Breeding of apple is a long-term and costly process due to the time and space requirements for screening selection candidates. Genomics-assisted breeding utilizes genomic and phenotypic information to increase the selection efficiency in breeding programs, and measurements of phenotypes in different environments can facilitate the application of the approach under various climatic conditions. Here we present an apple reference population: the apple REFPOP, a large collection formed of 534 genotypes planted in six European countries, as a unique tool to accelerate apple breeding. The population consisted of 269 accessions and 265 progeny from 27 parental combinations, representing the diversity in cultivated apple and current European breeding material, respectively. A high-density genome-wide dataset of 303,239 SNPs was produced as a combined output of two SNP arrays of different densities using marker imputation with an imputation accuracy of 0.95. Based on the genotypic data, linkage disequilibrium was low and population structure was weak. Two well-studied phenological traits of horticultural importance were measured. We found marker–trait associations in several previously identified genomic regions and maximum predictive abilities of 0.57 and 0.75 for floral emergence and harvest date, respectively. With decreasing SNP density, the detection of significant marker–trait associations varied depending on trait architecture. Regardless of the trait, 10,000 SNPs sufficed to maximize genomic prediction ability. We confirm the suitability of the apple REFPOP design for genomics-assisted breeding, especially for breeding programs using related germplasm, and emphasize the advantages of a coordinated and multinational effort for customizing apple breeding methods in the genomics era. Malus × domestica Borkh.) is one of the most economically valuable fruit crops in temperate regions1. Thousands of cultivars are grown in national and private repositories around the globe. Extensive genetic variation described in the European apple germplasm illustrates the available genetic diversity among cultivars3. Only a fraction of the existing apple cultivars is commercially used. Although ongoing breeding programs worldwide aim to create new cultivars adapted to consumer demands and changing climate, these goals could be difficult to reach within the narrow elite genetic pool of modern breeding material4.Apple  and to allow genomic prediction. Particularly, genomic prediction7. Genomic prediction in apple was tested for the first time by Kumar et al. in 20128. However, this and further studies have been based on a limited number of genetic markers and/or been carried out at a local scale14.For the application of genomic prediction in fruit trees, apple became a model species due to its economic importance and the range of available research resources15. Low population structure2 and rapid linkage disequilibrium decay in highly diverse apple germplasm3 underlie the need for dense SNP marker datasets for GWAS. Considerable progress has been made in the development of genomic resources in apple16. Creation of low and medium density SNP arrays, such as the Illumina Infinium® 20K SNP genotyping array (20K array)17 was followed by the establishment of the Affymetrix Axiom® Apple 480K SNP genotyping array (480K array) with more than 480K SNPs18. Using this SNP array for apple, markers significantly associated with phenological traits in several germplasm collections have been successfully discovered by GWAS3. Although the high marker density of the 480K array may lead to higher prediction accuracies than achieved before, no genomic prediction study was conducted using this array so far. Commercial apple breeding programs still cannot afford large-scale genotyping of their germplasm with expensive tools. Therefore, a balance between genotyping density, costs, and predictive ability should be found for the application of genomic prediction in breeding.The prediction accuracy of genomic prediction models generally increases with the number of markers used to genotype the training population, reaching a plateau depending on the architecture of the trait, the number of individuals in the training population, the size of the genome and linkage disequilibrium15. For the first time in apple, these aspects could be tested with (i) GWAS and genomic prediction using the high-density 480K array marker dataset, (ii) a comparison of the effects of SNP density on GWAS and genomic prediction, and (iii) the prediction precision analysis. Our further aim was to discuss the use of the apple REFPOP for genomic prediction in multiple environments, across multiple traits and multi-management practices and to facilitate the improvement of apple breeding using the established apple REFPOP.Here, we present an apple reference population: the apple REFPOP. The population has been replicated across six environments in Europe and designed for comparing two management practices, which will allow for a thorough and unique study of the effects of genotype, environment, and management as well as their interactions on apple phenotypes. The main objectives of this study were to consolidate the high-density SNP marker dataset for all apple REFPOP genotypes, apply the SNP marker dataset when describing population characteristics of the apple REFPOP and prove suitability of the apple REPOP design for genomics-assisted breeding. Success of the genomics-assisted breeding may depend on characteristics such as marker density, trait architecture or size of the training population2, 194 European accessions were classified according to their origin into (i) Northern and Eastern Europe incl. Russia and Baltic countries , (ii) Western and Central Europe , (iii) Southern Europe with accessions from Spain, Italy, and Portugal , and (iv) Southeastern Europe containing accessions from Romania, Northern Macedonia, Moldova, Bulgaria, and Turkey . The 69 non-European accessions originated from (i) Australia and New Zealand , (ii) Canada , (iii) Japan , (iv) United States of America , and (v) South Africa . Six accessions previously analyzed with the 480K array but of unknown origin were also included in the apple REFPOP.The apple REFPOP was ultimately built with (i) 269 diploid accessions representing a wide range of genetic diversity in apple, originating from various geographic regions around the globe and (ii) 265 diploid progeny from 27 parental combinations from several European breeding programs  increased the marker density from 7060 to 303,239 SNPs . Additionally, imputation accuracy of 0.96 and 0.94 when calculating Pearson correlations between imputed and original values across individuals and across markers, respectively, was estimated for 86 genotypes from two parental combinations, ‘Fuji’ × ‘Pinova’ and ‘Golden Delicious’ × ‘Renetta Grigia di Torriana’.Missing marker values in the reference set obtained from the 480K array , genotypes sorted by cluster membership within groups defined by geographic region of origin appeared highly admixed . EstimaPredicted values of genotypes adjusted for spatial heterogeneity within each environment showed that individual genotypes appeared to respond differently to the various environments, with an apparent broader variation among genotypes for harvest date than for floral emergence Fig. . When mop-values). Reported p-values were closely below the log-transformed Bonferroni-corrected significance threshold for GWAS performed with the full set of 480K array SNPs; all three associations were significant at density of 150,000 SNPs. Two SNPs were located at the top of chromosome 9 (proportion of explained phenotypic variance r2 of 0.07 and 0.03) and a third one on chromosome 11 (r2 = 0.10). Four SNPs were identified to be significantly associated with harvest date using the full set of 480K array SNPs . The strongest association was found on the chromosome 3 (r2 = 0.39) with another significantly associated marker at a distance of 5.3 Mb (r2 ≈ 0). Two SNPs on chromosome 10 (r2 = 0.15) and on chromosome 16 (r2 = 0.11) were also significantly associated with harvest date. The QQ-plots for both traits indicated a good model fit  may be expected only for simple, oligogenic traits (number of markers underlying the trait M ≤ 10). With a training population of the size of the apple REFPOP accession group (N = 269), more complex traits with M = 100 may be predicted with very high precision if the heritability was high (h2 = 0.8), but with a decrease in precision for a moderate heritability (h2 = 0.5). A training population size equal to that of the whole apple REFPOP (N = 534) may be sufficient to predict traits with M = 100 for both high and moderate heritabilities with very high precision. The precision analysis indicated that highly precise predictions for traits with very complex architecture (100 < M ≤ 1000) may be possible if heritability was high and the training population had approximately twice the size of the apple REFPOP (N = 1000). However, the increase in estimated precision from N = 534 to N = 1000 was comparably smaller than the increase from N = 269 to N = 534.The precision analysis of genomic prediction Fig.  allowed 21. The incorporation of both cultivated accessions and modern breeding material is expected to promote the applicability of the apple REFPOP for genomics-assisted breeding beyond the scope of most current breeding programs, whose genetic bases are generally narrow22. Also, since relatedness between training and breeding populations is a crucial factor for successful genomic prediction13, the European breeding programs can directly profit from the outcomes of the project because their breeding material has been included in the apple REFPOP. Furthermore, due to the high admixture of the accessions, which stem from across the globe, the levels of diversity in the apple REFPOP appear to be adequate to predict the performance of a broad spectrum of novel breeding material.This study is the first report on the apple REFPOP, a reference population created to advance apple breeding with genomics-assisted methods. The population is divided into an accession and a progeny group. Genotypes of its accession group  were chosen to represent a wide range of geographic origins and capitalize on the previously available high-density SNP array data. The progeny group stemmed from eight different European breeding programs to represent current tendencies in European apple breeding. For the progeny group, the choice of genotypes was mainly based on genetic distance sampling within progeny groups derived from a number of parental combinations. On the contrary, the choice of genotypes for the accession group did not correspond to a core collection design which generally aims at maximizing genetic diversity18, but using this array remained costly. Here, we combined the high-density marker information of the accessions with the recently inferred pedigrees for numerous cultivars19 to perform a large-scale marker imputation of the progeny group genotyped with the 20K array17. Although marker imputation has been routinely applied at large scales in well-studied organisms such as cattle before23, here we report for the first time a large scale, high-density imputation in apple. The imputation has multiplied the amount of marker information by ~43× for the progeny group at relatively low cost. A high imputation