Paeonia rockii, one of tree peony species, is a precious emerging woody oil crop. However, in this valuable plant, the study of functional loci associated with yield traits has rarely been identified. Therefore, to explore the genetic architecture of 24 yield quantitative traits, the association mapping was first reported in 420 unrelated cultivated P. rockii individuals based on the next-generation sequencing (NGS) and single-molecule long-read sequencing (SMLRS).Allelic variation underlying the quantitative traits in plants is caused by the extremely complex regulation process. Tree peony originated in China is a peculiar ornamental, medicinal and oil woody plant. P. rockii accessions. We observed a high level of genetic diversity  and low linkage disequilibrium (LD) between EST-SSRs. Moreover, four subpopulations in the association population were revealed by STRUCTURE analyses. Further, single-marker association analysis identified 141 significant associations, involving 17 quantitative traits and 41 EST-SSRs. These loci were mainly from AP2, TCP, MYB, HSF, bHLH, GATA, and B3 gene families and showed a small proportion of the phenotypic variance (3.79 to 37.45%).The developed 58 pairs of polymorphic expressed sequence tag-simple sequence repeat (EST-SSR) markers from 959 candidate transcription factors (TFs) associated with yield were used for genotyping the 420 P. rockii, and provide a precious resource that reveals allelic variation underlying quantitative traits in Paeonia and other woody oil crops.Our results summarize a valuable collection of functional loci associated with yield traits in  P. rockii (S. G. Haw et L. A. Lauener) T. Hong et J. J. Li belongs to the Paeonia section Moutan DC., Paeoniaceae, which is originated from northwest China and has become one of the most representative species of tree peonies. The varieties originated from the species have been cultivated widely in China as the second-largest cultivar group of Chinese tree peonies, including about 300 cultivars [P. rockii also presents an advantage agronomic trait for its seed yield and unsaturated fatty acid contents in seeds in recent years [P. rockii has been rapidly extended as an emerging woody oil plant. However, how to improve the breeding efficiency and seed yield by using the molecular breeding methods has become a top priority. The breeding system of tree peonies is predominantly outcrossing and the cultivated cultivars are of hybrid origin [P. rockii will be required to shorten the breeding cycle and improve the production value effectively.Woody oil crops are economically essential crops globally because of their high oil content in their seeds and/or fruits, strong resistance, and stable yield. Now they have become the critical source for human edible oil, lubricants, biodiesel, cosmetics, paint and other industries , 2. P. rultivars . In addint years . TherefoGossypium hirsutum L.), 172 cultivars in China and 331 polymorphic SSRs were used for association mapping of yield-related traits. Totally, 93 significantly associated loci for seven yield traits were identified across more than one environment [P > 1.30, P < 0.05) [Hordeum vulgare, a total of 379 cultivars were used for genome-wide association mapping to identify the alleles controlling yield-related traits, and 13 putative genes regulating grain traits in European cultivated barley were obtained [Currently, association mapping has been widely used in the identification and genetic testing of important quantitative trait locus (QTL) in various species –17. And ironment . To reve < 0.05) . In Hordobtained . In wheaobtained . These pAmong dozens of markers, although SNP markers are usually used in crop association mapping, SNP sites are generally biallelic polymorphisms, which are significantly lower than SSR markers, and the development and detection costs are higher. Therefore, SSR markers have become increasingly popular in association analysis because of their codominant inheritance, extensive genome coverage, chromosome-specific location, relative abundance and high throughput genotyping . In partTaNAC2-5A overexpressing transgenic wheat lines show higher grain yield and higher nitrogen accumulation in aerial parts; A wheat CCAAT Box-binding TF can increase the wheat yield with less fertilizer input [unbranched2 and unbranched3 can affect yield traits by regulating the rate of lateral primordia initiation; Nuclear factor Y (NF-Y) B subunits confer drought tolerance and lead to improved corn yields on water-limited acres [Brassica napus, overexpression of the brassinosteroid biosynthetic gene DWF4 simultaneously increases seed yield and stress tolerance [P. rockii.TFs can modulate gene expression and play a essential critical role in the regulation of yield. For example, IPA1  can promote both yield and disease resistance by sustaining a balance between growth and immunity in rice; The CCT domain-containing gene family has significant impacts on heading date, regional adaptation and grain yield , 42. In er input , 44. In ed acres , 46. In olerance . In treeP. rockii by combining association mapping and markers within TFs are rarely reported. Here, we sampled the cultivated P. rockii population for association mapping. After that, the genetic diversity and population structure were analyzed based on the developed EST-SSRs by comparative transcriptome. Moreover, LD and single-marker association mapping were conducted to explore the allelic effects on the natural variation of complex yield traits in the constructed population. Our results will lay a foundation to identify the linkage loci of yield traits in P. rockii and will be of great significance for the genetic improvement of yield traits of woody oil crops.Taken together, the studies on the allelic variation associated with yield traits in P. rockii. The one-way ANOVA analysis by R package showed a wide range of phenotypic variation among all the 24 quantitative traits measured. The variation coefficient ranged from 12.03 to 106.63% (mean 38.60%). The average variation coefficient of branch and leaf, flower and fruit traits was 22.57, 37.21 and 49.75%, respectively , among which 182 showed a highly significant correlation (P < 0.01)  ranged from 3 to 16, with an average of 8. The effective number of alleles (NE) ranged from 1.02 to 7.32, with an average of 2.83. The PIC values ranged from 0.021 to 0.849 (mean 0.514) and Shannon’s information index (I) ranged from 0.07 to 2.18 (mean 1.13). The mean values of observed heterozygosity (Ho) and expected heterozygosity (HE) were 0.529 and 0.561, respectively. Since Ho was higher than HE at 26 EST-SSR loci, the Wright’s inbreeding coefficient (FIS) ranged from − 0.828 to 0.867 with a mean value of 0.048  reached a mode at K = 4 before decreasing, and the highest delta K was detected when K = 4  were identified at K = 2–6, among which four major well-separated genetic clusters  were observed at K = 4–6 , 64.13, 58.08 and 47.91% of EST-SSR loci demonstrated significant LD at P < 0.05, P < 0.01 and P < 0.001, respectively. Based on r2 estimates, only 0.67% (r2 ≥ 0.05) and 0.18% (r2 ≥ 0.1) of the loci pairs showed significant LD. Therefore, the overall level of LD between EST-SSR loci was low, and most of them were in linkage equilibrium , such as PS10 (PB.32979.2), PS12 (PB.59960.1) and PS17 (PB.53756.4) in the MYB gene family. Then, of the 793 assessed loci pairs (P < 0.001), 479 showed r2 levels > 0.005 (60.40%). Among them, several loci showed significant LD values, such as PS50 within PSTCP11(PB.61740.1)  marker-trait association tests. Out of these, ten associations (4.31%) including 7 EST-SSR loci were significant at the P < 0.01 level. However, correction for multiple testing using the FDR method reduced the number to 8 (3.45%) at a significance threshold of Q < 0.05, involving three traits with 7 EST-SSRs. These loci explained 4.93 to 25.32% of the phenotypic variation, with an average of 11.49%. The number of associations varied across the traits was 2  to 3 . One EST-SSR (PS31) was associated with at least one trait. For 3 out of the eight associations, the gene effect showed overdominance (|d/a| > 1.25). The remaining 5 associations showed additive  or partial to full dominance   at a significance threshold of Q < 0.05, involving seven traits with 36 EST-SSRs. These loci explained 3.79 to 37.45% (mean 11.06%) of the phenotypic variation. The number of significant associations varied across the traits was 2  to 32 , as shown in Additional file For branch and leaf traits associated with yield, we performed 464 (58 EST-SSRs × eight traits) marker-trait association tests. Among them, 102 associations (21.98%) including 39 EST-SSR loci were significant at the threshold of P < 0.01. However, correction for multiple testing using the FDR method reduced the number to 46 (6.61%) at a significance threshold of Q < 0.05, involving seven traits with 26 EST-SSRs. These loci explained 4.45 to 30.29% (mean 11.47%) of the phenotypic variation. The number of significant associations varied across the traits was 3  to 12 (single fruit number), as shown in Additional file For fruit traits associated with yield, we performed 696 (58 EST-SSRs × twelve traits) marker-trait association tests. Out of these, 64 associations (9.20%) including 30 EST-SSRs were significant at the threshold of Based on the results of association mapping, we observed that the floral traits were significantly associated with SSR loci within TFs from 5 gene families , branch and leaf traits were significantly associated with 16 gene families . Fruit traits were significantly associated with 15 gene families   of the phenotypic variance. The number of significant associations varied across EST-SSRs was 1 to 7, and 11 out of the 19 EST-SSRs exhibited significant associations with at least one trait. The modes of gene effect for 21 associations were overdominance, 15 were additive, and the remaining 13 were partial to full dominance  were excluded. Further, the results showed that 49 associations were significant at the threshold of P. rockii. The results indicated that the average number of allele was 8, which was higher than that of Ficus carica [Pistacia atlantica [Cucumis melo [P. rockii [P. rockii [P. rockii. Simultaneously, the number and type of EST-SSRs and the characteristics of the test population are different.A vital prerequisite for dissecting population evolution and association analysis is to make clear the genetic diversity of the mapping population and the polymorphism of markers used . Here, ws carica , Pistacitlantica , Cucumismis melo  and cult. rockii , but low. rockii . Here, wFIS [P. rockii [Populus tomentosa [P. rockii [P. rockii. Therefore, our results prove that highly heterozygous redundancy is an important biological characteristic of P. rockii, and further support the view that the cultivated resources in P. rockii are complex hybrid origin [Additionally, the population FIS , 50 rang. rockii , which iomentosa  and P. r. rockii , etc. Mod origin .P. rockii (PIC = 0.514) [P. tomentosa [F. carica [P. atlantica [Prunus avium [P. rockii or the fact that we sample the accessions with significant genotype differences in this study.Comparing to other outcrossing woody plants, we detected a high level of genetic diversity in = 0.514) , 53, whi. carica , but lowtlantica  and Prunus avium . This isP. rockii [P. rockii is mainly divided into four subgroups, which is consistent with the source of cultivated germplasm in this study, as shown in Fig. The analysis of crop population structure can not only reflect the gene exchange and affinity among individuals, but also be the premise of association mapping, which is conducive to improving the mapping efficiency and avoiding the emergence of false positives . In this. rockii . We specP. tomentosa [Eucalyptus [Gossypium hirsutum [P. rockii [P. rockii. Moreover, the LD level of genic-SSR loci is not representative of the whole genome or the gene interval region level, which may also lead to the low LD levels [P. rockii limit the analysis for the decay of LD between markers, which remains to be studied further.The analysis of LD level in population is not only the genetic underpinnings for association mapping, but also provides a reference for the selection of appropriate association analysis strategies. Generally speaking, the LD level is low in cross-pollination plants, such as omentosa , 7, 56, calyptus , Gossypihirsutum  and P. r. rockii . The treD levels . AdditioP. rockii. Among them, SSR loci from MADS-box, AP2, MYB, and other gene families showed high genetic effects. Simultaneously, there were not only significant associations between one trait and SSRs in multiple gene families, but also pleiotropism or co-localized associations, which was consistent with the reported results [SSR markers based on candidate genes have higher genetic effects in regulating the expression and function of genes related to quantitative traits . In this results , 21, 39.In this research, we detected 176 combinations associated with three different types of traits. Still, this number was reduced to 141 after correction for multiple testing, which further improved the accuracy of the association results. Moreover, studies have shown that differences in population size and structure can cause variations in the results of association mapping. A typical association population should be a combination of multiple independent and unrelated individuals from the same region . TherefoAssociation mapping of complex quantitative traits in plant can detect many significantly associated markers, but explain a small portion of phenotypic variance . In thisP. rockii. Moreover, TFs with an AP2 domain in Arabidopsis thaliana and Oryza sativa can control seed weight and seed yield [d/a| = 1.517) and seed weight  in P. rockii, and the modes of gene effect were all overdominance (|d/a| > 1.25). Therefore, we speculate that PS19 is likely to be an essential marker for regulating the seed yield in P. rockii. In addition, TFs from the AP2 gene family are also significantly associated with other yield traits such as fruit size and fruit weight, which remains to be further verified in future studies.TFs with an APETELA2 (AP2) domain play significant roles in plant growth, development, and stress responses. Studies have also shown that TFs from the AP2 gene family are associated with crop yield improvement –68. In ted yield , 66. In P. rockii. Also, a study has shown that the novel MYB-like TF OsMPH1 can regulate plant height and improve grain yield in rice [P. rockii.The MYB family of proteins comprise a large family of plant transcription factors, participating in the regulation of plant growth and development –74. TFs  in rice . We alsoP. rockii, we first constructed an association population consisting of 420 individuals. Then, the developed 58 polymorphic SSR loci within TFs associated with yield were selected for association mapping. Moreover, the genetic diversity and population structure were evaluated with the polymorphic loci, which proved that the population showed a high level of polymorphism and four subpopulations. Further, the results of association analysis based on single-marker showed that the 17 yield quantitative traits were regulated by 41 EST-SSR loci from 16 gene families, and 141 significant association combinations were identified. All these results furnish practical information to explore the effective functional loci associated with yield traits in tree peonies, it is also of great significance for the selection of yield-related traits and the cultivation of high-yield cultivars for oil tree peony.For the association mapping in P. rockii were mainly identified and collected from Gansu Province in northwest China by Beijing Guose Peony Technologies Co., Ltd. All these materials represented diverse genetic resources related to yield quantitative traits and were cultivated with general agronomic practices in the open field of Beijing Guose Peony Garden in Beijing, China   Fig. . Then baThe 420 individuals from the association population were scored based on 24 candidate quantitative traits with at least three replicates per genotype. In total, four flower traits  were measured at the full bloom using one either digital caliper  or measuring tape. A total of 8 branch and leaf traits  were measured. Among them, plant height, crown breadth, compound leaf length, and compound leaf width were measured using a measuring tape, the maximum basal branch angle was measured with Protractor Edge, and the other traits were measured with CI-203 laser leaf area meter . In addition, a total of 12 fruit traits  were measured. The electronic balance was used to measure weight. The other traits were measured with the digital caliper and measuring tape  according to the manufacturer’s instructions with minor modifications. Five microliter of each total DNA was assessed by 1% Tris-acetic acid-EDTA (TAE) agarose gel electrophoresis, and 1 μL was assessed using NanoDrop ND2000  . Based on the sequencing data, the candidate 959 TFs from 21 gene families associated with yield based on previous reports were screened. Then a total of 166 EST-SSRs containing six nucleotide repeat types were identified, with an average of one SSR per 5.78 unigenes. Among them, 58 polymorphic EST-SSR markers have been identified and proven to be effective in Paeonia (Unpublished observationsWe have conducted an RNA-seq experiment of flower buds of nologies . The RNA2O and 1 μL (50 ng) template DNA. The amplification program was as follows: 5 min at 95 °C, 35 cycles of 30 s at 95 °C, 30 s at the appropriate annealing temperature, 1 min at 72 °C, and 10 min at 72 °C, 4 °C hold. The products were separated by capillary electrophoresis using an ABI3730XL capillary sequencer along with an internal size standard  after confirmation of PCR amplification by electrophoresis on a 1% agarose gel. The polymorphic EST-SSR loci were read with GeneMarker v1.80 software using LIZ 600 size standards . Subsequently, Micro-Checker v2.2.3 (http://www.microchecker.hull.ac.uk/) was applied to identify and to correct the genotyping errors [Each PCR reaction was performed in a total reaction mixture volume of 10 μL containing 5 μL 2 × Power Taq PCR MasterMix , 0.5 μL (10 pmol) each primer, 3.0 μL dd HDescriptive statistics were performed for 24 quantitative traits, including coefficient of variation (CV/ % = standard deviation / mean × 100%), one-way ANOVA , correlation analysis, principal component analysis (PCA), and cluster analysis. All the statistics were carried out by using IBM SPSS Statistics 20.0 software and R language package.NA, NE, Ho, HE, PIC, I and FIS were calculated by GenAlEx v6.501 [http://pritch.bsd.uchicago.edu/structure.html) [K) through an admixture model. For each value of K (K = 1–19), ten independent runs were performed with a burn-in period of 100,000 followed by 200,000 Markov Chain Monte Carlo (MCMC) replications. Then the results were submitted to the Structure Harvester (http://taylor0.biology.ucla.edu/struct_harvest/) [LnP(D) and ΔK were used to detect the optimum K value [The developed 58 polymorphic EST-SSRs were used to analyze the genetic diversity of association population. The summary statistics of x v6.501  and POPGx v6.501 . The devre.html) , was usearvest/) . As a re K value . Then th K value . The out K value . Structur2. The r2 values between pairs of EST-SSRs  were calculated with 105 permutations using the TASSEL v2.0.1 software (http://www.maizegenetics.net/). The pairs of loci were considered to show a significant LD when P < 0.001. In the association mapping, the TASSEL v2.0.1 software package was used for marker-trait analysis with 104 permutations by using the mixed linear model (MLM) [Q matrix estimating the membership coefficients for each accession was derived from the STRUCTURE runs. The relative kinship matrix (K) was determined by using SPAGeDi software v1.2 [LD was measured as the squared correlation of allele frequencies el (MLM) . The Q mare v1.2 . False dare v1.2 .d) to additive (a) effects, which was estimated from least-square means for each genotypic class. The values of 0.50 < |d/a| < 1.25, |d/a| ≤ 0.5 and |d/a| > 1.25 were defined as partial or complete dominance, additive effects and under- or overdominance, respectively. The algorithms of dominance and additive effects were d = GBb - 0.5 (GBB + Gbb) and 2a = |GBB - Gbb|, respectively  [The gene effect was assessed by using the ratio of dominance (enotype) .Additional file 1 Table S1. The descriptive statistics, correlation, principal component and systematic cluster analysis of 24 quantitative traits in the association population of P. rockii.Additional file 2 Figure S1. The clustering pedigree diagrams of 420 accessions and 24 quantitative traits in the association population of P. rockii.Additional file 3 Table S2. Summary of significant EST-SSR marker-trait pairs from the association test results of flower, branch and leaf, and fruit traits in the association population of P. rockii.Additional file 4 Table S3. The 24 investigation traits and measurement standard in the association population of P. rockii.Additional file 5 Table S4. Information of 58 polymorphic EST-SSRs for association mapping.


