Vrn-A1 locus. Historical selection for grain yield in Nordic wheat is associated with TaGS5-3A and TaCol-5 loci.Adaptation to the Norwegian environment is associated with polymorphisms in the −1 per year between 1972 and 2019 due to introduction of new varieties. These gains were associated with increments in the number of grains per spike and extended length of the vegetative period. However, little is known about the genetic background of this progress. To fill this gap, we conducted genome-wide association study on a panel consisting of both adapted  and important not adapted accessions used as parents in the Norwegian wheat breeding program. The study concerned grain yield, plant height, and heading and maturity dates, and detected 12 associated loci, later validated using independent sets of recent breeding lines. Adaptation to the Norwegian cropping conditions was found to be associated with the Vrn-A1 locus, and a previously undescribed locus on chromosome 1B associated with heading date. Two loci associated with grain yield, corresponding to the TaGS5-3A and TaCol-5 loci, indicated historical selection pressure for high grain yield. A locus on chromosome 2A explained the tallness of the oldest accessions. We investigated the origins of the beneficial alleles associated with the wheat breeding progress in the Norwegian material, tracing them back to crosses with Swedish, German, or CIMMYT lines. This study contributes to the understanding of wheat adaptation to the Norwegian growing conditions, sheds light on the genetic basis of historical wheat improvement and aids future breeding efforts by discovering loci associated with important agronomic traits in wheat.Grain yields in Norwegian spring wheat increased by 18 kg haThe online version contains supplementary material available at 10.1007/s00122-023-04424-9. Triticum aestivum L.) is among the essential and most traded staple foods, providing around 20% of daily protein and calorie intake for approximately 4.5 billion people worldwide . From 1972 to 2019, wheat breeding in Norway increased GY by 17.8 kg ha−1 (0.34%) per year and prolonged grain filling and vegetation periods by 2 and 3 days, respectively, showing better adaptation of new cultivars to the changing climate   and diversity array technology (DArT) markers with much more numerous single nucleotide polymorphism (SNP) markers, which provides an effective mean to identify associations between various traits and loci through genome-wide association studies (GWAS)  gene, with homoeologous copies on chromosomes 2A, 2B, and 2D  genes. Eps genes usually have small effects  and is hereafter referred to as the validation panels. Not every genotype was tested in each season/location combination due to different genotype content and number in every field season . The validation panels are considered adapted to the Norwegian growing conditions due to their origin.Field trials were carried out for the main panel during field seasons 2015–2021 at Vollebekk Research Station  and Staur farm . Those locations represent Norway’s two main and economically important wheat-growing areas: the somewhat warmer and milder climate of south-eastern Norway and the slightly colder and temperate climate of inland Norway, respectively.−1 of compound NPK fertilizer (YaraMila 22-3-10) and planted each season on the break of April and May in both locations (exact planting dates in Table S1). Following germination, trials were kept disease and weed free according to local management practices using herbicides  and fungicides  in doses tailored to the needs. Irrigation was applied in case of drought that could affect the growth of the plants. Alleys within the trials were created by spraying Glyphosate shortly after seedling emergence. The trials were harvested each season toward the end of August after all varieties had reached full ripeness.The trials were fertilized at sowing with 120 kg N haSeason 2018 in both locations was marked by very little rainfall and high temperatures during the early growth stages of the plants , which, despite irrigation efforts, caused severe damage to the trials. This damage reduced GY by nearly 60% and caused many plant agronomical characteristics to be abnormal (data not shown). Therefore, we excluded the 2018 field season at both locations from the analysis.Field trials of the validation panels were carried out following the same procedures as for the main panel in field seasons 2019–2022 at Staur and Vollebekk locations.The trials were designed as an alpha-lattice with two replicates per genotype, block size of 6, and positions of every accession randomized each year in each location. Each column was planted with buffer variety at its start and end to eliminate border effects. Each field trial plot was 5 × 1.5 m in size at harvest, with gaps between the plots of 30 cm and a central alley of 1 m. Not every variety was tested for the main panel in each season/location. The number of genotypes tested varied from 100 to 295 per season/location, with 301 and 295 unique accessions in Vollebekk and Staur, respectively (Table S2).The collection was phenotyped for days to heading (DH), days to maturity (DM), grain yield (GY), and plant height (PH). Not every trait was phenotyped in every environment (season/location combination) Table .Table 1O2. PH was assessed by measuring the distance between the ground and the top of spikes  for a random tiller sample when plants reached their final height.DH and DM were assessed by recording when approximately 50% of the tillers in an experimental plot had reached the respective stage. GY was measured by harvesting and threshing the trial plots, drying the yield until approximately 13.5% moisture, weighing it, and recalculating it to g per mData for plots that lodged early in the season was removed due to the heavy impact on their development. If lodging occurred later in the season , data were double-checked for consistency and possible impact on the traits and judged if they should be included in the dataset.For each trait, three types of genotypic means (lsmeans) were calculated: location/season  means, location mean , and a global mean, where all the locations and seasons were combined.As it was common to observe extra spatial variability within the trials (due to soil gradients) that could not have been captured by blocking, an additional covariate was introduced (columns) into the models to correct it.The lsmeans were calculated using packages “lme4” and “lmerTEST” and custom scripts in R, version 4.2.1.Field trial lsmeans were calculated using the mixed model :1\documeCross-season lsmeans for each location were calculated using the mixed model :2\documeGlobal means  were calculated using the mixed model :3\documeField trial (season/location), location, and an overall mean  are hereafter referred to as environment, location, and global mean, respectively.For the validation panel, only environment means were calculated due to varying genotype content in each environment.2) was used to assess data quality (replicability), calculated for individual trials using Eq. .Samples were prepared and genotyped with the TraitGenetics 25 K SNP chip as described in Nannuru et al. .The physical positions of the markers were determined using the chip’s documentation, and markers not mapped to any physical chromosome position were placed on a fictional chromosome Un.Markers were filtered, leaving only the ones with less than 10% missing data and minor allele frequency (MAF) larger than 0.05. Heterozygous markers were treated as missing data. After the quality check, the dataset contained 19,874 high-quality markers mapped to sub-genomes A (7999), B (7905), and D (2111) on chromosomes 1A (1156), 1B (1147), 1D (391), 2A (1232), 2B (1377), 2D (437) 3A (1074), 3B (1336), 3D (256), 4A (699), 4B (602), 4D (111), 5A (1340), 5B (1406), 5D (311), 6A (1126), 6B (1082), 6D (319), 7A (1372), 7B (955), 7D (285) and Un (1859).The main panel exhibits a strong population structure due to the presence of “adapted” and “exotic” groups of lines; therefore, additional correction for population structure was applied by including principal genomic components in the model. Due to poor adaptation, the exotic lines often exhibit unusual phenotypes under Norwegian growing conditions. To mitigate the risk of confounding SNPs with line adaptation and to discover possible sources of adaptation, two series of GWAS were carried out for each phenotype: on the whole collection, and adapted part only. Detailed description of the population structure of the main panel can be found in Nannuru et al. .GWAS and LD (linkage disequilibrium) analysis were performed using GAPIT v3.2 , but with a stronger signal. FarmCPU is a multi-locus model based on the MLM method, which relies on iterative and alternative use of fixed and random effect models to minimize the proportion of false positives. Markers are tested one by one using random models. Then the resulting significant associations are used as covariates in a fixed model . FarmCPU is well-suited for highly quantitative trait analysis  = 5.6). MTAs that crossed the threshold at least for the global mean, and two other environments were reported. However, all traits are highly quantitative and