accuracy was achieved, which is comparable to a similar study in poplar24. To evaluate the imputation accuracy, two parental combinations ‘Fuji’ × ‘Pinova’ and ‘Golden Delicious’ × ‘Renetta Grigia di Torriana’ consisting together of 86 progeny with known high-density marker data were used. The parents ‘Fuji’ and ‘Pinova’ are present in the pedigree of five and three parental combinations of the imputation set, respectively. The parent ‘Golden Delicious’ can be found in all of the pedigrees from the imputation set, and therefore, relates to the whole progeny group of the apple REFPOP. Although the pedigree of ‘Renetta Grigia di Torriana’ is unknown, both parental combinations ‘Fuji’ × ‘Pinova’ and ‘Golden Delicious’ × ‘Renetta Grigia di Torriana’ are strongly related to the imputation set and therefore may provide a useful estimate of the imputation accuracy in other imputed parental combinations. An attempt to improve the imputation accuracy might include expanding the reference set with all 19 parents of the parental combinations as well as some of their ancestors for which high-density marker genotype data are not yet available.Lately, resources for high-density marker genotyping in apple became available with the development of the 480K array25. In concordance with previous findings, we found a strong linkage disequilibrium decay over short distances in the apple REFPOP dataset, the pattern of decay being very similar to that described by Urrestarazu et al.3 The linkage disequilibrium decay was observed in the apple REFPOP from a distance as short as ~2.5 kb. Given the genome size of a doubled haploid derivative of ‘Golden Delicious’, estimated to 651 Mb26, and the number of markers in this study, our marker resolution corresponded to one marker per ~2.1 kb on average. Based on this value, each group of loci in linkage disequilibrium should be on average represented by one marker. Thus, the marker coverage we report seems appropriate for genome-wide analyses, which is supported by our GWAS and prediction analyses. Due to the heterogeneity in the marker density over the genome, the statistical power could be reduced in specific regions with low SNP density.Earlier studies with lower density of genome-wide SNPs found that their number of markers was insufficient for GWAS because of a rapid decay in linkage disequilibrium in apple10 The weak latitudinal cline in the European accessions may reflect the population structure reported in this germplasm by Urrestarazu et al.2 The overall weak population structure in the apple REFPOP accession group, which was similar to a previously described weak genetic structure in apples of European origin, presumably reflected the generally highly admixed apple germplasm that is a result of the prominent gene flow characteristic of the cultivated apple gene pool27.Partial differentiation between European and non-European accessions in our material is consistent with significant differences between Old World and New World varieties found by Migicovsky et al.28, which accounts for potential confounding effects of kinship and population structure. Thus, this method allows to combine highly related plant material, like in a pedigree-based-analysis, and more diversified, unrelated individuals to integrate different levels of linkage disequilibrium in the same analysis, hence maximizing the chances of finding regions associated with the target trait. By performing GWAS on the apple REFPOP dataset, SNPs associated with phenotypic variation could be identified and assigned to previously known genomic regions. A genomic region located on chromosome 9 was significantly associated with the trait floral emergence. Quantitative trait loci (QTL) at close locations were previously identified for floral bud break, floral emergence, and flowering period30. The second SNP association with floral emergence was located on chromosome 11 approximately 1 Mb downstream from a SNP identified by Urrestarazu et al.3 This association may be related to a minor QTL on chromosome 11 discovered using best linear unbiased predictors for genotype by year interaction effect of one season for the mapping of QTLs associated to bud break date  in the study of Allard et al.30 For harvest date, one significantly associated SNP on chromosome 3 was located 14,610 bp upstream from the transcription factor NAC18.1 listed as gene MD03G1222600 on the GDDH13 v1.1 genome26. Other studies have identified associations between NAC18.1 and harvest date, and the gene is a known member of a family of conserved transcriptional regulators involved in ripening10. Another SNP on chromosome 3 associated with harvest date was located ~1 Mb upstream from a marker reported before by Urrestarazu et al.3 The remaining two SNP associations were found on chromosomes 10 and 16 where QTL for harvest date have also been discovered before31. The identification of SNPs associated with both phenology traits in well-characterized genomic regions and for one possible minor QTL indicates the suitability of the apple REFPOP for discovering other alleles with large and small effects on trait variability in apple. Although novel marker–trait associations could not be identified and their number was lower than in Urrestarazu et al.3, who also used genotypic data of the 480K array, the number of reported marker–trait associations in this work was higher than in GWAS studies using lower SNP densities obtained by genotyping by sequencing32.We applied GWAS using the multi-locus mixed-model (MLMM) method13, although cross-validation may have inflated predictive ability compared to a potential independent validation with a test set33. To our knowledge, floral emergence has not been predicted in apple before; in this work, an average predictive ability of 0.57 was reached for this trait. The predictions for harvest date had an average predictive ability of 0.75, which was higher than any previously reached accuracies of this, or equivalent, traits in apple11. The presented genomic prediction methodology may be directly applied for the breeding of floral emergence and harvest date. In particular, breeding programs using germplasm related to the apple REFPOP may capitalize on this work.Applying a genomic prediction model with cross-validation, we were able to predict both phenology traits with moderate to high predictive ability when compared to the predictions for different apple traits reported previously15, the SNP density at which the plateau of predictive ability is reached may be specific to the apple REFPOP independently of the traits, but may differ for other populations of the same species. These results can have a practical impact on apple breeding, where cost-effective genotyping of 10K SNPs may be sufficient for precise genomic prediction. In breeding research, the same genotyping coverage may be adequate to perform GWAS of oligogenic traits. For complex traits under strong environmental control such as floral emergence, high-density SNP marker datasets remain desirable in GWAS. Future modeling including the effects of environment and genotype by environment interaction may contribute to a higher precision of genomic prediction in complex traits.The high SNP density in this study allowed for powerful GWAS and genomic prediction analyses, with overall lower performance for floral emergence than harvest date. Floral emergence appeared under weak genetic control with the majority of phenotypic variance explained by the effects of environment and genotype by environment interaction. Markers significantly associated with the trait explained a low proportion of the phenotypic variance in our study, pointing to a complex genetic architecture of floral emergence with many influential genomic regions yet uncovered. With SNP density increasing up to 150,000 SNPs, increasing amount of the phenotypic variance of floral emergence can be explained with GWAS. Environment-specific GWAS or GWAS with phenotypes from across several seasons and locations may allow for improved GWAS performance in floral emergence. For harvest date, a trait under strong genetic control with a large proportion of the phenotypic variance explained by a few major genomic regions, our results suggest that SNP density as low as 10,000 markers may be required to discover genomic associations with the trait. The 10,000 marker subset was also sufficient to reach a plateau of the predictive ability in genomic prediction of both traits, with the difference in predictive ability between traits possibly attributable to the trait architecture. As previously shown in American cranberryIn our study, the size of the SNP marker dataset seemed to affect the genomic prediction ability stronger than the feature selection method. On the contrary, a higher power of GWAS to detect marker–trait associations can be obtained with a smaller SNP marker dataset than with a larger set of SNPs depending on the representation of genes underlying the traits in the SNP marker dataset. This way, more marker–trait associations could be revealed with the 7060 SNPs of the 20K array than using SNPs pruned for linkage disequilibrium and such pruning should be avoided prior to GWAS.In the light of prediction precision analysis, the lower predictive ability for floral emergence may be explained by a higher complexity of this trait, together with lower heritability. Importantly, the results were very likely impacted by the low phenotypic variability of floral emergence in the season of 2018. Additional phenotyping seasons will likely contribute to a better representation of the flowering variability in the population.34. We found a moderate but noticeable effect of the genotype by environment interaction on both phenology traits evaluated in 2018, which contrasts with the limited effect of genotype by environment interaction on a trait similar to harvest date reported in sweet cherry34. The replication of the apple REFPOP across six environments will enable the inclusion of these interactions into genomic prediction models. Furthermore, GWAS across separate environments can be performed in the future to identify environment-specific associations and evaluate the stability of associations across environments.The performance of breeding material in tested as well as untested but similar environments can be predicted accurately using genomic prediction models taking into account genotype by environment interactionsThe apple REFPOP was also designed for comparing different management practices: one part of every orchard was grown under the conventional practice of each region, to evaluate the response of the germplasm to environmental effects; the second part can be managed in order to evaluate response to managements such as reduction of irrigation or pesticide application. However, the second management practice has not been applied so far to allow the trees to mature. Incorporating genotype by management and genotype by environment by management interactions in prediction models may help select new material adapted to drier climates or with stronger resistance to apple pests and diseases.36.In addition to the multi-environment and multi-management design, protocols for phenotyping of various traits have been applied since 2018 to evaluate the apple REFPOP. More than 10 different traits including yield, fruit quality and phenology are being simultaneously phenotyped with the same method at