The entire collection of cultivated barley germplasm accessions conserved in the Indian National Genebank (INGB) was characterized for nine qualitative and 8 quantitative traits to assess the nature and magnitude of prevailing genetic variability and to develop a core set. A wide range of variability was observed for days to spike emergence (51–139 days), days to physiological maturity (100–152 days), plant height (45.96–171.32 cm), spike length (3.44–13.73 cm), grain number/spike (10.48–82.35), and 100-grain weight (1.20–6.86 g). Initially, seven independent core sets were derived using 3 core construction tools– MSTRAT, PowerCore, and Core Hunter 3 by employing the maximization method, heuristic sampling, and optimisation of average genetic distances, respectively. The core set-3 generated by Core Hunter 3 by simultaneous optimisation of diversity and representativeness, captured maximum genetic diversity of the whole collection as evident from the desirable genetic distance, variance difference percentage , coincidence rate of range  and variable rate of coefficient of variance , which were more than threshold value of VD (80%), CR (80%), and VR (100%) required for good core collection. The coefficient of variation and Shannon–Weaver diversity indices were increased in the core set as compared with the whole collection. The low value of Kullback-Leibler distance (0.024–0.071) for all traits and quantile-quantile plots revealed a negligible difference between trait distribution patterns among the core set and entire assembly. Correlogram revealed that trait associations and their magnitude were conserved for most of the traits after sampling of the core set. The extraction of the INGB barley core set and identification of promising accessions for agronomically important traits in different genetic backgrounds will pave the way for expedited access to genetically diverse and agronomically important germplasm for barley breeding. Hordeum vulgare ssp. vulgare) evolved from its wild progenitor H. spontaneum (C. Koch) Thell, in the Fertile Crescent of Middle East about 10,000 years ago  and six-rowed (H. vulgare ssp. hexastichum). In two-rowed barley, only one spikelet at each node is fertile while all three spikelets are fertile in the six-rowed variant. Another classification is based on the presence of distinct caryopsis types. Most cultivars have intact husk cover of caryopsis (hulled), wherein the outer lemma and inner palea are firmly adherent to the pericarp at maturity, but a few variants are of the free threshing type (with a loose husk cover which gets easily separated from grain upon threshing) and are called naked or hulless barley (H. vulgare var. nudum L.) , brewing malts (30–40%), and the remaining percent for food purposes Ullrich, . Cultivaspontaneum and cultivated forms , Gatersleben  at the Indian Council of Agricultural Research-National Bureau of Plant Genetic Resources (ICAR-NBPGR), New Delhi, conserves the base collection with about 7,500 accessions of barley which were characterized for this study. After removing the duplicates and accessions in which data could not be recorded for one or more traits, finally, 6,778 accessions were subjected to data analysis to assess genetic diversity and develop a core set in barley. The objective of this work was to assess the nature and magnitude of prevailing diversity and to provide a manageable and representative selection in the form of a core set for use in research and breeding. Initially, seven independent core sets were assembled using different core construction softwares- MSTRAT, PowerCore, and Core Hunter 3 (CH3) which were subjected to quality evaluation based on different criteria  and 2nd at flowering stage (65–70 DAS). Recommended agronomic practices were followed during various stages of crop growth. Each accession was harvested and threshed manually. Additionally, a selected set of around 206 diverse accessions showing superiority for different agronomic and phenological traits was further validated in the subsequent years (2018–19 and 2019–20) in an Augmented Block Design with 40 entries in the first 5 blocks and 42 entries in 6th block including the above-mentioned checks.A total of 6,778 barley accessions, of which 5,351 were indigenous collections (IC) assembled from 21 different states of India and 1,427 exotic collections (EC) mainly from Syria, Canada, the USA, and Mexico were used in this study . The accviz. days to 75% spike emergence (DSE), days to 80% maturity (DPM), plant height , spike length , spikelet triplet groups per spike (STG), grain number per spike (GNS), hundred-grain weight , and grain yield per meter row  were measured quantitatively, while another 9 traits viz. growth class (GC), growth habit (GH), early plant vigor (EPV), spike row type (SR), awn type (AT), spike density (SD), grain type (GT), grain pericarp color (GPC) and lodging tendency (LT) were assessed qualitatively as per descriptors for barley  according to Augmented Randomised Complete Block Design Federer,  and adjuVP Lush, , where VRobinson . Expecten et al. , where kCompiled data on agro-morphological and phenological traits were standardized to eliminate scale differences and employed in core set identification. Initially, seven different core sets were developed which consisted of one core set developed using MSTRAT  maximizing E-NE distances (CH3- Core set 1);(ii.) maximizing A-NE distance (CH3- Core set 2);(iii.) maximizing both E-NE and A-NE with equal weightage of 1:1 (CH3- Core set 3);(iv.) E-NE and A-NE with unequal weightage of 0.3:0.7 (CH3- Core set 4);(v.) E-NE and A-NE with equal weightage of 0.7:0.3 (CH3- Core set 5).A set of selected 83 accessions was fixed for inclusion in all core sets based on the superior expression for one or more traits visualized in the field, trait-specific promising accessions, and limited representation in the genebank. The size of the core set was fixed as approximately 10% of the entire collection, considering the neutral allele theory Brown, .t-test. For quantitative traits, the homogeneity of variances of the entire collection and the selected core set was examined with Levene's test , the promising accessions were identified and validated , which were more than the threshold value of VD (80%), CR (80%), and VR (100%) and high value of average Shannon-Weaver diversity index (H') required for a good core collection. Although the MD in CH3-core set 3 was 62.5% which is more than the desired value. The inter-relationships between traits were conserved in all the analyzed core sets with reference to the whole collection as indicated by Mantel correlation. Based on various evaluation indices described above, the CH3-Core set-3 (hereafter referred to as INGB barley core set) appeared to capture the prevalent diversity and representativeness of the whole collection to a maximum extent. Therefore, we selected this core set for further comparative analysis with the entire collection. This core set was constituted by 678 accessions comprising 521 accessions of six-rowed and 157 two-rowed barley including 220 accessions having hulless caryopsis. List of INGB core set accessions along with the source of collection sites, biological status, and characterization data on 9 qualitative and 8 quantitative traits is presented in t-test provided a non-significant difference for three traits . Levene's test revealed non-significant differences among variances for traits PH and GY, and significant for other traits such as DSE, DPM, SL, STG, GNS, and HGW. Frequency distribution plots  in the core set and entire collection . The extr = 0.58 in the entire collection, r = 0.69 in the core set) and between PH and GY   possible with eight quantitative traits, 26 were significant in the entire collection and 23 in the core set, and were conserved after sampling of the core set in terms of trait association as well as magnitude.The estimates of trait associations revealed that significant and positive correlations exist among the traits such as DSE and DPM (ore set) . PH was Principal component analysis (PCA) based on the correlation between eight quantitative traits was done to examine the spatial distribution of entries/accessions in the core set and entire collection. The first five principal components (PCs) explained the major portion of variance (78%) in the barley core set. This value was comparable with that of the entire collection (76%) . In addietc., which forms the basic platform for detailed evaluation for feed, food, and malt purpose and also colored barley for functional food purpose per se. The high variability recorded in spike and grain traits in the present study shows the remarkable adaptability in terms of morphological structure and environmental conditions in which barley is cultivated throughout the world  are largely unknown  of which 1% (65 accessions) showed extra early heading. For maturity also, around 6.26% of accessions showed early maturity in less than 120 days, among which only 1.08% (73 accessions) attained maturity in <115 days. Early types are essential in most barley-producing areas owing to rain-fed cultivation. In India, about 44% of the area under barley cultivation is rain-fed. Hence early maturity is an obvious breeding target to escape drought and terminal heat stress at the end of the growing season. Besides this, the short duration and fast-growing genotypes of barley perfectly fit the major cropping system cereal-legume (for food and feed) in dryland areas of arid/semi-arid zones. About 24% of the total accessions were late heading (>100 days) of which 40% were exotic, mainly received from Syria and Mexico. This may be due to the fact that winter in these countries is much prolonged and cooler and selection is for late plant types to escape frost damage. Around 50 accessions constituting about 0.74% of the total assembly showed dwarf plant height (<75 cm), which is a highly desirable trait as barley is a lodging-prone crop. Although studies on diversity assessment in Indian barley , Shannon-Weaver diversity index, correlation coefficient analysis, and PCA. We could obtain a higher CV for all the traits in the core set as compared to the whole collection which is indicative of capture of more variability in the core set. The interquartile range was almost similar for all the traits such as DPM, HGW, PH, SL, STG, and GY, except DSE and GNS  which shr = 0.53, P0.05) indicated that plant height is directly associated with the yield potential of the plant in addition to being an important fodder trait in barley. In addition, PH was also significantly and positively correlated with other yield components such as SL, GNS, STG. These results are