement Table S5). However, multiculturalism is different as increasing education and ROH are associated with a more liberal attitude towards multiculturalism (supplement Table S5). The results remain consistent whether Family ID & kin or only family ID is included as random factor. Thus, overall, we cannot exclude SES effects and interactions between SES, ROH and in-group ethnic favoritism, but on the basis of our data, we are not able to make any final conclusions.We did search for some additional “phenotypic evidence” that a more in-group ethnic favoritism attitude may foster inbreeding and thus lead to an increase in homozygosity. In support of our assumptions, on the basis of data from 18 countries from the World Value Survey (supplement Table S6), we found that a more restrictive attitude towards ethnic diversity and the percentage of first and second order cousin marriage is positively correlated  indicating that indeed there might be an association between ethnocentrism and inbreeding.We know from twin studies that in-group favoritism is partly genetic, albeit the contribution of genetics to in-group ethnic favoritism and in-group favoritism in general is less clear compared to other traits such as for instance political attitude Below is the link to the electronic supplementary material.


The testcross performance of each maize inbred line was tester dependent. When lines were crossed to a tester within the heterotic group, many yield components related to ear size and kernels per ear were significantly reduced, but kernel size was rarely impacted. Thus, the effect of heterosis was more noticeable on traits that increased kernels per ear rather than kernel size. Hybrids of DTMA inbred lines crossed to PHP02 exhibited phenotypes similar to testcrosses of Stiff Stalk and Non-Stiff Stalk heterotic groups for yield due to significant increases in kernel size to compensate for a reduction in kernels per ear. Kernels per ear and ear length were correlated  with and more heritable than yield, suggesting these traits could be useful for inbred selection.As the plant variety protection (PVP) of commercial inbred lines expire, public breeding programs gain a wealth of genetic materials that have undergone many years of intense selection; however, the value of these inbred lines is only fully realized when they have been well characterized and are used in hybrid combinations. Additionally, while yield is the primary trait by which hybrids are evaluated, new phenotyping technologies, such as ear photometry (EP), may provide an assessment of yield components that can be scaled to breeding programs. The objective of this experiment was to use EP to describe the testcross performance of inbred lines from temperate and tropical origins. We evaluated the performance of 298 public and ex-PVP inbred lines and 274 Drought Tolerant Maize for Africa (DTMA) inbred lines when crossed to Iodent (PHP02) and/or Stiff Stalk (2FACC) testers for 25 yield-related traits. Kernel weight, kernels per ear, and grain yield predicted by EP were correlated with their reference traits with  In the early 20th century, maize was commonly grown as an open-pollinated variety and yield improvement was stagnant. Since the implementation of double-cross and subsequently single-cross hybrids, maize yields have increased at a rate of 48 and 119 kg ha–1, respectively (USDA NASS). Maize production in the United States totaled 363.2 billion kg on 33.5 million hectares with an average yield of 10,860 kg haIn 1970, the Plant Variety Protection Act (PVP) allowed commercial breeding programs to register varieties and inbred lines as intellectual property restricting the use, sale, and importation of this material for 20 years . Inbred 1 cross of inbred lines from divergent heterotic groups to leverage heterosis  panel from CIMMYT were assessed for 25 yield-related traits when crossed to SS and/or IO testers. Representative ears were hand harvested from each plot for EP studies. The objectives of this experiment were to (1) validate the use of ear photometry on a diverse set of hybrids representing temperate and tropical maize, (2) characterize the relationships among and heritability of ear photometry traits, and (3) describe the heterotic patterns of temperate and tropical inbred lines in testcross hybrids using ear photometry.–1 of mono-ammonium phosphate (11-52-0) and 224 kg ha–1 of potash (0-0-60), and in the spring of 2017, 180 kg ha–1 of pre-plant ammonium nitrate was applied. Weed control  was applied pre-plant at a rate of 3.7 kg ha–1. In 2018, nitrogen was applied in mid-March at a rate of 224 kg ha–1 of ammonium nitrate. Weed control , was applied pre-plant at a rate of 4.7 kg ha–1. Additionally, , was applied after planting at a rate of 210 g ha–1. Prior to silk emergence in 2018, insecticide  was applied due to a Japanese Beetle infestation.This experiment was grown in the summer of 2017 and 2018 at the Purdue University Agronomy Center for Research and Education . The soil type at this location is a Chalmers silty clay loam  (Purdue Agriculture Data Engine). Experimental plots followed a maize-soybean crop rotation with planting dates of June 1, 2017 and April 30, 2018. In both years, the fields were cultivated prior to planting. Fertilizer was applied in the fall of 2016 as 168 kg ha–1 in each year. The hybrids were blocked by temperate or tropical origin and tester to promote pollination among hybrid types and evaluated in a randomized complete block design with two replications.Experimental plots were two rows 4.5 m long by 1.5 m wide with a spacing of 76 cm in 2017 and 3 m long by 1.5 m wide with a spacing of 76 cm in 2018 planted to a population of 74,000 seeds haper se performance . The choice of a commercial IO tester for the tropical germplasm differentiates this study from previous work which tested formance  and combformance . AdditioPrior to machine harvest, 10 representative ears were selected from the plots in 2017 and 5 representative ears were selected from the plots in 2018 and dried to about 15% moisture followed by red-green-blue (RGB) imaging. These ears were imaged from a single angle using a Canon EOS Rebel T6i camera and an imaging system from Corteva Agriscience formerly DuPont Pioneer . Before Common image processing techniques such as filtering, thresholding, edge finding, edge enhancement, color selection, spectral filtering, and water shedding were used to process images in a semi-automated process . Using aEP was used to measure or predict 25 traits to provide unique insight into the characteristics of an ear. Traits measured or predicted in EP include, but are not limited to, grain yield (PHTYLD), kernels per ear (PHTKPE), average single kernel weight (KERWGT), and ear length (EARLGT). For a full description and heritability of the 25 EP traits, please refer to max + Tmin)/2] − 10. When the maximum and minimum temperatures were greater than 30°C or less than 10°C, then Tmax and Tmin were set to 30 and 10°C, respectively  divided by REFKPE (count ear–1) and was used as the reference