controlled by many small effect loci; therefore, the Bonferroni correction of p values can be too conservative  > 3) for the global mean and at least two environments/means. Peak markers alongside significant markers in the window were used to construct haplotypes. The search for MTAs with the MLM method was carried out in the adapted and complete datasets, similarly to the FarmCPU method.Consistent peak markers discovered using the FarmCPU method (section above) were used to anchor haplotypes. A window of 40 Mbp  around a peak marker’s position was studied using the MLM method . Markers were considered based on appearing significant  posthoc test, α = 0.05. Rare haplotype alleles (appearing in less than ten accessions) were discarded from the analysis due to insufficient statistical power to detect their associations. The proportion of phenotype variance explained by each SNP and each putative QTL was estimated using linear models and reported separately as a percentage in the whole panel and its adapted part.Varieties in the adapted part of the main panel were assigned a breeding line year of creation by analyzing their documentation. For varieties for which it was only possible to establish the year they were released to the market, seven years were subtracted to obtain the year of creation (based on the average time it took from variety creation and release to the market in the collection). It was possible to establish the year of creation (YOC) for 180 lines in the adapted part of the main panel, assigned to the following seven periods: pre-1960 (2 lines), 1960–1969 (4), 1970–1985 (6), 1986–1995 (9), 1996–2005 (24), 2006–2010 (41), and 2011 onwards (94). Allele frequency for each discovered haplotype and MTA in GWAS was calculated for each period and analyzed for trends over the years.Effects of the significant SNPs discovered in the main panel (full panel and its adapted part) were tested using an independent set of varieties and breeding lines originating from Graminor AS  spring wheat breeding program . The validation panels were genotyped using TraitGenetics 25 K SNP chip, identically as described for the main panel.Field trial data were analyzed using mixed models as described in the section “−2 (GY) and reach lower plant height by 4.5 cm (PH) compared to Vollebekk. The trials conducted in Staur exhibit higher variability in DH, DM, and GY , mature 2.5 days earlier (DM), have higher grain yield by 90 g mThe most substantial difference between the exotic and adapted lines of the main panel is seen for GY, with a severe reduction of GY in non-adapted lines accounting for 64% of the total phenotypic variance in GY. Adapted lines also tend to head earlier, mature earlier, and be slightly taller, but with the grouping explaining much less of the phenotypic variance Table , Fig. 1.2 > 0.63). DH showed the highest heritability , followed by DM, GY, and PH (0.63). PH achieved the highest variability in H2 (0.39–0.9) compared to other traits (differences around 0.2) in different environments. Heritability estimates from Vollebekk and Staur experiment sites were comparable  except for PH   were assigned to the following seven periods: pre-1960 (2 lines), 1960–1969 4), 1970–1985 (6), 1986–1995 (9), 1996–2005 (24), 2006–2010 (41), and 2011 onwards (94). Significant trends over the years using this grouping can be seen for all traits except days to heading. Lines belonging to the time periods from 1996–2005 onwards mature later than lines created in the 1960s, and old accessions (until 1970) are significantly taller than later lines. For GY, there has been consecutive increases with the lines created during 1971–1995 yielding significantly higher than older ones, but less than the lines created after 1995 , where the peak markers were discovered using the criterion of p < 0.001 across the global mean and two other environments and two MTAs within a 5 Mb window. The number of significant SNPs (detected using FarmCPU and MLM methods) in each QTL varied from 1 to 18, and no QTL was associated with more than one trait . Two QTL were discovered for DH on chromosomes 1B and 7B, two for DM on chromosomes 6B and 6D, three for GY on chromosomes 3A, 5A, and 7B, and five for PH on chromosomes 2A, 4A, 4B, 4D, and 6B. All these regions met the stringent Bonferroni threshold for the most significant marker, except for the plant height QTL on 4B .Two QTL regions were detected for DH on chromosomes 1B and 7B, explaining 14 and 11% of the variance and with two and one-day effects, respectively. Both consisted of a few SNPs . QMat.nmbu-6B consisted of 10 markers, while QMat.nmbu-6D included only one marker discovered using the FarmCPU method. QMat.nmbu-6B showed a considerable effect of around five days, explaining approximately 25% of the variance in both datasets. Similarly, QMat.nmbu-6D was detected consistently across the datasets, explaining 9 to 10% of the variance, with a minor effect of 0.8 days. No adaptation-specific QTL was discovered for DM .For DM, two QTL regions were detected on chromosomes 6B and 6D, consistently associated in the complete and adapted datasets. −2 and explaining between 16 and 67% of the variance in GY in the complete set. QYld.nmbu.5A is associated with line adaptation, showing a very high effect and proportion of variance explained in the entire dataset  while exhibiting no significant effect in the adapted set. Also, all the MTAs of QYld.nmbu.5A were discovered in the entire dataset. However, the remaining two QTL (QYld.nmbu.3A and QYld.nmbu.7B) were consistently associated with GY in both datasets, with smaller effects  (Table S7).Three QTL regions were detected for GY with effects (without correcting for population structure) ranging from 38 to 193 g ms Tables , S6. ValQHt.nmbu-6B . The QTL had effects ranging from 2 to 10 cm and explained 5 to 33% of the variance in PH in the entire dataset. None of the QTL appeared to be adaptation-specific, as all showed significant and comparable effects in both adapted and complete datasets. As the presence of exotic lines increases the variance in PH considerably . QHt.nmbu-2A could not be validated due to residual minor allele frequencies of the SNPs comprising it in the validation sets (Table S7).The highest number of QTL regions (5) was detected for PH, on chromosomes 2A, 4A, 4B, 4D, and 6B. All the QTL regions for PH consisted of more than 3 SNPs except for QHd.nmbu-1B and QYld.nmbu-5A) consistently appeared highly significant for their respective traits in the entire dataset while showing no polymorphism/effect in the adapted part of the dataset  region  and captured 67% of GY variance in the entire dataset. The high proportion of variance explained by the QTL makes it likely that QYld.nmbu-5A is the leading cause for the observed differences between the adapted and exotic lines. Interestingly, even though QYld.nmbu-5A showed no significant effect in the main panel’s adapted part, three SNPs belonging to it showed significant association with GY in the validation panels, however, with effects not nearly as high as in the entire main panel (Table S7). QYld.nmbu-5A is effectively represented by five haplotypes (occurring in more than ten lines) and several underrepresented variants (present in less than ten lines). The allele associated with lower GY (AAAGGTCC) occurs exclusively in exotic lines, while high-GY alleles are present in adapted lines only. The rare alleles are present in 13 and 21 adapted and exotic lines, respectively. Exotic lines carrying one of the underrepresented alleles also exhibit lower GY .The on Table  showed aQHd.nmbu-1B (1–2 Mb), capturing 14% of the variance in DH in the entire dataset .s Tables ,  This Qs Tables c. The nes Tables c. QYld.nQYld.nmbu-3A but not as radically as QYld.nmbu-7B. QYld.nmbu-3A comprises a single SNP, consistently detected using FarmCPU and MLM methods (Table S6) and explained 14 and 22% of GY variance in adapted and complete datasets, respectively , while the later accessions mostly carry the shortening allele (ACACC). However, the tall allele could still be found in 3 lines created between 1986 and 1995 and two more recent breeding lines , it can be observed that SNP alleles associated with increased GY and DM are visibly dominating in the population  (Table S7).Crossing adapted germplasm with exotic parents is an essential source of variation and valuable alleles , is comprised of multiple SNPs, and coincides with the chromosomal location of the Vernalization1 locus Vrn-A1. Vernalization response is a well-described, crucial component of genotype adaptation to particular growing conditions , the heading and flowering time differences were much more pronounced (data not shown), indicating that the vernalization genes are playing a crucial role in adaptation to the Nordic growing environment. The fact that QYld.nmbu-5A has effect on both GY and DH is convincing that GY benefits from phenological adaptation and not from some other linked gene in the vicinity of the Vrn-A1 locus.Line adaptation to the Norwegian growing conditions is most visible for GY: more than half of the variance in GY can be attributed to line adaptation, with much smaller proportions for the other investigated traits. By comparing significant loci for the entire