ARAP2 and TSN genes concerning the IBW trait. The genomic prediction ability is improved using deregressed estimated breeding values including parental information as a response variable despite Bayesian methods and genotyping platforms for the IBW trait in Korean Yorkshire pigs.The individual birth weight (IBW) of pigs is an important trait regarding its relevance to mortality at weaning, sow prolificacy, and growth performance. This study investigates the variance component estimation, informative window regions, and the efficiency of genomic predictions associated with IBW traits in Yorkshire pigs. The low heritability (0.13) is estimated on the basis of a full model including individual genetic, sow genetic, and common environmental effects. Two common window regions of the genome are identified under three different genotyping platforms found within the This study estimates the individual birth weight (IBW) trait heritability and investigates the genomic prediction efficiency using three types of high-density single nucleotide polymorphism (SNP) genotyping panels in Korean Yorkshire pigs. We use 38,864 IBW phenotypic records to identify a suitable model for statistical genetics, where 698 genotypes match our phenotypic records. During our genomic analysis, the deregressed estimated breeding values (DEBVs) and their reliabilities are used as derived response variables from the estimated breeding values (EBVs). Bayesian methods identify the informative regions and perform the genomic prediction using the IBW trait, in which two common significant window regions (SSC8 27 Mb and SSC15 29 Mb) are identified using the three genotyping platforms. Higher prediction ability is observed using the DEBV-including parent average as a response variable, regardless of the SNP genotyping panels and the Bayesian methods, relative to the DEBV-excluding parent average. Hence, we suggest that fine-mapping studies targeting the identified informative regions in this study are necessary to find the causal mutations to improve the IBW trait’s prediction ability. Furthermore, studying the IBW trait using a genomic prediction model with a larger genomic dataset may improve the genomic prediction accuracy in Korean Yorkshire pigs. MYOG, MSTN, and DBH have been reported to affect birth weight [https://www.illumina.com/products/by-type/microarray-kits/porcine-snp60.html), Neogen GeneSeek (https://genomics.neogen.com/en/ggp-porcine), and Affymetrix (https://genomics.neogen.com/en/affymetrix-axiom-porcine-array). Regarding the birth weight trait in pigs, a previous study [Litter size and birth weight have been used as representative traits of sow productivity . Howeverh weight ,14,15. Gh weight , poultryh weight , beef cah weight , sheep [h weight , and pigh weight , using gus study  identifius study  found 12us study . HoweverHere, the IBW trait was recorded between 2005 and 2020 in the GGP farm in Korea. The pedigree and phenotypic records of 76,108 and 38,864 Yorkshire pigs, respectively, were used to estimate the variance components and the genetic parameters to identify the most optimal statistical model. The average and standard deviation of IBW were 1.372 ± 0.284 kg, ranging from 0.60 kg to 2.70 kg.A total of 3858 Korean Yorkshire pig genotypes were used as a reference set across three SNP genotyping platforms of Illumina porcineSNP60 v2  and Axiom porcine55K and Axiom porcine660K , which consisted of 61,565, 55,372, and 658,692 SNP markers, respectively. Quality control measures of the SNP markers and animals included the exclusion of unmapped SNPs, sex chromosome SNPs, SNPs with a poor call rate (<0.90), and duplicate SNP map-positions. Additionally, animals with a poor call rate (<0.90) were excluded, as well as animals that did not have a registration number and animals with a poor call rate for duplicate genotypes within and among genotyping platforms. Consequently, the number of available SNP markers was 47,567, 52,398, and 539,459 across the 55K, 60K, and 660K SNP panels, respectively, using the Sscrofa 11.1 mapping information. This resulted in 429, 2,579, and 406 animals across the 55K, 60K, and 660K SNP panels, respectively, which were used in the GWAS and genomic prediction modeling. Briefly, the imputation process of the three SNP genotyping platforms was performed separately as follows: all the genotypes were imputed to their respective SNP genotyping panels using the FImpute v2.2 software  with defTo establish an optimal statistical model for estimating the variance components and the genetic parameters of the Yorkshire pigs’ IBW, four animal models that considered the maternal genetic effects, the common environmental effects, and the animal genetic effects, in addition to the fixed and covariance effects were used. The birth weight of each individual was used as a response variable, in which the first model (Equation (1)) applied an animal model that only considered the individual genetic effect, whereas the second model (Equation (2)) considered the maternal genetic effect, and the third model (Equation (3)) considered the common environmental effect that occurs during the pregnancy of full-siblings. Finally, the fourth model (Equation (4)) applied a full model that included the sow genetic effect and the common environment effect as well as the individual genetic effect. During this statistical model, the effects of sex, parity of dam, and contemporary group (farm-year-season) were included as fixed effects. To correct the IBW, which is a response variable, the litter size of dams was applied to each model as a covariate term effect, in which the variance components and the genetic parameters were estimated by fitting all the models using the restricted maximum likelihood (REML) procedure that was implemented in the statistical software R using the ASReml v4.1 package . The fouEquation (1): Animal model with a direct additive genetic effect:To determine the most suitable model for estimating the genetic parameters, the log-likelihood values (LogL) of the four different models were compared.The Chi-Square statistical test , and the reliability of each individual were estimated by a single-trait animal model accompanied by a full model (Equation (4)) using the ASReml v4.1 package in R . Two typed model . FinallyTwo Bayesian methods, BayesB  and Bayesoftware  for genosoftware .y, and y is a vector of one of the response variables (DEBVexcPA or DEBVincPA) of the validation set.During this study, a five-fold cross-validation method was used to estimate the genome accuracy, and the k-means clustering method was used for cross-validation. The reference set with both phenotypes and genotypes was divided into the training and validation sets, in which the relatedness was configured to be as small as possible through the k-means clustering method . The cluUsing the four models, the optimal model for IBW was found through the likelihood ratio test, in which the estimated variance component and genetic parameter result of each model, as well as the comparison result for identifying the most optimal model, are summarized in To identify the most informative 1 Mb window regions (over 0.5% of the additive genetic variance) as well as the significant SNP markers, we based our estimations on the model frequency within these window regions that were used in the GWAS analysis of the IBW trait across three commercially developed porcine SNP genotyping platforms . We employed the BayesB method with a large value of π (medium-density: 0.99 and high-density: 0.999) with DEBVincPA acting as a response variable in the Yorkshire pigs. The results of these association studies of the IBW trait are summarized in ARAP2 gene. These results were similar when using the Axiom660K genotyping platform, in which the most significant SNP marker was AX-116342374, which was located within the ARAP2 gene. Moreover, when using the Illumina60K genotyping platform, we found that the DBWU0000855 SNP marker located on SSC15 (29.71 MB) was the most significant, which was located within the TSN gene. However, we also found the same informative region (SSC8 at 27 Mb) using the two Axiom genotyping platforms with the Illumina60K genotyping platform. Hence, across the three genotyping platforms, the highest percentage of additive genetic variance (3.31%) was found in Illumina 60K, whereas the Axiom55K (3.17%) and Axiom660K (3.16%) had similar values. Taken together, we identified consistent informative regions (SSC8 at 26 or 27 Mb and SSC15 at 29 Mb) with same gene annotations (ARAP2 and TSN) in all platforms. Fine-mapping is needed to identify causal variants for IBW in SSC8 at 26–27 Mb in the future. The ARAP2  gene is known to affect the actin cytoskeleton through mediating RhoA [TSN (translin) gene is known to act as a modulator of mesenchymal cell proliferation and differentiation in mice [We identified 10 significant SNPs in the four windows detected by the Axiom55K, which were the same number of markers in the Illumina60K, whereas in the Axiom660K, we identified nine significant SNPs in the two detected windows. To summarize, the most significant detected window in each panel was on chromosome SSC8 at 27 Mb using the Axiom55K, on chromosome SSC15 at 29 Mb using the Illumina60K, and on chromosome SSC8 at 27 Mb using the Axiom660K platform, which explained 3.17%, 3.31%, and 3.16% of the variance, respectively. Concerning the Axiom55K panel, the most significant SNP marker AX-116342380), which was based on the model frequency of the SNP markers, was located on SSC8 at 27.89 Mb within the ing RhoA . Especia2380, whi in mice . Taken tThe genomic prediction accuracy of the studied IBW trait across the three genotyping platforms, two response variables, and two Bayesian methods are summarized in Contrasting to our expectation, a high extent of linkage disequilibrium (LD) between SNP and quantitative trait loci (QTL) via increasing marker density having the potential to improve prediction accuracy ,37 was nDuring the current study, we observed an increase in the genomic accuracy when using DEBVincPA as a response variable as compared to DEBVexcPA across the SNP genotyping platforms and Bayesian methods. These results are consistent with previous reports in terms of growth and productive traits in Duroc pigs . During During this study, we estimated a low heritability and identified candidate genes of the IBW trait of Korean Yorkshire pigs; hence, applying genomic technology can rapidly improve this trait. To realize this improvement, we evaluated and compared the genomic prediction ability across various genotyping platforms, response variables, and Bayesian methods. Altogether, two common informative 1 Mb window regions were identified across the three genotyping platforms, where the prediction ability was higher when using DEBVincPA as a response variable relative to using the other response variable. Thus, we suggest that future fine-mapping studies should include target sequencing of informative regions to identify the causal mutations and improve the prediction ability of IBW traits. Furthermore, a genomic prediction model that encompasses a larger genomic dataset reflecting the IBW trait may be useful in future genetic evaluations of Korean Yorkshire pigs.