in congruence with earlier reports by Jabbari et al.  may be utilized in future selection and breeding in barley to cater to different agro-ecologies and end-uses. Based on the genetic variability laid out in the present study, the INGB barley core set comprising 678 accessions has been developed after comparative quality evaluation of seven different core sets derived using different software and strategies. The core set captured maximum diversity and representativeness of the whole collection as evident from various evaluation indices based on comparison of mean, variance, range , QQ plots, Shannon-Weaver diversity index along with the optimisation of average genetic distance described in this report. The development of barley core set and trait-specific germplasm identified in this study will provide expedited access to genetically diverse and agronomically important genetic resources, which would be useful in widening the genetic base of barley and thus more effective breeding programs. Besides the diverse germplasm in the form of the core set may be subjected to field evaluation for various biotic and abiotic stresses and subsequently genome-wide association studies to identify the underlying genes/alleles/markers.The original contributions presented in the study are included in the article/VK: conceived, designed and conducted the experiment, collected and compiled the data, and wrote the manuscript. JA: analyzed the data. M and JK: sowing and collection of phenotypic data. SJ: provided seed material from National Genebank. BP: facilitation for completion of the experiment. NP: layout, sowing, and collection of phenotypic data. JR: reviewed the manuscript. AP: conservation of diverse specimen in National Herbarium of Cultivated Plants and NBPGR and reviewed the manuscript. AK: facilitation and guidance for the success of large-scale characterization of germplasm. All authors contributed to the article and approved the submitted version.This study was supported by institutional funding resources from ICAR-NBPGR Institutional Project (PGR/GEV-BUR-DEL-01.01).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


The dominance effect is considered to be a key factor affecting complex traits. However, previous studies have shown that the improvement of the model, including the dominance effect, is usually less than 1%. This study proposes a novel genomic prediction method called CADM, which combines additive and dominance genetic effects through locus-specific weights on heterozygous genotypes. To the best of our knowledge, this is the first study of weighting dominance effects for genomic prediction. This method was applied to the analysis of chicken (511 birds) and pig  datasets. A 5-fold cross-validation method was used to evaluate the genomic predictive ability. The CADM model was compared with typical models considering additive and dominance genetic effects (ADM) and the model considering only additive genetic effects (AM). Based on the chicken data, using the CADM model, the genomic predictive abilities were improved for all three traits , and the average improvement in prediction accuracy was 27.1% compared with the AM model, while the ADM model was not better than the AM model. Based on the pig data, the CADM model increased the genomic predictive ability for all the three pig traits , with an average increase of 26.3%, and the ADM model did not improve, or even slightly decreased, compared with the AM model. The results indicate that dominant genetic variation is one of the important sources of phenotypic variation, and the novel prediction model significantly improves the accuracy of genomic prediction. With the continuous growth of the global population, human demand for food and security continues to increase. Hybridization is an important tool for increasing meat and grain production. It has been successfully applied to the production of animals (such as chickens and pigs) and plants (such as corn and rice). The performance of hybrid individuals is affected by genetic factors such as additive, dominance, and epistatic genetic effects. Traditional genetic evaluation methods only consider additive genetic effects but not nonadditive genetic effects (dominance and epistatic effects). Many studies have shown that nonadditive genetic effects are an important component of phenotypic values  estimating the dominant degree based on the deviation between the heterozygous and homozygous marker genotypes; and (2) using the estimated degree of dominance as weights on heterozygous genotypes to construct a genomic relationship matrix. The details of the approach are as follows.1 homozygous (A1A1), heterozygous (A1A2), and A2 homozygous (A2A2) genotypes be coded as 0, 1, and 2, respectively. The prior degree of dominance at a locus is defined as1A1, A1A2, and A2A2, respectively.Let the Ad) is defined as:The weighted heterozygous genotype  model for estimating the genetic values, including additive and dominance effects. The genomic relationship matrix can be built using the same method as those for the additive genomic relationship matrix , eviscerating percentage (EP), which is percentage of eviscerated weight to body weight before slaughter, and breast muscle percentage (BMP), which is percentage of breast muscle weight to eviscerated weight. The phenotypes in the chicken data (from one herd) were corrected for fixed effects (sex and batch), and the fixed effects were estimated using linear least squares approach by linear fixed effects model. The birds were genotyped using the Illumina Chicken 60K SNP BeadChip. SNP markers with a minor allele frequency (MAF) lower than 0.01 were deleted. After editing, 46,672 SNPs were used to build the relationship matrix.The novel model was tested using two published datasets from chickens  were analyzed in this study, and the traits had 2804, 2715, and 3141 phenotypic records, respectively. The three traits were either corrected for environmental factors  and rescaled by correcting for the overall mean (T3) or was a rescaled, weighted mean of corrected progeny phenotypes (T1 and T2), for which many pigs have no individual phenotype  integrates additive and dominance genetic effects and can be written as:Gad was constructed using the modified marker genotype coefficients (Cd), where locus-specific weights were exerted on heterozygous genotypes, and a method similar to the additive genomic relationship matrix was applied (VanRaden Mad is a (n × m) matrix  that specifies SNP genotype coefficients at each locus. The coefficients of the ith column in matrix Mad are (0–2pi) for A1A1, (Cd–2pi) for A1A2 where Cd was as defined earlier, and (2–2pi) for A2A2, where pi is the frequency of allele 1 (A1) at locus i.The combined additive and dominance genomic relationship matrix VanRaden . BrieflyCADM can be considered as a (co)variance matrix, but the definition is not exactly the same as the one in conventional breeding model. In CADM, we considered dominance effect as 0 for homozygous and non-zero for heterozygous, i.e., a genomic model  is:G was constructed using the original SNP marker information (VanRaden M are coded as (0–2pi) for A1A1, (1–2pi) for A1A2, and (2–2pi) for A2A2 at locus i.The additive genomic relationship matrix VanRaden , in whicd is the vector of dominance effects, Zd is the corresponding incidence matrix. It is assumed that d ~ N  is:G is the same as in the AM model. The dominance genomic relationship matrix D is constructed by H is a (n × m) matrix of heterozygosity coefficients. The coefficients of the ith column in matrix H are (−2pi2) for A1A1, (2piqi) for A1A2, and (−2qi2) for A2A2, where qi and pi are the frequencies of allele 1 (A1) and allele 2 (A2) at locus i, respectively.The method for constructing the additive genomic relationship matrix The variance-covariance components were estimated using the average information restricted maximum likelihood (AIREML) . The cross-validation was repeated 10 times.Prediction accuracy was defined as the correlation between the predictions and corrected phenotypic values. Differences between the correlations from different models were tested by bootstrapping Efron  and BonfTable Similar to the situations with chicken traits, the variance component values estimated from the three genomic models were different in pig traits Table . For T1 As shown in Table The phenotypic performance of a trait is affected not only by additive genetic effects but also by dominance and epistatic effects  of heterozygous genotype coefficients. However, according to our experience, relaxation sometimes leads to problems with convergence or abnormal solutions caused by the uncertainty of the estimated degree of dominance. Lower MAF together with linkage disequilibrium will strongly affect the estimates. In this study, we used MAF ≥ 0.01 because it is popularly used threshold for editing marker genotype data in genomic prediction. For calculating difference between three genotypes of a locus, how to handle the low MAF loci is a challenge.In this study, overdominance was not considered in the CADM model. This may not completely match the actual situation. In fact, the CADM model is available for overdominance by relaxing the limitation . Some traits may be mainly affected by additive genetic effects, and some traits may be mainly affected by nonadditive genetic effects (Xu For different traits, the dominance effects on phenotypic variation are different, so the combined additive and dominance relationship matrix (Gfects Xu . The CADWith our CADM model that combines additive and dominance genetic effects through defining heterozygous genotype coefficients, the abilities of genomic prediction are greatly improved. The results from this study indicate that dominant genetic variation is one of the important sources causing phenotypic variation, and the novel prediction model integrating dominance effects can significantly improve the accuracy of genomic prediction.Supplemental File 1 - simulation for CADMSupplemental File 2 - Tables