the six environments. Genotypes are replicated at least twice at each of the environments; each tree is evaluated for all traits separately to allow for variance decomposition up to the individual level . Using multi-trait genomic prediction models, prediction of traits with low heritability or labor-intensive phenotyping can be supported by genetically correlated traits with higher heritability and available phenotypesThis study benefits from a collaborative European approach dedicated to the improvement of apple breeding via genomics-assisted methods. A reference population, which sampled diverse apple germplasm and current European breeding material at larger scales than most current breeding programs, has been established. An extensive set of high-density SNP marker data has been assembled via cost-effective validated marker imputation while making use of the recently available SNP arrays and pedigrees. The imputation method of localized haplotype clustering together with the consolidated high-density SNP marker dataset can be implemented as a standard for cost-effective genomics-assisted breeding. Our diversity and quantitative genetics analyses showed that the reference population is representative of the current apple diversity and breeding material, and that the associated genotypic resources and experimental design allow for the development and application of genomics-assisted breeding methods in apple. This work emphasized the positive effects of high marker density on GWAS and the role of trait architecture in both GWAS and genomic prediction. The apple REFPOP with its unique multi-environment, multi-management and multi-trait design represents a rich source of data for future environment-specific GWAS and genomic predictions. Particularly, the predictions produced with models accounting for the interaction effects between genotype, environment, and management, as well as using multi-trait modeling can help untangle the effects underlying the traits and ultimately improve the efficiency and success of apple breeding. The apple REFPOP will be the cornerstone of many future projects including the application of genomic selection in apple and the work on apple in the EU-H2020-INVITE project (2019–2024).7. The accession group consisted of old and modern diploid accessions representing a wide range of genetic diversity in apple. Simple sequence repeat data obtained by Fernández-Fernández37, Lassois et al.21 and Urrestarazu et al.2 were used to allocate unique genotype code  to the accessions included in these studies, which resulted in 1292 unique genotypes available for further choice. When possible, passport data of the accessions belonging to each unique genotype were used to identify its country or region of origin. To form the accession group, a subset of the unique genotypes was created. All possible unique genotypes were chosen when <15 genotypes were available per each country or region of origin. For origins represented by a larger number of accessions, priority was given to the genotypes already analyzed with the Axiom®Apple480K array18. Additional genotypes of each origin were chosen randomly so that the overall number of selected genotypes per origin was proportional to the number of genotypes of this origin in the whole collection of unique genotypes. Unique genotypes previously analyzed with the 480K array but of unknown origin were also included. Additionally, five accessions  considered as founders in the progeny group pedigree were added to the accession group. Most accessions were chosen from the apple germplasm collection of the National Fruit Collection, Brogdale, United Kingdom in order to simplify collection of the plant material. The budwood of the founders stemmed from two sources: France’s National Research Institute for Agriculture, Food and Environment (INRAE), Angers, France and Wageningen University and Research (WUR), Wageningen, The Netherlands. Availability of budwood from trees affected the numbers of chosen accessions. Therefore, accessions often had to be either (i) replaced with a different accession of the same MUNQ or (ii) excluded in case no other accession corresponding to the unique genotype was available or could provide enough budwood. Additionally, the triploid accession ‘Biesterfelder Renette’ (MUNQ 1106.1) and the accession ‘Karinable’ (MUNQ 7828) with no available SNP data were excluded from the analysis, although planted in the orchards.The apple REFPOP collection composed of accessions and progeny was designed and established by the collaborators of the FruitBreedomics project7. These full-sib parental combinations originated from eight different breeding programs and they were obtained from 32 parents while 13 of the parents were included in the accession group. For most parental combinations, genotypic information was available ahead of this study, with different genotyping density depending on the parental combination. Twenty-two parental combinations had been genotyped with the 20K array38. In addition, in the frame of a pilot study of genomic selection9, three other parental combinations were genotyped with a custom 512 SNPs array using the TaqMan OpenArray technology covering the whole genome at a very low density. Finally, for two parental combinations, whole genome data were not available.The progeny group of the apple REFPOP included 27 full-sib parental combinations previously used in the European project FruitBreedomics39. In all cases, the 10 individuals formed the center of each of the clusters defined by genetic distance. Where budwood was not available in sufficient numbers, they were either (i) replaced by individuals closest to the center of the same cluster or (ii) excluded from the progeny group leading to fewer than 10 genotypes per parental combination being chosen . From the parental combination ‘Jonathan’ × ‘Prima’, 11 progeny were included in the REFPOP. One progeny of the ‘Dalinette’ × X6681 parental combination (NOVADI/0830) was found as triploid using 20K genotypic data and thus excluded from the analysis, although planted in the orchards. For the two parental combinations without whole genome marker data available, individuals were chosen randomly.A subset of 10 individuals per parental combination was chosen to form the progeny group of the REFPOP. For the 25 parental combinations for whom the whole genome marker data was available, 10 individuals were chosen using a genetic distance sampling strategy40. Depending on the environment, planting distance within and between tree rows ranged from 0.9 to 1.3 m and 3.2–3.6 m, respectively. All orchards were divided into two parts: the first part was to be managed with the common agricultural practice of the country, the second was to receive alternative management conditions . So far, both parts have been managed in the same way. The first part consisted of two randomized complete blocks, totaling together 1068 trees, each block containing one replicate per genotype. The second part also consisted of two randomized complete blocks, each containing one representative of approx. one-third of the genotypes (on average 184 genotypes). Every environment shared about half of these genotypes (92 on average) with one of the other countries . Additionally, each environment shared on average 34 genotypes with three further countries. The blocks within parts were used to ensure that two replicates of the same genotype were not planted at a close proximity to each other, but were not intended to block for environmental effects. The two parts were physically separated by a row of trees comprised of additional representatives of genotypes included in the apple REFPOP as well as other material. Since the alternative management regimes were not applied in the initial years, the trees in the barrier, as well as trees in what would later be the alternative management scenario may have contributed phenotypic values for traits in 2018. Three control genotypes ‘Gala’, ‘Golden Delicious’, and Modì® ‘CIVG198’ were each replicated 48 and 18 times in the first and the second part of the orchard, respectively.In 2015, budwood from each apple genotype was collected and grafted onto ‘M9’ rootstocks. The grafting was performed in three different nurseries, i.e., at (i) INRAE Angers, France, (ii) Better3Fruit, Rillaar, Belgium, and (iii) Consorzio Italiano Vivaisti, San Giuseppe, Italy. The following year, grafted trees were planted across six contrasting environments, each located in (i) Rillaar, Belgium, (ii) Angers, France, (iii) Laimburg, Italy, (iv) Skierniewice, Poland, (v) Lleida, Spain, and (vi) Wädenswil, Switzerland. The environments ranged across several biogeographical regions in Europe, i.e., the Mediterranean in Spain, Atlantic in France and Belgium, Alpine in Italy and Continental biogeographical region in Switzerland and Poland19. The SNP marker dataset included all apple REFPOP accessions (including 13 parents of the apple REFPOP progeny group) and additional unique genotypes later used as a reference set for marker imputation. The applied filtering strategy differed from the original one described by Bianco et al.18 in discarding the quality prediction based on metrics of the SNP clusters and making use of the pedigree, which was reconstructed in a recent study using all genotyped diploid unique genotypes19. For more details about SNP filtering, see Supplementary Methods 26 were used. Markers unassigned to the 17 apple chromosomes were excluded, resulting in a dataset of 303,239 biallelic SNPs.A SNP marker dataset for the apple REFPOP was produced using two overlapping SNP arrays of different resolution. The genotypic data generated with the 480K array for a total of 1356 unique genotypes were retrieved from previous studies38. The 49 remaining progeny from parental combinations X338 × ‘Braeburn’, ACW 11303 × ACW 18522, ACW 13652 × ACW 11567, ‘Dalinette’ × X6681, and X6398 × ‘Pinova’ were genotyped with the 20K array within the framework of this study. All 20K array SNPs were filtered and the allele data for the remaining SNPs were curated to ensure the data made logical marker inheritance and co-segregation patterns following the methods and principles described by Vanderzande et al.41 The set of 20K-array-generated markers was aligned to the 480K array marker set and 7060 of the 20K array SNPs were retained for further analysis.Genomic data for the apple REFPOP progeny group were generated using the 20K array. For 210 progeny from 22 parental combinations, the data were already available19. Second, the imputation set was formed of the remaining 259 progeny from 27 parental combinations . Third, 40 additional progeny of the parental combination ‘Fuji’ × ‘Pinova’ and 46 progeny of ‘Golden Delicious’ × ‘Renetta Grigia di Torriana’ which had all been genotyped using the 480K array18, but none of which had been chosen for inclusion in the apple REFPOP, were designated as a validation set.Due to the difference in marker resolution of the SNP arrays that were used to generate the SNP marker datasets, marker imputation was performed to provide high-density SNP marker information across the whole apple REFPOP. Genotypes included in the apple REFPOP and additional genotypes involved only in the imputation were used either as (i) reference for the imputation or (ii) imputation set or (iii) validation set Table . First, 42. In the first step, reference genotypes  