Advances in genotyping and phenotyping techniques have enabled the acquisition of a great amount of data. Consequently, there is an interest in multivariate statistical analyses that identify genomic regions likely to contain causal mutations affecting multiple traits . As the demand for multivariate analyses increases, it is imperative that optimal tools are available to assess their performance. To facilitate the testing and validation of these multivariate approaches, we developed simplePHENOTYPES, an R/CRAN package that simulates pleiotropy, partial pleiotropy, and spurious pleiotropy in a wide range of genetic architectures, including additive, dominance and epistatic models.We illustrate simplePHENOTYPES’ ability to simulate thousands of phenotypes in less than one minute. We then provide two vignettes illustrating how to simulate sets of correlated traits in simplePHENOTYPES. Finally, we demonstrate the use of results from simplePHENOTYPES in a standard GWAS software, as well as the equivalence of simulated phenotypes from simplePHENOTYPES and other packages with similar capabilities.https://github.com/samuelbfernandes/simplePHENOTYPES.simplePHENOTYPES is a R/CRAN package that makes it possible to simulate multiple traits controlled by loci with varying degrees of pleiotropy. Its ability to interface with both commonly-used marker data formats and downstream quantitative genetics software and packages should facilitate a rigorous assessment of both existing and emerging statistical GWAS and GS approaches. simplePHENOTYPES is also available at  The wealth of data available from high-throughput phenotyping platforms used in modern agronomic experiments enables unprecedented study into the genomic underpinnings of genotype-to-phenotype relationships , 2. In phttps://github.com/samuelbfernandes/simplePHENOTYPES.Several useful software packages have been developed to simulate correlated traits –6. Howevcreate_phenotypes function. In particular, the user has the option to indicate the degree of pleiotropy among the QTNs, the number of additive and non-additive QTNs, the degree of correlation between multiple traits, and the heritability of each simulated trait.simplePHENOTYPES is capable of simulating traits controlled by a wide range of genetic settings, as depicted in Fig. Trait j and Trait j, and nine QTNs only control Trait j, as well as another QTN controlling type_of_ld input parameters of create_phenotypes (see Listing 1 below).When simulating multiple traits, the user has control over whether all QTNs control all traits (pleiotropy), a subset of the QTNs control all traits , or separate QTNs in linkage disequilibrium (LD) control individual traits (spurious pleiotropy). To illustrate these three different scenarios, consider a set of 20 QTNs and two traits  QTNs controlling each trait, as well as their effect sizes. These effects may either be manually inputted in a list with a vector of effect sizes for each trait, or as a single value from which simplePHENOTYPES will create a geometric series of effect sizes . The effTrait k and Trait k and 0.40 and 0.16 for trait It is possible to both indirectly and directly control the genetic correlation between traits simulated in simplePHENOTYPES. The genetic correlation between traits can be indirectly controlled by assigning different effect sizes to their shared QTNs. Thus, if the same two additive QTNs control two traits, denoted Alternatively, simplePHENOTYPES allows users to assign specific Pearson correlations between genetic values of the traits using a process known as whitening/coloring transformation . To illucor input parameter inside create_phenotypes), the Cholesky decomposition is first applied to L is a lower diagonal matrix defined from the Cholesky decomposition of To modify cor_res). Thus, the variance of each simulated trait is equal to the sum of i.) the variance of the genetic values from the QTNs and ii.) the variance of these random error terms. Although the current implementation of simplePHENOTYPES explicitly dichotomizes trait variability into these two sources, we anticipate that future versions will allow the user to specify the contributions of background genetic effects and non-genetic covariates to the simulated traits.Another feature of simplePHENOTYPES is the ability to specify the heritabilities of each simulated trait. These heritabilities are subsequently used to simulate normally distributed random error terms that represent non-genetic sources of trait variability. By default, these random error terms are independent, but the user may optionally specify a user-defined residual correlation  genetic and residual correlations with those specified by the user, as well as confirm details on the specified genetic architecture. In addition, the variance explained by each QTN . Here, the same data set of 280 maize lines form the Goodman-Buckler diversity panel is used to simulate two traits controlled by three additive QTNs (http://soybase.org/snps/download.php). This data set was comprised of 42, 291 SNPs obtained with the SoySNP50K [In a different scenario, we also simulated a pair of traits controlled by 20 pleiotropic QTNs (Listing 2), with a different heritability for each trait and QTNs with a minor allele frequency between 0.05 \documently GEMMA , which iTo demonstrate the equivalence of simulated trait results between simplePHENOTYPES and similar packages, we compared traits simulated by simplePHENOTYPES to those from AlphaSimR , SimPhe simplePHENOTYPES makes it possible to simulate multiple traits controlled by loci with varying degrees of pleiotropy. Its ability to interface with both commonly-used marker data formats and downstream quantitative genetics software and packages should facilitate the rigorous assessment of both existing and emerging statistical GWAS and GS approaches.Project Name: simplePHENOTYPEShttps://github.com/samuelbfernandes/simplePHENOTYPESProject Home page: Operating system: Tested on Linux, Windows and macOSProgramming languages: ROther requirements: R 3.5 or higherLicense: MIT licenseAny restrictions to use by non-academics: No (free software)Additional file 1. Description of the R code used for benchmarking analysis, GWAS conducted on the simulated data sets, and to estimate the run time of simplePHENOTYPES.


Sus scrofa). In this study, we identify several host genomic features having a microbiome-mediated effects on fat deposition. This demonstrates how the host genome can affect the phenotypic trait by inducing a change in gut microbiome composition that leads to a change in the phenotype. Host genomic variants identified through our analysis are different than the ones detected in a traditional genome-wide association study. In addition, the use of latent dependent variables allows for the discovery of additional host genomic features that do not show a significant effect on the measured variables. Microbiome-mediated host genomic effects can help understand the genetic determination of fat deposition. Since their contribution to the overall genetic variance is usually not included in association studies, they can contribute to filling the missing heritability gap and provide further insights into the host genome – gut microbiome interplay. Further studies should focus on the portability of these effects to other populations as well as their preservation when pro-/pre-/anti-biotics are used (i.e. remediation).A large number of studies have highlighted the importance of gut microbiome composition in shaping fat deposition in mammals. Several studies have also highlighted how host genome controls the abundance of certain species that make up the gut microbiota. We propose a systematic approach to infer how the host genome can control the gut microbiome, which in turn contributes to the host phenotype determination. We implemented a mediation test that can be applied to measured and latent dependent variables to describe fat deposition in swine ( Other effects are usually included in the model to control for other design factor effects. These can be genetic gp or environmental ep. Likewise, microbiome-wide association studies (MWAS) are performed to identify associations between M and P. A graphical representation of a generic MWAS model (Mod2) is reported in p and ep effects can be fit to account for other factor effects. Lastly, a GWAS study can be performed using M as the dependent variable of interest. In this case the generic model (Mod3) is as reported in m or environmental em.In the context of a genome-wide association study (GWAS), the effect of a given G feature on a P of interest is tested for its magnitude and significance. Other genetic and environmental effects are included in the  model used to perform the association in order to adjust for effects that could be present due to the characteristics of the experimental design. An acyclic graph representation of a generic model used in GWAS (Mod1) is reported in association is emphasized in the acronym though the regression coefficient effect of G on P. The term effect carries a causal meaning, which is often neglected in the interpretation of GWAS studies. However, in this study we will refer to the estimated regression coefficients as effects, implying causality. Thus, we will refer to p number of paths through which G affects P, with p-1 paths having null effect and one path having a non-null effect. The In GWAS studies, the term In the case of multiple paths with non-null effects but of opposite signs, the resulting A potential solution to this problem is offered by mediation analysis Examples of such phenomenon are reported in behavioral and marketing research. For instance, Pollack et al. measuring a phenotype.In all the models outlined above, it was implicit that the variables G, M and P were directly measured. In reality, the same models could be applied to latent, non-measured variables through Structural Equation Models (SEM) which can combine mediation analysis with latent variable analysis The example could also apply to a G → M → Π path analysis, where M is mediator variable exerting an effect on the latent variable Π. A potential implementation for the model (Mod4L) described above is depicted in a priori and then tested on the data available data. MWAS results are usually not causally interpretable, although the need to move from association to causality has been emphasized by several authors A mediation analysis implies a causal process, which has to be hypothesized Sus scrofa) is a relevant species to study fat deposition patterns when they depend on the host genomic background Sus scrofa as a model organism, kept either under experimental or commercial conditions. In this case, our group and its partners have generated a vast dataset, which contains several measures of fat deposition together with characterization of host genomic background and gut  microbiome composition.Swine (The objectives of this study were to 1) to provide a framework for the implementation of a microbiome-mediated search of host genomic features with effect on phenotypes of interest; 2) search for host genomic variants that affect fat deposition through the modification of the gut microbiome and 3) to search for host genomic variants exerting a microbiome-mediated effect using latent variables constructed on multiple measures of fat deposition in swine.22.1Sus scrofa) raised under commercial conditions by The Maschhoffs LLC. . For each individual, several performance measures were collected, both in vivo and post mortem. Fecal microbiome samples were obtained at different time points during the trial. A total of 1,183 records with complete host genomic, host phenotypic and fecal microbiome information were available for subsequent analyses.Data used in this study came from an existing database and partial results of the research have been previously published 2.1.1The phenotypic traits used in this study have already been described in other studies by our group P) included measures of backfat depth taken in vivo at the age of 118.1 ± 1.16 d (BF1); 145.9 ± 1.53 d (BF2) and 174.3 ± 1.43 days (BF3) of life, together with the day before slaughter which occurred at 196.6 ± 8.03 days (BF4). Measurements were taken on the right side of the pig’s back in the area corresponding to the 10th rib. These measures were collected using an ultrasound equipment  at the facility where the animals