Improving yield prediction and selection efficiency is critical for tree breeding. This is vital for macadamia trees with the time from crossing to production of new cultivars being almost a quarter of a century. Genomic selection (GS) is a useful tool in plant breeding, particularly with perennial trees, contributing to an increased rate of genetic gain and reducing the length of the breeding cycle. We investigated the potential of using GS methods to increase genetic gain and accelerate selection efficiency in the Australian macadamia breeding program with comparison to traditional breeding methods. This study evaluated the prediction accuracy of GS in a macadamia breeding population of 295 full-sib progeny from 32 families , along with a subset of parents. Historical yield data for tree ages 5 to 8years were used in the study, along with a set of 4113 SNP markers. The traits of focus were average nut yield from tree ages 5 to 8years and yield stability, measured as the standard deviation of yield over these 4 years. GBLUP GS models were used to obtain genomic estimated breeding values for each genotype, with a five-fold cross-validation method and two techniques: prediction across related populations and prediction across unrelated populations.2=0.30 and 0.04, respectively). Prediction accuracy for yield was 0.57 for predictions across related populations and 0.14 when predicted across unrelated populations. Accuracy of prediction of yield stability was high (r=0.79) for predictions across related populations. Predicted genetic gain of yield using GS in related populations was 474g/year, more than double that of traditional breeding methods (226g/year), due to the halving of generation length from 8 to 4years.Narrow-sense heritability of yield and yield stability was low (hThe results of this study indicate that the incorporation of GS for yield into the Australian macadamia breeding program may accelerate genetic gain due to reduction in generation length, though the cost of genotyping appears to be a constraint at present.The online version contains supplementary material available at 10.1186/s12864-021-07694-z. Nut yield is the most economically important selection trait of macadamia . In 2017In addition to increased yield, precocious cultivarsthose that produce nuts at an early agemay be commercially attractive due to cash flow at an early age. However, it is not yet known how precocity might affect the rate at which yield begins to plateau in macadamia varieties. In coffee and apple, early-yielding varieties are desirable, particularly those with stable yields over time , 9. For Selection of new macadamia varieties involves two stages: thousands of seedlings are produced by cross-pollination to create diversity and are assessed in an unreplicated seedling progeny trial (SPT) (sometimes across multiple sites due to space restrictions), then the best performing trees are clonally propagated and evaluated in replicated trials across multiple environments in a candidate cultivar regional variety trial (RVT) . Trees bGenomic selection is a form of marker-assisted selection (MAS) that utilises genome-wide markers to predict genomic estimated breeding values (GEBVs) of individuals, after which the best performers are selected, possibly without phenotyping candidates , 15. As Genomic selection was first used in dairy cattle and is being increasingly used to improve genetic gain in both animal and plant breeding programs. With the potential to shorten breeding cycles, long-lived species with slow maturation times may have the most to gain from MAS and GS , 20. Gra272=0.2 (average distance of 0.128cM between markers) were superior to those at lower densities. Accurate phenotyping of a large training population, preferably over multiple environments and years , is required for perennial crops to derive accurate predictions due to the interactions between these factors [40High prediction accuracy of GS models will improve confidence in selecting elite candidates. Prediction accuracy depends on many factors, including the model, crop, size of the reference population, extent of linkage disequilibrium (LD), marker set, and heritability of the trait of interest . Genetic factors , 4042.M. integrifolia genome (v2) was published with 4098 scaffolds anchored to 14 pseudo-chromosomes  [Recently, an updated version of the 0 413kb) . In a st0 413kb)  found thNarrow-sense heritability for yield in the study population was 0.300.08. For yield stability across 4 years, heritability was close to zero Table. VariancModerate prediction accuracy was achieved for yield from cross-validation (CV) using randomly masked individuals . In comparison, yield prediction accuracy was not significantly different from zero for prediction across unrelated populations where families were grouped . However, when families were grouped, prediction accuracy was not significantly different from zero  using a selection index. SPT is then followed by a RVT for at least 8 years, where selected elites are clonally propagated and evaluated for more economically important traits across multiple environments.Genomic selection: After germination, the first leaves of each progeny seedling are genotyped for a large number of markers. Genomic prediction is then used to predict GEBVs for yield . Elite candidates are selected, using a weighted selection index for multiple traits, for establishment and evaluation in the RVT.Two breeding strategies were compared to demonstrate how implementing GS could decrease the breeding cycle and subsequently increase genetic gain Table. The numHere, we consider the generation length  as the time taken to select individuals to use as parents to produce the next generation of seedlings. Generation length for traditional breeding was 8 Table , as elitFor traditional breeding methods, r was calculated as the square-root of yield heritability 0.30=0.55; Table5; Table5This study is the first to investigate the use of genomic prediction to improve genetic gain for yield and yield stability in macadamia breeding. Our results suggest that yield-based traits are complex and highly polygenic, as indicated by low heritability, and that GS offers a suitable method to select genotypes to improve yield. Prediction accuracy is strongly influenced by the relatedness between training and validation populations , and unrThe CV method of family-grouped prediction represents an extreme version of the potential real-world application of GS in macadamia where predictions are performed across unrelated populations. It is likely that the training and target populations will actually be more closely related as there is often an overlap of cultivars used as parents between breeding populations, and elite individuals from one population are commonly used as parental germplasm in subsequent generations . It is eThe implementation of GS in macadamia may include prediction and deployment across environments. The current study population had limited replication of genotypes across environments and did not include G x E interactions in prediction models as preliminary results found no evidence of G x E in this experimental material . Previou2=0.30, h=r=0.55). These similar values for r demonstrate that the genomic prediction accuracy estimated in the current study will provide similar gain as phenotypic analysis, regardless of the time advantage in GS strategies. The prediction accuracy achieved in GS in this study was not as high as reported in some other horticulture crops, which may be attributed to several factors. Estimates of macadamia yield in the current and previous studies [The prediction accuracy for yield in the current study was moderate for randomly-grouped individuals r=0.57), and comparable to the prediction accuracy of yield as measured by phenotypes  had an average LD of r2=0.124, with LD decaying rapidly over short distances and more moderately over long distances [2=0.2 between markers were more accurate than models with fewer markers and lower densities. Future analysis of LD in macadamia could employ the use of an updated macadamia reference genome (45) to determine the distribution of markers across chromosomes, and include corrections for population structure and cryptic relatedness.LD between markers and genes controlling target traits is essential for GS . Previouistances . These ristances , 38. Incistances , where mGenetic recombination occurs with successive generations of breeding, which may affect the linkage between markers and genes controlling target traits . FurtherThe results of this study indicated that genetic gain in macadamia breeding was particularly influenced by the length of the breeding cycle. Genotyping seedlings at a very early age, for example using their first leaf after germination, to identify high-yielding individuals through GS could halve the length of the SPT. Subsequently, elite trees could be cross-pollinated to produce the next generation as soon as they begin to flower, which is usually around the age of four. From there, clonally replicated trees could be phenotyped for other economically important traits, and candidate cultivars identified using a selection index. Similarly in apples, Muranty, Troggio  suggesteIn their review of GS in apple by Kumar et al. , 55, vanThe opportunity to employ GS in a wider range of crops is increasing with declining genotyping costs and advancements in technology , 51, 57.Currently, costs involved in genotyping may restrict the implementation of GS in the Australian macadamia breeding program. To reduce genotyping costs, delaying GS to deploy on a smaller population size may be a viable option, similar to a strategy proposed by Gardiner, Volz ; to reduFuture work employing GS to increase genetic gain in macadamia could investigate other economically important traits, such as tree size. In the same population as the current study, O'Connor et al.  found 16Further work could also include multi-trait models to investigate whether the inclusion of additional traits, such as trunk circumference and nut weight, increases the accuracy of yield prediction. Jia and Jannink  found thFinally, future GS analyses could involve more genetic markers and/or more evenly-distributed markers across the genome. This approach may ensure that small-effect loci are captured, since LD in macadamia decays rapidly over short distances . With thWe found that genomic prediction accuracy of nut yield in macadamia in randomly-grouped individuals was moderate, at r=0.57, and similar to the accuracy of traditional breeding. Prediction accuracy across unrelated populations (r=0.14) was lower than for prediction across randomly-grouped individuals. However, due to the relatedness in parental germplasm between subsequent breeding generations, a realistic prediction accuracy would likely be similar to that of randomly-grouped rather than family-grouped individuals. Additionally, we believe that this study is the first to estimate heritability of yield stability across years for a nut tree, as well as genomic prediction for this trait. Genetic gain for yield using GS (474g/year) was more than double that of traditional breeding methods (226g/year), largely due to the generation length being halved in GS. Our results indicate that GS is a viable option to increase genetic gain of yield in macadamia, though validation in