trait for KERWGT. The average EP predicted PHTYLD, PHTKPE, and KERWGT was correlated to their corresponding reference measurement. Subsequently, this validation dataset was split into temperate (n = 989) and tropical (n = 424) origin to verify the use of EP in these perspective backgrounds and are shown in The accuracy of EP predicted traits PHTYLD, PHTKPE, and KERWGT was assessed through manual measurements of the reference traits. The abbreviations for reference traits start with –1) to validate the EP platform, reference yield (REFYLD18) (kg ha–1) was measured on a per plot basis  in 2018 using a plot combine  with grain weights standardized to 15% moisture. Stand count was used as a covariate in the linear model between REFYLD18 and PHTYLD to limit the variability in yield due to differences in stand. Moisture was measured as the percent moisture in the grain at harvest with the plot combine. This validation dataset was split into temperate  and tropical (n = 448) origin to verify the use of EP in these perspective backgrounds  is the fixed effect of the kth rep nested in the jth year. ε is the random residual error term associated with each phenotypic measurement. Significant differences of heterotic groups were determined using analysis of variance (ANOVA) of the BLUPs. When ANOVA was significant, Tukey test was performed to distinguish between the heterotic groups in R library agricolae::HSD.test.Where YBroad-sense heritability  using va2 represents broad-sense heritability of a given trait. Hybrid, hybrid × year interaction, and error variance components are denoted by y = 2) and number of reps per year (r = 2) were y and r in equation 2. Phenotypic correlations were computed using R function cor and visualized using corrplot::corrplot. Hierarchical clustering of the EP traits was performed through stats::hclust using Ward’s Minimum Variance (ward.D2). The Ball-Hall Index was used to determine the appropriate number of clusters among the traits. To visualize the dendrogram, the R function plot was used with stats::cutree for colorization and ape::as.phylo to convert our object to class phylo. Principal component analysis (PCA) was performed in PLINK v1.9   were ectively . When thr = 0.49 . PHTYLD ctively) .Multivariate analyses were used to assess the relationship among EP traits including PCA , hierarcPCA was employed on the EP traits to gain a greater understanding of their relationships . The firBroad-sense heritability was estimated for the 25 traits evaluated in this study on an entry-mean and plot-mean basis . Among EThrough visual assessment using the elbow method, four PCs were found to sufficiently explain the population structure among these inbred lines with 55.5% of the total variation explained in the PCA of SNP data. PC1 explained 20.2% of the total variance and visually separated the temperate and tropical inbred lines . PC2 expThe heterotic patterns of the temperate and tropical inbred lines were evaluated for their testcross performance with 2FACC  and PHP0p value < 0.05) reduced included PHTYLD, PHTKPE, EARAREA, EARBOX, EARLGT, EARPER, EARVOL, PHTKPR, REFKPE, and REFYLD. There was also a significant  reduction in heterotic potential of the IO heterotic group as compared to NS in testcrosses to 2FACC for PHTYLD, PHTKPE, EARAREA, EARCW, EARVOL, EARWTH, ETB, KERCC, PHTKR, PHTKPR, SCTTER, REFKW, REFKPE, REFYLD, REFYLD18, MOISTURE, AD, SD, and PH. Traits KERWTH, KERMIND, AD, SD, and ASI (GDD) were the only traits significantly greater in the SS as compared to NS heterotic group with IO material as an intermediate not significantly different from either SS or NS for KERMIND, KERWTH, and ASI. In testcross performance with 2FACC, kernel attributes were generally not significantly improved as a result of heterosis.A decrease in testcross performance was seen when 2FACC was crossed within the SS heterotic group compared to NS and IO . Traits p value < 0.05) reduced were PHTYLD, PHTKPE, KERWGT, EARAREA, EARCW, EARLGT, EARPER, EARVOL, EARWTH, KERCC, KERLEN, PHTKPR, PH, and EH  different for EARBOX, EARTR, ETB, PHTKR, TKERAB, and REFYLD18 when crossed to PHP02.Many agronomic and EP traits were significantly reduced when PHP02 was crossed within the IO heterotic group as compared to SS and NS heterotic groups. Traits significantly  reduced. The reduction in kernel number attributes was present due to a significant  increase in SCTTER compared to NS and SS heterotic groups and TKERAB compared to NS. PHTYLD was not significantly different between SS, NS, and DTMA heterotic groups though due to a significant  increase in KERWGT, EARPER, KERARE, KERLEN, KERMAXD, KERMEAND, KERMIND, KERPER, and KERWTH in DTMA compared to NS and SS inbred lines. In addition to EP traits, hybrids from DTMA inbred lines exhibited significantly  greater AD, SD, ASI (GDD and Days), PH, and EH as expected due to their tropical origin.In testcross performance with PHP02, the DTMA inbred lines exhibited similar performance to SS and NS heterotic backgrounds . PHTYLD,p value < 0.001) within-plot variance than plots of temperate descent . In 2018, mean within-plot variance per plot was 316.3. DTMA testcrosses had significantly greater  within-plot variance than temperate testcrosses .Variance of PHTYLD was estimated on a per plot basis from 10 ears in 2017 and five ears in 2018. Due to the differences in number of ears sampled per plot, analysis was not combined between years. In 2017, mean within-plot variance per plot was 427.5. DTMA testcrosses had significantly greater  and on a per ear basis in 2017 . The correlation between photometry-estimated yield and reference yield in 2018 was r = 0.39. When stand count was used as a covariate in the model, the correlation increased to r = 0.47  (r = 0.88) (r = 0.49) (r = 0.38) compared to the temperate germplasm (r = 0.51) (r = 0.49) as compared to the temperate germplasm (r = 0.86). Pioneer Hi-Bred International also validated many of the traits in this platform including kernels per ear  and yield  in temperate germplasm  . Kernel  = 0.88) . Photome = 0.49) . The cor = 0.51) . As suchermplasm . This stR2 = 0.7. R2 = 0.99 and 0.74, respectively. r = 0.99 and 0.97, respectively). Yield components such as kernel count and kernel weight were also correlated to their reference measurements .The phenotyping platform described in this paper presents a potential improvement over the previously mentioned phenotyping strategies as the kernels do not need to be shelled from the ears and the ears are only imaged from one angle. The ease of using this platform enables it to be scaled to the level needed in a breeding program; however, the accuracy of kernel weight assessment was reduced in this study from the platform described in H2 = 0.52). H2 = 0.60), ear length (H2 = 0.71), and kernel perimeter (H2 = 0.75) are a subset of yield components with an increased heritability. Heritability of a given trait is a function of the germplasm under evaluation and the effect of the environment . In our p value < 0.001, 2017; p-value < 0.05, 2018) increase in within-plot