panel and its adapted part alone, two loci were highly significant in the whole panel, with no effect in its adapted part, hinting that those regions may either play a role in adaptation to the Nordic growing environment, be a remnant of line origin, or be random (spurious). s et al. ). Lines QHd.nmbu-1B, captures over 14% of the variance in DH in the whole set. QHd.nmbu-1B’s peak marker (BS00022180_51) has been previously discovered for DH in the same panel ; however, still retaining a high degree of diversity in the loci.Unlike most studies on historical genetic gains, this study attempted to use a mix of registered varieties and advanced breeding lines based on the creation timeline rather than the year of release. This was unavoidable due to the scarcity of registered varieties  and the resulting problems with reaching a large enough sample size. Despite this shortcoming, the GY increase over time shows similarity to many collections  to QYld.nmbu-7B (701 Mb), the TaCol-5 gene was discovered and experimentally confirmed to be associated with the number of spikelet nodes per spike in wheat , which was a product of a cross between Runar  and the German variety Sirius. Since Runar carries the low GY allele (TCCT), the high GY allele must therefore come from Sirius . The high GY haplotype (CTAC) is also found in a group of Swedish varieties . The other favorable allele (CTCC) is found in modern Norwegian varieties with CIMMYT parentage , indicating that this haplotype was introduced into Norwegian wheat breeding by crossing with CIMMYT parents. Indeed, the CTCC haplotype is present in Australian varieties with CIMMYT parents like Avocet and Kukri as well as the landmark Brazilian variety Frontana . However, despite this finding being of value for documenting breeding progress, this locus appears to be almost “fully utilized” in the most recent lines and shows no room for future improvement with the current collection of alleles present in the germplasm.From the breeding progress standpoint, the most exciting finding is the QYld.nmbu-3A, which, in contrast to QYld.nmbu-7B, still shows a high degree of polymorphism in the most recent lines. Despite detecting only one significant SNP in the locus, its association was consistent in the validation sets. QYld.nmbu-3A’s only MTA appears in a similar region to the chromosomal location of the TaGS5-3A gene, a locus selected during breeding in Chinese wheat associated with increased kernel size, resulting in higher GY  of QYld.nmbu-3A first appears with Møystad, an old Norwegian variety released in 1966. Møystad is a product of a cross between a sister line  of Norrøna  with the Swedish variety Kärn II. Since Norrøna carries the G allele (associated with negative effect on GY), the favorable allele (A) likely comes from Kärn II. The presence of the same allele in Swedish varieties like Dragon and Avle supports this hypothesis. The allele has been further transmitted from Møystad to important Norwegian varieties like Bastian and Bjarne, and later became dominating in the Norwegian spring wheat breeding material.Another locus showing signs of selection in Norwegian wheat is QHt.nmbu-2A locus, which became almost monomorphic over time with regard to the short allele. The oldest line with favorable (short) allele (ACACC) is the breeding line MS273-150 (YOC 1975) which is a progeny from the cross of Møystad with the landmark semi-dwarf variety Sonora 64. As Møystad carries the tall allele (GTCTT), it is likely that Sonora 64 was the source of the short allele. The short allele is also present in line T7347, which must have inherited it from Sirius. Moreover, the short allele is also found in Swedish varieties like Tjalve, Dragon, and Avle, which all have been used as crossing parents. Therefore, there are at least three plausible sources of the short allele in the Norwegian spring wheat breeding program. Significant MTAs with PH in a similar region were previously detected  genes originating from the Japanese variety Norin-10 played a crucial role in the Green Revolution by introducing semi-dwarf posture to new varieties, which became spread worldwide during consecutive breeding efforts  show polymorphism and significant effects in the validation panel, with late alleles dominating the population.Due to the risks associated with wet periods at the end of the growing season in Norway , early-maturing varieties of spring cereals are generally desired. However, due to climate change, it was estimated that from the 1970s until 2005, the vegetative season in Norway was extended by approximately seven days , later validated using independent sets of recent Norwegian breeding lines. The results indicated that adaptation to the Nordic growing conditions is seen mainly in changes in grain yield and is genetically associated with a phenological response due to polymorphisms in the Supplementary file1 (XLSX 20 KB)Supplementary file2 (XLSX 206 KB)Supplementary file3 (XLSX 1747 KB)Supplementary file4 (XLSX 160 KB)Supplementary file5 (DOCX 10414 KB)Below is the link to the electronic supplementary material.


R/StageWise enables fully efficient, two-stage analysis of multi-environment, multi-trait datasets for genomic selection, including support for dominance heterosis and polyploidy.https://github.com/jendelman/StageWise.Plant breeders interested in genomic selection often face challenges to fully utilizing multi-trait, multi-environment datasets. R package StageWise was developed to go beyond the capabilities of most specialized software for genomic prediction, without requiring the programming skills needed for more general-purpose software for mixed models. As the name suggests, one of the core features is a fully efficient, two-stage analysis for multiple environments, in which the full variance–covariance matrix of the Stage 1 genotype means is used in Stage 2. Another feature is directional dominance, including for polyploids, to account for inbreeding depression in outbred crops. StageWise enables selection with multi-trait indices, including restricted indices with one or more traits constrained to have zero response. For a potato dataset with 943 genotypes evaluated over 6 years, including the Stage 1 errors in Stage 2 reduced the Akaike Information Criterion (AIC) by 29, 67, and 104 for maturity, yield, and fry color, respectively. The proportion of variation explained by heterosis was largest for yield but still only 0.03, likely because of limited variation for the genomic inbreeding coefficient. Due to the large additive genetic correlation (0.57) between yield and maturity, naïve selection on an index combining yield and fry color led to an undesirable response for later maturity. The restricted index coefficients to maximize genetic merit without delaying maturity were identified. The software and three vignettes are available at The online version contains supplementary material available at 10.1007/s00122-023-04298-x. During the first decade of the twenty-first century, the focus of genomic selection research was the development of theory and methods , then for ploidy When marker data are provided, the software decomposes G can be blended with the pedigree relationship matrix A  dominance model, which follows the classical framework of Fisher  and Kempd in the classical diploid model of Vitezica et al.  DesignQ for ploidy X  isThe dominance value of an individual is the sum of its dominance effects and can be written as VD, is m loci, the dominance value is In Eq. , \documegenic variance, which depends on allele frequencies but not LD between loci. The second term is the disequilibrium covariance, which can be positive or negative.The first term in Eq.  is the dQ denote the n × m matrix of dominance coefficients for n individuals at m loci. The vector of dominance values D is defined by interpreting its variance component In classical quantitative genetics, the substitution effects are fixed parameters, but to compute dominance values by BLUP, we switch to viewing them as random normal effects  according to L can represent some other factor, such as management). Using the subscript k to designate location, the linear model . The non-additive correlation parameter was therefore fixed at 1 and accepted as a model limitation. When markers are included as fixed effect covariates, different regression coefficients are estimated for each location. Similarly, different regression coefficients for genomic inbreeding are estimated per location.A similar framework is used for multi-trait analysis, with trait replacing location in Eq. , except Ej . The core idea is to compute variances based on the method of Legarra (The aim is to quantify the proportion of variance (PVE) explained by each effect in the Stage 2 model, excluding the main effect  Legarra , and thesij  y with mean Vy can be computed using the following general formula for quadratic forms , W represents the centered matrix of allele dosages for the fixed effect markers , F is the vector of genomic inbreeding coefficients, and c is the vector of economic weights for multiple traits or locations, then the genetic merit vector for the population isGenetic merit is a linear combination of random and fixed effects. For random effects, the structure of u and