Genome‐wide marker effect heterogeneity is associated with a large effect dormancy locus in winter malting barley

Abstract

Prediction of trait values in plant breeding populations typically relies on assumptions about marker effect homogeneity across populations. Evidence is presented for winter malting barley (Hordeum vulgare L.) germination traits that a single, causative, large‐effect gene in the Seed dormancy 1 region on Chromosome 5H, HvAlaAT1 (Qsd1), leads to heterogeneous estimated marker effects genome wide between groups of otherwise related individuals carrying different Qsd1 alleles. This led to reduced prediction accuracy across alleles when a model was trained either on individuals carrying both alleles or one allele. Several genomic prediction models were tested to increase prediction accuracy within the Qsd1 allele groups. Small gains (5–12%) in prediction accuracy were realized using structured genomic best linear unbiased predictor models when information about the Qsd1 allele was used to stratify the population. We concluded that a single large‐effect locus can lead to heterogeneous marker effects in the same breeding family. Variance partitioning based on large‐effect loci can be used to inform best practices in designing genomic prediction models; however, there are likely few cases for which it may be practical to do this. For malting barley, if germination traits are highly associated with malting quality traits, then similar steps should be considered for malting quality trait prediction.

Core Ideas

• A single large‐effect seed dormancy locus leads to genome‐wide marker effect heterogeneity.

• Prediction accuracy between individuals with different dormancy alleles is lower than within allele prediction.

• A structured GBLUP model can be used to increase prediction accuracy across all individuals.

• The effects of large‐effect loci on allele substitution should be accessed when present in a population.

Abbreviations

BLUE

best linear unbiased estimator

BLUP

best linear unbiased predictor

GBLUP

genomic best linear unbiased predictor

PM

physiological maturity

SNP

single‐nucleotide polymorphism

1. INTRODUCTION

Predicting traits with genome‐wide markers without measuring those traits in all individuals is of great interest in plant breeding and can save resources while increasing the rate of genetic gain (Heffner et al., 2009; Meuwissen et al., 2001). Different prediction frameworks have been developed to increase accuracy based on regularization method and/or assumptions about the distributions of marker effects (Gianola, 2013). In most cases many of these models perform approximately equally well (dos Santos et al., 2020; Heslot et al., 2012; Lyra et al., 2020; Merrick & Carter, 2021).

One of the most difficult aspects of genomic prediction is accurate prediction across populations (i.e., different breeding pools). If subpopulations differ in average phenotype, then prediction of group membership is often adequate for a model to produce a reasonably high overall correlation between the model prediction and the true values. However, the within‐subpopulation prediction accuracy may be extremely low (Berro et al., 2019; Windhausen et al., 2012). This may be because of the decreased genomic heritability due to the explanation of a substantial portion of variance by the population factor or due to other factors, such as inconsistent allele substitution effects across the populations (de los Campos et al., 2015). Allele substitution effect homogeneity must be assumed for each marker across all individuals in the typical genomic best linear unbiased prediction (GBLUP) method and most other regression methods (de los Campos & Sorensen, 2014). Allele substitution effects have been shown to differ across populations (Legarra et al., 2021; Lehermeier et al., 2015; Veturi et al., 2019).

A large‐effect locus may have various non‐additive effects on the rest of the genome from the perspective of regression modeling. For example, in a family segregating for a seedling fatal mutation, a model trained on all the homozygous individuals carrying the mutation for plant lifetime will produce different allele substitution effects than a model trained on those not homozygous for the mutation. This example is illustrative but not practical because no active breeding program would include the phenotypes of the individuals carrying the homozygous fatal mutation in prediction models. It does raise the question of whether this sort of genome‐wide epistasis can occur within a typical breeding population. Can the status of large‐effect locus cause marker effect heterogeneity between groups of otherwise related individuals (i.e., from the same family) carrying different alleles? If allele substitution effects are heterogeneous due to a single large‐effect locus, it is likely that genomic prediction models trained on individuals containing both (or multiple) alleles of that locus will have a suboptimal within‐allele group prediction accuracy. The genomic prediction model will likely not accurately estimate the marker effect magnitude. The marker effects may be estimated as the combination of two or more different marker effects, with one effect size per marker from each group of individuals carrying each large effect allele. Heterogeneity of marker effects has been established across diverse populations (Guillenea et al., 2022; Legarra et al., 2021; Lehermeier et al., 2015; Liu et al., 2011; Rio et al., 2020; Schulz‐Streeck et al., 2012; Veturi et al., 2019); however, no study has explored this possibility in the context of large‐effect loci in related populations. Common ways tested to increase prediction accuracy across populations have included stratified analysis or the addition of random group‐specific marker deviation terms to standard regression models (Lehermeier et al., 2015). Both methods seek to more accurately estimate marker effects of each group to increase prediction accuracy.