variance compared to temperate testcrosses. Many of the temperate inbred lines used in this study were the result of intensive selection where inbred lines were evaluated in multi-environment trials within commercial breeding programs where yield stability was an important consideration  . Multiplper se performance   . Pre-brer = 0.88) and kernel weight (r = 0.49) were both correlated with their reference measurements. Grain yield on per ear basis and plot basis were also correlated with reference measurements with correlations of r = 0.75 and r = 0.47, respectively. Twenty-five ear traits were assessed. Traits related to ear size and kernels per ear were found to be more related to yield than kernel attributes. Similarly, traits related to ear size and kernels per ear were found to be affected by heterosis to a greater degree than kernel size when evaluating inter-heterotic group crosses compared to intra-heterotic group crosses. Yield components were generally found to be more heritable than grain yield indicating their potential in inbred selection. Temperate, commercial United States heterotic groups had a wide range of phenotypes when inter- and intra-heterotic group testcrosses were evaluated. DTMA inbred lines, when evaluated using an Iodent tester, were found to have comparable yields to temperate material due to an increase in kernel weight that overcame the decrease in kernels per ear. Detailed phenotypic description of inbred lines is instrumental in the use of ex-PVP inbreds in public breeding programs and the incorporation of diverse germplasm to sustain long-term genetic gain in the commercial United States maize industry.Ear photometry methods can be used to identify and quantify traits that were previously difficult to measure at scale in a breeding program. In this study, kernels per ear (https://purr.purdue.edu/publications/3623/1.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 below: Best linear unbiased predictions (BLUPs) for the 25 yield-related traits measured by ear photometry for the 831 testcross hybrids evaluated in this study can be found in the Purdue University Research Repository, MT initiated, conceived, and coordinated all the experiments. ST and AS performed most of the experiments. ST wrote the manuscript with contributions of all the authors. All authors contributed to the article and approved the submitted version.AS was employed by the company Advanta Seeds. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


A second major locus for fruit longitudinal shape (qSHL5.1), probably also affecting fruit size, was found co-localizing at locus G, suggesting pleiotropic effects of peach/nectarine traits. An additional QTL for fruit longitudinal shape (qSHL6.2) was identified in the distal end of chromosome 6 in a cross with an ornamental double-flower peach and co-localized with the Di2 locus, controlling flower morphology. Besides assisting breeding activities, knowledge of loci controlling fruit size and shape paves the way for more in-depth studies aimed at the identification of underlying genetic variant(s).Fruit size and shape are critical agronomical and pomological attributes and prime targets in peach breeding programs. Apart from the flat peach type, a Mendelian trait well-characterized at the genetic level, ample diversity of fruit size and shapes is present across peach germplasms. Nevertheless, knowledge of the underlying genomic loci remains limited. In this work, fruit size and shape were assessed in a collection of non-flat peach accessions and selections, under controlled fruit load conditions. The architecture of these traits was then dissected by combining association and linkage mapping, revealing a major locus on the proximal end of chromosome 6 ( Peach (Prunus persica L. Batsch) is the most cultivated species of the Prunus genus in temperate regions. Remarkable breeding efforts during the last century have led to a dramatic improvement of fruit appearance and the release of commercial cultivars with intense skin coloration, large size, and regular shapes2.Fruit external attributes play a crucial role in the definition of quality market standards. Size, color, shape, and absence of defects directly affect consumer’s preferences and acceptance. Not surprisingly, these traits continue to be the major breeding targets in horticultural crops3. Other shape characters include height and width of stalk cavity, tip-end presence and shape, suture prominence, and fruit symmetry4. In particular, suture deformation can modify the length-to-width ratio , causing a deviation from the spherical shape of the fruit5. Varietal improvement has privileged the selection of roundish (globose) fruits in almost all commercial peach and nectarine cultivars. The flat fruit type, known as ‘Pantao’ in China and ‘saucer’ or ‘donut’ peach in western countries, has been a notable exception, gaining a breeding interest starting from 1980 (with the release of the ‘Stark Saturn’ variety) and remaining a target trait in some breeding programs6. While peach cultivars are broadly classified into flat or non-flat (or round) types, a huge variability of fruit shapes have been reported across non-flat peach accessions, widely varying from oblate to ovate/elongated. Based on longitudinal  and transversal sections, Blake & Edgerton7 classified peach standards into 12 classes for the longitudinal section and 9 for the transversal one, respectively. While being part of the routine breeding evaluation, fruit shape attributes have rarely been evaluated through objective quantitative measurements  and roughly categorized through visual assessment, particularly focusing on the overall shape and/or the scoring of tip and suture prominence8.Basic descriptors such as height, length, width, and aspect ratios , are major determinants of peach fruit shape. The optical impression of roundness by the human eye is associated with a height-to-width ratio of about 1.05, subtending to slightly oblate-shaped fruitsS locus initially described by Lesley9 and fine-mapped to the distal part of chromosome 613. Apart from this locus, knowledge of other genetic factors contributing to shape variation in non-flat-type fruits is still limited. A moderate correlation with fruit size and an intermediate heritability estimate have been reported for the ratio between height and average suture and cheek diameter8. A genotypic contribution to fruit shape is supported by the distribution of round and ovate shapes in some breeding progenies5. Blake14 suggested a dominance of ovate over round shape, in contrast to Smykov15, reporting an almost fully inherited roundish over ovate shapes from visual analysis of several segregating progenies. A more quantitative inheritance has been proposed based on the wide range of variability obtained by crossing round and ovate cultivars, albeit with a slight bias towards round3. Genetic analysis of fruit shape may be complicated by the influence of environmental conditions—in particular pre- and post-blooming temperatures seem to strongly influence