The value of  Gallais . Becausen by Eq.  with u ac, the software divides the user-supplied weights by the standard deviations of the breeding values (estimated in Stage 2); it also applies an overall scaling such that Index coefficients entered by the user are interpreted as relative weights for standardized traits (or locations). To generate the vector i is the squared correlation with its true value i, and , then the random effects component of The reliability V inversion method, The final equality in Eq.  relies ox under selection intensity i isThe breeder’s equation provides the expected response to truncation selection on predicted merit  see Eq. , and then on n individuals in the population, which differs slightly from the covariance of a vector with respect to its MVN distribution  effects for t traits/locations nested within m markers, with variance–covariance matrix , and from Eq. , vine maturity , and potato chip fry color (Hunter L) after 6 months of storage. The G matrix was used for multi-trait analysis, instead of H, due to convergence problems with the latter.The potato dataset is an updated version of the data from Endelman et al. , which smerge_impute from R package polyBreedR (https://github.com/jendelman/polyBreedR). This command performs one iteration of the EM algorithm described in Poland et al.  from genotyping with potato SNP array v2 or v3 (which contains most of v2)  for individuals and GWAS scores for markers. Three vignettes, or tutorials, come with the software to give detailed examples of using the commands. The following results represent a condensed version of this information.The workflow to analyze data with StageWise is illustrated in Fig. FD, from the directional dominance model, (2) FG, from the diagonal elements of the additive genomic relationship matrix, and (3) FA, from the diagonal elements of the pedigree relationship matrix. The FG and FD coefficients from the genomic models were highly correlated (r = 0.98) and have the same population mean, − 0.08, which indicates a slight excess of heterozygosity compared to panmictic (Hardy–Weinberg) equilibrium. Although there was some concordance between the genomic and pedigree coefficients for the most inbred individuals, there was little agreement at small values of FA  or as dominance values. In the context of genomic prediction, directional dominance models use inbreeding coefficients to estimate heterosis. Figure e model,  FG, fromsummary command to the output from Stage2 generates a table with the proportion of variation explained (PVE). The PVE for additive effects, which can be called genomic heritability, ranged from 0.34 (yield) to 0.43 (maturity) , with similar results for fry color 0.25–0.74) and maturity (0.38–0.74) . The benefit of including Stage 1 errors in the Stage 2 model was assessed based on the change in AIC, which ranged from − 29 for maturity to − 104 for fry color , in the vicinity of the well-known regulator of potato maturity summary command returns the additive correlation matrix for the traits. For the potato dataset, late maturity was correlated with higher yield (r = 0.57) and slightly with lighter fry color (r = 0.23). There was no genetic correlation (r = 0.00) between yield and fry color.Multi-trait analysis follows the same general workflow as a single trait. In addition to the PVE, the blup is used to specify the selection index coefficients, which determine the relative weights of the traits (after standardization to unit variance) for genetic merit.  For the potato chip market, it is reasonable to give equal weight to yield and fry color. However, naïve selection on these traits alone will generate offspring with later maturity, which is undesirable. One way to avoid this is by using vine maturity as a covariate in the analysis.The “index.coeff” argument for gain command in StageWise can be used to compute the coefficients of a restricted selection index, in which the response for some traits is constrained to be zero  model  for yield, we should expect small PVE when there is limited variation for inbreeding. The standard deviation of p > 1/3; for p < 1/3, duplex dosage contributes more.From the theory of directional dominance, the average dominance coefficient is the covariate for estimating heterosis. Xiang et al.  used aveA more general approach to restricted selection indices was developed in StageWise by investigating the geometry of the problem Eq. . Until nblup_prep makes it easy to investigate the potential benefit of using a correlated, secondary trait to improve genomic selection. Many plant breeding programs are exploring the use of spectral measurements from high-throughput phenotyping platforms to improve selection for yield. For example, Rutkoski et al. .Typically, the number of traits a breeder must consider for selection is too large to analyze jointly in StageWise based on the current implementation with ASReml-R. New algorithms may alleviate this limitation in the future Supplementary file2 (PDF 157 KB)Supplementary file3 (ZIP 14439 KB)Below is the link to the electronic supplementary material.


Coffea canephora, evaluated across multiple years and locations, our contribution is 3-fold: (1) first, we demonstrated that the number of harvest evaluations may be reduced leading to accelerated implementation of molecular breeding; (2) we showed that stability metrics are predictable; and finally, (3) both stable and high-performance genotypes can be simultaneously predicted and selected. While this research was carried out on representative environments for coffee production with substantial crossover in genotypic ranking, we anticipate that genomic prediction can be an efficient tool to select coffee genotypes that combine high performance and stability across years and the target locations here evaluated.Coffee is one of the most important beverages and trade products in the world. Among the multiple research initiatives focused on coffee sustainability, plant breeding provides the best means to increase phenotypic performance and release cultivars that could meet market demands. Since coffee is well adapted to a diversity of tropical environments, an important question for those confronting the problem of evaluating phenotypic performance is the relevance of genotype-by-environment interaction. As a perennial crop with a long juvenile phase, coffee is subjected to significant temporal and spatial variations. Such facts not only hinder the selection of promising materials but also cause a majority of complaints among growers. In this study, we hypothesized that trait stability in coffee is genetically controlled and therefore is predictable using molecular information. To test it, we used genome-based methods to predict stability metrics computed with the primary goal of selecting coffee genotypes that combine high phenotypic performance and stability for target environments. Using 2 populations of  Coffee is one of the most consumed beverages and traded agricultural commodities in the world. Globally, an estimated 125 million people along the supply chain depend on coffee for their livelihood , therebyContrasting other initiatives to confront these issues, modern plant breeding techniques can meet these challenges. Conventionally, coffee breeders have centered their decisions on visual selection collected over multiple generations, which is time-consuming and costly . Modern Jointly with genomic prediction implementation, the relevance of genotype-by-environment interaction (GEI) is an important variable when evaluating the phenotypic performance of coffee plants. For most perennial crops, genomic selection and GEI have been simultaneously evaluated to predict the phenotypic performance of target genotypes in different environments , in whicAdvances in analytical methods have provided the research community with a breadth of tools to quantify the relevance of GEI in plant breeding. One avenue to study GEI is to search for individuals with stable fitness across environments. To this end, the use of linear regressions, in the form of Finlay–Wilkinson (FW) regressions, has gained popularity, given its parsimonious input requirements. In FW regression, the expected performance of a genotype varies as a function of the environmental effects, and plants are either classified on their stability or responsiveness to environment potential . Using aIn coffee, environmental stability is mainly addressed in terms of spatial and temporal variations  the minimal number of harvests necessary to predict different coffee traits in a context of genomic prediction; (2) the most stable genotypes predicted across locations and years, using FW and AMMI approaches; and, (3) the best strategy to predict stability metrics when data from target populations are collected. Altogether, we hypothesized that genomic prediction could be an efficient tool to select coffee genotypes that combine high phenotypic and stable performance across years and locations.Considering the importance of GEI for coffee breeding, in this study, we address the following main question: can we predict trait stability using a genome-based approach? Motivated by the potential to use genomic prediction to reshape traditional coffee breeding schemes, we used