were raised. An additional measure of backfat (BFt) was taken post mortem using a Fat-O-Meater system , again at the site of the 10th rib. Carcasses were then dissected into commercial cuts, each of which was weighted. We used the weight of the belly cut (BEL) for its high fat content Briefly, phenotypes analyzed . After quality control the number of SNP remaining for further analyses was 40,542, distributed on the 18 autosomes. Genotypes were coded as the number of copies of the minor allele, i.e. 0 for AA, 1 for Aa or aA and 2 for aa, where a is the minor allele and A is the major allele. The SNP will hereinafter be referred to as host genomic features (G).All individuals were genotyped with the PorcineSNP60 v2 BeadChip . Quality control of the markers was performed by removing single nucleotide polymorphisms (SNP) with a call rate of less than 0.99, minor allele frequency of less than 0.05 and deviation for Hardy-Weinberg equilibrium (2.1.3S1), 118.2 ± 1.18 (S2) and 174.3 ± 1.43 (S3). Fecal samples were subjected to 16S rDNA amplicon sequencing as previously described by Maltecca et al. cmultrepl from package “Zcompositions” clr from package “compositions” M).Rectal swabs were obtained on all individuals at the ages of 18.6 ± 1.09 d , CG is the fixed cross-classified effect of the contemporary group ; S is the fixed cross-classified effect of the sire of the individual (28 levels); b is the random effect of the batch of individuals  where the individuals were allotted (331 levels); Since models had to be tailored to the SEM framework and the use of cross-classified effects is discouraged given the large number of solutions that need to be computed, cross-classified effects were transformed to linear covariates. This was carried out in two steps. First, a model was fitted for each phenotypic trait using the following specifications:thp trait; thp trait; thp trait; thp trait; thp trait.In the second step, incidence matrices and vectors of solutions were used to define new explanatory variables as follows:thm M.The same process was applied using M as the dependent variable and generating the variables For further use, all the four newly generated variables were centered to show mean equal to 0 and standard deviation equal to 1.2.2.2D, thg G on the thp P; thp phenotypic trait on the thg selected host genomic feature.The first analysis consisted of selecting the G features that were significantly associated with the phenotypic traits of interest . The model was specified as:it as in ; Mm is t2.2.4thp P, thm M, thg G on the thm M, thm M on the thp P, thg G on the thp P; thm M; thp P; thp P and thm M, respectively. This model allows to estimate the effect of G on both M and P. While estimating such effects the other effects are simultaneously estimated, in this case, the effects of CG, dam line and pen for their effect on both M and P.Model Mod4  was used2.2.5Measured variables contain information that is limited by the equipment and time of recording as well as the inability of the measuring technology to describe the whole biological process that is manifested in the phenotype. A SEM can be used to test the mediation through M on latent variables, providing further insights on the mediation paths provided that the latent variables built on correlated variables recover more information than the sum of the information contained in the measured variables. Model Mod4L  was implFATg) describing the (back) fat deposition over the life of the individual using the variables BF1, BF2 and BF3. A second latent variable (FATt) was defined using the measured variables BF4, BFt and BEL. This second variable aimed at describing the fat deposition at the end of the trial, merging information measured on the back of the body by two different instruments (BF4 and BFt) to the weight of the cut with the largest fat content (BEL). The Pearson correlations among the six variables are reported in We defined a first latent variable  was declared if the value 0 did not fall within the confidence intervals, i.e. the empirical distribution did not include null values. A permutation test was specifically designed to disrupt the P smaller than 0.05) if the non-permuted estimate did not fall within the confidence intervals, i.e. the null-hypothesis distribution did not include the estimate values from the intact data.Significance of the fitted effects in models Mod1, Mod4 and M5 . First, markers that fell within a contiguous window of 10 SNP were grouped together. The whole Sus scrofa QTL database was downloaded and previously discovered QTL were merged to each of the marker windows of interest. Then, the count for each QTL category  was calculated for each of the analyses conducted .The analysis performed to discover the G variants exerting a significant total or mediated effects gave a list of markers that were compared to the existing Animal QTL database biomaRtwww.ensembl.org/index.html).In addition, the R package 33.1Peptococcus but showed a different rate of presence (frequency of non-zero counts). S2a showed a presence of 0.523 and absorbed 2.70, 2.13 and 2.08 percent of phenotypic variance for BF1, BF2 and BF3, respectively. S2b showed a stronger presence of 0.793 and absorbed 6.49, 5.08 and 3.53 percent of total variance for the three phenotypic traits.Peptococcus, while S3b and S3c belonged to the genus Butyricicoccus. S3a showed stronger presence compared to S2a (0.995 vs 0.523) meaning that the relative abundance of this OTU increases as pigs age. S3a absorbed 9.02, 6.43 and 9.57 percent of the total variance for BF4, BFt and BEL, respectively, being the M feature with the strongest impact on the studied traits. S3b and S3c showed a similar presence (0.903 and 0.972) and absorbed 2.82, 2.10 and 1.87 percent of the total variance of BF4, BFt and BEL, while S3c absorbed the 4.46, 2.63 and 1.53 percent of the variance of the three P traits. It should be noted that S3c did not show a significant effect on BEL after Bonferroni correction but the effect was still significant after FDR correction. This M feature was still chosen as a mediator for the large percentage of variance absorbed on the three variables.The other three chosen M features belonged to samples collected at S3, contemporary with the recording of BF4, BFt and BEL. These M features were not tested on BF1, BF2 and BF3 for an evident conflict with the causal M → P structure with P appearing before M could be recorded. The variables S3a belonged to the same OTU as S2a and therefore to the genus 3.2The number of features identified as significant after bootstrapping varied across the traits, ranging from 237 for BF1 to 497 for BFt, with intermediate values of 314 for BF2, 273 for BF3, 482 for BF4, and 265 for BEL. The latent variables identified a different number of significant G features as compared to the measured component traits. 3.33.4Results for the mediation analysis are presented in The mediator variable used is the one that allowed the largest number of discoveries, namely S2b for FATg and S3c for FATt . In the 3.5www.animalgenome.org) that were found in proximity to the G features discovered in this study . The results for the Total effect are equivalent to the results that can be obtained with a traditional GWAS.Meat and Carcass Traits category, here referred to as Meat.In the online database, the QTL are grouped based on the trait category they were found in association to. These categories are reported on the y-axis, while the number of QTL hits is reported on the x-axis. According to the database categories, the six traits used in this study belong to the Meat category. S2a-mediated effects were the largest for BF3 and FATg while S2b (Peptococcus) mediated effects showed the largest number of hits for BF1, BF2, BFt, BEL and the latent variable FATt. The largest number of hits in the Meat category was always reached by one of the mediated effects. For BF4, the total effect showed a larger number of hits in the Health group, followed by the S3c-mediated effect in the same group. Yet, there was a consistent number of hits in the Meat group, with ~100 hits from the total effect and the S3a-/s3b-mediated effects.With the exception of BF4, the largest number of hits per trait was reached by a mediated effect on the 44.1direct effect but also as an effect on the microbiome features, which in turn affect the phenotypic trait of interest. While the direct effect assumes that a change in the host genome causes a change in the phenotypes with no assumption on the biological path that could lead to that change, the mediated effect assumes that the mediator (the gut microbiome composition) is involved in the path to test. The mediation analysis, therefore, compares a specific biological path (the mediated effect) to a generic path (the direct effect). Because of the nature of this study, our discussion does not deeply focus on the results about the G and M features discoveries, but on how mediation analysis implemented in a SEM can help recover host genomic variance for fat deposition traits.This study discovered several host genomic variants that affect fat deposition in swine involving gut microbiome as a mediator. In the analysis implemented, the effect that the host genome exerts on the phenotypic traits of interest is modeled as a Several hypotheses on the biological mechanisms involved in mediated effects are possible. For example, some G features could alter the microbiota composition . These two mediator variables were also the ones with the strongest and most consistent effects on the phenotypic traits  allowed the overall discovery of 464 features for FATg and 279 for FATt  and total G → P (below) effects are depicted in total and mediated effects were generally different. Sus scrofawww.animalgenome.org). There was seldom an agreement between the total and mediated effects for their allocation on the QTL categories since the number of hits for the two effects was different for most of the traits. The total effects were predominantly associated with Health and Meat QTL. The fact that the Health category showed several hits for the total effect could be due to the fact that the animals used in this study were raised in commercial conditions while most of the GWAS studies are performed in nucleus farms, which have more stringent biosecurity controls. The relevance of Health hits could therefore result from an immunity component embedded in the traits used in this study. The mediated effects colocalized with Meat QTL for most of the traits. This shows again the difference in the biological processes that the total and mediated effects are pointing at and, at least in this study, there was more consistency with previous literature by looking at the mediated than total effects. The G features that determine the P trait for the total effects are those associated with the trait (G → P). Conversely, the explicit modeling of the M−mediated path implies that a change in the G variable leads to a change in the M variables, in other words the genes associated with the G feature controls the gut microbiome composition (G → M). Once the latter is altered, i.e. a change in the abundance of the selected M features occurs, some physiological process leads to a change in fat deposition (M → P). The G features identified for the mediated effect would primarily affect the abundance of the mediator M feature. If such M mediator strongly impacts the fat deposition of the host, the mediated effect will be visible. Since some of the previously identified QTL for fat deposition in regions are in proximity to the G features identified for the mediated effect in this study, we could also hypothesize that the previous study captured genetic variation for the M mediator abundance, that was realized in the fat deposition phenotypes.The host genomic regions that are responsible for the total and mediated effects on the two latent variables. Several genes identified withing the significant genomic regions for the mediated effects point at cognitive development. DYNLRB1 was found to be associated to neuronal survival 4.4The G features with a significant mediated effect cannot be found in a traditional GWAS, unless they show a significant total effect, as would be the case in this study. This proves the value of a mediation analysis.Mediation analysis has been used in other studies that aimed at estimating indirect effects that G could