pistil tip and suture prominence16. For example, high-chill peach cultivars grown in tropical climate often show elliptic  fruit with accentuated tip and/or suture bulge17, suggesting a role of inadequate chilling or prolonged endo-dormancy on flower bud and early ovary development18. Analysis of some progenies from low-chill breeding programs suggests low heritability of these traits and strong genotype-by-environment interaction19. Studies on the effect of tree cultivation management on fruit shape are scarce, although excessive fruit thinning seems to increase the incidence of fruit deformation, at least in some cultivars20.Genetic analysis of peach fruit shape mainly focused on the Mendelian flat trait controlled by the dominant 21. However, differences in endocarp size 22 or fruit shape  among genotypes could bias the correlation between fruit size and mass, making them de facto well-distinct traits. Fruit size in stone fruits is a complex trait affected by genotype, environment, and their interactions19. Also, orchard management, including rootstock, fertilization, irrigation, and/or pruning has significant effects on this trait23. At physiological level, final drupe size is a function of mesocarp cell number, cell size, and intercellular space25. Fruit growing potential is primarily determined by cell number , which in turn depends on genetic factors (possibly related to the number of ovary cells at bloom)28 and source-sink limitations occurring during specific growth phases (driven by the competition for assimilates among fruits)31. Assimilates supply is controlled through the adjustment of fruit load by thinning , a cultivation practice with a tremendous effect on fruit size, particularly on genotypes with high growth potential32. At genetic level, a wide range of heritability estimates have been reported for peach size (suture and cheek diameter), varying from lower than 0.30 to higher than 0.90 depending on the study and occurrence of transgressive segregation34. Apart from population-specific genetic factors, such differences in heritability estimates may at least in part be due to differences in environmental conditions and tree management practices 35. The knowledge of the genetic bases underlying fruit size variation would bring significant benefits to the selection process, including markers or genomic assisted approaches. QTL mapping studies for fruit size have been performed in peach as well as other stone fruits, most of them using bi-parental progenies or pedigree-based approaches. In peach, QTLs for fruit size have been reported in inter- and intra-specific progenies on chromosomes 1, 2, 3, 4, 5, 6, and 7, although their presence, position, and/or explained phenotypic variance widely differed depending on the genetic background used for dissection34. In other Prunus species, such as sweet cherry, major overlapping QTLs for drupe size were repeatedly found on chromosomes 2 and 6, with additional loci reported on 1 and 537.Fruit size is another important external quality attribute but also a component of yield and, thus, a fundamental characteristic for developing novel cultivars. Peach fruit size is generally estimated measuring equatorial diameter, often highly correlated with fruit mass  within a genotypeqSHL/Fs6.1) explaining most of the phenotypic variability for longitudinal shape and also affecting fruit size. The effects of this QTL on fruit longitudinal shape were confirmed in two different segregating progenies, while those on fruit size seem more dependent on the genetic background. An additional QTL for longitudinal shape (qSHL5.1) was identified on chr 5 co-localizing with the G locus, suggesting a putative pleiotropic effect of the peach/nectarine trait. Finally, a QTL for longitudinal shape (qSHL6.2) was identified in a cross-progeny derived from an ornamental double-flower peach and co-localized with the Di2 locus controlling flower morphology.Objective of this study was to dissect the genetic architecture of fruit size and shape traits in a collection of 172 non-flat accessions and selections representative of occidental peach cultivation and breeding. To this end, the collection was phenotyped using objective measures and indices during two consecutive seasons under controlled crop load conditions. Association mapping revealed several loci associated with fruit size and shape, including a major locus on the proximal end of chromosome 6  width , and depth . Fruit size (Fs) was determined by averaging maximum w and d. The w/h  and w/d  ratios provide estimates of fruit shape in the longitudinal and transversal sections, respectively. For both indices, a value of 1.05 is associated with a visual perception of round fruits, while lower or higher values correspond to ovate and oblate shapes, respectively. In the longitudinal section, the ratio of proximal to distal width  allows differentiating the ovate from the elliptic (heart-shaped) form. The same could be also applied to the transversal section . In the transversal section, the degree of suture indentation was also visually scored (γ). Proximal fruit end shape was evaluated by the indices: width of stalk cavity (α), estimated as the angle formed by the top cheeks points and the site of stalk attachment; height of stalk cavity (HST) as the vertical distance between the stalk attachment point and the tangent line to the maximum cheeks points; proximal indentation (ΔCH) as the relative height difference between cheek points . In the distal fruit end, tip length and (in case of tip absence) the indentation angle formed by the distal cheek points and fruit apex (β), were also evaluated.Quantitative data for fruit size and shape were estimated by using standard indices and others relevant for peach drupe  and 2–2.5 (heavy)—were applied in a subset of 26 accessions representative of the range of size and shape variability. As expected, the reduction of fruit load significantly increases fruit size (Fs), with a magnitude dependent on the maximum growth potential of each accession (from 5 to 14 mm on average). Interestingly, fruit load also affects fruit shape, increasing SHL  independently from the year or genotype, while SHT was less affected   on fruit size, two thinning treatments—i.e., light and heavy, based on fruits number per cmFs and both SHL and SHT were observed under these load conditions , ranging from 49.0 mm to a maximum of 80.6 mm  , although most of the accessions were characterized by nearly round-shaped fruits   , with an average of 1.17.05) Fig. . The upp05) Fig. . SHL valSHT showed a lower range of variation  compared to SHL  , although it was affected by high within-accession variability (pooled standard deviation = 0.082) and low correlation between-years  . The maximum value of this index was observed in accession ‘Pacific Star’  reported in old classification systems for peach was not present in the collection. Regarding STT in the transversal section, fruits showed no appreciable variability, except for the out-ranking accessions ‘Pillar’ and ‘Groc d’Alto’, having a high incidence of triangular-shaped fruits (caused by tissues swelling at the suture level)  did not show appreciable variability, being flat or slightly shallow in almost all accessions, excluding ‘Buco Incavato’, with an evident and deep indentation  Fig. . Also, sion Fig. .