a historical data set collected in 2 breeding populations of C. canephora were evaluated, with different fruit maturation times, referred to here as Premature and Intermediate populations. For the Premature population, a total of 9 parents were used, with an average earlier fruit maturation in February to March and harvest in May. The Intermediate population was designed from 16 parents from the Incaper Germplasm Bank, with fruit ripening in March to April and harvest in June. Parents from both populations were established in separated and isolated seed orchards. After 1 cycle of recombination, seeds were derived from each maternal plant and planted in 2 separate fields. Progenies in both populations were first submitted to a visual screening based on yield, disease resistance, and drought tolerance. After screening, the 103 best progenies in the Premature population, and the 118 best progenies in the Intermediate population, were cloned into separate trials established in a randomized complete block design with three replications and five plants per plot —latitude 19°24 south, longitude 40°31 west, 70 m altitude and Sooretama Experimental Farm (FES)—latitude 15°47 south, longitude 43°18 west, 40 m altitude. Additional historical data was included for the FEM location, in which traits were evaluated over eight harvests. More details about the plant material and experimental design are described in Ferrão et al. ; Espirito Santo State, Brazil; in partnership with Embrapa Café, Brazil. Two recurrent selection populations of per plot . The Preo et al. , 2018 anPremature and Intermediate populations, a total of 20 phenotypic traits were evaluated. Herein, we classified the traits into 4 categories:For the A group of 6 traits was visually scored for morphological and physiological traits related to coffee growing. The maturation time (FL) was evaluated using a 1- to 7- rating scale where 1 indicated precocity and 7 represents late maturation. Uniformity of the maturation period (UNIF) was measured on a 1 to 3 scale, where 1 represented uniformity of fruit maturation and 3 lack of uniformity. Bean size (GSIZ) was on a 1 to 7 scale, with the lowest value indicating the smallest beans. Plant architecture (PRT) was related to the size of the bush, and it was assessed using a 1 to 3 scale, where 1 meant small plant size and 3 large. Vigor (VIGOR) was a metric associated with healthiness and was evaluated using a 1 to 9 scale, where 1 indicated low vigor and 9 high vigor. Finally, the general scale (GSCE) was a visual metric assessed by breeders and indicated the overall performance of a genotype classified by breeders. It was evaluated using a 1 to 9 scale, where 1 represented poor genotypes and 9 more promising ones.Hemileia vastatrix, whose symptoms include pale yellow spots on upper leaf surfaces, followed by powdery orange-yellow lesions. Coffee leaf mine (LMINER) is caused by Leucoptera coffeella, a moth in the family Lyonetiidae. Cercospora leaf spot (CERC), also called Brown eye spot or Berry blotch, is caused by the fungus Cercospora coffeicola, and the main symptoms are brown spots on foliage, which enlarge and develop a gray-white center and red-brown margin.A total of three traits were visually evaluated for disease resistance, all using a 1 to 9 scale, where 1 represents no visual symptoms and 9 visible and severe symptoms. Coffee leaf rust (RUST) is caused by the fungus The total production (kilograms of mature coffee fruit in the cherry stage) of each progeny were harvested and weighed. In accordance with internationally accepted practices in coffee research and production, yield was reported as bags of 60 kilograms per hectare.After being harvested, a sample of 2 kg of ripened fruits were processed in 2 stages. The first was to use a natural drying method (sun drying), and obtain the weight (in grams) of coffee fruits afterward, named as CHERRY_g. The second was depulping (getting rid of the skin and mucilage) and weighing the resulting dry processed and unroasted beans, herein GREEN_g. The ratio between CHERRY_g and GREEN_g was measured as a new trait, named as CHE:GREE. Because it is known that coffee bean size can affect the roasting process and influence drink quality , for addApeKI restriction enzyme was used for the digestion of the DNA samples, and 96 samples were multiplexed per Illumina flow cell for sequencing. GBS analysis pipeline implementation, SNP filtering, and manipulation were described in Ferrão et al. (Genotyping by sequencing (GBS) was used to genotype the populations in the Genomic Diversity Facility at Cornell University. Leaf samples from each genotype were collected and lyophilized. DNA extraction was made using Qiagen DNeasy Plant, and the genomic libraries were prepared following o et al. , 2018. SPhenotypic analyses were carried out with the following 2 main objectives: (1) determine the impact of number of harvests on the predictive ability and (2) estimate the predictive ability of trait stability metrics. To this end, we reasoned the following statistical approach to modeling the phenotypic data and use in subsequent genomic prediction models:To investigate the impact of number of harvests on genomic prediction, we considered 8 years of phenotypic data collected at the FEM location. The impact of including more harvest data in predictive studies was tested under 2 different scenarios of validation as described in After dividing our population into training and validation, we used our historical data to systematically include more years in the testing set and predict the validation set. For example, case I represents data collected only in 2007 and was used to predict phenotypes in 2014 and 2015. In the other extreme (case VI), we predicted 2014 and 2015 using the data collected from 2007 to 2012. All linear models were fitted using the ASReml R package , n axis in the PC axes (PCAs), ith genotype and jth environment eigenvectors for the nth PC, respectively. where: N is the number of PCs in the model for the ith genotype (The sum of squares of the PC (SPC) scores was used to calculate the AMMI stability index using the following equation: SPC = A second popular approach to address GEI is based on linear regression models. A FW regression express the interaction in the form of heterogeneity of the slopes computed across individual genotypic performance under an environmental index. The inference is performed in two main steps: (1) estimate environmental effects from the environmental means using the main effects model and (2) estimate of intercepts and slopes of each genotype.μ is the overall mean (intercept); ig is the main effect of ith genotype; jh is the main effect of the jth environment; ib + 1 is the change of expected individual performance per unit of change of jh (slope); jĥ is the estimate of jth environment effect; jje is the error term. The stability index of individual ith is the deviation of the corresponding individual slope (ib) from zero. Herein, we considered an individuals with “high stability” when its corresponding slope is close to zero—since they can keep their performance over different environment conditions. FW regressions were carried out using the FW R package  assumes that the marker effects are normally distributed with fixed variance, which could align better for trait predictions that follow this infinitesimal model. The BayesB model induces variable selection and assumes that most loci do not affect the phenotypic variation, a fact that aligns better for traits controlled by relatively few loci. Both models were fitted following linear regression, as proposed by A second point of analysis in this study was how multi-population (MP) data could be integrated to better predict trait stability. To answer such a question, three statistical modeling approaches were implemented: (1) a single population (SP) model obtained by regressing phenotypes on markers separately in each coffee population; (2) a combined analysis where marker effects were treated as homogeneous across populations [across-population (AP) model]; and (3) a combined analysis where marker effects were assumed heterogeneous across populations, and marker x population interaction was accounted for. All the reference models were originally implemented by j = {yij}, where i represent lines  and j represent populations, on markers using the following linear model:A SP GS model is obtained by regressing the phenotype vector containing the trait records for each population, yij is the phenotype of ith individual  of the jth environment  and kth markers ; jµ is an intercept of jth population, j = {xijk} is a marker matrix; jβ = {jkβ} is a vector of marker effects and je is a vector of model residuals. X1 represents the number of reference alleles at a specific locus in the coffee genome and is coded as 0, 1, 2. Marker effects are the same, X1 = X2 = … Xs, for lines evaluated in all environments in a full-factorial design. Marker effects and model residuals are assumed to be independent and normally distributed: jβ ∼ N and ej ∼ N.where y1β = 2 = ββ following the regression model described in matrix notation:In this model, marker effects are assumed to be the same across populations, such that: where y is a vector of the