between pairs of SNPs on each chromosome with the R package snpStats43. To reduce computational time, SNPs of each chromosome were sampled randomly to include one tenth of the markers per chromosome in the r2 calculation, which resulted in 4.6 × 108 marker combinations. A loess smoother (α = 0.5) was fitted to 100,000 randomly chosen r2 values across the whole span of chromosomes. Additionally, the loess smoother (α = 0.5) was calculated for all obtained r2 values for pairs of SNPs within a 5 kb distance. To determine the distance between SNPs at which the r2 dropped below 0.2, average r2 was calculated at 100, 5, 1, and 0.1 kb (100 bp) as a mean of all r2 within a window of 100 bp around each of the values.Linkage disequilibrium statistics were calculated as a square of the correlation coefficient  with supplementary individuals was performed with the R package FactoMineR45. Tenfold cross-validation for the number of populations K = {1, 2, …, 20} was performed with ADMIXTURE 1.3, a program for estimating ancestry in unrelated individuals46. ADMIXTURE was used with default settings and a subset of markers filtered according to the program’s manual. To avoid spurious effects of high linkage disequilibrium between adjacent markers, SNPs were removed in sliding windows of 50 SNPs advanced by 10 SNPs when squared correlation was >0.1 for pairs of variants, leading to a subset of 12,374 SNPs. The correct K value was identified at the lowest cross-validation error. As structure is best estimated among unrelated (or weakly related) individuals, the neighbor-joining tree and ADMIXTURE were estimated for the accession group only. For the population structure analyses, the European accessions were divided into several broad regions of origin to compensate for the uncertainty around the exact origin of old varieties2.The neighbor-joining method as implemented in the R package ape47. Harvest date was measured as the date when more than 50% of the fruits reached full physiological maturity, as determined by iodine coloration or expert knowledge47. Both traits were evaluated for each of the replicate trees individually. Deviation from the phenotyping protocol for harvest date led to exclusion of harvest date recorded in Poland. After measurements, dates were converted to counts of days starting at the beginning of the year in which they were measured.Two phenotypic traits were evaluated at the six plantation sites in 2018. Floral emergence of each tree was recorded as the date when 10% of flowers openedRaw phenotypic values were corrected for spatial heterogeneity individually within environments to obtain the adjusted phenotypic values of each tree. The corrected as well as uncorrected (raw) phenotypic values were used to estimate the individual-location clonal mean heritability. The adjusted phenotypic values of each tree were further used to fit a mixed model including the effects of genotype, environment and their interaction. The variance of each effect was calculated from the fitted mixed model to estimate multi-location clonal mean heritability and the fraction of phenotypic variation associated with the effects. Finally, the adjusted phenotypic values of each tree were used to obtain phenotypic least-square means of genotypes across environments, i.e., a single mean phenotypic value for each genotype.20. To specify the smooth component, a two-dimensional penalized tensor-product of marginal B-spline basis functions based on the P-spline ANOVA approach (PS-ANOVA) was defined with the default settings as a function of covariates plantation row and column, further denoted as f. The following linear mixed model was fittedy being the vector of phenotypic values measured for each tree, u and v denoting the numeric positions, i.e., rows and columns, the vectors cg, cr and cc being the random effect coefficients for the genotypes, rows and columns (as factors) associated with the design matrices Zg, Zr and Zc, respectively, the ε denoting the random error vector. Spatial independence assumption of the error vector was visually assessed using a residuals’ spatial plot for each model fit as described by Rodríguez-Álvarez et al.20 To characterize the importance of model components, effective dimensions associated with each random factor , the PS-ANOVA spatial trend (fv(v), fu(u),uhv(v),vhu(u) and fu,v) and the total effective dimension EDs  were assessed20. Predicted values of genotypes adjusted for spatial heterogeneity within each environment were produced with random model terms of the smooth component and the random row and column effects excluded from the predictions. These values were used to visualize variability between traits and sites. Residuals for each tree  were extracted from the model fit and summed with the corresponding predicted values of genotypes adjusted for spatial heterogeneity within each environment to obtain adjusted phenotypic values of each tree.To account for spatial variation of the complete block design, e.g., due to different soil composition or water availability in the orchards, and to predict adjusted phenotypic values of each tree, spatial heterogeneity in the phenotypic data was modeled separately for each environment and trait using the spatial analysis of field trials with splines (SpATS)H2 was estimated for each of the traits and environments before and after the spatial correction. A random-effects model was fitted for each environment via restricted maximum likelihood (R package lmer48)yik was the kth phenotypic value from genotype i , µ was the grand mean, gi was the random effect of the ith genotype and εik was the error term. Individual-location clonal mean heritability was calculated from variance components of the model as total genotypic variance To evaluate the efficiency of the spatial correction method when comparing raw data with data adjusted for spatial heterogeneity, individual-location clonal mean heritability The individual-location clonal mean heritability was used to eliminate one trial with the heritability value below 0.1.48)yijk was the kth adjusted phenotypic value of each tree from genotype i in environment j, µ was the grand mean, gi was the random effect of the ith genotype, lj was the fixed effect of the jth environment, glij the interaction effect between the ith genotype and jth environment (random) and εijk was the error term. Then, multi-location clonal mean heritability was calculated using Eq.  of genotypes across environments were calculated with the R package doBy49. The phenotypic least square means of genotypes across environments were used later for genome-wide association analyses and genomic prediction.Phenotypic least-square mean of each genotype across environments was estimated from the adjusted phenotypic values of each tree corrected for spatial heterogeneity within the environments. First, a multiple linear regression model was fitted for each trait28, a stepwise mixed-model regression for mapping complex traits under population structure, was applied to perform GWAS for both apple REFPOP groups together. As a response variable, the phenotypic least-square means of genotypes across environments were used. MLMM was used as implemented in the R package GAPIT 3.050 with default settings and SNPs with low minor allele frequency (0.05) removed. Marker–trait associations were found as significant for p-values falling below a Bonferroni-corrected significance threshold α* = α/m with α = 0.05 and m representing the number of tested markers. The proportion of phenotypic variance explained by each SNP marker significantly associated to the phenotypic least-square means of genotypes across environments was estimated as a coefficient of determination (r2). The r2 was estimated from a simple linear regression model fitted using the numeric marker values of a single SNP as predictor and phenotypic least-square means of genotypes across environments as response.The multi-locus mixed model (MLMM) method51 was used for genomic prediction of breeding values. The model was defined asy being the vector of phenotypic least-square means of genotypes across environments, W the design matrix relating genotypes to y, G the SNP matrix, ε the vector of errors. Five-fold cross-validation was applied with the model and data of the whole apple REFPOP, each run masking 20% of the genotypes as validation set. Marker effects (BLUPs) were generated from the remaining 80% of the genotypes to make predictions for the validation set. Predictive ability was estimated as an average value of Pearson correlation coefficient calculated between observed phenotypic least-square means of genotypes across environments from each validation set and predictions for the same genotypes. The cross-validation was repeated 100 times, the five folds being chosen randomly without replacement before each of the repetitions.The RR-BLUP model52, the markers were chosen evenly spaced from a random starting point. Since the 480K array was designed to cover not only the genic regions, but also to reach a uniform coverage of non-genic regions18, the order of the markers on chromosomes was used as a proxy for their physical distance when sampling. For each of the nine SNP densities, the SNP choice was repeated with 10 different seeds resulting in 90 subsets. For these subsets, GWAS and genomic prediction were performed as described above, with the five-fold cross-validation of the genomic prediction being repeated 10 times for each subset. The number of significant associations detected by GWAS was determined as the number of regions containing SNPs with p-values falling below a Bonferroni-corrected significance threshold. Mean number of the significant associations in GWAS and mean prediction ability of the genomic prediction as well as their 95% confidence interval were calculated for each number of chosen markers.Additionally to the analyses with the full set of 303,239 SNPs produced with the 480K array, different subsets of SNPs were used to perform the GWAS and genomic prediction to investigate the effect of feature selection approaches on model performance. SNPs in subsets were chosen according to three main feature selection strategies, (i) the SNP set from the 20K array (7060 SNPs) available in the full SNP marker dataset, (ii) the SNP set thinned according to linkage disequilibrium , and (iii) an unsupervised SNP choice. For this latter strategy, data subsets were built for densities of 500, 1000, 5000, 10,000, 50,000, 100,000, 150,000, 200,000, and 250,000 markers. As suggested by Bermingham et al.53. The approximation of the precision  or 0.8 (high). To interpret the output, trait architecture was classified using M into oligogenic (M ≤ 10), complex (10 < M ≤ 100), and very complex (100 < M ≤ 1000). Precision of genomic estimated breeding values was considered very high when equal or larger than 0.8. All statistical analyses and data formatting in this article were performed with R54 and visualized with the R package ggplot255, unless stated otherwise.Expectations of the precision of genomic estimated breeding values were approximated based on Eq. , i.e., ESupplementary figuresSupplementary table 1Supplementary table 2Supplementary table 3Supplementary table 4Supplementary table 5Supplementary table 6Supplementary methods