a separate population is required. Further research and validation into the use of marker-assisted selection for other key traits in the seedling stage, including kernel recovery and tree size, are needed. Additionally, increasing the number and spread of markers across the genome may capture more causal polymorphisms through LD and lead to higher prediction accuracy.This study involves a subset of individuals from a progeny population in the Australian industry macadamia breeding program, from which seedlings were produced, established and assessed in field trials by Horticulture Australia Limited, CSIRO and the Queensland Government. The entire progeny population consisted of approximately 2000 seedlings across 141 full-sib families from crosses between 47 publicly available parents, with 136 progeny per family (mean 14) . Trees wAs described by OConnor, Kilian , 295 unrHistorical data were used in this study. Yield was evaluated on an individual tree basis from ages 5 to 8 after planting. Each year, nuts-in-husk were manually harvested from the ground in multiple harvests from February to August. A final strip harvest was undertaken at the end of the season, in which the nuts remaining in the tree were removed with poles and hooks. Nuts were dehusked mechanically and weighed to obtain a wet nut-in-shell weight. For each tree, a 1kg sample was taken (where available) and dried to approximately 1.5% moisture content at 35C for 48h, 45C for 48h, and 55C for 48h, based on protocol by Prichavudhi and Yamamoto . SamplesYield was the standardised yield of an individual tree in 1 year; Site was the fixed effect of the location of the tree ; Block was the fixed effect of planting block within a Site; Type was the fixed effect of method used to propagate the tree ; Number Neighbours was the fixed effect of the number of trees on either side of that tree within the planting row, to allow for influence on phenotype of gaps created by the death of neighbouring trees; Age was the fixed effect of age after planting of the tree; Year was the fixed effect of calendar year that yield was harvested (as trees were planted in different years across the sites); Tree was the random effect of individual tree (with no replication of genotypes) within Site, without any pedigree or genetic relationship information, and error was a vector of random deviations e~N  using yield data across the four years (ages 5 to 8):PstI and HhaI restriction enzymes and barcoded adaptors. After PCR, samples were pooled, applied to c-Bot (Illumina) bridge PCR, and then sequenced using Illumina Hiseq2500 for 77cycles. Sequences were processed using proprietary DArT pipelines, with SNP markers detected based on parsing sequence clusters. Missing calls were imputed using the probabilistic principal components analysis (PPCA) method [This study used genetic markers obtained as described by OConnor, Kilian  and brie) method  with 97.Accession is the tree effect modelled as the additive genetic effect of the individual, assumed random ~ N , and SiteTree is the permanent environment random effect of each tree within site across years, uncorrelated among trees, assumed random ~ N  was constructed among all individuals using the 4113 SNPs, as per VanRaden  and detaYield SD is the standard deviation of PBLUPs for ages 5 to 8 across all sites.To determine the accuracy of genomic prediction for yield stability over multiple years, GEBVs were obtained using the following model:2) of average yield was made based on the variance components of Eq. 2 was calculated as An estimate of genomic narrow-sense genomic heritability h of averaThe prediction accuracies of the GEBVs from the models above were determined using five-fold cross-validation (CV). In turn, 20% of phenotypes were masked (set to missing) in a validation set, and data for the remaining 80% of individuals were used as a training set to train the model and predict the masked values. This process was repeated five times until all subsets were used in the validation set, with each individual used only once in the validation set.Individuals were assigned to one of five groups for the five-fold CV using two grouping techniques for predictions: random and related family groups. For the random CV, individuals were selected for the training and validation group at random (randomly-grouped). Here, full-sibs were randomly allocated across the training and validation groups, and so predictions were performed on individuals that were related to the training population. For the second method, individuals were grouped by family and related families (those with common parents) and grafted parents (family-grouped), to give approximately equal-sized groups. Thus, entire full-sib families were either in the reference set or in the validation set, and predictions were performed on families unrelated to the training population (unrelated population). This second method represents a more extreme version of the application of GS, where the two populations are not closely related.2) was estimated from Eq. Prediction accuracy (r) for each of the five CVs was calculated as:mentclass2pt{minimi is selection intensity as a function of the proportion of the population selected, r is square-root of yield heritability for traditional breeding or the prediction accuracy of the GS model, and L is generation length in years. Here, is the genetic standard deviation, which was calculated as the standard deviation of PBLUPs from Eq. i=2.665 and 2.338, for 1 and 2.5% selected, respectively, as taken from Falconer and Mackay [A simple comparison of breeding strategies was made to demonstrate how GS could be effectively incorporated into the macadamia breeding program to reduce selection time and increase genetic gain. Genetic gain  was calculated for yield for traditional breeding and GS methods using the following equation derived from Falconer :6\docummentclass2pt{minimd Mackay . We assuAdditional file 1: Supplementary Table1. Variance components for phenotypic BLUPs derived from Eq. Supplementary Table2. Variance components for genomic BLUPs derived from Eq. Supplementary Figure 1. Boxplots showing the observed relationship distributions from the GRM for: full siblings, half siblings, parent offspring, parent-parent, and unrelated relationship groups. Supplementary Figure 2. Boxplot showing the observed relationship distributions from the GRM for the diagonals (identity).


Aesthetic chills, broadly defined as a somatic marker of peak emotional-hedonic responses, are experienced by individuals across a variety of human cultures. Yet individuals vary widely in the propensity of feeling them. These individual differences have been studied in relation to demographics, personality, and neurobiological and physiological factors, but no study to date has explored the genetic etiological sources of variation. To partition genetic and environmental sources of variation in the propensity of feeling aesthetic chills, we fitted a biometrical genetic model to data from 14,127 twins (from 8995 pairs), collected by the Netherlands Twin Register. Both genetic and unique environmental factors accounted for variance in aesthetic chills, with heritability estimated at 0.36 . We found females more prone than males to report feeling aesthetic chills. However, a test for genotype x sex interaction did not show evidence that heritability differs between sexes. We thus show that the propensity of feeling aesthetic chills is not shaped by nurture alone, but it also reflects underlying genetic propensities. They are frequently self-reported by individuals during peaks of hedonic9 and emotional experiences14, such as sadness and happiness15, being moved14, feeling touched10, and the sensation of awe6.Aesthetic chills16), with participants reporting sidewise sensation of thrills in the upper dorsal part of the neck, or in the spine and back5, shivers down the spine17, tingling sensations in the arm18, and more general diffuse bodily reactions10. Bodily reactions that are associated consistently across studies with concurrent dynamic peripheral changes, mainly by increases in phasic skin conductance, and changes in heart rate, and less consistently with drop in temperature or increase in respiratory rate, occur before, during and after chill onset23. Besides being associated with self-reported and somatic manifestations, aesthetic chills usually correlate with activity in brain regions that play a role in the representation of visceral and somatic states24, such as the bilateral insula (Ins)25 and the anterior cingulate cortex7, as well with several other brain regions that overlap with general reward mechanisms in the basal ganglia25, and in the orbitofrontal cortex7, plus other areas such as the supplementary motor area25, the thalamus, and the cerebellum25.An extensive body of research has documented the physiological and neurobiological correlates of aesthetic chills, although sample sizes tend to be small. Chills occur with somatic manifestations  tend to experience more chills, as measured both by self-report36. Further, preliminary evidence obtained on small samples of individuals, suggests that the individual tendency of experiencing chills also correlates with structural brain differences, such as higher tract volume between the superior temporal gyrus and both the anterior insula and the medial prefrontal cortex20, and resting physiological arousal, such as higher resting state skin conductance level30.Variation in the frequency of experiencing chills has also been accounted for by functional brain differences. For example, data obtained from resting-state functional Magnetic Resonance Imaging (rs-fMRI) on 1000 subjects indicates that individuals more prone to experiencing chills have enhanced connectivity between the network composed by the Ins and the cinglulate cortex (anterior and posterior cingo-opercular network) with ventral default network, by the latter network with the anterior visual and the posterior temporal networks, by the lateral and the dorsal default networks, and by a decrease in functional connectivity between the cerebellum and the somatomotor cortex31, modulation of negative affect21, and stress-related growth37 have been found in the past. For example, Johns et al.37 recently highlighted, in a moderately large sample, the relationship between proneness to feel aesthetic chills to the tendency of approaching stressful events in a way that facilitates positive growth.Beyond physiological correlates of chills, several psychological correlates, such as empathy43, many of which specifically focused on narrow aspects of aesthetics . These studies applied the Classical Twin Model (CTM) to distinguish