adjusted phenotype of the individuals in populations I and II, X is the design matrix of marker effects for each population and P indexes markers), as follow: In this model, marker effects are estimated in two components: a main effect across both populations and a specific effect computer per population. The final marker effect was computed after summed effects that are cluster-specific  and predicted GEBVs using: (1) marker effect estimated in one set of years to predict the genotype performance for other years  and positively correlated with VIGOR (0.55) and GSCE (0.64); and negatively correlated with RUST (−0.36), CERC (−0.24), and CHE:GREE ratio (−0.25). RUST, an important disease in coffee, was positively correlated with CERC (0.30), M15 (0.29) and M17 (0.21); and negatively correlated with UNIF (−0.26), VIGOR (−0.26), the postharvest traits M10 (−0.21), and RES (−0.28). In the Intermediate population, the correlation among traits was similar to what was obtained in the Premature population, but differences include significant negative correlations between YIELD with RES (−0.29), LMINER (−0.25), and GREEN (−0.20).A second piece of relevant information extracted from PCA analyses is the relationship between coffee traits . Traits Intermediate population showed superior phenotypic performance. Heritability estimates ranged widely among most traits in both populations, from 0.15 for CHE:GREE in the Premature population, to 0.92 for GSIZ in the Intermediate population. YIELD, an important coffee trait, showed large heritability values in both populations. Heritability values were also consistent across both locations.The descriptive summary of phenotypic performances, heritability, and average stability using AMMI and FW models are presented in Premature population, while it ranged from 0.32 for LMINER to 8.41 for GREEN_g in the Intermediate population. When evaluated in terms of regression analyses, the mean for the FW stability index was approximately zero for all traits in both populations, and the standard deviation showed heterogeneity among slopes. We further quantified the importance of GEI effects by estimating variance components for all traits, and the percentage of GEI variation explained by the first two components using AMMI models (P < 0.001) across populations, confirming the relevance of temporal and spatial variation in C. canephora.GEI was first noticed by crossover interactions observed when the relative difference between genotypic means were investigated over the environments . Trait sI models . EstimatIntermediate population. In contrast, RUST had a negative and low correlation (−0.11) for the AMMI metric only in the Premature population. Based on the AMMI results, consistent low correlations observed across both populations were observed only for VIGOR, CHERRY_g, M13, and RES traits. When contrasted with the computed FW slopes, Person's correlation between phenotypic performance and stability metric for most traits were significantly associated. The only trait that was consistently scored as statistically nonsignificant across both coffee populations was the GREEN_g trait.The linear relationship between phenotypic performance and environmental stability projects future improvements in selecting individuals with high performance and desirable stability. Non-significant associations were observed, which were more related to the AMMI estimates. In particular, a low correlation (0.09) value was observed between YIELD and the AMMI metric computed for the For genomic prediction, we tested three main scenarios addressing (1) the relevance of testing genomic selection models with different statistical assumptions; (2) the importance of collecting multiple-year harvest data; and finally (3) the predictability of trait stability.Premature population to 0.51 for the FL trait in the same population, in both models. The most extreme differences between models were observed for the M13 trait measured in the Premature population and the LMINER trait collected in the Intermediate population. Average prediction accuracies were higher generally in the Intermediate population (0.433 vs 0.341). We also observed great variation across the traits. For example, in both populations, large predictive abilities were noted for the postharvest traits; in particular, CHERRY_g, M12, and M13 traits.When contrasting the predictive abilities of BRR and BayesB models, both models showed similar performance across all traits in both populations . The cloThe second question underlies the effectiveness of increasing the number of years as a means of improving the predictive ability of a model. Overall, in both populations, prediction accuracies for all traits increased when more years were included in the training set. Results are better illustrated in Premature population trait stability was slightly better than observed in the Intermediate population. When FW and AMMI metrics were contrasted, trait stability measured by FW regressions was more predictable using genomic information than AMMI metrics. In view of model parametrization, we could not observe larger differences between the three different models, suggesting that a more parsimonious implementation (SP model) is sufficient to maintain good predictive abilities across all traits in both populations  positive correlations (ranging from 0.44 to 0.96) between trait values and stability estimated with AMMI and FW in both populations. Herein, the top 10% of best genotypes for each trait were ranked and compared to the top 20% of genotypes selected from the AMMI stability (lowest ASV) and the top 20% for FW stability (absolute b ∼ 0). In Our last research question addressed whether genotypes with high phenotypic performance and stability across years and locations could be simultaneously selected. Both the summary of average stabilities  and PearC. canephora beans correspond to more than 45% of national production  across locations and years.To quantify the importance of GEI, we first observed substantial crossover genotypic ranking when the relative difference between genotypic means over different environments was studies. In the sequence, we used AMMI models and observed that interaction variation accounted by PC1 and PC2 was above 50% for most of the traits in both populations. We complemented our investigation using FW regression models. At the genotypic level, we classified some genotypes with approximated absolute phenotypic stability for most traits. This implies that a good number of coffee genotypes can be selected for poor and favorable environments. For the specific goal raised in this study, coffee breeders are looking for genotypes that combine wide adaptability and high yield, in combination with other favorable traits. Interestingly, most traits demonstrated significant correlations (0.18–0.96) between phenotypic performance and trait stability estimated with either AMMI or FW in both populations. Hence, it is reasonable to suggest that phenotypic performance and trait stability can be simultaneously selected for the target environments evaluated in this study.Intermediate population, which could be due to the differences in genetic architecture and expression of phenotypic characteristics in different populations. In general, the high accuracy of GEBV obtained from this study indicates that GS could be effective for all coffee traits.Our second contribution relies on using genomic selection in a practical breeding program. To our knowledge, there are no studies in coffee addressing predictive performances in a such diverse set of traits, evaluated in multiple coffee populations and environments. Therefore, when morpho-agronomic, disease resistance, yield, and postharvest traits were investigated, we observed low-to-moderate (0.28–0.51) predictive abilities. The average prediction accuracy was slightly higher for traits evaluated in the Critical at the implementation level, when a new set of traits are investigated for genome-based prediction, an important question is what statistical method might better describe the relationship between the phenotypic and genetic variation , similar finding was also observed in cattle and corn  in general, good predictive abilities could be found when data was collected in 3 years, an information that opens new avenues to reducing coffee breeding cycles, reduce costs, and ultimately leverage genetic gains; (2) stability metrics could be predicted, in particular, using the FW regression; and finally (3) more parsimonious models, with populations trained separately, is a valid alternative to combine predictive ability and computational cost. Overall, the methods and approaches we used here allow for the simultaneous selection of genotypes with large GEBVs and stability across target environments. It should be emphasized that such findings are restricted to 2 populations evaluated in very specific locations and timeframes, a fact that could narrow down our conclusions. For a big picture on the genetic architecture associate to stability in coffee traits, we emphasize the need for experiments that contemplate a larger number of representative (and contrasting) site, evaluated over multiple years.jkad062_Supplementary_DataClick here for additional data file.