exert on P, even if using other host phenotypes rather than gut microbiome as a mediator. In a study on beef cattle performed with a different approach, Leal-Gutiérrez et al. Therefore, the estimation of microbiome-mediated effects could help discover additional genetic variance for many traits. The role of gut microbiome has been previously proposed and as a partial explanation for the missing heritability problem 4.5The current study was performed under commercial pork production conditions, and animals were fed standard diets. It is well known that the gut microbiome can be heavily influenced by feeding different diets or using pro-/pre-/anti-biotics. For this reason, the mediated effect should be studied in other populations or experiments because of its specificity. For example, let’s assume that the use of feed additives alters the gut microbiome composition, including a change in the M feature that is involved in the mediated path. We will call such external intervention as Z → M, where Z is some variable measuring the additive dosage. While the M → P effects would not be altered and would probably be observed on P, the G → M could be altered due to Z → M since the two effects are competing. If the external intervention ‘overwrites’ G → M, this effect could be nullified as Z is probably designed to totally control M. Alternatively, both effects could be magnified if some biological interaction between G and Z occurs, i.e. (GZ) → M. It is important to note that such susceptibility to external interventions could be found for the total effect as well, although the possibility for that effect to incorporate multiple paths makes it less prone to change under different conditions.From a methodological standpoint, this study proposed a relatively simple method to test for mediations. Models that allow mediation through multiple variables should be studied. The discovery of genomic markers associated with (or affecting a) phenotype of interest should be performed with methods that can fit all markers within the same model, accounting for linkage disequilibrium and perhaps performing variable selection The option to use more than one mediator variable should be allowed to fully describe the biological processes of mediation, especially if the proposed mediators show some degree of correlations. In this regard, Preacher and Hayes 5Sus scrofa) where different measures of fat deposition served as phenotypes of interest.In this study we propose a simple method to study the causal relationships between host genome, gut microbiome and host phenotypes. We used a dataset that included information collected on swine  variance for certain traits could help solve the so called ‘missing heritability problem’. Future research should be aimed at studying the longitudinal causal network among the different variables as well as implementing models that allow the selection and regularization of exogenous and mediator variables.F.T. and C.M. conceived the study. F.T. performed the statistical analysis and wrote the first draft of the manuscript. C.M. contributed to the manuscript writing and the interpretation of results. J.F., Cl.S. and Ca.S. acquired the phenotypic data. All authors have read and approved the final manuscript.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


ABO, and replicated many previously detected large-magnitude G×S interactions impacting waist-to-hip ratio. We also discovered many new G×S interactions impacting such traits as height and body mass index (BMI) within regions of the genome where both male- and female-specific effects explain a small proportion of phenotypic variance (R2 < 1 × 10−4), but are enriched in known expression quantitative trait loci.Many complex human traits exhibit differences between sexes. While numerous factors likely contribute to this phenomenon, growing evidence from genome-wide studies suggest a partial explanation: that males and females from the same population possess differing genetic architectures. Despite this, mapping gene-by-sex (G×S) interactions remains a challenge likely because the magnitude of such an interaction is typically and exceedingly small; traditional genome-wide association techniques may be underpowered to detect such events, due partly to the burden of multiple test correction. Here, we developed a local Bayesian regression (LBR) method to estimate sex-specific SNP marker effects after fully accounting for local linkage-disequilibrium (LD) patterns. This enabled us to infer sex-specific effects and G×S interactions either at the single SNP level, or by aggregating the effects of multiple SNPs to make inferences at the level of small LD-based regions. Using simulations in which there was imperfect LD between SNPs and causal variants, we showed that aggregating sex-specific marker effects with LBR provides improved power and resolution to detect G×S interactions over traditional single-SNP-based tests. When using LBR to analyze traits from the UK Biobank, we detected a relatively large G×S interaction impacting bone mineral density within  In this way, sex provides two well-defined conditions in which allele frequencies and linkage disequilibrium (LD) patterns are equivalent, but nevertheless genetic effects of one or many autosomal loci may differ.SEX differences are widespread in nature, and observed readily among many human traits and diseases. For quantitative traits, sex may affect the distribution of phenotypes at various levels, including mean-differences between genetic males and genetic females  as well as differences in variance. Sex differences are likely due to myriad factors, including differential environmental exposures and unequal gene dosages for sex-linked genes, as well as sex-heterogeneity in the architecture of genetic effects at one or more autosomal loci  SMR selected an average of 50.7 SNPs with an estimated power of 0.436 and estimated FDR of 0.451. Altogether, these results suggest that for G×S discovery, LBR offers higher power and lower FDR than SMR—the method most widely used in GWA studies—at least when G×S interactions are observed.We also compared the two methods based on arbitrary, albeit commonly used, mapping thresholds for SMR and LBR. At ery rate ], LBR seP-values from an F-test  as metrics for LBR and SMR methods, respectively. Again, LBR showed higher power with lower FDR than a standard SMR P-value . At traditional mapping thresholds, LBR and SMR had similar power but LBR achieved that power with much lower FDR; at P-value ≤ 5 × 10−8, the number of SNPs selected was 374.56 with an estimated power of 0.794 and FDR of 0.66.When trying to map SNPs that had effect in at least one sex, we used P value-diff for SMR; P value-diff ≤ 5 × 10−8, estimated power and FDR were 0.22 and 0.006. As seen in In a second round of analyses, we removed all causal variants from the panel of SNPs used in the analysis to represent a situation where causal variants are not observed, and genotyped SNPs are tagging causal variants at varying degrees. We initially assessed the relative performance of LBR to infer segments harboring G×S interactions. Power and FDR were assessed at several resolutions: 1 Mb, 500 kb, and 250 kb regions around each causal variant. At each resolution, a discovery was considered true if the finding laid within a segment harboring a G×S causal variant. In this scenario, we again observed that LBR had small variability in power and false discoveries between MC replicates (Table S3). Power and FDR were computed at different thresholds .j and window j*.We analyzed four complex human traits  measured among ∼259,000 distantly related Caucasians from the UK Biobank . For each trait, we fit the LBR model  across tTo compare both the magnitude and sign of sex-specific SNP effects, we plotted each nst β^mj . The traGDF5 locus, previously known to strongly associate with adult height  had a ABO, the gene controlling blood type.To make G×S inferences at the level of window variances irrespective of the magnitude of sex-specific effects, we adopted a ulations , provideLYPLAL1, MAP3K1, COBLL1, RSPO3, and VEGFA, among others. We also detected numerous novel G×S interactions  for the discovery of G×S interactions among traits to compare j within window j*) were enriched in eQTL, then compared to eQTL enrichment from P value-diff-selected SNPs as a function of the number of SNPs selected . P value-diff-selected SNPs for all traits except WHR. For instance, at P-values were 2.39 × 10−4, 1.52 × 10−12, 2.01 × 10−12, and 8.33 × 10−4, for height, WHR, BMD, and BMI, respectively. When selecting the same number of SNPs using P value-diff, enrichment P-values were 2.25 × 10−2, 1.56 × 10−28, 5.54 × 10−8, 1.93 × 10−1, for height, WHR, BMD, and BMI, respectively.As seen previously, many G×S interactions inferred using LBR have exceedingly small sex-specific effects. To further investigate whether G×S detections using the P-value of 2.6 × 10−4 . Interestingly, BMD G×S signals are very strongly enriched in eQTL with associated eGenes (including ABO and CYP3A5) expressed in the adrenal gland, among other tissues. For height, we observed small enrichment P-values across many tissues since G×S focal SNPs are enriched in eQTL with associated eGenes (including LOC101927975 and CNDP2) expressed across many tissues. Lastly, for WHR, we observed G×S detections to be heavily enriched in eQTL with associated eGenes expressed in fibroblast, adipose, and skin tissues.To provide more information about how genetic regions bearing G×S interactions may impact gene expression in specific tissues, we determined whether focal SNPs at fic eQTL . For heiWe have investigated the degree to which sex-specific genetic architectures differ at local regions, using large biobank data  and Bayesian multiple regression techniques that estimate sex-specific marker effects accounting for local LD patterns. The flexibility of the Bayesian approach enables multi-resolution inference of sex-specific effects, from individual SNP effects to window-variances that aggregate SNP effects within chromosome segments. These inferences can all be drawn using the results of the same model fit , but difThe Bayesian multiple regression technique performed in this study, along with estimation of window variances, was largely inspired by Through simulations, we showed that LBR provides superior power and precision to detect causal variants and those specifically bearing G×S interactions. We rationalize improvements in power upon traditional SMR methods by noting that the magnitude of a typical causal variant or G×S interaction is exceedingly small, and can elude hypothesis testing, due partly to the burden of multiple test correction. We also note that the resolution (peak size) in SMR signals is relatively large when using large sample sizes . To overcome this problem, we provided evidence that LBR methods—either by estimating conditional  marker effects or by aggregating conditional marker effects within relatively small regions—can achieve improved resolution when working with large sample sizes such as biobank-level data.ABO, and that G×S interactions are highly enriched in adrenal gland-specific eQTL. This encourages the hypothesis that some G×S are eQTL that may modulate gene expression in the adrenal gland, with gene function dependent on the level of sex hormones. This was also an intriguing finding given that ABO blood groups have been known to associate with osteoporosis and osteoporosis severity , or when using different sample sizes or samples from different populations. With large sample sizes, the increased power and flexibility of LBR comes at the cost of a significantly larger computational burden than that involved in the traditional SMR approach; however, working with large datasets can be made manageable by adjusting the size of each fitted segment  and paraTo conclude, we have demonstrated the powerful and flexible use of local Bayesian regressions for GWA to infer sex-specific genetic effects and G×S interactions using the UK Biobank. This was done largely by showing various means to utilize estimates of conditional , sex-specific SNP marker effects for GWA even when causal variants are not on the SNP panel for analysis. We anticipate that many more traits will be analyzed with this method to increasingly learn more about what is contributing to differences between males and females in human populations.