Cleft lip with or without cleft palate (CL/P) is one of the most common congenital malformations in humans involving various genetic and environmental risk factors. The prevalence of CL/P varies according to geographical location, ethnicity, race, gender, and socioeconomic status, affecting approximately 1 in 800 live births worldwide. Genetic studies aim to understand the mechanisms contributory to a phenotype by measuring the association between genetic variants and also between genetic variants and phenotype population. Genome-wide association studies are standard tools used to discover genetic loci related to a trait of interest. Genetic association studies are generally divided into two main design types: population-based studies and family-based studies. The epidemiological population-based studies comprise unrelated individuals that directly compare the frequency of genetic variants between  cases and controls. The alternative to population-based studies (case–control designs) includes various family-based study designs that comprise related individuals. An example of such a study is a case–parent trio design study, which is commonly employed in genetics to identify the variants underlying complex human disease where transmission of alleles from parents to offspring is studied. This article describes the fundamentals of case–parent trio study, trio design and its significances, statistical methods, and limitations of the trio studies. Cleft lip with or without cleft palate (CL/P) is one of the most common congenital birth defects with a complex etiology,Genetic association studies are generally divided into two main design types: population-based studies and family-based studies.The alternative to population-based studies (case–control designs) includes various family-based study designs that comprise related individuals.The model of Mendelian inheritance offers a straightforward rationalization of the genetic design of a trait. It prescribes that one gene locus produces the trait in either recessive or dominant pattern in families. However, many traits do not follow such a straightforward model of genetic architecture. Based on Mendelian inheritance principles, every parental allele has a 50% probability of being transmitted.Under the null hypothesis of no association between the disease and the marker, every parent transmits one of their two alleles to each offspring at random with a probability of 50/50 and independently of the other parent and any other oﬀspring. For the example inCase–parent trio studies are commonly employed in genetics to identify the variants underlying complex human disease. It involves the diseased/affected child and their parents (father and mother). In these studies, the affected children are selected from a population and then the affected children and their parents are genotyped.Case–parent trio designs study the effects of a gene marker and gene–environment (GxE) interaction.The family-based association studies were initially proposed by Falk and Rubinstein to avoid false-positive association test results.genomic imprinting.In most of the genetic association studies, investigators compare an allele or genotype frequencies in unrelated case and control subjects or examine preferential allele transmissions from parents to affected offspring. It is important to contemplate parent of origin effectsGxE interactions have significant scientific and public health implications.This design has the most significant advantage of being robust to population structure bias as the estimation of gene transmission would be within the families, conditioning on parental genotypes, and it is an unbiased method as all the subjects are from the same family.Several genetic studies focused on numerous complex genetic and epigenetic effects associated with a nonsyndromic CL/P, suggesting that the mother transfers half of her genome to the offspring and provides the environment for the fetus. Variation within the mother's genome could affect the intrauterine environment to the development of the fetus. Parent-of-origin effects, where the effect of inherited DNA depends on whether it is transmitted from the mother or the father, may be difficult to study with a population-based case–control design. More complex genetic effects such as maternal genotype effects, maternal–fetal interactions, and parent-of-origin effects can be best studied using the case–parent trio design, where affected cases and their parents are genotyped.The advantages of case–parent trio design studies are as followsRobustness in sample collection and false conclusions because of population stratification and ethnic heterogeneousness.Testing directly for maternal versus paternal effects.It permits the effects of fetal genotype versus parental origin in a very robust manner.Correct mutations are often obtained.It is unbiased as they share the same genetic ancestry.Simplex families (only the affected member) will be used effectively to check for linkage in the presence of disequilibrium.Family information will be helpful to check maternal genotype and parent-of-origin effects.It minimizes problems with confounding that plague traditional case–control designs as a result of the observed case is always compared with “controls” obtained from the same family.It is useful to check for GxE interaction under the conditional logistic or logistic regression framework.Case–parent trio design studies employ a distinct statistical procedure to examine the linkage and association of a gene with the trait. When studying families, the transmission of alleles from the parent to the offspring is analyzed. In this sense, parents are used as genetic controls for their children.Transmission Disequilibrium Test (TDT): it compares the offspring to its antiself, and the unobserved instance of an offspring with each nontransmitted allele.Conditional on parental genotype (CPG): it compares the proband to unobserved pseudosiblings with all possible transmission patterns. Again, these pseudosiblings are not determined; however, the results of conditioning on the parental genotype are used to make a matched analysis.Combined likelihood approach: this method collectively models the likelihood of parental and case genotypes.The most common statistical procedure used in case–parent trio design study is the TDT introduced by Spielman et al. It is a robust test for the linkage and disequilibrium in a variety of complex diseases that are associated with genetic etiology. It is more sensitive than haplotype sharing tests and requires only simplex families.The CPG approach developed by Schaid and Sommer models the probability of an affected child's genotype CPG as a function of the genotype relative risks (GRRs) of the child.http://www.goldenhelix.com) and freely accessible software system PLINK.There are various commercially available software suites for case–parent trio study designs such as Golden Helix , some are intrinsically uninformative about allele transmission.They provide a robust assessment of gene effects; however, they do not impart complete information on GxE interaction.Not all of the parental genotypes (one or both) are available for the study because of death, separated parents (divorced), or false paternity.Some families/parents may refuse to participate in clinical research.The cost of genotyping is expensive for the case–parent trios (three persons) than for the case–controls (two persons) without a corresponding linear increase in statistical power.Difficulty in recruiting large samples and time-consuming.Discarding those families with missing one or both parental genotypes will cause statistical power loss.If there is no deviation from multilocus Hardy–Weinberg equilibrium, the case–parent trio design will have no power to discover even tight linkage.Case–parent trio studies are commonly used in genetics to identify the variants underlying complex human disease. They are useful to study the transmission of genetic variants between parents and oﬀspring and how genetic variants diﬀer between the aﬀected individual(s) and the unaﬀected individuals within a family. This design has the most significant advantage of being robust to population structure bias and can test for more complex genetic effects such as maternal genotype effects, maternal–fetal interactions, and parent-of-origin effects that are significantly relevant when studying congenital birth defects.In the absence of GxE interactions, using cases and their parents has proved to be a powerful test to assess disease associations with candidate genes. Case–parent trio study designs are adequate to estimate the genetic effects, and therefore the aim of collecting genetic information from family members enrich the genetic analysis, increase the power of study, help in obtaining correct mutations, and address the priority regarding population structure bias and methods of combining genetic information from unrelated cases and controls.


At present, little is known about the asymptotic distribution of the γ-statistic when conducting association analyses for rare variants. One advantage of OV-RV is that it provides a robust estimation of the distribution of the γ-statistic by employing the permutation approach proposed by Fisher. We also perform extensive simulations to investigate the numerical performance of OV-RV under various model settings. The simulation results reveal that OV-RV is valid and efficient; namely, it controls the type I error approximately at the pre-specified significance level and achieves greater power at the same significance level. We also apply OV-RV for rare variant association studies of diastolic blood pressure.In recent years, there has been an increasing interest in detecting disease-related rare variants in sequencing studies. Numerous studies have shown that common variants can only explain a small proportion of the phenotypic variance for complex diseases. More and more evidence suggests that some of this missing heritability can be explained by rare variants. Considering the importance of rare variants, researchers have proposed a considerable number of methods for identifying the rare variants associated with complex diseases. Extensive research has been carried out on testing the association between rare variants and dichotomous, continuous or ordinal traits. So far, however, there has been little discussion about the case in which both genotypes and phenotypes are ordinal variables. This paper introduces a method based on the  However, recent evidence suggests that only a small proportion of the phenotypic variance can be explained by common variants , which is obviously unreasonable in GWAS. Recent studies have shown that ignoring the different directions and magnitudes of rare variant effects may lead to loss of testing efficiency  be the genotype at the m loci, where Gij is the number of mutations in variant j for subject i. In general, Gij ∈ {0, 1, 2}. The genetic score of the genotype for subject i is defined aswi is a weight and g( · ) is a link function. In practice, the selection of the weight and the use of the link function can be of various types as long as they are justified. For example, one can choose the weight utilized in Madsen and Browning (wi = 1 and the link function (.) is an indicator function. At last, according to the genetic score, the genotype levels are sorted from small to large. Correspondingly, the phenotypes can be sorted from small to large in terms of the degree of the disease. For i = 1, …, n, let i and j be the numbers of different Yi and different Gi, respectively. For ease of notation, denote by Y the phenotype and denote by G the genotype score at the m loci. Let 0, 1, …, I − 1 and 0, 1, …, J − 1 be the levels of Y and G, respectively.Suppose there are Browning  to ensur2.1.