Glu-D1, Pinb-D1, and non-gluten proteins are associated with sedimentation values and falling number in European wheat.Sedimentation values and falling number in the last decades have helped maintain high baking quality despite rigorous selection for grain yield in wheat. Allelic combinations of major loci sustained the bread-making quality while improving grain yield. Glutenin (Glu-1) and Puroindoline (Pin-1) with ZSV provided positive analytic proof of our studies. We report novel candidate loci associated with globulins and albumins—the non-gluten monomeric proteins in wheat. In addition, predictive breeding analyses for ZSV and HFN suggest using genomic selection in the early stages of breeding programs with an average prediction accuracy of 81 and 59%, respectively.Zeleny sedimentation values (ZSV) and Hagberg-Perten falling number (HFN) are among the most important parameters that help determine the baking quality classes of wheat and, thus, influence the monetary benefits for growers. We used a published data set of 372 European wheat varieties evaluated in replicated field trials in multiple environments. ZSV and HFN traits hold a wide and significant genotypic variation and high broad-sense heritability. The genetic correlations revealed positive and significant associations of ZSV and HFN with each other, grain protein content (GPC) and grain hardness; however, they were all significantly negatively correlated with grain yield. Besides, GPC appeared to be the major predictor for ZSV and HFN. Our genome-wide association analyses based on high-quality SSR, SNP, and candidate gene markers revealed a strong quantitative genetic nature of ZSV and HFN by explaining their total genotypic variance as 41.49% and 38.06%, respectively. The association of known The online version contains supplementary material available at 10.1007/s00122-023-04450-7. Wheat producers and downstream value chains place a high premium on grain’s baking quality because it affects the end-user value and yields high monetary profits. Baking quality, therefore, becomes an important selection criterion in wheat breeding programs across the globe. In Germany, wheat varieties are released according to different quality classes, and several traits form the basis for determining a given class (Sortenliste Glu-1) loci, i.e., Glu-A1, -B1, and -D1, are present on the long arm of group-1 wheat chromosomes (Payne and Lawrence Glu-3), on the other hand, are Glu-A3, -B3, and -D3 that are present on the short arm of group-1 homoeologous chromosomes  loci (Brown and Flavell Pin-1) genes—present at the Hardness locus—which mainly affects the grain texture —that are widely distributed in cereals—have also been associated with improved rheological properties of flour doughs, loaf volume, crumb structure, and overall bread making  represents high gluten content, strength, and quality—a means for predicting the bread-making quality of flour Zeleny . Major he Morris , were ale Morris . In addiHagberg-Perten falling number test indicates starch degrading enzyme α-amylase’s activity in wheat flour Perten . Higher Most grain quality traits harbor quantitative genetic control, i.e., their total genetic variance is controlled by the concerted action of large- as well as small-effect loci. In such a scenario, prediction of the total genetic value based on a large number of marker genotypes conferring both large and small effects on the trait becomes a method-of-choice  comprising 372 varieties  was evaluated for two major grain quality traits viz. Zeleny sedimentation values  and Hagberg-Perten falling number . The phenotypic data of these two traits were gathered from eight and four environments, respectively. Each environment was considered as a location-by-year combination. The field trials were conducted using an alpha lattice design with two replications per environment. We did not observe conditions conducive to pre-harvest sprouting  that can strongly influence HFN. A major reason is that data were gathered by keeping in view the German registration authority’s (Bundessortenamt) practices to obtain quality traits’ data from field trials where standard crop protection and plant growth regulator applications (intensity level-2) are executed: this reduces lodging and consequently impacts quality profiles, including HFN. A further detailed description of field trials, agronomic practices, climatic conditions, and calculation of the adjusted entry means per environment was given previously  are considered during the variety registration trials, we retrieved their phenotypic data  from a previously conducted study based on multiple environments , grain hardness , and grain yield  covering three decades starting from the year 1980 as Rht-D1 alleles  in scatterplots to show their distribution across the years of registration.To test the genetic trend or progress mentclass2pt{minimPath analysis—an extension of multiple regression—allows determining the best-fit hypothesis to explain the relationships between the dependent and independent traits by comparing different models Streiner . We set 2 test, comparative fit index (CFI), Tucker–Lewis’ index (TLI), and standard root mean square residual (SRMR) were used to analyze the goodness of fit of the model as χ2In model 1 Eq. , all the.08 Suhr . In mode.08 Suhr , in whicT be the trait number. In the first step of model 2  was first genotyped with 732 simple sequence repeat (SSR) markers that resulted in scorable 770 loci and 3176 alleles  and grain hardness puroindoline (Pin-1) genes are reported to have a significant impact on wheat end-use quality, we sequenced the whole panel to observe their allelic frequency and impact in European wheat. Each Glu-1 locus on chromosomes 1AL (Glu-A1), 1BL (Glu-B1), and 1DL (Glu-D1) consists of two tightly linked genes encoding x- and y-type HMW-GS. PCR-based candidate/functional markers were applied to distinguish the wheat varieties for null-, x-, and y-type glutenin subunits. For Glu-A1, as described in Liu et al.  and Bx7OE (overexpressed) subunits  genes resulted in significant improvement in GY in wheat , boxplots were drawn for the complete set of varieties (BLUEs) and those harboring reference and variant alleles. We used Welch’s two-sided t-test to observe if there existed significant differences between the means of varieties harboring different alleles.For all candidate markers  was calculated based on the second solution, as described by VanRaden (We performed genome-wide association studies (GWAS) based on the BLUEs calculated across environments and molecular markers that passed the quality criteria of < 5% missing values and > 5% minor allele frequency. We combined the SSRs, SNP arrays, and functional-gene markers for the molecular markers set. Following Yu et al. , a standVanRaden .p is the number of quality markers used in the GWAS. Since Bonferroni’s correction amounted to P values in a multiple linear regression model; R2, N and H2 denote the regression coefficient, number of observations, and the broad-sense heritability calculated in Eq. To declare the marker-trait associations (MTA), we employed the Bonferroni correction z et al. , the genentclass1pt{minimaThe genetic gain per unit time and cost become co-extensive with the genotypic variance explained by the trait-associated markers. For example, if the quantitative trait loci (QTL) underlying a given trait explain a small proportion of genotypic variance, marker-assisted selection for these QTL becomes cost and time intensive. Hence, we selected the markers that explained We evaluated the genome-wide prediction (GP) accuracies of ZSV and HFN by using five genomic selection (GS) models with different marker variance assumptions. The GS models were genomic best linear unbiased prediction (GBLUP), BayesA, BayesB, BayesC, and reproducing kernel Hilbert space regression (RKHSR)  and Hagberg-Perten falling number (HFN) were assessed on a panel of 372 wheat varieties registered in European markets (Table S1). The field trials to collect data were performed in replicated trials in eight and four environments, respectively. Boxplots based on adjusted entry means drawn for individual environments showed consistent performance of both traits yielding positive average Pearson’s product-moment correlation P < 0.001) larger than zero for both ZSV and HFN, with their BLUEs approximating normal distribution  decreased by 0.17% per annum  increased  genetic trends were observed for ZSV, HFN, and GH  correlation was observed between GPC and GY  followed by ZSV (R2 = 0.26), and (2) there, nevertheless, exist varieties with