The BVA/KC (British Veterinary Association/Kennel Club) and FCI  are the main screening schemes used to evaluate the status of canine hip dysplasia (HD) in Europe. Jointly utilizing HD records from both BVA/KC and FCI schemes could improve the reliability of genetic evaluation within and across countries. In this study, HD scores for German shepherd dogs (GSDs) in the UK (using the BVA/KC scheme) and Sweden (using the FCI scheme) were used to investigate how to better operate joint genetic evaluations across the two schemes. It was shown that under a bivariate model, which regarded BVA/KC and FCI scores as different traits, the estimated genetic correlations between the UK and Swedish GSD populations were the same when using BVA/KC total or worse hip scores and for single-country or joint analysis of both the UK and Swedish populations. Under a univariate model that converted BVA/KC scores into FCI scores, the predictability of estimated breeding values was slightly improved by performing a joint analysis. Canine hip dysplasia (HD) is one of the most common orthopedic disorders in large and giant dog breeds . It was Until now, national genetic evaluations based on HD screening schemes have been implemented in several European countries, . However, with the increasing number of exchanges of breeding animals and semen between European countries , joint gIn this study, using the German shepherd dog (GSD) as an example breed, BVA/KC scores in the UK and FCI grades in Sweden were utilized to investigate how to better operate joint genetic evaluations across countries with different screening schemes. First, genetic correlations between total or worse hip BVA/KC scores with FCI grades were estimated under a bivariate model . Secondly, instead of performing a bivariate model across HD schemes, BVA/KC scores for UK dogs were converted from continuous scores into categorical grades to perform a univariate model together with FCI grades for Swedish dogs .Data used for analysis was provided by kennel clubs from the UK (The Kennel Club) and Sweden (Svenska Kennelklubben), including the pedigree and HD records of GSDs in each country. Dogs that occurred in both UK and Swedish pedigree databases (duplicated IDs) were detected by matching the individual's own and parental IDs. After replacing the duplicates with a unique ID, pedigrees of GSD from the two countries were merged into a combined database containing 877,280 registered animals. If HD was recorded with no screening date, recorded when the dog's age was <12 months or recorded before the year of 2000, then the HD record was removed from data analysis. The HD screening schemes in Sweden changed in 2000 (into FCI grades); thus, for simplicity, we chose to base our study on records since 2000. In total, 17,064 BVA/KC scores from the UK population and 30,909 FCI grades from the Swedish population were used to perform the study. There were no dogs with HD records in both screening schemes. The distribution of BVA/KC scores in the UK GSD population and FCI grades in the Swedish GSD population are shown in For the bivariate model, both total hip scores (HS) and the hip scores for the worse hip (WS) from the BVA/KC scheme were transformed by natural logarithm into transformed total hip scores (THS) and transformed worse hip scores (TWS), as performed for the genetic evaluation of HD in the UK :Five), following the method used for genetic evaluation of HD in Sweden (Five) used in the bivariate model are shown in Hip grades A, B, C, D, and E of the FCI scheme were converted into scores 1.0, 2.0, 2.5, 3.0, and 3.7  following a suggested conversion originally published by the BVA   and converted FCI grades (FCIFive) in the bivariate models. XBVA/KC (XFCI), ZBVA/KC (ZFCI), and WBVA/KC (WFCI) are incidence matrices, and bBVA/KC (bFCI), aBVA/KC (aFCI), and uBVA/KC (uFCI) are solution vectors for fixed effects, additive genetic effects, and litter effects, respectively. The vectors of fixed effects for both countries consisted of sex, birth year, birth month, and age at screening. In the bivariate model, the vectors of additive genetic effects were assumed to follow a multivariate normal distribution with covariances as where yFCI is the vector of combined HD phenotypes for UK and Swedish dogs (FCIFive+Five). XFCI, ZFCI, and WFCI  are incidence matrices (solution vectors) for fixed effects, additive genetic effects, and litter effects in the univariate model, respectively. The vector of fixed effects in the univariate models consisted of sex, birth year, birth month, and age at screening, with an additional fixed effect, country, compared to the bivariate models. In the univariate model, the vector of additive genetic effects was distributed as where Five was the corresponding phenotype for the EBVs of FCIFive (bivariate and univariate models) and FCIFive+Five (univariate model). Correlations between EBVs and corresponding phenotypes using single-population datasets were also calculated for THS and TWS in the UK population and for FCIFive separately in the UK and Swedish populations to test whether the predictability was improved through joint-population analysis. Further details of the data used in the analysis are shown in Following the variance components estimation described above, heritabilities and genetic correlation (for the bivariate model) were calculated. For each trait/model, the Pearson correlation between EBVs and corresponding phenotypes was calculated to measure the predictability of EBVs, where THS was the corresponding phenotype for the EBV of THS (bivariate and univariate models), TWS was the corresponding phenotype for the EBV of TWS (bivariate model and univariate models), and FCIFive (Swedish dogs) were the same (0.27) whether the corresponding trait for UK dogs was THS or TWS (Five and THS (0.67) was the same as that with TWS (0.67). In the univariate models, the estimated heritability for FCIFive+Five was 0.23, which was lower than the estimate for FCIFive in the bivariate model (0.27).In the bivariate models, estimated heritabilities for FCIS or TWS ; the herFive) to 0.95 for joint-population analysis (FCIFive+Five).In the UK population, the correlation between EBVs and corresponding phenotypes was slightly higher for THS (0.88) than that for TWS (0.87) in the bivariate models . The corFive, was 0.92 in the single-population analysis  for the joint-population analysis using the univariate model.For the Swedish population, the correlation between EBVs and corresponding phenotype, FCIanalysis . In the By combining the UK and Swedish HD data (including pedigrees and phenotypic records), we investigated two main questions: whether THS or TWS is more appropriate for joint evaluation with FCI grades and whether BVA/KC scores for UK dogs converted to FCI grades are compatible with FCI grades for joint genetic evaluation across screening schemes, so that they can be treated as the same trait in a univariate model.Five and FCIFive+Five estimated in this study were 0.27 and 0.23, respectively, which are close to 0.25 as previously estimated for the GSD population in Germany  but lower than that for the Labrador retriever breed (0.82) when performing a joint genetic evaluation (bivariate model) between the UK and Sweden (Five), the correlations between EBVs and corresponding phenotypes for the UK population  were the same for the single-population analysis  and the joint-population analysis . Similarly for the Swedish population, the correlations between EBVs and corresponding phenotypes of FCIFive estimated from single- and joint-population analyses were both 0.92. The lack of improvement in performing a joint analysis may be due to two factors: (1) the number of phenotypes in each country was sufficient to guarantee high estimation reliability within each population, and (2) there were no dogs with screening records in both countries . After converting BVA/KC scores into FCI grades (UK dogs) and performing genetic evaluation with FCI grades as a common trait , the predictability in both the UK and Swedish populations was slightly improved by the addition of dogs from the other country, which suggests that there may be a benefit of “borrowing” BVA/KC scores from the UK to implement HD genetic evaluations. This may be particularly useful for countries (unlike Sweden) with few accumulated HD records.The estimated genetic correlation 0.67) between transformed BVA/KC scores and converted FCId Sweden . This di7 betweenFor BVA/KC scores used in the UK population, our results suggest that neither THS nor TWS is a better trait on which to perform joint bivariate analysis with FCI grades. However, for the British national genetic evaluation under a univariate model using BVA/KC scores, the total hip score has previously been suggested to be a more appropriate trait for breeding against HD than the worse hip score due to the presumption that the differences between left and right hips derive from environmental influences rather than genetic effects . We onlyFor both the UK and Sweden, under the joint-population analysis, the univariate model gives a higher correlation between EBVs and the corresponding phenotypes. However, for the UK population, this may in part be an artifact of the non-linear relationship between EBVs  and the original (non-transformed) BVA/KC scores , which dJoint genetic evaluation across countries has been implemented in dairy cattle since 1983, using a well-defined Multiple Across-Country Evaluation (MACE) model , and mucRecently, a small improvement in accuracy of genomic selection was seen for UK dogs in a joint genomic prediction of Norberg Angle score (one of diagnostic characteristics of HD) between US and UK Labrador retrievers ; thus, fThe data is not publically available because the authors don't hold permission to share it. It was provided by The Kennel Club and Svenska Kennelklubben. Requests to access the data should be addressed to these organizations directly.Radiographs were taken by veterinarians for submission to the British Veterinary Association/Kennel Club (UK) and Svenska Kennelklubben (Sweden) as part of the canine hip scoring schemes in the respective countries. We received approval for the study from the Veterinary Ethical Review Committee (VERC) and Human Ethical Review Committee (HERC) at the Royal (Dick) School of Veterinary Studies, The University of Edinburgh.SW, ES, and PW designed the study. SW and JF analyzed the data. All authors contributed to the assembly of the data and preparation of manuscript.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.