α to 0.37 for HST , except for ‘Pesca a Cuore Capuozzi’, consistently characterized by a stylar tip length over 10 mm  showed low variability among accessions, being flat or slightly depressed (data not shown).The other parameters showed moderate to low correlation among years, ranging from 0.57 for  mm Fig. . Also, iα and HST (r-squared −0.61), all other parameters were not significantly related.The correlation among the various indices was also evaluated by Spearman’s test; however, excluding the negative correlation between 35. The second cluster (group 2) included various genetic materials, such as Occidental traditional accessions, early USA breeding materials, and a few individuals with Oriental origins. The remaining were admixed genotypes. In Principal component analysis (PCA) of size and shape, the 2 first principal components were found to be relevant following the scree plot method, accounting for 51.8% of the total variation. The first and second PC account for 31.4% and 20.4%, respectively  was correlated to HST, Fs, and α  while the second (Dim2) to the main shape attributes SHL, SHT, and STL . The projections of the accessions on the PCA graph show no evident differentiation among clusters, maybe except for some genotypes of group 1  characterized by negative values of Dim1, and of group 2 presenting high positive values for Dim2.As inferred by the Admixture program, the predictive accuracy of population structure in the panel was maximized for two a priori clusters (K) , identifying SNP_IGA_683904 as the most associated marker at position 25,033,223 bp , by adding 11 flat genotypes to the panel of 172 non-flat accessions. Based on previously published mapping information, the best accuracy was achieved using the FarmCPU algorithm adjusted for population structure  and using the average of yearly records and associations were detected for size and shape traits.SHL), signals at the proximal end of chromosome (chr) 6 were detected by all models and in both years, although the top SNPs were different: Peach_AO_0600284 for 2018  and Peach_AO_0601598 for 2019  (Table SHL between-years (0.77), average values were also used for the analysis, confirming the main locus at the beginning of chr 6 with top marker at SNP_IGA_609531 . Other loci above the Bonferroni threshold were detected on chr 1 and 4 , stable loci were identified at the same marker positions by all models on the proximal ends of chr 4 and 6: Peach_AO_0424020, located at 4,578,765  and SNP_IGA_605104, located at 4,132,770 bp   allows testing average phenotypic values: other than the two major loci on chr 4 and 6, several significant signals were detected on chr 1 , 3, 5, and 7 , stable signals were identified by all models on chr 8, at markers SNP_IGA_825124  for 2018 and SNP_IGA_817953  for 2019 with a maximum p-value of 4.72e−04 and 2.25e−04, respectively, above the permutation threshold of 8.49e−04. For proximal indentation (ΔCH) a stable association in both years was detected by all models on chr 8 at SNP_IGA_864911, located at 14,668,631  above the permutation threshold (3.84e−03). For the width of stalk cavity (α), associated loci were detected on chr 1 and 5 for 2018, and chr 5 and 8 for 2019. Finally, for the height of stalk cavity (HST) and shape triangle index (STL) signals were only identified for 2018 or 2019, respectively.Regarding the other shape traits, only signals above the respective permutation thresholds were identified, mostly depending on the year Table . CumulatFs trait is close to the signals identified for SHL . Associated markers map to a local high LD region spanning about 1.2 Mb delimited by Peach_AO_0600618 and Peach_AO_0605368 , named qSHL/Fs6.1 , round (1.05), and slightly oblate (1.08) shapes, respectively, and explaining 31.6% of the phenotypic variance in the panel. Association of these haplotypes with Fs trait was only significant for H2, being associated with an increase of drupe size  for qSHL/Fs6.1 locus, two bi-parental progenies segregating for different SNP blocks were investigated (Supplementary File 1 progeny (BxO) from the cross ‘Bolero’  × ‘Oro A’ ; an F2 progeny (CxEL2) derived from cross ‘Contender’  × ‘Elegant Lady’ .To further explore the involvement of Fs and SHL traits were highly to moderately correlated in the two analyzed seasons , with broad-sense heritability of 0.62 and 0.58, respectively. SHT did not show appreciable variability (data not shown). Average Fs values showed an almost bimodal distribution, while SHL was normal but negatively skewed. Interestingly, the two traits were correlated (r-squared −0.78), as fruit size increase along with the decrease of SHL . Linkage analyses in the BxO map detected a major QTL at the proximal end of chromosome 6, peaking for both Fs and SHL traits at SNP_IGA_608970 , with maximum LOD of 28.2 and K-score of 41.12, respectively . Interestingly, the H1H2 is also associated with increased fruit size compared to H2 .In BxO, 2 seedlings segregated 1:2:1 (chi-square = 1.60) for the H1, H1H2, and H2 blocks, respectively; broad-sense heritability of Fs and SHL was of 0.61 and 0.30, respectively. Even in this progeny, 1-year phenotyping revealed a significant association between qSHL/Fs6.1 segregation and the range of SHL value, varying from about 1.00–1.07 on average. In contrast, effects of this QTL on fruit size were not significant in this progeny , co-localizing at the G locus  . However, when accounting for qSHL/Fs6.1 haplotypes, the effect of G trait on Fs was only significant in the H2 background , with the minor allele homozygous or heterozygous in all ultra-early maturing accessions . This marker seems associated with a decrease of Fs, although differences were only significant for homozygous genotypes  from the cross of ornamental peach ‘NJ Weeping’  × ‘Bounty’ . In WxBy, SHL and SHT both showed a normal but slightly negatively skewed distribution. Correlation between the two seasons was high for SHL and low for SHT . Linkage analyses in WxBy map showed a major QTL signal for SHL in the middle of chr 6, peaking at the Di2 morphological marker  with a maximum LOD of 8.3% and 27.8% of explained variance  was stable when considering yearly data and co-localized within the dominant Di2 locus that controls flower petal number. Indeed, segregation of the Di2/di2 locus was significantly associated with SHL values, which additively increase from ovate in homozygous double-flower (Di2/Di2) individuals (SHL around 0.95) to progressively rounder shapes in heterozygous (Di2/di2) double-flower and single flower ones .43. In peach, EFD has been mainly used to also define the influence of the position of the center of gravity, curvature, and degree of roundness44. However, width-to-height and length-to-width ratios seem to account for most of the variability