genetic from environmental influences. Two studies from the 1970’s (Barron39) focused on individual differences in aesthetic sensitivity –defined by the authors as the extent to which one individual’s aesthetic judgment is in line with the opinion of experts- for paintings and drawings in a small sample of twins. The authors found contradicting results, with non-trivial heritability estimates ranging from 55 to 67% in the first study39, and trivial estimates in the latter38. Most recent studies from Zietsch et al.43, Germine et al.41, and Sutherland et al.42 focused on aesthetic preferences for faces. Heritability estimates were 33% for specific preferences for dimorphic male traits43, and 22–30% for more general individual preferences for faces respectively. The only study we are aware of going beyond preferences, from Butkovic et al.40, found 40% of individual differences in flow proneness from music—a subjective, pleasurable, and fully absorbing experience—to be explained by genetic factors.The etiological sources of variation in aesthetic chills, i.e., how much of the observed variation can be explained by genetic and environmental factors, is yet unknown. Such lack of knowledge about the etiology is not unique to aesthetic chills alone but is shared among many studies on aesthetics. To our knowledge, there are only a few empirical investigations addressing the etiological sources of variation underlying individual differences in aesthetic experiences/appraisal44 as a proxy for the propensity of feeling chills. This item was selected, because explicitly asking individuals if they feel chills is a good indicator of actual experienced chills measured in experimental settings26. For example, Colver and El-Alayli26 found the subjective reports of the experience of chills correlate with chills measured by a combination of button presses and galvanic skin responses (r = 0.90). Kleipzig et al.25 found a modest correlation between self-reports of how often individuals experience shivers and report chills while undergoing fMRI (r = 0.63). Further, Item 43 seems capable of tapping into individual differences which are highly shared among cultures, being the first or the second best predictor of OE1; to significantly correlate (r = 0.29) with chills measured by the co-occurrence of self-reported feelings and physiological changes26; and to capture neurophysiological differences between individuals36, by being significantly associated , collected in 2004 (NTR survey 746) on 6760, in 2009 (NTR survey 847) on 10,176 and in 2013 on 9419 twins (survey 1048). In all surveys, participant consent was obtained . Written informed consent was obtained from individuals when volunteering to become a participant in the NTR. The studies were in accordance with the declaration of Helsinki and were approved by the Central Ethics Committee on Research Involving Human Subjects of the VU University Medical Centre, Amsterdam, an Institutional Review Board certified by the U.S. Office of Human Research Protections . For ANTR Survey 7: METC 03/181; for ANTR Survey 8: METC 2008/244; for ANTR Survey 10: METC 2012/433. After excluding 320 pairs, for which no data for the item 43 were available across surveys, and data from 5 twin pairs due to missing information on age for both twins, we analyzed data on 14,127 twins , ranging from 14 to 97 years old, with mean age = 30 (SD = 13). Our procedure for data selection when multiple surveys had been completed, is detailed below. Table 45. The outcomes of linear discriminant analysis of the training set were used to predict zygosity in the testing set (N = 1362). Zygosity prediction based on survey items was accurate in 95.9%. The item that distinguished best between MZ and DZ twins was “Were you each other’s spitting image as children?” (see Appendix. Zygosity in45 for details.) Test-reliability correlations for the twins who have completed more than one survey (N = 6923) were calculated for males and females separately. To avoid confounding effects due to familiar resemblances, data from one randomly selected twin per family were analyzed.The data were obtained from the Netherlands Twin Register (NTR), a longitudinal cohort established in 1987 by the department of Biological Psychology at the Vrije Universiteit Amsterdam. Data on the self-reported propensity of feeling aesthetic chills were collected by mailed surveys (see44). The NEO-FFI consists of 60 items rated on a five-point scale . The Openness to Experience (OE) scale contains an item (43) “Sometimes when I am reading poetry or looking at a work of art, I feel a chill or wave of excitement” which was selected as a proxy for the propensity of experiencing aesthetic chills.Self-report of chills was obtained from the short version of the NEO-personality Five Factor Inventory  we prioritized complete answers from twin pairs, i.e., twin pairs were selected when both twins reported scores for the Item 43 on one of the surveys; (2) if one of the two twin’s response was missing for all three surveys, we randomly selected a survey with the response for the other twin; (3) if twins took part in different surveys, we randomly selected data for the pair from one of the complete surveys. Of the reported combined sample size, 5132 were twin pairs who both completed the survey, of which 2790 were MZ, 1306 were same-sex DZ (DZss), and 1036 were opposite-sex DZ (DZos) twin pairs.49. The A component captures all additive effects of alleles across genetic loci, while the D component captures non-additive and interactive effects of alleles at contributing genetic loci. For the environmental components, the C captures all environmental factors that are shared between twins. When twins are raised together, home-environment effects can be captured by C. The E component captures all factors that are non-shared between twins nor explained by genetic factors. Thus, the E component captures all the unexplained unsystematic variance, comprising measurement errors.We analyzed the data using the CTM to estimate the proportion of variance explained by genetic and environmental factors. Within the CTM, the observed phenotypic variance (P) can be decomposed into additive genetic (A), dominance genetic (D), common environmental (C), or unique environmental (E) components51). MZ twins thus share 100% of both additive as well as dominance genetic effects. DZ twins, on the other hand, derive from two fertilized eggs and share only 50% on average of the additive genetic effects, and only 25% of the dominance genetic effects (see52). Thus, within the CTM, the correlation between the A component within MZ twin pairs is equal to 1, while within DZ twins is equal to 0.5. Similarly, the correlation between the D component within MZ twin pairs is also 1, while for DZ pairs is 0.25. Further, since the C component captures all shared environmental effects and the E component captures all non-shared effects, the correlation for both MZ and DZ twins are set to 1 for the C component and 0 for the E component. As a consequence of these premises, when MZ twins resemble each other more than DZ twins on a given trait the heritability of such trait is considered to be non-trivial. Here, it is important to note that a model with four components cannot be statistically identified within the CTM, given that there is only enough information to estimate three components. Therefore only A, C and E or A, D, and E components can be estimated simultaneously52. A rule of thumb is to assess the twin correlations and fit an ACE model accordingly when the MZ correlation is not larger than twice the DZ correlation. In comparison, an ADE model is fitted when the MZ correlation is larger than double the DZ correlation. Components within a model  are then dropped  to assess whether they contribute to phenotypic variation. If the model with fewer components  fits the data as equally well as the model with more components, then the dropped component is evaluated to be not explaining any significant phenotypic variance.The decomposition of the variance is possible because different genetic association exist for MZ and DZ twins. Since MZ twins derive from the same fertilized egg their genetic material is ~ 100% shared , we expect MZ male-male correlations to be equal to MZ female-female correlations and DZ male-male, and female-female correlations also to be similar. When there is no difference in the expression of the genes in men and women , we expect that the correlation in same-sex DZ twins is equal to that of opposite-sex DZ twins. Under the assumption of no sex effects, the amount of phenotypic variance is expected to be accounted for by a similar amount of A, D, C, and E, and similar genes are expected to influence phenotypic variation in both sexes56, in R-Studio, R version 3.6.2. Significance of the covariate (age), birth order effect and mean differences across zygosity were tested by a series of models nested inside the saturated model. The goodness of fit of the model was evaluated by 1) likelihood ratio, that is by the difference in minus twice the value of the log-likelihood (− 2LL) between the two models, which has a χ2 distribution, with the degrees of freedom equal to the difference in the number of parameters, and by 2) the Akaike’s Information Criterion (AIC), by keeping the model with the lowest AIC as the best fitting model.The models were specified in OpenMx version 2.17.253, the significance of differences in means, variances, and covariances across sexes was tested by a series of models nested inside the saturated model. A sex-limitation model was evaluated to examine whether quantitative sources of etiological variation statistically differed between the sexes by constraining variance components to be equal for men and women. The goodness of the fit and the significance of the sub-models with variance components constrained to be equal across sexes were compared to the full model. Qualitative sex differences were tested by allowing genetic correlations (rg) between DZos to be freely estimated. The goodness of the fit and the significance were obtained by comparing the more parsimonious model in which rg within DZos was constrained to 0.5. Mean, standard deviations, 95% CI, and within twin pair correlations were estimated in a saturated model. A variance decomposition model was compared to the saturated model. Subsequently, we test nested models, which were obtained by constraining one of the genetic or environmental variance components to zero. Heritability estimates were obtained as the proportion of genetic variance over the phenotypic variance.Genotype x sex interaction was tested for both quantitative sex differences  and qualitative