γ-statistic explicitly, we first provide a brief description of the cross-contingency table for rare variant association studies. The cross-contingency table of the genotype level at m loci by the phenotype level is listed in xij is the number of subjects that occurs in the cell in row i and column j. Denote by πij the joint probability of  in the cell of row i and column j and by {πij}I×J the joint distribution of .The cross-contingency table is a tool that can properly display the joint distribution of categorical variables and has been widely used in categorical data analysis. In order to express the framework of the 2.2.Y and G are ordinal, one would expect to test the monotone trend association between Y and G, where the monotone trend association refers to Y trending to increase to higher levels or trending to decrease to lower levels as the level of G increases. Define that a pair of subjects is concordant if there exists a subject that ranks higher on G and Y simultaneously. Similarly, define that a pair of subjects is discordant if there exists a subject that ranks higher on G but ranks lower on Y. Consider two independent observations randomly sampled from the joint distribution {πij}I×J. For this pair of subjects, we can express the probabilities of concordance and discordance as follows:c − Πd.When both Y and G; in other words, the probability of ties Yi = Yj or Gi = Gj is zero. Then, Πc/(Πc + Πd) and Πd/(Πc + Πd) are the probabilities of concordance and discordance, respectively. Goodman ;Randomly permute the original phenotype ;Generate the new cross-contingency table by matching the permuted phenotype  is an indicator function.Step 2. Estimate the distribution of the In this section, we provide a detailed permutation approach for estimating the distribution of the 3.et al., et al., α level. Without loss of generality, the prespecified α levels are set to be 0·05 and 0·01 in the simulations. Second, we compare the power of these methods at the same significance level. According to the scheme for generating simulated data, the simulations are divided into two cases, including a designed parameter-based simulation and a real genotype-based simulation. The simulation results are based on 1000 replications.In this section, we explore the numerical performance of our method (OV-RV) and five existing methods, including CAST  of the corresponding rare variants. Within each region, we randomly sampled pj from the uniform distribution U. Under the assumptions of the Hardy–Weinberg equilibrium law, the probabilities that the genotype score Gij has a value of 0, 1 and 2 are (1 − pj)2, 2pj(1 − pj) and Gi, i = 1, …, n are classified into j ordinal categories, where For each locus Ti, i = 1, …, n are generated by the following linear model:ɛi, i = 1, …, n are independent and β = d · T if m = 20 and β = d · T if m = 40. In the following simulation, the values of d are set to be 0, 0·2, 0·4, 0·6 and 0·8, respectively. It is clear that Ti and Gi are independent when d = 0. Hence, examining the control of type I errors yielded by these testing methods is under the model setting d = 0. We use the 20%, 30% and 40% sample percentiles to discretize Ti, i = 1, …, n and generate ordinal phenotype variables Yi, which take values of 0, 1, 2 and 3. The simulation results are exhibited in To focus on the main points, we select 12 and 18 rare variants from the region of 20 and 40 rare variants as disease-causal variants, respectively. The intermediate variables m = 40 and α = 0.01. From the lower part of α = 0.05. Although the empirical type I error of WSS is relatively large when m = 40 and α = 0.05, it is still acceptable. These simulation results confirm the validity of the eight methods in Simulation I.d varies from 0·8 to 0·2. Note that the larger the value of d, the stronger the trend association between the ordinal phenotype variable and the ordinal genotype variable. It is easy to interpret the aforementioned simulation results. We can also observe that the power of OV-RV uniformly dominates the other competing methods. This indicates that our OV-RV is more efficient, especially when both the phenotype and the genotype are ordinal.3.2.http://www.1000genomes.org). Specifically, we select two genes, TG and COL6A3, as candidate genes. The TG gene contains 146 single-nucleotide polymorphisms (SNPs), among which 113 out of these 146 SNPs are rare (MAF <1%), whereas the COL6A3 gene consists of 187 SNPs, and 143 out of these 187 SNPs are rare. The means of action of these genes have been revealed in several studies . The GAW19 dataset contains whole genome and exome sequences for odd chromosomes, gene expression measures, systolic blood pressure and diastolic blood pressure (DBP), as well as related covariates in 20 large families and 1943 unrelated individuals. Here, we focus on the 1943 unrelated individuals provided by GAW19 and consider the DBP phenotype. A series of procedures for data pre-processing are performed before carrying out association studies. We eliminate individuals who have missing phenotypes, and a total of 1851 individuals are left for analysis. In addition, we complete the missing genotype by a random sample based on the MAF.EBF1 and NPR3 on chromosome 5, as well as gene TMEM133 on chromosome 11, are associated with DBP , we can obtain the gene starts and gene ends of these three genes. For each gene, genotypes are generated by selecting rare variant loci with MAF <5%. The significance level is set to be 0·05. The phenotypes are divided into four levels in terms of DBP. To be specific, phenotypes with DBP <60, 60 ⩽ DBP <80, 80 ⩽ DBP <90 and DBP ⩾ 90 correspond to levels 0, 1, 2 and 3, respectively. Due to the poor performance of the CAST, SUM and WSS methods in simulations, we only compare the performance of the remaining five methods. Detailed results are shown in p-values yielded by OV-RV are uniformly smaller than those of the competing methods. We can also see that OV-RV identifies all three DBP-related genes, whereas the other competing methods identify at most one related gene. This indicates that OV-RV is more efficient at detecting disease-related genes.DBP is measured in millimetres of mercury (mmHg) when the heart is at rest between beats. It has been reported that genes 5.γ-statistic has been successfully applied to the field of searching for the trend associations. However, the asymptotic distribution of the γ-statistic derived by Goodman (γ-statistic under the null hypothesis. Both the designed parameter-based simulation and the real genotype-based simulation illustrate that OV-RV is valid and more efficient compared with its competitors. A real data analysis on the GAW19 dataset shows that OV-RV achieves greater efficiency and can detect more disease-related genes.In this paper, we propose a novel method, called OV-RV, for the detection of the trend associations between ordinal genotypes and ordinal phenotypes. The  Goodman  is no loOur OV-RV can also be extended in several ways. First, it has been shown that different diseases or traits usually share similar genetic mechanisms. Conducting an integrative association analysis of several traits can significantly improve testing efficiency. Hence, it is desirable to develop a method for testing associations between ordinal genotypes and multiple ordinal phenotypes. Second, as illustrated in simulations, the power of OV-RV decreases as the proportion of effects in different directions increases. This means that OV-RV is conservative when a large proportion of effects are of different directions. It would be of interest to obtain a more powerful genetic score for extending OV-RV to these situations. Third, the permutation method brings large computation costs when there is a large number of rare variants. Recently, algebraic statistics has been successfully applied in testing independence from the sparse contingency table. It may give rise to a novel method for testing trend associations from the sparse contingency table.


Pinus radiata) population, possibly due to the presence of strong and well-estimated correlation with other highly heritable traits. Conversely, we did see benefit in a shining gum  population, where the primary trait had low or only moderate genetic correlation with other low/moderately heritable traits. Marker selection in multivariate analysis can therefore be an efficient strategy to improve prediction accuracy for low heritability traits due to improved precision in poorly estimated low/moderate genetic correlations. Additionally, our study identified the genetic diversity as a factor contributing to the efficiency of marker selection in multivariate approaches due to higher precision of genetic correlation estimates.Multivariate analysis using mixed models allows for the exploration of genetic correlations between traits. Additionally, the transition to a genomic based approach is simplified by substituting classic pedigrees with a marker-based relationship matrix. It also enables the investigation of correlated responses to selection, trait integration and modularity in different kinds of populations. This study investigated a strategy for the construction of a marker-based relationship matrix that prioritized markers using Partial Least Squares. The efficiency of this strategy was found to depend on the correlation structure between investigated traits. In terms of accuracy, we found no benefit of this strategy compared with the all-marker-based multivariate model for the primary trait of diameter at breast height (DBH) in a radiata pine ( Heritability is one of the most important genetic parameters to consider for breeding, defined as the proportion of phenotypic variance explained by underlying genetic factors  and shining gum [Eucalyptus nitens (H. Deane & Maiden) Maiden], a proxy for productivity in forest trees and thus considered the most economically important trait for those species. Non-target traits involved in the multivariate analysis represent operationally measured attributes related to stem form and wood quality.The aim of this study is the improvement of genomic prediction for traits with relatively low heritability and poor prediction accuracy, such as those related to forest tree productivity , structured into 42 full-sib families each represented by ~10 individual genotypes, part of The New Zealand Radiata Pine Breeding Company's (RPBC) program, selected for growth and form attributes. The field experiment was established as an incomplete block design containing nine blocks, each comprising six families with five replicates per family. All individuals were evaluated for the following traits: branch cluster frequency (BR9), visually assessed using a 9-point scale from 1  to 9  , measured as basic wood density through the maximum moisture content method  platform , wood stiffness (ST [km/s]), growth strain (GS [mm]), and average tangential air-dry shrinkage (TS [%]) measured on two different logs: log 1 from 1.4 to 3 m (index 1) and log 2 from 3 to 6 m (index 2) at the age of 7 , g is the vector of random additive genetic values following var(g)~N~N~N for genotype in y is the vector of individual-tree