for fruit shape in peach45, as also observed in our collection.The main peach shape descriptors reported in the UPOV guidelines are based on the qualitative ranking of fruit into discrete classes through visual analyses. Such subjective scoring systems pose limitations for genetic analyses. Therefore, a first goal of this work was the collection of quantitative phenotypic data based on objective, standard indices for shape traits, determinable through measurements with a digital caliper and/or image-based software. Other than allowing precise quantification of phenotypic variation, such indices have the advantage of being relatively easy to collect and comparable among different studies. Among other approaches to evaluate shape traits, 2D or 3D imaging-based approaches involving elliptic Fourier descriptors (EFD) have been also adopted in fruit species46. Among the various non-genetic factors affecting size, fruit load is probably the most important, as it can account up to 84% of size variability within a single accession47. As an example, fruit size in a typical large-sized peach commercial cultivar  can range from 50 until 90 mm as a sole function of the fruit load47. This range is close to the whole variability measured in our collection (about 50–80 mm). Imposing two divergent fruit load regimes in a subset of accessions clearly indicated that thinning-induced increase of fruit size also tended to modify shape, particularly, increasing SHL. Thus, in order to minimize confounding effects due to source-limitations, we set a light fruit load (0.7–1 fruits per cm2 of TCSA), ideally allowing accessions to express their maximum fruit growth potential. The tight control of fruit load allowed the reduction of year-to-year differences within accession, resulting in 0.69 Fs correlation among the two years of assessment. Clearly, specific recommendations for thinning intensity in terms of fruit number per TCSA (such as the range of fruit load adopted in this work) are not universally valid for all environments and cultivation conditions; nevertheless, management and specific fruit load conditions are crucial for an accurate assessment of peach fruit size and shape, as well as to ensure a reliable comparison across studies. Also, estimating genotype × management  interactions at the whole panel level  may be a matter of future studies, although imposing different fruit loads is not always feasible in breeding progenies or in collections of genotypes characterized by different growth vigor and productive habitus.In several species, fruit shape is often altered following the size alteration and viceversaFs) trait, in other studies at peach germplasm-level34, the range of phenotypic variability has not been reported in detail, hindering a direct comparison with our work. In 14 non-flat intra-specific peach breeding progenies, average population Fs values ranged from about 65 to 80 mm5, as also observed in our work, while in a BC2 peach × P. davidiana progeny and BC1 ‘Texas’ × ‘Earlygold’ the lower limit of the range reached less than 40 mm48.For fruit size   and transversal shape (SHT)  are particularly relevant in peach breeding, since they subtend to ovate, round or oblate forms of the fruit and its regularity, respectively2. A germplasm-wide analysis of these traits in peach has not been reported in the literature. In our work, the phenotypic variability recorded for these two shape traits can be considered as representative of the intra-species variability in Occidental accessions. Although additional diversity may be present in Oriental materials, the observed ranges of variation for SHL and SHT  are comparable to those reported in a pool of accessions including also peach hybrids with wild species, such as davidiana (0.95–1.08 and 0.96–1.07)45 or almond48. Most accessions in our panel (particularly those recently released) showed values for SHL attributable to a nearly round form or slightly oblate, as a consequence of the strong selection activities towards this consumers’ preferred attribute. While SHT showed a more limited range of variability, this parameter was less stable within the two years of evaluation, implying more pronounced effects of environmental conditions compared to SHL. SHT is visually associated to fruit shape regularity and tends to be strongly altered by morphological defects such as triangular-shaped fruits and/or prominent suture 49. Protruding tips and sutures can be bruised during handling and shipping, and are thus undesirable traits for commercial peaches50. The presence of genotypes more prone to these defects has been variously reported, as confirmed in our panel by the out-ranking accessions  with a high incidence of triangular-shaped fruits. These accessions may be used as cross-parents for studying the trait in a more restricted genetic background, although broad-sense heritability of suture prominence seems to be very low51. Longitudinal Shape Triangularity index (STL) was developed to quantify the degree of fruits ellipticity. The heart shape is considered a fruit defect, particularly when highly accentuated (STL above 1.20) and associated with a pronounced tip. Most of the accessions showed values around 1.10 for this index and a low frequency of extreme phenotypes. The degree of ellipticity and tip prominence tend to increase in sub-tropical peach cultivations, mainly as a consequence of insufficient chilling accumulation but also elevated post-bloom temperatures53. Not surprisingly, this shape trait has considerable importance in low-chill cultivar development17, although the selection is hindered by year-to-year variability  and strong genotype-by-environment interactions19. Growing condition of our collection, ensuring complete satisfaction of cold requirement even in the most demanding accessions, are probably the reason for the poor variability observed for tip morphology or protruding tip incidence. An interesting accession (‘Pesca a Cuore Capuozzi’) with heart shape and the evident tip could be useful to analyze these traits in temperate climates. The limited range of variability and low yearly stability found for other shape traits, such as proximal indentation (ΔCH) width and height of stalk cavity  or indentation angle (β), will require additional studies in other germplasm collections for clarifying the actual presence of relevant phenotypic diversity in peach.Regarding shape, among the measured indices, SHL) and fruit size (Fs) (around 0.60) and low for the other shape traits. A major effect locus for longitudinal shape (SHL) was identified at the beginning of chr 6 (qSHL/Fs6.1) within an LD region of about 1.2 Mb. Allelic variation at this locus was largely represented by two haplotype blocks (named H1 and H2) accounting for over 30% of the phenotypic variance for SHL in the collection panel, with H1, H1H2, and H2 genotypes, respectively, associated to ovate, round and oblate shapes. Interestingly, homozygosity for the ovate-associated H1 haplotype was underrepresented compared to the other two genotypes (only 8%), suggesting