White Guinea yam is mostly a dioecious outcrossing crop with male and female flowers produced on distinct plants. Fertile parents produce high fruit set in an open pollination polycross block, which is a cost-effective and convenient way of generating variability in yam breeding. However, the pollen parent of progeny from polycross mating is usually unknown. This study aimed to determine paternity in white Guinea yam half-sib progenies from polycross mating design. A total of 394 half-sib progenies from random open pollination involving nine female and three male parents was genotyped with 6602 SNP markers from DArTSeq platform to recover full pedigree. A higher proportion of expected heterozygosity, allelic richness, and evenness were observed in the half-sib progenies. A complete pedigree was established for all progenies from two families (TDr1685 and TDr1688) with 100% accuracy, while in the remaining families, paternity was assigned successfully only for 56 to 98% of the progenies. Our results indicated unequal paternal contribution under natural open pollination in yam, suggesting unequal pollen migrations or gene flow among the crossing parents. A total of 3.8% of progenies lacking paternal identity due to foreign pollen contamination outside the polycross block was observed. This study established the efficient determination of parental reconstruction and allelic contributions in the white Guinea yam half-sib progenies generated from open pollination polycross using SNP markers. Findings are useful for parental reconstruction, accurate dissection of the genetic effects, and selection in white Guinea yam breeding program utilizing polycross mating design. Dioscorea of the family Dioscoreaceae, order Dioscoreales. Dioscorea is the largest genus of Dioscoreaceae comprising about 614 species [Enantiophyllum, Lasiophyton, Combilium, Opsophyton and Macrogynodium [Dioscorea rotundata Poir, D. alata L., D. cayenensis Lam, D. opposite Thumb and D. japonica Thunb belong to Enantiophyllum and are distinguished by clockwise twining on support [Dioscorea rotundata Poir) is native to West Africa [Yam belong to the genus gynodium . Dioscor support . White Gt Africa . White Gt Africa . Allotett Africa  and disot Africa .White Guinea yam is a highly prized African food crop cultivated for its underground starchy tubers. It is a food of choice in West Africa, where it has a deep-rooted connection with the social and cultural facets of the people . White GBreeding is among the tools to release the yam potential as food source and industrial raw material. Yam breeding utilizes both sexual and asexual reproduction where an artificial hand or natural open pollination applied for the generation of full-sib or half-sib progenies segregating for desired traits and subsequent selection of their clonal derivatives for performance reproducibility and stability over seasons and locations . Yam speD. rotundata and D. alata mapping populations. The progenies of each of the mapping populations showed combinations of their parental alleles, indicating the success of hybridization.Open pollination produces half-sib progenies with unstructured pedigree. DNA profiling of progeny and possible parents and comparing their alleles for determination and validation of existing relationships  is a viaPaternity testing improves selection gains by increasing parental control in the selection gain equation . AccuratThe genetic parameter estimates of half-sib progenies are presented in Generally, there were unequal proportions of half-sib progenies confirmed as true hybrids among crossing parents . Of the The pedigree recovery of families TDr1686, TDr1687, TDr1688, TDr1689, TDr1690 and TDr1691 are displayed in We also checked maternal identity in the progenies and found a mismatch in one out of the eight maternal parents that successfully produced offspring from open pollination polycross block. Our analysis revealed that maternal parent ‘Ojuiyawo’ had a low allelic contribution to the progenies despite the highest putative male contributors assigned to the progenies in family TDr1692 .The proportion of gametes in the studied materials are presented in Transition SNPs were higher in number and frequency in all progeny families studied . The C tYam breeding is a two-step process that involves both sexual and asexual reproduction. Sexual reproduction generates recombinant progenies either through artificial hand or natural open pollination. Generating a reasonable number of recombinant progenies for valid selection from potentially interesting parental sources with the controlled cross is a challenging task in yam due to its tiny sized flowers and partial asynchrony ,13. HoweSexual fertility and flowering synchrony are essential for success with open natural pollination in yam. Our results showed variations in the proportion of gametes among families . GeneralHibiscus moscheutos [Betula pendula [Picea abies [Hibiscus moscheutos. Paternal contributions were affected by pollen–pollen interactions in artificial crossing experiments using pollen mixtures in Pinus sylvestris [Pseudotsuga menziesii [Cryptomeria japonica [Thysanoptera) usually play key role with natural open pollination in yam [Coleoptera, Diptera, Hymenoptera and Hemiptera reported visiting the yam field during the flowering period presumably contribute to natural open pollination [More interestingly, the paternal contribution under natural open pollination was unequal, suggesting unequal pollen migrations or gene flow among the crossing parents. The causes of the varying parental ability and their unequal contribution to progenies have also been noted in other species. In scheutos , Betula  pendula  and Piceea abies , unequalea abies  also obslvestris . Moreoveenziesii  and polljaponica . Detailen in yam . Howeverlination .The average minor allele frequency of the risk allele tested for all families was greater than 10% indicating its significance in detecting genetic effects in the studied populations. The findings are also in concurrence with Ardlie et al. , who notD. rotundata. This suggests the enormous potential of parentage analysis for selection, pedigree identification, and accurate dissection of the genetic effects that could contribute to accurate prediction of the extent of gene flow in heterogeneous populations of yam, as well as other root and tuber crops. Similar analysis could also be applied to other crops too. Telfer et al. [Eucalyptus nitens. Sartie and Asiedu [D. rotundata and D. alata controlled pairwise crosses. Tamiru et al. [Reliable pedigree information is useful for the accurate dissection of the genetic effects, and thereby maximize selection gain in crop breeding. Molecular markers have been effectively applied in many crops for the reconstruction of pedigree and understand the footprint of breeding history of contemporary germplasms ,38. Our r et al.  reportedd Asiedu  reportedu et al.  confirmeManihot esculenta Crantz) [Solanum tuberosum L.) [Ipomoea batatas L.) [Parental reconstruction has also been successfully done in other root and tuber crops such as cassava ( Crantz) ,41,42, posum L.) ,44 and satas L.) . In thesatas L.) ,47. A deatas L.) .D. polystachya plastid genomes [The numbers and patterns of SNP mutations in this study indicate a bias in chloroplast genome evolution in half-sib progenies of white yam. The diversity and patterns of SNP mutations in the studied half-sib progeny families were possibly due to the function of genes as previously suggested by Cao et al. . The mea genomes . Small m genomes . However genomes . The scoD. rotundata comprising nine females and three males with desired complementary traits for fresh tuber, dry matter, tuber shape, earliness and tolerance to yam mosaic virus [The experimental materials were botanic seeds generated using polycross mating designs. The polycross design was established at the International Institute of Tropical Agriculture, Ibadan, Nigeria, using 12 genotypes of ic virus . The matPrior to establishing the prenursery and nursery, cocopeat and topsoil samples were collected and analyzed at IITA soil analytical lab using standard procedures described by the International Soil Reference and Information Centre (ISRIC) and the FAO . The cheThe prenursery was laid out in a completely randomized design with two replicates in the glasshouse. The cocopeat was put in perforated polyethylene seedling trays and slightly soaked. Different botanic seeds were sown in 5 cm holes created in the growth medium in early March 2017. The trays were well labeled at planting and irrigated every other day until 4 weeks after sowing (WAS). The growing seedlings were fertigated to field capacity every other day for 4 WAS; and fumigated with cypermethrin at the rate of 15 mL per 1 L water at 6 WAS prior to transplanting in the seedling nursery at 8 WAS.The nursery was laid out in a randomized complete block design in the screen house. Seedlings were transplanted in early June in blocks of 20 plots per block, with inter- and intra-spatial block spaces of 0.5 m apart. The seedlings were transplanted in holes created in the crest of the sterilized topsoil and irrigated to field capacity every three days until 6 months after transplanting (MAT).Approximately 1 g young, healthy and fully expanded leaves were collected per genotype. Approximately 54 samples comprising 50 progenies, three putative male and one maternal-bearing fruit parents were collected per family. Genomic DNA was extracted from representative samples using modified CTAB protocol with slight modification . The genThe raw HapMap file from DArTseq genotyping platform  was first converted to a variant call format (VCF) file using perl programming language and TASSEL v.5.2.43 ,54. The Various population genetic analyses were conducted to explore the genetic properties of the markers. The number of alleles and allele frequencies for the selected SNPs were estimated using the VCFtools . The proThe Penalized and doMC libraries were used to estimate the contribution of the male and female parents in the offspring. The value of each parent was estimated using the multinomial model of the penalized function formula as described by McIlhagga .i, j)th element j occurred in observation i. Each element The log-likelihood of parentage of the observations studied was calculated as:The observation vectors The probability vectors The probability vector (L with respect to β was estimated using the chain rule as:The gradient (intercept) of dL/dp is simply y/p, where the division is element-by-element. The Jacobian dp/dβ isThe gradient Each of the submatrices The values generated for each progeny were ranked and the true hybrids were identified based on the estimated male and female coefficients. The profile values of progeny samples of each family and maternal parent were surrounded by the three putative male parents and analyzed for possible alignments. Helium pedigree visualization software was used for pedigree transmission patterns, and visualization of the various polycross families generated as described by Shaw et al.  and ShawIn the current study, the identification of parentage relationships in the half-sib progenies of white Guinea yam using SNP markers aids the accurate traceability of genotypes with unknown identity, and determination of genetic diversity across families and generations that could be exploited for breeding.