trait measurements, β is the vector of fixed effects , e is the vector of random residual effects following var(e)~N , where X is the scaled matrix of marker genotypes and Y is the scaled matrix of clonal values for measured traits, and u and v are vectors of coefficients maximizing the covariance. The coefficients in u measure the importance of variables in X (genetic markers) to latent variables, and were therefore used as criteria for selection of markers to calculate the marker-based relationship matrix. Since prior knowledge of genetic architecture in studied traits and complexity of pleiotropy and QTL collocation is usually lacking, exploration of the whole matrix of combinations of selection intensity for potentially informative genetic markers was required. First, marker coefficients in the vector u associated with each component were truncated by the 90th, 80th, 70th, 60th, and 50th percentiles, and loadings for selected markers were transformed to either 1 or 0. For each percentile level, different numbers of components were included into the marker selection process.The BLUE estimates for genotypes for P. radiata) and prediction accuracy using the “BGLR” statistical R package  or marker information (GBLUP) were used to estimate narrow-sense heritability , g is the vector of additive genetic effects following var(g)~N~N (scenario MVGBLUP1). However, the relationship between traits is not driven only by markers acting in the same direction; some markers act in the same direction only for certain sets of traits, and in opposite directions for other traits (negative pleiotropy). To investigate the impact of such markers, we tested a second scenario where markers involved in the construction of the relationship matrix were selected from both positive and negative tails of the loading distribution (scenario MVGBLUP2). For example, in the 90th percentile scenario, markers were selected from both above the 90th percentile and from below the 10th percentile. The other scenarios continued to select the markers having loadings closer to the middle of their distribution. Again, this marker selection strategy was applied across the variable number of components included in this study. The improved marker-based estimates of genetic correlation were performed using marker weights implemented in the construction of a trait-specific marker-based relationship matrix ~N, where G1 is a variance-covariance structure for additive genetic effects following G1=G, where 1ana and σna1a are additive genetic covariances between the 1st and nth trait, ⊗ is the Kronecker product and G is the marker-based relationship matrix estimated either as follows:where Gw) as defined above, e is the vector of random residual effects following var(e)~N, where R is the residual variance-covariance structure following R = I, where 1ene and σne1e are residual covariances between the 1st and nth trait. The number of iterations in BGLR was set to 300,000, with a burn-in period of 50,000 iterations, thinning to 10. Given the different percentiles of marker loadings and numbers of latent variables used in marker selection, the best scenario was identified on the basis of the deviance information criterion (DIC). Additionally, single-trait model (scenarios BLUP and GBLUP) were implemented for each investigated trait to evaluate the benefit of the multivariate model over univariate analysis. Trait heritability was estimated following:where p_i is the frequency of the alternative allele at the ith loci, or estimated on the basis of weighted markers . The prediction accuracy was estimated as correlations between EBVs and GEBVs predicted through cross-validation. The statistical significance of difference in prediction accuracy between benchmark and the best scenario using selected markers, non-parametric Wilcoxon rank test was implemented  and 3.44–3.79% (P. radiata) of the total variance attributed to the first two principal components   as well as marker-based (GBLUP) univariate model in P. radiata. Heritability estimates were moderate to high, ranging from 0.093 (ST2) to 0.282 (WD) using sib-ship (BLUP) and from 0.089 (DBH) to 0.559 (WD) using markers (GBLUP) in E. nitens, and from 0.046 (ST9) to 0.588 (WD) using pedigree (BLUP) and from 0.126 (ST9) to 0.529 (WD) using markers (GBLUP) in P. radiata (Trait heritabilities were estimated using variance components inferred from a sib-ship reconstruction-based (BLUP) as well as marker-based (GBLUP) univariate model in  radiata . In geneE. nitens, genetic correlations ranged from −0.459 (between WD and GS2) to 0.859 (between GS1 and GS2) using sib-ship (MVBLUP)  to 0.548 (between WD and PME) using the pedigree (MVBLUP)  resulted in the number of selected markers ranging from 1,940 to 9,697 in E. nitens and from 9,838 to 58,636 in P. radiata (Using PLS-CA resulted in the construction of marker-based relationship matrices using different numbers of markers. When only markers with positive loadings (MVGBLUP1) were used, the number of selected markers ranged from 970 to 9,627 in  radiata .E. nitens population resulted in the worst model fit in terms of deviance information criteria (DIC). The model fit continually improved with more relaxed parameters on marker loadings. This pattern was observed for both tested strategies (MVGBLUP1 and MVGBLUP2). The best scenario appeared close to the one using all markers (MVGBLUP) (using seven components and the 40th percentile)  . There wrcentile .E. nitens. Similarly, in P. radiata, correlations reached values from 0.57 to 0.99. In both populations, the genetic correlations increased as the number of components as well as the proportion of markers selected within components increased  to 0.653 (BR9) in P. radiata. In marker-based models (GBLUP), this ranged from 0.183 (DBH) to 0.764 (WD) in E. nitens, and from 0.388 (DBH) to 0.645 (WD) in P. radiata. In general, the implementation of single-trait models (BLUP and GBLUP) resulted in lower prediction accuracies when the marker-based model (GBLUP) was compared to the pedigree/sib-ship based model (BLUP) (Prediction accuracy in the pedigree/sib-ship based model (BLUP) ranged from 0.246 (DBH) to 0.782 (WD) in l (BLUP) , 4.E. nitens, and from 0.553 (PME) to 0.679 (BR9) in P. radiata. In the marker-based model (MVGBLUP), this ranged from 0.529 (DBH) to 0.768 (WD) in E. nitens, and from 0.435 (ST9) to 0.618 (WD) in P. radiata. Generally, the implementation of multi-trait models (MVBLUP and MVGBLUP) followed a similar pattern as the single-trait model, in that the pedigree/sib-ship based model (MVBLUP) mostly outperformed the marker-based model (MVGBLUP), with a few exceptions, such as WD in E. nitens and DBH and WD in P. radiata (The prediction accuracies from the multi-trait model (MVBLUP and MVGLUP) were higher compared to the single-trait model (BLUP and GBLUP). Prediction accuracy in the pedigree/sib-ship based model (MVBLUP) ranged from 0.541 (DBH) to 0.754 (WD) in  radiata , 4.E. nitens and from 0.446 (ST9) to 0.627 (WD) in P. radiata. For models with markers selected using both positive and negative loadings (MVGBLUP2), prediction accuracies ranged from 0.414 (ST2) to 0.766 (WD) in E. nitens, and from 0.436 (ST9) to 0.631 (WD) in P. radiata. The marker-based models using marker selection (MVGBUP1 and MVGBLUP2) resulted in increased prediction accuracy of the primary trait while maintaining similar accuracies for other traits in E. nitens. No impact of marker-selection on prediction accuracy of the primary trait was observed in P. radiata (E. nitens when the MVGBLUP2 model was implemented (Prediction accuracy of the models with markers selected using only positive loadings (MVGBLUP1) ranged from 0.434 (ST2) to 0.759 (WD) in  radiata . The hig radiata –5. The slemented .E. nitens, reaching values from −0.952 (TS) to −0.559 (DBH) in scenarios where marker selection was based on positive marker loadings, and from −0.951 (TS) to −0.332 (WD) in scenarios where marker selection was based on both positive and negative marker loadings. The correlations between prediction accuracy and DIC were relatively weak in P. radiata reaching values from −0.721 (WD) to 0.115 (BR9) in scenarios where marker selection was based on positive marker loadings, and from −0.583 (DBH) to 0.623 (BR9) in scenarios where marker selection was based on both positive and negative marker loadings.The prediction accuracies estimated for each trait and marker selection scenario were correlated with DIC and number of selected markers. The correlations between prediction accuracy and DIC were strong for E. nitens, reaching values from 0.467 (DBH) to 0.910 (ST1) in scenarios where marker selection was based on positive marker loadings and from 0.274 (WD) to 0.923 (TS) in scenarios where marker selection was based on both positive and negative marker loadings. Conversely, the correlations between prediction accuracy and number of selected markers were rather weak in P. radiata reaching values from −0.235 (BR9) to 0.841 (DBH) where marker selection was based on positive marker loadings and from −0.613 (BR9) to 0.439 (DBH) where marker selection was based on both positive and negative marker loadings. For our primary trait (DBH), in both species the opposite pattern was found between prediction accuracy and number of selected markers compared with prediction accuracy and DIC . The efficient coordination of the pathways responsible for each particular attribute requires a certain level of organization in space and time, developed through modularity in the biological processes . Markers with strong associations to this alignment (large loadings) are likely positioned within the genomic regions showing pleiotropy or an accumulation of QTLs responsible for studied traits. Due to evolutionary trade-offs of gene functions on overall fitness, pleiotropy can act in opposite directions for affected traits  through their shared variances . Since the method maximizes covariance between the latent variables from each block (phenotypes vs. genetic markers) through the coefficients in vectors E. nitens population. Including more traits with no strong relationships . Finding markers associated with the underlying genetic correlation structure can therefore potentially further improve the precision of genetic correlation estimates and thus the prediction accuracy of involved traits. However, it is worth noting that the scenarios showing the highest prediction accuracy for low heritability DBH were not supported by the model fit patterns (DIC) in either the E. nitens or P. radiata populations tested. Therefore, model fit is not a good indicator for selecting the best model in this case.Our analysis found there was a benefit to using marker selection (MVGBLUP1 and MVGBLUP2) in the multivariate analysis in the H and WD , the preP. radiata. Traits in the same biological module usually show a high level of phenotypic integration, with pleiotropy likely contributing to this  and show low to moderate genetic correlations in order to benefit from this approach. On the other hand, there is no further benefit of the proposed method when the estimated genetic correlation between the traits is high, such as the genetic correlation between WD and DBH in The efficient implementation of genomic selection in forestry requires the consideration of at least three groups of factors: (1) the genetic architecture of measured traits, (2) the structure of the