at least in our collection, a negative selection toward this allelic configuration. The effects of this QTL were further validated in two progenies (BxO and CxEL2), where segregation of qSHL/Fs6.1 explained most of the observed phenotypic variability for SHL.To our knowledge, this work is the first effort to characterize the genetic architecture of fruit shape variability in non-flat peach cultivars. Association mapping revealed several genomic loci associated with fruit shape; information about their positions will be useful as a starting point for extending research to other germplasm collections. Cumulative heritability explained by GWAS loci was moderately high for longitudinal shape (SHL (qSHL5.1) was found co-localizing at locus G. The correlation among traits due to pleiotropy or strong linkage among QTLs seems to be an important driver of fruit quality multi-trait evolution. For example, a strong linkage between flat trait and a reduction of fruit weight has been reported in peach progenies5, also supported by co-localization of locus S with fruit mass QTLs54. As observed in bud sports, peach/nectarine mutations would appear to have a pleiotropic or strong linkage effect on some traits, particularly fruit size and shape55. The effect of this locus was clear when comparing longitudinal shape in nectarine versus peach accessions, the first showing significantly lower SHL value, and more round shape. Putative pleiotropy of the nectarine trait seems also evident when accounting for qSHL/Fs6.1 segregation, although not significant in the H1-ovate background. The exclusion of nectarines in a multi-progeny study significantly reduces heritability for fruit size, from 0.40 to 0.0919. However, G trait effect on Fs was elusive in our panel. Given its relevance for breeding, the role of nectarine trait on both SHL and Fs should be more specifically addressed, particularly in progenies segregating for both G and qSHL/Fs6.1 loci. Apart from these two major loci, other QTLs were also identified by GWAS on chr 1 and 4, although the first only by two of the three tested algorithms. However, the low LD level found around top associated SNPs did not allow haplotypes inference and reliable estimates of the contribution to SHL variability.A second major QTL for 21. In another study involving materials from the UC Davis Breeding Program including introgressions from wild relatives , QTLs for Fs were identified on chr 2, 3, and 7 although in a different position compared to the previous analysis (21–22.5 Mb)34. In WxBy progeny, a QTL on chr 7 explained the majority of size variation, but it was located in a different interval compared to the previous studies (maximum LOD for SNP_IGA_776826 at 15.2 Mb), with additional stable loci detected on chr 1 (11.8 Mb) and 3 (13.7 Mb)33. In the BxO progeny, a major QTL for Fs perfectly co-localizing at the qSHL/Fs6.1 locus was detected in the same region previously reported on chr 634. The range of fruit size segregation (from less than 50 to more than 70 mm) and the high proportion of explained variance (about 60%) further support the relevance of the QTL in this genetic background. The co-localization of Fs and SHL QTLs in the BxO progeny suggests a pleiotropic effect of qSHL/Fs6.1, however, recombination events around this locus did not allow to confidently narrowing the interval (data not shown). Therefore, whether qSHL/Fs6.1 harbors multiple QTLs or a single QTL with pleiotropic effects remains an important question for future research. Association of segregating haplotypes at qSHL/Fs6.1 and Fs was less evident in the CxEL2 progeny and the germplasm panel, suggesting a more complex architecture of this trait compared to SHL. Indeed, other loci were detected by GWAS, with the most significant signal at the proximal end of chr 4. This QTL seems to be mainly linked to the small fruit size characterizing early maturing accessions  suggesting either the presence of a linkage between Fs and maturity date (MD) loci or pleiotropic effects of MD. MD effects on fruit size or mass have been already reported in peach and other species, supported by an overall moderate correlation in several breeding progenies56. However, excluding very early maturing accessions, the relationship between Fs and MD in our panel was not significant. Moreover, the position of this QTL does not coincide with a major MD locus previously reported57.The dissection of fruit size has been reported in several studies. In a pedigree-based analysis, QTLs on chr 6  and 7 (6.6–9.5 Mb) were stable across seasons, and a QTL on chr 5 (2.5–3.2 Mb) was detected in one yearFs variation in WxBy has uncovered a complex genetic inheritance, controlled by several major and minor QTLs33. Using the same dataset, a major QTL (qSHL6.2) for SHL was uncovered at the Di2 locus, controlling the double-flower trait. This locus seems to be regulated by a deletion of the miR172 target site in the AP2/TOE-type family gene PETALOSA altering flower morphology through the development of supernumerary petals58; additional studies should be performed to explore the possible pleiotropic effects of this variant, as previously demonstrated for heat-requirements in the same background59. Indeed, this aspect would provide insight into the link between environmental growing conditions  and fruit morphology. In apple, the AP2-miR172 module influences fruit size, since a transposon insertion in a miRNA172 allele co-located with a major QTL for fruit size in large-sized cultivated and wild progenitor apple species, whereas over-expression of miRNA172 in transgenic apple significantly reduces fruit size60.The particular genetic background of the WxBy progeny  allows to expand the diversity associated with fruit size and shape and evaluate the re-introgression of wild-related traits in a modern breeding background . A previous linkage analysis of α, ΔCH, STL or SHT), our genomic scan did not allow to find stable and highly significant loci, as they seem to be affected by the environment . Unraveling the genetic bases of such traits will require additional studies and particular experimental designs (such as replicated multi-site collections)61. Also, novel phenotyping methods should be tested, including the use of machine learning or 3D imaging in morphometric approaches, as tested in other fruit species43. Considering the high within-tree variability of these traits, quantification in terms of incidence  could be useful to improve phenotyping resolution, although this will require the analysis of a large number of fruits, which is not always feasible in large collections.For other shape traits  involved in transcriptional repression leading to fruit elongation64; lc putatively encoding the ortholog to WUSCHEL controlling meristem size and locule number65; fw2.2 encoding a member of the Cell Number Regulator family66 and fw3.2 encoding a cytochrome P450 enzyme of the CYP78A class ortholog to KLUH67. Other QTLs have been recently cloned, such as ENO, an AP2/ERF transcription factor that regulates tomato fruit size by affecting