Malting barley (Hordeum vulgare L.) is a subclass of barley grown for malting, a process of controlled germination. The malted barley, “malt,” is then used in the production of beer, liquors, and numerous other products. The collection of malt quality phenotypes is expensive (Schmitt & Budde, 2011), but germination traits may be indicative of malting traits (Frančáková et al., 2012; Woonton et al., 2005). This has not been evaluated for breeding populations, but it is clear that barley that does not germinate readily, either with a low germination rate or percentage, is not suitable for malting. Germination traits change with after‐ripening, as does malting quality, though the relationship between them is not well characterized on a population scale (Bradford et al., 2008; Briggs et al., 1994; Gothard, 1984; Rooney et al., 2021; Woonton et al., 2005). Germination traits evaluated soon after physiological maturity (PM) can be used as a measure of pre‐harvest sprouting resistance, a trait that has become increasingly important due to sporadic weather patterns and expansion of malting barley acreage. Seed dormancy is the most viable method of pre‐harvest sprouting resistance in malting barley (Rodríguez et al., 2015); however, dormancy may have negative effects on malting quality. Accurately predicting germination traits at several different times after maturity is critical for predicting pre‐harvest sprouting resistance and when a line may have germination traits suitable for malting.

Core Ideas

• A single large‐effect seed dormancy locus leads to genome‐wide marker effect heterogeneity.

• Prediction accuracy between individuals with different dormancy alleles is lower than within allele prediction.

• A structured GBLUP model can be used to increase prediction accuracy across all individuals.

• The effects of large‐effect loci on allele substitution should be accessed when present in a population.

Barley germination and seed dormancy have been the subject of several mapping studies (Edney et al., 2013; Han et al., 1996; Hickey et al., 2012; Hori et al., 2007; Lin et al., 2009; Nagel et al., 2019; Oberthur et al., 1995; Sweeney et al., 2021). These studies consistently found two major loci associated with dormancy, Seed dormancy 1 (SD1) and Seed dormancy 2 (SD2) (Nakamura, 2018). Both loci occur on chromosome 5H, and a causative gene has been identified at each. At SD1 there is an alanine amino transferase (HvAlaAT1, HORVU.MOREX.r2.5HG0398940) that affects primary dormancy and dormancy duration, and at SD2 there is a mitogen‐activated kinase kinase (HvMKK3, HORVU.MOREX.r2.5HG0447180) that has been shown to have similar effects (Nakamura et al., 2016; Rooney et al., 2021; Sato et al., 2016; Sweeney et al., 2021; Vetch et al., 2020). Both SD1 and SD2 have large effects, with both explaining large portions of genetic variance for primary dormancy in populations segregating for them. The HvMKK3 is thought to affect dormancy through reduced enzymatic activity in the dormant alleles (Nakamura et al., 2016). The alleles of HvAlaAT1 in the SD1 are thought to have approximately equal activity but differ by a single amino acid on the surface of the protein, perhaps leading to changes in regulation between them during after‐ripening (Sato et al., 2016).

The objective of this study was to investigate whether a large‐effect dormancy locus could affect allele substitution effects (marker effects) within a set of four biparental winter malting barley families and to investigate how to improve within‐allele and overall prediction accuracy if this was the case. This work will inform pre‐harvest sprouting and dormancy prediction in barley and could have implications on the wider prediction sphere.