training population, and (3) the quality of the phenotypic and marker data. A trait's genetic architecture is measured through factors, such as heritability, mode of inheritance  and the effective number of chromosomal fragments , co-segregation and linkage disequilibrium between markers and QTLs , depending on selection intensity and reduction in additive genetic variance Bijma, . The redEucalyptus species (~0.56 Gb) has allowed the rapid and cost-effective development of the multi-species Eucalyptus SNP chip, based on SNP discovery from whole genome sequencing data  and large amount of repetitive sequences required a different SNP discovery and genotyping approach based on reduced representation sequencing of the genome  and ~ 35% (considering both positive and negative loadings) of markers were included in the marker-based relationship matrix in E. nitens, and ~94% and 99% markers in P. radiata  and other moderately heritable traits, this approach does not show benefit beyond that observed with the multivariate model using all genetic markers. One drawback is that this approach requires all individuals in the training population to be phenotyped for all traits included in the analysis to perform the marker selection procedure (PLS-CA).10.5281/zenodo.4040042.The datasets generated for this study can be found in the ZENODO data repository: doi: JK performed the analyses and drafted the manuscript. MS, HD, ET, NG, and YL designed the study, assisted with drafting the manuscript, and secured the funding. RM developed the phenotyping protocols for wood quality attributes. All authors significantly contributed to the current study.The authors declare that this study received funding from NZ Ministry of Business, Innovation and Employment and Radiata Pine Breeding Company Ltd. The Radiata Pine Breeding Company Ltd. was involved in phenotypic data collection. The funders were not involved in the study design, analysis, interpretation of data, the writing of this article or the decision to submit it for publication. JK was employed by the company Scion. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


With the rapid development of the poultry industry, outbreaks of certain avian diseases such as avian influenza, Newcastle disease, and salmonellosis can cause severe loss to local economies. An effective method to avoid this problem may be developing resistant lines on the basis of immune response traits. In our study, when the number of genotyped reference animals was small, the traditional pedigree-based method (BLUP) was more efficient than the genetic linear unbiased prediction of genomes (GBLUP) method in predicting the genetic parameters of sheep red blood cell antibody titer (SRBC), the ratio of heterophils to lymphocytes (H/L), the spleen immune index (SII) and the spleen weight at 100 d (SW) in Beijing oil chickens.Poultry diseases pose a large threat to poultry production. Selection to improve immune traits is a feasible way to prevent and control avian diseases. The objective of this study was to investigate the efficiency of estimation of genetic parameters for antibody response to avian influenza virus (Ab-AIV), antibody response to Newcastle disease virus (Ab-NDV), sheep red blood cell antibody titer (SRBC), the ratio of heterophils to lymphocytes (H/L), immunoglobulin G (IgG), the spleen immune index (SII), thymus immune index (TII), thymus weight at 100 d (TW) and the spleen weight at 100 d (SW) in Beijing oil chickens, by using the best linear unbiased prediction (BLUP) method and genomic best linear unbiased prediction (GBLUP) method. The phenotypic data used in the two methods were the same and were from 519 individuals. With the BLUP model, Ab-AIV, Ab-NDV, SRBC, H/L, IgG, TII, and TW had low heritability ranging from 0.000 to 0.281, whereas SII and SW had high heritability of 0.631 and 0.573. With the GBLUP model, all individuals were genotyped with Illumina 60K SNP chips, and Ab-AIV, Ab-NDV, SRBC, H/L and IgG had low heritability ranging from 0.000 to 0.266, whereas SII, TII, TW and SW had moderate heritability ranging from 0.300 to 0.472. We compared the prediction accuracy obtained from BLUP and GBLUP through 50 time 5-fold cross-validation (CV), and the results indicated that BLUP provided a slightly higher accuracy of prediction than GBLUP in this population.  In poultry breeding, the main objective traits are growth and reproduction traits, whereas, little attention has been paid to the selection of immune traits. Regular immunization is a large expense in poultry production, and the problem of poultry diseases remains very serious ,2,3. SelSalmonella typhimurium resistance and has suggested that H/L is highly heritable in chickens. In general, SRBC and H/L can be more suitable as indicators for the breeding of new strains with high disease resistance. Both can measure the body’s general disease resistance and have stable heritability; consequently, selecting the traits can improve general disease resistance in chickens.SRBC is a non-pathogenic multivalent antigen that has been widely used in animal humoral immune response studies, it reflects the level of antibodies produced by the body . SRBC anAccurate and reliable estimation of genetic parameters is a prerequisite for rational breeding programs during the animal breeding process. In recent years, with the detection of single nucleotide polymorphism (SNP) markers and the rapid development of biochip technology, new genetic-prediction methods have been developed, notably the genetic linear unbiased prediction of genomes (GBLUP) method . GenomicThe objective of this study was to estimate genetic parameters of nine immune traits and to compare the accuracy of BLUP and GBLUP in genomic prediction on immune traits in Beijing oil chickens.Ethical approval on animal care and experimental procedures were performed in accordance with the Animal Ethics Committee of the Institute of Animal Sciences, Chinese Academy of Agricultural Sciences  with the following reference number: IASCAASAE-03.The data were collected from 519 Beijing oil chicken cocks raised at the Chang ping Experimental Base of Institute of Animal Sciences. The Beijing oil chicken is an indigenous Chinese breed characterized by slow growth and high meat quality. All birds were from the same batch, the offspring of 53 cocks and 199 hens. At 100 d of age, the chickens were killed, and blood and serum samples were collected. We recorded immune traits including Ab-AIV, Ab-NDV, SRBC, H/L, IgG, SII, TII, TW and SW . 2 value of the corresponding dilutions. H/L was measured by using blood smears made with fresh blood [Ab-AIV, AI-NDV, and SRBC antibody levels in the serum samples were measured with hemagglutination inhibition tests according to previous studies ,23,24,25SII (%) = weight of spleen(g)/weight of carcass(g)TII (%) = weight of thymus(g)/weight of carcass(g)Genomic DNA was extracted from blood samples with a conventional phenol method, and then genotyping was performed with 60K SNP chips . All 519 chickens with immune trait records were genotyped. PLINK (V1.07) software was used to control for the quality of chip genotype data, with individual call rates > 90%, SNP locus call rates > 95% and minor allele frequency > 1%. After quality control, 46 876 SNP markers and 519 individuals were used.In this study, two methods, a pedigree-based BLUP method with a pedigree-based relationship matrix and a GBLUP method based on genomic relationship matrix, were used to predict the breeding value.y was the vector of phenotypic values , μ was the overall mean, 1 was a vector of 1, a was the vector of additive genetic effects, following a normal distribution of N, where A was the pedigree-based genetic relationship matrix, and σa2 was the variance of additive genetic effects. Z was the incidence matrix associating a with y, and e was the vector of random residuals with distribution of N , in which I was the identity matrix, and σe2 was the variance of residuals.The traditional animal model with a pedigree-based relationship matrix was applied to predict breeding values for each trait separately . The mody, Z and e were the same as those in the BLUP model, g was the vector of genomic breeding values to be estimated, following a normal distribution of N, in which σg2 was the variance of additive genetic effects, and G was the marker-based genomic relationship matrix. Z was the incidence matrix linking g to y, and e was the vector of random residuals following a normal distribution of N , in which σe2 was the variance of residuals. The estimation of variance components and the prediction of breeding values were performed with the Asreml package [The GBLUP model was used to predict the GEBV of all genotyped individuals .(2)y=1μ package .Cross-validation (CV) is usually used to obtain a reliable and stable model, and to evaluate the quality of the model ,29. In tPredictive Ability: Correlation between phenotype and breeding value  values of estimated heritability for all traits were less than 0.110. The heritability of Ab-NDV and IgG was almost 0, and Ab-AIV, SRBC, H/L, TII and TW had low heritability ranging from 0.185 to 0.281. However, SII and SW had high heritability of 0.631 and 0.573, respectively. With the GBLUP model, SRBC, Ab-NDV and IgG had the lowest heritability. Ab-AIV and H/L had low heritability of 0.266 and 0.128, respectively. SII, TII, TW and SW had moderate heritability ranging from 0.300 to 0.472. The SE of estimated heritability was less than 0.090.As shown in p = 0.081), For H/L, as shown in In this study, the estimated heritability of nine immune traits ranged from 0.00 to 0.631 with a pedigree-based BLUP model and from 0.000 to 0.472 with the GBLUP model. Therefore, the estimate of heritability was higher with the BLUP method. For the BLUP model, the estimates of heritability for the two main selected immune traits, SRBC and H/L, were 0.185 and 0.265, respectively. SRBC and H/L had low heritability in Beijing oil chickens, which is in line with findings from previous studies. Boa-Amponsem has reported that maternal antibody levels affect antibody titers in next-generation chickens, and the heritability of chickens responding to antibodies produced by SRBC is relatively stable . Al-MurrThe SEs of heritability estimates were low. Although the dataset in our study was small, there are some possible reasons that may explain this finding. First, the individuals were from a single farm and lived in the same environment during the same period; thus, the model was simple, and relatively few parameters needed to be estimated. Second, the dataset had good structure in estimating genetic parameters because of the appropriate numbers of half-siblings and full-siblings.We selected SRBC and H/L as the target immune traits to detect the accuracy through 50 time 5-fold CV. Compared with the GBLUP method, the traditional BLUP method had slightly higher accuracy for the two immune traits, and the accuracy of prediction for H/L was higher than that for SRBC. Our results differed from those in previous reports ,35, in wOur research aimed to analyze the efficiency of BLUP and GBLUP in genomic prediction on immune traits in chickens. Estimates of heritability of SRBC, H/L, SII and SW were higher with the BLUP model than the GBLUP model. Importantly, the BLUP model led to slightly higher accuracy in genetic parameter prediction than the GBLUP model in our study.