floral meristem development68 or sov1, encoding another member of the OFP family (SlOFP20)69. Apart from their functional conservation, the presence and effect of genetic variation associated with these genes remained to be elucidated in peach and other stone fruits. Members of the previously described gene families localize within confidence intervals of major QTLs in other taxa, suggesting that organ shape and size variability may have a common genetic basis70. For example, a candidate gene of the FW2.2/CNR clade, PavCNR12 co-localize with a major QTL on chr 2 explaining the highest portion of the phenotypic variation in modern cherry germplasm71. In peach, a 1.7 Mb chromosomal inversion putatively affecting an OFP gene (PpOFP1) has recently been identified as the most promising candidate for flat trait39. The whole‐genome sequence of peach72 is a useful resource for the identification of candidate genes underlining QTLs for fruit size and shape. Focusing on chr 6 QTLs, other than the PpOFP1 gene, two additional members of the OFP gene family, PpOFP5 and PpOFP15, encoded by transcripts Prupe.6G042700.1 (at 3.13 Mb) and Prupe.6G042800.1 (3.14 Mb)73 co-localize at qSHL/Fs6.1, representing promising candidates for this major locus  encoded by transcript Prupe.6G240600 (at 23.9 Mb) was present within the 2-LOD interval of qSHL6.2 .2 TCSA) was set based on a previous work74 and taking into account average yield per tree density in close commercial orchards. The F1 cross (BxO) from ‘Bolero’ × ‘Oro A’ parents comprising 126 seedlings located in the experimental field of the University of Milan, Azienda Didattico Sperimentale ‘F. Dotti’ 75. The F2 cross (WxBy) from ‘NJ Weeping’ × ‘Bounty’ parents comprising 123 seedlings located at the CRPV orchards in Castel S. Pietro 33. The F2 cross CxEL2 derived from self of F1 CxEL individual #071 comprised 100 individuals located at the CRPV orchards in Imola . BxO and CxEL2 progenies were grafted onto GF677 rootstock, while WxBy were own-rooted, and all planted at distance of 1 × 4  and trained as slender spindle . In the three progenies, fruit thinning was performed as previously described33, leaving 1–3 fruits per fruiting shoot and harvesting the 10 largest fruits from each tree. Climatic conditions of growing areas allow the complete fulfillment of chilling requirement also in high-chill accessions.The panel used in this study is comprised by 172 ‘round’ and 11 ‘flat’ accessions derived from MAS.PES peach germplasm collection located in the experimental farm ‘M. Neri’ of CRPV  in Imola  , width (w), and depth (d) were determined by a digital caliper, and the results given in millimeters. The degree of suture indentation in the transversal section (γ) was visually scored. The indices shape triangle index (STi), width of stalk cavity (α); height of stalk cavity (HST), proximal indentation (ΔCH), and indentation angle (β), were evaluated through image analysis: ten fruits were transversally and longitudinally sectioned, placed on a rigid graph paper in the center of the camera’s field of view, capturing two RGB color images for accession. Images were manually processed using ImageJ software77, after calibration performed using the set scale function. Descriptive statistic of data was performed in R environment. Correlation between traits was analyzed using the Spearman correlation coefficient. Normal distribution was tested using the Shapiro–Wilk test (p < 0.05).Fruits were collected at commercial maturity on seasons 2018–2019 for the accession panel, on 2011–2012 for WxBy, 2013–2014 for BxO and 2017 for CxEL78 plus a 9K SNPs add-on derived from high-coverage whole-genome re-sequencing data79 was used to genotype the analyzed panel of 172 accessions and CxEL2 progeny. Genotyping data were filtered for marker missing rate <10% and minor allele frequency (MAF) > 5%, finally retaining a total of 12,473 high-quality SNPs for GWA analysis. The Peach Genome assembly V2.0 was used as a reference for SNP marker positions69. BxO and WxBy progenies were genotyped using the IPSC peach 9K SNP array, as previously described57. Population substructure was inferred using the model-based clustering algorithm ADMIXTURE v1.22, Successive values of K (a priori genetic clusters) were imposed, choosing the K which maximize the predictive accuracy through a cross-validation procedure. Principal Component Analysis (PCA) was also performed using the full set of filtered SNPs through the R function prcomp. The optimal number of PCs to be included for the considered phenotype was determined by using Bayesian information criterion (BIC). Genotyping and map construction in BxO and WxBy progenies was previously described57.The novel released 18K SNP array peach, composed by the IPSC peach 9K SNP arrayQ = 2 matrix as covariate: Mixed Fixed and random model Circulating Probability Unification (FarmCPU), Multi-locus Mixed Linear Model (MLMM), and linkage disequilibrium iteratively nested keyway (Blink). A naive Generalized Linear Model (GLM) without correction for population structure was also used. The performance of all tested GWA algorithms was evaluated by comparing the observed vs. expected p-values under null hypothesis through quantile–quantile (QQ) plot inspection. For association significance, thresholds were calculated based on Bonferroni correction for a type I error rate of 0.05 (4.01e−06) and less stringent (trait-specific) permutation tests. SNP-based broad-sense heritability was estimated by GREML method using GCTA tool after fitting GWAS top SNPs. Intra-chromosomal LD patterns were calculated using r-squared correlation for all pairwise SNPs comparisons and visualized using HAPLOVIEW v4.2. SNP haplotype blocks at qSHL/Fs6.1 were deduced through identical-by-state (IBS) phasing.For association analysis, different algorithms were adjusted using a 80. According to normality distribution (Shapiro–Wilk test) the non-parametric Kruskal–Wallis (KW) rank-sum test or interval mapping (IM) were used to search for phenotype-marker associations. A QTL was considered significant for LOD values higher than 3 in IM and p = 0.005 for the individual test in KW. In case of not-normal data, IM approach was used for an approximate estimate of the QTL-explained percentage of phenotypic variance. Association of qSHL/Fs6.1 haplotype class and SHL and Fs in the BxO and CxEL2 progenies was determined using in non-recombinant individuals. Comparison among phenotypic values of each segregating class was estimated by ANOVA, Kruskal–Wallis, and two-tailed Student’s test (p < 0.01). Statistical analyses were carried out in an R environment.Linkage maps and genotypic data used for QTL analysis in BxO and WxBy progenies were already available from previous studies. QTL analyses were carried out using the MapQTL 6.0 softwareSupplemental File 1Supplemental File 2Supplementary materials descriptionSupplemental Figure 1Supplemental Figure 2Supplemental Figure 3Supplemental Figure 4Supplemental Figure 5Supplemental Figure 6Supplemental Figure 7Supplemental Figure 8Supplemental Figure 9