sex differences  in etiology. First, similarly to Vink et al.r(1488) = 0.58  and r(578) = 0.61  between survey 7 and survey 8 for female and male respectively, r(2118) = 0.58  and r(830) = 0.52  between survey 8 and survey 10 for female and male respectively, and r(1078) = 0.58  and r(410) = 0.51  between survey 7 and survey 10 for female and male respectively .Test–retest reliability was obtained for data from surveys 7 and 8 (5 years apart), surveys 8 and 10 (4 years apart), and surveys 7 and 10 (9 years apart). Single-item reliability estimates range from 32.The distribution of the item 43 scores is given in Fig. r = 0.39  and r = 0.35  for MZ male and MZ female respectively, r = 0.07  and r = 0.21  for DZ male and DZ female respectively, and r = 0.14  for DZos  = 255.07, p < 0.001). On the other, removing birth order and subsequently zygosity mean and variance differences did not deteriorate the overall model fit , indicating that mean and variance were not different across the first and the second-born and across zygosity. As expected, constraining mean scores to be equal across sexes resulted in a deterioration of the fit (− 2LL = χ2(17) = 113.68, p < 0.001), However, constraining variance to be equal across sexes, as well as constraining covariance to be equal across DZss and DZos, did not deteriorate the overall fit of the model (− 2LL = χ2(17) = 6.64, p = 0.99 and − 2LL = χ2(20) = 13.93, p = 0.83, respectively).Twin correlations from the saturated model, were 0.35  and r = 0.14  respectively. The pattern of correlations between DZss and DZos indicates an absence of evidence of genotype x sex interaction effects  = 106.32, p =  < 0.001). However, constraining DZos rg to be equal to 0.5 did not deteriorate the model fit (− 2LL = χ2(1) = 2.16, p = 0.14). This indicated etiological sources of variation to not qualitatively differ across sexes. Moreover, constraining variance components across sexes to be equal did not deteriorate the model fit (− 2LL = χ2(3) = 2.19, p = 0.53). This indicated etiological sources of variation to not quantitatively differ across sexes either.Phenotypic correlations for DZss and DZos, extracted from the model in which covariance across sexes were constrained to be equal (Sex:DZss same covariance model), were  r = 0.37  within MZ and r = 0.15  within DZ twin pairs. Phenotypic correlations suggested once more the AE model as the most appropriate model to describe the data.Phenotypic correlations, obtained from the most parsimonious model Table p ≤ 0.001). As expected, the final model AE  equal to 2.03 for males and 2.25 for females (SD = 1.13), was the most parsimonious well-fitting one (− 2LL = χ2(1) ≤ 0.001, p ≥ 0.999). As shown in Table The final genetic univariate model fitting results and comparison are presented in Table  AE Fig. , with meThis research investigates and reports genetic and environmental sources of variation for the propensity of feeling aesthetic chills. We analyzed the variance of the NEO-FFI Item 43: “Sometimes when I am reading poetry or looking at a work of art, I feel a chill or wave of excitement”, which is a proxy measurement for the propensity of feeling aesthetic chills. We found that 36% of the variance in feeling aesthetic chills can be explained by additive genetic factors and the remaining 64% by environmental sources of variation. If we consider these results in the view of the test–retest reliability, which we obtained for data from surveys 4, 5 and 9 years apart, which ranged from around 0.51–0.61, the environmental variance reflects to a substantial extent reliable non-genetic causes of individual differences.57. Moreover, we confirmed, in the largest sample used to investigate the role of demographic factors on chills to date, that females and older individuals are more prone than males and younger individuals to experience aesthetic chills. This is in line with some of the results previously obtained from the general population29. Additionally, it is also important to note that the directionality of the sex effect as found in this study was also consistent, as far as we know, with all of the studies that reported non-significant trends toward females reporting more frequent chills than males33.A lack of shared environmental sources of variation in the propensity of feeling chills should not come as a surprise, given that variation in most of the psychological human traits investigated so far show no relationship with shared environmental effects15, our results are only partially supporting his hypothesis. Panksepp argued that chills are a genetically influenced trait that “resonate with ancient emotional circuits that establish internal social values”15, and that they probably evolved over time from a need for physical closeness induced by the separation between a mother and her infant. Such mother-infant relationships should have produced an enhanced selective propensity of experiencing chills in females. Our findings that variation in chills is influenced by genetic factors, and that females are more prone to experience chills, therefore partially support this hypothesis. However, our findings that no qualitative, nor quantitative, genotype x sex interaction effects affect variation in propensity on aesthetic chills do not support the separation-call hypothesis. Indeed, in line with results on a majority of other human traits58, our results are consistent with the hypothesis that the same genetic sources of variation in males and females influence variation in the propensity of feeling aesthetic chills.We would like to note that, although apparently consistent with the separation call phenomena proposed by Panksepp36 argued that the enhanced connectivity between sensory and salience/default networks as found in their study, based on resting-state fMRI data of 1000 subjects from the Human Connectome Project (HCP), indicates that individuals who are more prone to experience chills from art and poetry, as measured by the item 43, are also individuals that can better integrate sensory information with internal emotional experiences. Moreover, preliminary evidence on a small sample recently indicated that augmenting sensory signals that mimic the physical experience of aesthetic chills can enhance individual social-affective cognition .We believe our results bring into focus questions that go beyond the descriptive nature of this study. Williams et al.36 or is it more a priori predisposition that makes individuals better at integrating sensory information with their internal states, or alternatively more sensitive to bottom-up somatosensory signals, that makes them more likely to reach such peaks of emotional-hedonic experiences? Clearly, further genetic informative studies, such as cross-trait cross-twin studies displaying both proneness of feeling chills and, for example, functional or structural brain metrics, are needed to answer these questions. However, our finding that approximately one-third of the variance in the propensity of feeling chills can be explained by genetic influences sheds some light on such questions.Yet, how can one reinterpret such results in light of our present findings? Is it environmental exposure over one’s own lifetime to art and poetry that is causally shaping the connectivity as seen in Williams et al.61, we were constrained by what measurements were available. This reduced the complexity of the variation in the propensity to feel aesthetic chills to variation in a single item. Additionally, it is worth noting that the NEO-FFI item 43 explicitly asks for the propensity of feeling chills, or wave of excitement, only from art or poetry. As such, Item 43 neglects the possibility of drawing any distinction between different types of chills63 and omits many other possible causes of chills. This limited our capacity to obtain a more nuanced estimate of aesthetic chills. For example, although a previous study found the item 43 to be correlated with the number of chills experienced from music26, further studies are still needed to claim that etiological sources of variation influence the propensity of feeling chills from music specifically. Moreover, even though the test–retest reliability for the item 43 may be considered good for a single item, it was not perfect. However, if this had any impact on our results it was through increasing the measurement error, which by definition is included in the estimate for the unsystematic environmental sources of variation. As such, our estimates on the effect of additive genetic variation should be considered to be, at worst, a lower bound for the real effect of genetic influence on the propensity of aesthetic chills. Another consideration is that the study of the etiology of a trait detached from any personality background represents a rather unorthodox approach to etiological studies. Our approach is motivated by the specific interest to what item 43, as highlighted above, pertains to be, that is, variation in the proneness to aesthetic chills and not by its relative weight on OE. Although not common, such an approach  has found support in recent literature64. For example, Franic et al.64 showed, in a partially overlapping sample to the one used in this study, the role of independent genetic contribution on the variation of single items by finding evidence against the hypothesis of personality factors as full mediators of genetic effects. Further, Williams et al.36, while exploring the association of Item 43 with the strength of the functional connections between different resting-state networks, found that an item being part of a broader personality factor can be more strongly associated with variability in a biological trait of interest than a personality factor itself.Further, it is important to consider the limitations of our study. As other studies investigating complex traits in large samples65 . It would be tempting to speculate on the role that genes coding for proteins playing in such neuromodulatory mechanisms have on the genetic variation as found in this research. However, the recent past taught us that heritability estimates from twin studies are usually explained by thousands, if not hundreds of thousands of tiny genetic effects, even for traits for which the causal chain from genes to behavior seems to be shorter than expected (see for example69).We thus warn against any speculation on single putative causes, and thus call for further genetic informative studies. Genome wide association and functional annotation studies would be especially useful in exploring the whole genome in order to inspect which genetic variations can be associated with variation in the propensity of aesthetic chills, and to inspect whether