above average values for each combination .The genetic correlation among all five investigated traits based on their BLUEs revealed that all quality traits, viz. ZSV, HFN, GPC, and GH showed a negative correlation with GY. The most pronounced significant negative . For QZsv.ipk-1D, the functional marker for the glutenin gene Glu-D1 (UMN25 and UMN26) that distinguished between Dx5 + DY10 and Dx2 + Dy12 subunits was significantly associated with the ZSV and explained 25.56% of the genotypic variance . The QTL QZsv.ipk-1D was also represented by the marker BS00022768_51 (gene ID: TraesCS1D02G317300) that explained 26.05% of the genotypic variance with functional annotation of globulin—a non-gluten wheat protein that is associated with wheat quality . QZsv.ipk-5D, represented by BS00000020_51 (TraesCS5D02G004300), explained 11.39% of the genotypic variance and corresponded to Puroindoline-b (Pinb-D1)—a known gene at the Hardness locus responsible for controlling wheat grain texture (Morris AX-94430348 (TraesCS1A02G200400) representing the QHfn.ipk-1A explained 12.74% of the genotypic variance and corresponded to Albumin-2 protein—another non-gluten protein in wheat’s endosperm  yielded highly plausible candidate genes. For example, a SNP e Morris . For HFNGlu-1, Pin-1, and Rht-D1; Table S1, Fig. The entire wheat panel was genotyped for major loci associated with grain quality and yield  and Ax2* (10.56%) subunits. Welch’s two-sided t-test revealed that the presence of Ax-null was associated with significantly (P < 0.05) higher values for HFN and GY  Bx6 and Bx7 or Bx17, and (2) Bx7NE and Bx7OE subunits, revealed their frequencies as 29.91, 70.08, 93.82, and 6.18%, respectively. For the first marker, the presence of Bx7 or Bx17 subunit was associated with significantly higher values for ZSV and GH; however, the effect was negative for GY where the varieties harboring Bx7 or Bx17 subunit was associated with decreased (P < 0.05) values  higher values for all quality traits while  lower values for GY  and short (Rht-D1b) alleles on quality and GY. The difference between the means of varieties harboring tall (42.01%) and short (57.99%) alleles were non-significant for HFN and GH  for ZSV, GPC, and GY  and null Pina-D1b (7.57%) alleles in the investigated varieties. However, the allelic influence on varieties was non-significant , -D1b (42.90%), -D1c (11.08%), and -D1d (32.67%). Besides Glu-D1, Pinb-D1’s allelic influence was observed as most pronounced: the use of Pinb-D1b and -D1d to alter the grain texture in wheat varieties was evident from their frequencies  allele was associated with a significant decrease in all investigated quality traits whereas—except for HFN—the higher values were observed for mutant Pinb-D1c. As expected, wild-type Pinb-D1a and -D1c were associated with significantly higher and lower GY values, respectively. Moreover, the Pinb-D1b’s presence, compared to Pinb-D1a, was associated with significantly higher values for all quality traits while decreasing GY . Welch’s two-sided t-test revealed that hard wheats harbored significantly (P < 0.001) higher values for all the quality traits  practices and the environment. However, there exists variation among wheat varieties that could be ascribed to the underlying genetic factors. Because of the German Fertilizer Ordinance’s obligatory regulations for reduced fertilizer applications Justiz , exploitFor both ZSV and HFN, we observed a large genotypic variance and broad-sense heritability estimates—this is consistent with the previous reports  while GPC decreased (– 0.17%) significantly. Cormier et al.  observedd Friedt  reportedg et al.  reportedg et al.  reportedg et al. , who repg et al. e.Septoria tritici blotch, Drechslera tritici-repentis, and Fusarium head blight in the same GABI wheat panel.Wheat quality traits’ negative association with grain yield is historically well known  marker systems , (2) chromosome maps  or physical (bp) positions), and (3) nature of mapping populations . Moreover, the studies on the association mapping for ZSV and HFN are limited and do not provide marker sequences, especially in winter wheats. Hence, we compare our QTL to the recent and relevant studies in the following.QZsv.ipk-1A, -1B, and -1D explained > 25% whereas the MTA representing the fourth ZSV-QTL (QZsv.ipk-5D) corresponding to Pinb-D1 gene explained 11.39% of the genotypic variance. Würschum et al. (QZsv.ipk-1A harbored the gene for peroxidases (POD). To our knowledge, this is the first GWAS that identified an SNP linked with POD for ZSV—most possibly because PODs can improve the physical characteristics of gluten —is likely to be linked with Glu-D1, and, thus, may constitute the same QTL. Yu et al. . Also, Fradgley et al. . Pinb-D1’s association with ZSV suggests its possible role in controlling the ZSV—several previous studies have shown this gene’s association with other quality traits, including ZSV  by a certain margin and thus, the new high-yielding varieties inevitably show sustained/improved baking parameters. At this juncture, it can be safely assumed that wheat breeders seem to have exploited the ZSV/GPC ratio for which a stable and slightly positive genetic trend was observed in our study.Of the four QTL, three, viz. m et al.  also detghs Gale . In addiu et al.  recentlyy et al.  identifie Morris . QZsv.ipQHfn.ipk-1A’s significant marker  explained 12.74% of the genotypic variance and corresponded to the albumin protein . Albumin, like globulin, is a non-gluten minor protein in wheat endosperm that has a significant bearing on wheat’s quality  identified in this study explained 9.38% of the genotypic variance. To our knowledge, no previous reports, especially in winter wheats, identified HFN-QTL on 5B at or near 618.1 Mbp, thus, making it a novel QTL.For HFN, seven MTA present on individual wheat chromosomes were identified. Of these seven, only two explained ~ 10% of the variance, and, thus, were designated as HFN-QTL. The Glu-D1 and Pinb-D1. Nevertheless, although helpful in breeding programs for speedy selection gain, the QTL and corresponding candidate genes reported in this study need further genetic and functional validation.Taken together, our GWAS showcased ZSV’s genetic control to be less complex than HFN as its QTL showed more genotypic variance and were more significant than HFN—most possibly because of the action of known quality-related genes, e.g., Glu) loci bear a strong effect on the dough and baking quality  using candidate markers for the corresponding genes. In addition, the Rht-D1 and Pin-1 (Pina-D1 and Pinb-D1) loci were evaluated to observe their allelic influence on the investigated traits. Of the investigated loci, Glu-A1 alleles (Ax-null and Ax2*) did not significantly differentiate the ZSV; however, the presence of Ax2* resulted in a significant decrease in both HFN and GY. Glu-D1 locus  form the majority of the wheat storage proteins and the glutenin . The presence of Rht-D1a resulted in either decreased or commensurable values for GY. However, varieties harboring Rht-D1b alleles showed either increased or on par GY values. Taken together, our analyses show that Bx7orBx17, Dx5 + Dy10, and Pinb-D1b–d subunits/alleles have been necessary for improved and sustainable breeding for GY and quality traits. Hence, these can be used in two to three combinations depending upon the target GY and quality class. Also, Hap-2 and Hap-8 may be used to breed for targeted E  and C (cookies or stock feed) class GY groups, respectively.In the context of using major quality loci, it is vital to observe how breeders have exploited combination of alleles (haplotypes). As stated elsewhere, new varieties—depending on the quality class—must be superior to the checks (current top-yielding varieties) in terms of GY, disease resistance, and grain quality. In this regard, our haplotype analyses shed light on some of the breeders’ “favorite” haplotypes to sustain the bread-making quality while improving grain yield in wheat Fig. . For exaWe employed high-density SNP arrays, SSRs, and diagnostic markers with multi-environment robust phenotypic data for GWAS. However, the genotypic variance imparted by the identified MTA amounted to roughly 40% for ZSV and HFN. Hence, the remaining ~ 60% unexplained genotypic variance point to many small-effect maker loci, each explaining less than 10% genotypic variance. The prospects of genome-wide prediction—to predict the total genetic value of a trait based on all maker loci irrespective of their effect size—could be utilized Supplementary file 2 (XLSX 97 KB)Below is the link to the electronic supplementary material.