genetic variations associated with the propensity of feeling chills are enriched in brain tissue or elsewhere in the body. Further, although our study focused solely on the propensity of feeling aesthetic chills, its relationship with any other item is not uninteresting per se. For example, item 43 shares its etiology with other OE  and non-OE  personality items, making it an interesting candidate for further descriptive associations studies.Finally, it is important to note that it would be premature to reach any conclusions regarding the putative mechanisms underlying the genetic factors influencing aesthetic chills on the basis of the findings of this study alone. Some theoretical work makes predictions regarding biological mechanisms that might contribute to the experience of aesthetic chills. For example, under the knowledge-instinct theoretical perspective, positive chills emerge when the similarity between sensory information and the a priori mental representation of such information is maximized, a phenomenon that has been attributed to the modulation of the activity in the neural circuitry playing a role in the experience of chills, mainly via opioidergic or/and dopaminergic transmission57.Aesthetic chills are a somatic marker of peak emotional hedonic responses. Previous inconsistent evidence suggested that demographic, and somewhat more consistent evidence has suggested that personality and neurobiological factors, can account for part of the observed variation in feeling chills. Here, we confirmed that females are more prone than males, even if to a small degree, to experience aesthetic chills and that older individuals tend to report experiencing chills more than younger ones. Critically, we revealed that genetics play a role in the individual differences in the propensity of feeling chills, thus indicating that the tendency of experiencing hedonic peaks of emotional reactions to art and poetry is not shaped by nurture alone, but is also influenced by genetic predispositions, as thousands of other human traits are


Polygenic risk scores (PRSs) have wide applications in human genetics research, but often include tuning parameters which are difficult to optimize in practice due to limited access to individual-level data. Here, we introduce PUMAS, a novel method to fine-tune PRS models using summary statistics from genome-wide association studies (GWASs). Through extensive simulations, external validations, and analysis of 65 traits, we demonstrate that PUMAS can perform various model-tuning procedures using GWAS summary statistics and effectively benchmark and optimize PRS models under diverse genetic architecture. Furthermore, we show that fine-tuned PRSs will significantly improve statistical power in downstream association analysis.The online version contains supplementary material available at 10.1186/s13059-021-02479-9. Accurate prediction of complex traits with genetic data is a major goal in human genetics research and precision medicine . In the p-value threshold in traditional PRS, the penalty strength in penalized regression models, and the proportion of causal variants in LDpred [With great popularity, there also come great challenges. Prediction accuracy of PRS remains moderate for most phenotypes . Methodsn LDpred . Tuning n LDpred . HoweverWe introduce PUMAS , a novel method to fine-tune PRS models using GWAS summary data. As a general framework, PUMAS can conduct a variety of model-tuning procedures on PRS, including training-testing data split, cross-validation, and repeated learning. Through extensive simulations on realistic genetic architecture, we demonstrate that the performance of PUMAS is as good as methods based on individual-level data. Additionally, we apply PUMAS to GWAS traits with distinct types of genetic architecture and validate our results using well-powered external datasets. Furthermore, we systematically benchmark and optimize PRS for numerous diseases and traits and showcase the immediate benefits of fine-tuned PRSs in downstream applications.R2) of PRS using summary statistics in the validation set so that we can select the best model based on its superior performance (Eq. (20), the “Here, we outline the PUMAS framework. Detailed derivations and technical discussions are included in the “p-values. Next, we applied PUMAS to perform 4-fold repeated learning on marginal association statistics and selected the optimal number of SNPs to include in the prediction model by maximizing the average R2 across folds. Additionally, we implemented a traditional repeated learning approach with the same simulated individual-level data as a reference. Details about our implementation of PUMAS and repeated learning are described in the “We conducted simulations using genotype data from the Wellcome Trust Case Control Consortium (WTCCC) to investigate if PUMAS can achieve similar performance compared to classic model-tuning procedures. A total of 15,567 individuals and 322,235 genetic variants were included in the simulation after quality control. We simulated phenotype data with a heritability of 0.5, varying assumptions on SNP effects and proportion of causal variants the “” sectionp-value cutoffs in PRS models and validate their performance on large independent cohorts. First, we applied PUMAS to a recent GWAS of educational attainment (EA) conducted by the Social Science Genetic Association Consortium  [N = 54,162) [Next, we demonstrate our method’s performance using a gold-standard approach—we apply PUMAS to the summary statistics from well-powered GWASs to select the optimal 742,903) . 4775 sa742,903)  and 10,2742,903)  were use 54,162)  to optim 54,162)  from the 54,162) .p-value cutoffs of 0.8, 0.8, and 0.7 were the most predictive models suggested by PUMAS, HRS, and Add Health cohorts, respectively. Results on AD were also consistent between PUMAS and external validations. The optimal p-value cutoffs suggested by PUMAS, ADGC validation, and UK Biobank validation were 5e−6, 1e−9, and 1e−10, respectively. PRS models based on p-value cutoffs more stringent than 1e−5 showed good predictive performance in two validation sets for AD. Notably, as more SNPs are included in the model, the predictive performance of PRS sharply declines. Our model-tuning results based on GWAS summary statistics accurately predicted this pattern. Additionally, since we used an AD-proxy phenotype in the UK Biobank, the reduced predictive R2 is expected. But the trend of predictive performance remained consistent with the validation result in case-control data from the ADGC.Our summary statistics-based analyses showed highly consistent results compared with external validations  [N value as the sample size for the validation dataset and used the remaining samples of each SNP in the training subset. Overall, PUMAS results showed consistent patterns under these four scenarios  cholesterol from the Global Lipids Genetics Consortium   and the p-values based on the full sample have been used during LD clumping, directly applying the same model-tuning methods to clumped data may lead to information leak and overfitting. We applied PUMAS to clumped summary statistics of the IGAP 2013 AD GWAS  and 0.0034 (62.5% improvement) compared to PRSs with p-value cutoffs of 0.01 and 1, respectively , smoking behavior (cigarettes per day), and AD. PRSs with fewer SNPs showed superior performance for these traits. Among immune diseases, systemic lupus erythematosus, primary biliary cirrhosis, rheumatoid arthritis, multiple sclerosis, and eczema all favored a sparse model, while the optimal PRSs for inflammatory bowel diseases and celiac disease had substantially more SNPs. We also note that molecular traits such as blood lipids and 25-hydorxyvitamin D favored sparse PRS models, possibly due to stronger genetic effects and more homogeneous genetic mechanisms. These results also shed light on the differences in the predictive power of diverse types of diseases and traits. PRSs for height, systemic lupus erythematosus, inflammatory bowel diseases, and schizophrenia showed substantially better predictive performance, while the R2 for most behavioral/social traits remained moderate despite the large sample size in those studies. We also investigated the computational efficiency of our approach in real GWAS applications. Using only one CPU, PUMAS has an average computation time of 8.3 s and maximum of 38.23 s in the analyses of 65 traits  [p-value cutoff of 0.01. We applied the BADGERS [N = 63,926) [N = 318,773) [Finally, we demonstrate that fine-tuned PRS will lead to power gain in association analysis. We generated PRSs for 211 neuroimaging traits based on two recent studies conducted using samples from the UK Biobank (ctively) , 29. We  BADGERS  approach318,773) , 26. Samp = 1.7E−05) and axial diffusivities (p = 2.7E−05) whereby genetic risk for worse white matter integrity in the fornix was associated with risk of AD. No significant associations were identified using PRSs with an arbitrary p-value cutoff . Additionally, effect size estimates for top associations were consistent in two independent AD GWASs  [The complete association results of 211 neuroimaging traits with AD are summarized in Additional file off Fig. A. AssociASs Fig. B. Althou228,951) . ResultsFine-tuning PRS models with GWAS summary statistics has long been considered an impossible task. In this work, we introduced a statistical framework to solve this challenging problem. First, using GWAS summary data as input, PUMAS simulates training and validation summary statistics without accessing individual-level information. Then, PUMAS evaluates and optimizes PRS models on the simulated validation summary statistics. Both steps in the PUMAS framework are statistically rigorous, computationally efficient, and highly novel. Through simulations and analysis of real GWAS data with diverse genetic architecture, we demonstrated that PUMAS can effectively conduct sophisticated model-tuning tasks using GWAS summary statistics. We also showed that optimizing PRSs improves the statistical power in downstream association analysis and identified neuroimaging traits significantly associated with AD.This work will bring multiple advances to the field. First, it is no longer necessary to leave one dataset out in the GWAS for model-tuning purpose. With PUMAS, researchers can safely use effect size estimates from the largest available GWAS for PRS model training, which will lead to improved prediction accuracy. Second, when an independent validation set is not available, most studies in the literature select tuning parameters using one of the two strategies. Some studies fine-tune PRSs on testing samples that are used again in downstream applications, creating an overfitting problem, while other studies use a subset of testing samples to tune the model, reducing the sample size and power in the testing data. PUMAS allows researchers to apply fine-tuned PRS models to the full testing samples, thus avoiding overfitting and improving statistical power. Third, selecting the optimal tuning parameter is not the only application of PUMAS. Given a PRS model, our method allows researchers to calculate cross-validated predictive accuracy, providing a systematic approach to benchmark model performance without requiring external samples.p-value cutoff that needs to be tuned. Despite the simplicity, it remains one of the most widely used PRS models in the field. However, more sophisticated PRS methods have emerged [R2 metric is less interpretable. A future direction is to explore other metrics  to quantify prediction performance for binary traits. Third, our method assumes that GWAS is performed on independent samples. It is an open question whether PUMAS can be directly applied to family-based GWAS results [Our proposed framework has some limitations. First, our analyses so far have only focused on a classic PRS model with pruned SNPs and a varying  emerged –39. Futu results –43.Our results have provided strong evidence that it is possible to fine-tune PRS models with GWAS summary data. This new approach, in conjunction with widely available GWAS summary statistics, will have a long-lasting impact on future PRS model development and genetic prediction applications.Y follows a linear model:We assume the quantitative trait X =  denotes the random vector of p SNP; β = T is a p-dimensional vector representing fixed SNP effect sizes; ϵ is the error term following a normal distribution with zero mean. Let y and x =  denote the observed N × 1 phenotypic and N × p genotypic data of N independent individuals. For simplicity, we assume y and xj’s are centered. The summary association statistics in GWAS are obtained from the marginal linear regressions. Then, for j = 1, …, p, we can denote the regression coefficients and their standard errors as follows:where j is the error term for the marginal linear regression of phenotype on the jth SNP and jth marginal regression. If we have access to the full data set, most model-tuning approaches involve randomly sampling a subset of N − n individuals as the training set, i.e., ytr)( and xtr)( and xv)⊤(ytr)( and xv)⊤(yv) and (v) to indicate whether any summary statistics are computed from xtr)⊤(ytr)( or xv)⊤(yv), Σ is a symmetric matrix whose diagonal and non-diagonal elements can be denoted asTo subsample summary statistics, we now estimate the covariance matrix of j = 1, …, p and i ≠ j. Here, βj) is typically very small in GWAS and Σ can be estimated withFor  Project . Taken twhere xtr)⊤(ytr) is the weight for SNPs in PRS. In a traditional PRS, marginal regression coefficients from GWAS are used as the weight values, i.e., R2, a commonly used metric to quantify PRS predictive performance, from subsampled GWAS summary data, but our method can be extended to other metrics  can be calculated aswhere .g., AUC ) as wellwhere Y does not affect model tuning, it affects the scale of R2 and is thus critical for interpreting the results. This term can be approximated byAlthough empirical variance of Y) is always greater than j, the gap between these two is negligible in real GWAS due to the small effect size of each individual SNP. Thus, a simple estimator for Var(Y) can beAlthough Var.In practice, we use the 90% quantile of λ that maximizes the predictive accuracy. In the simple setting we introduced above, we will generate summary statistics for training and validation datasets. After specifying a tuning parameter λ, SNP weights in PRS can be trained by applying the model to the training summary statistics. Then, the prediction accuracy R2 on the validation summary statistics will be a function of λ. Therefore, we can select λ so that it maximizes model performance.So far, we have introduced strategies to subsample association statistics on training and validation sets and evaluate model performance using GWAS summary statistics. Combining these two key steps, we will be able to perform model tuning using GWAS summary data. Suppose a PRS model uses GWAS marginal estimates R2 will be a function of the model and we can choose the best-performing model by optimizing R2More generally, if the goal is to compare different models, both the summary statistics subsampling and performance evaluation steps remain unchanged. In this case, R2 on the validation set) K times. The average R2 across K folds can be used to select the best model. Similarly, if K-fold cross-validation needs to be implemented, we can first independently simulate K − 1 sets of training subsample xtr, k)⊤, M is the total number of SNPs, and p is the proportion of causal variants. We chose two values of p  to represent sparser and more polygenic genetic architecture. Following the LDAK paper [α =  − 2, − 1, 0, 1, 2 to better evaluate the performance of PUMAS under various genetic architecture. Thus, in total, we conducted simulations under 10 different settings. In each setting, causal SNPs were randomly selected across the genome and the effect sizes of non-causal SNPs were set to be 0. Using these simulated effect sizes, we generated continuous trait values in GCTA [We conducted simulations using real genotype data from WTCCC. The WTCCC dataset contains 15,918 samples with 393,273 genotyped SNPs across the whole genome. We removed SNPs that are not available in 1000 Genomes Project Phase III European samples from the simulations since 1000 Genomes data were used as the LD reference panel. We excluded individuals with genotype missingness rate higher than 0.01 and removed SNPs that satisfy any of the following conditions: (i) having minor allele frequency less than 0.01, (ii) having missing rate higher than 0.01 among all subjects, and (iii) having AK paper , we then in GCTA . We then in GCTA . These sN samples into k non-overlapping folds, which is what a k-fold cross-validation does, repeated learning randomly selects k times to obtain an averaged prediction accuracy  across k folds of analysis for each prediction model. Here, we implemented a 4-fold repeated learning approach. In each fold, we randomly select 75% of WTCCC samples . We repeated this procedure 4 times and reported the average R2 for each PRS model. In this simulation, we consider PRS models with p-value cutoffs ranging from 1e−5 to 1.We compared PUMAS with repeated learning . Instead of partitioning To show that PUMAS can be applied to binary traits, we conducted additional simulations under settings described above. For each simulation setting, we kept the same SNP effects, heritability, and proportion of causal variants. However, instead of generating quantitative phenotypes, we simulated binary phenotypes using a population prevalence of 50% and case-control ratio of 1:1 in GCTA . We perfxTy, we performed additional simulations in WTCCC. We implemented a total of 8 settings with different sample sizes, heritability, and proportion of causal variants. We simulated quantitative trait values and performed marginal linear regression to obtain GWAS summary statistics. Then, we calculated and compared diagonal elements Σj and ji and j  and negligible off-diagonal elements . Imputed genotype data for Add Health  and HRS  were accessed through dbGap (phs001367 and phs000428) and the EA phenotypes were defined following the SSGAC GWAS [https://addhealth.cpc.unc.edu/wp-content/uploads/docs/user_guides/AH_GWAS_QC.pdf. For HRS, SNPs with imputation quality score < 0.8 were removed from the dataset. After matching samples with accessible phenotypic information, 4775 Add Health samples and 10,214 HRS samples with self-reported European ancestry were used to validate EA PRS. The IGAP 2013 AD GWAS  dataset was accessed through the IGAP website (http://web.pasteur-lille.fr/en/recherche/u744/igap/igap_download.php). GWAS summary statistics  for 7050 ADGC samples can be accessed through the NIAGADS database (NG00076). Predictive performance on ADGC samples was assessed using summary statistics-based R2. Following a recent paper, we constructed the AD-proxy phenotype in the UK Biobank based on each sample’s AD status, AD history of parents, whether parents are still alive, and parental age (or age at death) [N = 355,583; number of SNPs = 9,605,099) were accessed through the UKB. The UKB genotype data was imputed to the Haplotype Reference Consortium reference. We removed samples who are not of European ancestry and SNPs with minor allele frequency < 0.01 or imputation R2 < 0.9. In addition, we applied PUMAS to benchmark PRS performance on 65 GWASs. Details on these studies are summarized in Additional files GWAS summary statistics on EA was shared to us by Dr. Aysu Okbay. In this dataset, samples from Add Health, HRS, 23&me, and Wisconsin Longitudinal Study were excluded (GAC GWAS . Both Adr2) threshold of 0.1 using PLINK [p-value grid was used to search for the optimal p-value cutoff . We constructed the AD-proxy phenotype in the UK Biobank following a recent paper [GWAS results for imaging traits were accessed from nt paper . To avoint paper , age, sent paper . BADGERSnt paper . Meta-annt paper .Additional file 1: Supplementary notes and figures.Additional file 2: Table S1. Compare model tuning techniques in WTCCC simulation with continuous phenotype.Additional file 3: Table S2. Compare model tuning techniques in WTCCC simulation with binary phenotype.Additional file 4: Table S3. R2 based on PUMAS and external validations for EA and AD.Additional file 5: Table S4. PUMAS results on LDL cholesterol and EA with various sample size specifications.Additional file 6: Table S5. Predictive performance on external validation for AD PRS based on pruned and clumped summary statistics.Additional file 7: Table S6. Summary of optimized 65 GWAS summary statistics.Additional file 8: Table S7. Summary of improvement of optimized 65 GWAS summary statistics comparing to PRS with arbitrary p-value cutoff.Additional file 9: Table S8. Computation time for analysis of 65 publicly available GWAS summary statistics.Additional file 10: Table S9. Summary of fine-tuned PRSs for UK Biobank imaging traits.Additional file 11: Table S10. Cross-trait LD score regression intercept estimates for 211 imaging traits with UKBB AD-proxy GWAS.Additional file 12: Table S11. Complete association results between 211 neuroimaging trait PRSs and AD.Additional file 13: Table S12. Simulation settings for investigating the estimation accuracy of covariance of summary statistics.Additional file 14. Review history.