2. MATERIALS AND METHODS

2.1. Winter malting barley germplasm

Four bi‐parental half‐sibling populations were created as part of a winter malting barley breeding program at Cornell University (called “DH”). The DH population was created by crossing ‘Lightning’ (Hayes et al., 2021) to four modern malting barley cultivars: ‘Wintmalt’, ‘Flavia’, ‘SY Typee’, and ‘KWS Scala’. Doubled haploids were developed at Oregon State University according to Cistué et al. (2003) through anther culture of F₁ plants of each cross. Lines were planted in the fall of 2019 and 2020 in two fields in Ithaca, NY. Fields in 2019 were planted according to an augmented block design with parents, and the check ‘Charles’ was replicated across family groups in 1‐m by 1‐m plots. Fields in 2020 were planted according to a randomized augmented block design with the checks Charles and ‘Endeavour’ and parents KWS Scala and Lightning in 1‐m by 2‐m yield plots. Data were unbalanced across years due to discard of a few undesirable lines and partial sampling of one of the fields in 2021. There were approximately 450 lines phenotyped with 76, 117, 128, and 124 lines in the Flavia/Lightning, Scala/Lightning, SY_Tepee/Lightning, and Wintmalt/Lightning families, respectively.

2.2. Germination trait/dormancy phenotyping

Average PM within a plot was recorded as the date 50% of the plot lost green color from the peduncle and spike. Two days after PM, bundles of 30–50 mature spikes were harvested, dried for 2 d at 35 °C, threshed, and stored at −20 °C to halt after‐ripening (Bahin et al., 2011; Briggs et al., 1994; Nagel et al., 2019). This enabled simultaneous observation of traits at the same number of after‐ripening days for all lines. Germination traits were measured with petri plate assays based on a method from the American Society of Brewing Chemists (ASBC, 1997) and equivalent to those used by Sweeney et al. (2021). Briefly, 30 kernels were plated in a 90‐mm petri plate containing two Whatmann #1 filter papers and 4 ml of tap water. Germinated (radicle emergence >2 mm) kernels were counted and removed every 24 h over 3 d. On the last day the ungerminated kernels were counted. Two replicates were performed per plot. Germination percentage (GE) was calculated as the proportion of kernels that germinated out of all kernels plated. A germination rate (GI) based on an inverse mean germination time was calculated as GI = 10 × (n ₂₄ + n ₄₈ + n ₇₂) × GE/(1 × n ₂₄ + 2 × n ₄₈ + 3 × n ₇₂), where n ₂₄, n ₄₈, and n ₇₂ are the numbers of kernels that germinated at 24, 48, and 72 h, respectively (Frančáková et al., 2012). All samples were removed from the freezer 24 h before the first germination assay was started at PM + 5 and kept at room temperature.

In 2020, assays were conducted at five timepoints after PM: PM + 5, 19, 47, 96, and 152 d of after‐ripening, which are labeled PM₅, PM₁₉, PM₄₇, PM₉₆, and PM₁₅₂, respectively. In 2021, assays were conducted at the same post‐PM dates as 2020, with the addition of assays at PM + 12, 33, and 68 d, which are labeled PM₁₂ PM₃₃, and PM₆₈. At every timepoint except for PM₅ in 2020, the full set of lines was observed with two germination assay replicates per plot. These dates were chosen to capture dormancy break and to give an estimate of germination traits after dormancy was lost based on a study of spring malting barley performed by Rooney et al. (2021). Additional times were added in 2021 based on the 2020 data to better capture the winter barley phenotypes, which differed from the spring barleys.

2.3. Genotyping data

All lines were genotyped with the barley 50K single‐nucleotide polymorphism (SNP) chip (Bayer et al., 2017) at the USDA Small Grains Genotyping Laboratory in Fargo, ND. Marker positions were based on the Morex v2 genome assembly (Monat et al., 2019). All markers with a minor allele frequency <0.05 and markers with heterozygosity >0.01 were removed. Markers with >10% missing data for lines were also removed using Tassel version 5 (Bradbury et al., 2007), resulting in 15,467 markers for analysis. The remaining missing marker sites were imputed by taking mean values for each marker in R using rrBLUP R package (Endelman, 2011). The SNPs were filtered by linkage disequilibrium pruning using the SNPrelate R package (Zheng et al., 2012) with a 25,000‐bp sliding window and a cutoff of 0.95, which resulted in 8,383 markers. Linkage disequilibrium declines to r ² < .2 in 30 Mbp overall families and was more extended within each family (Flavia, 94 Mbp; Scala, 61 Mbp; SY Tepee, 116 Mbp; Wintmalt, 87 Mbp).

All lines were genotyped with the KASP assays developed by Sweeney et al. (2021) for MKK3_E165Q and AlaAT_L214F (referred to as “Qsd1”). MKK3_E165Q genotypes a nonsynonymous SNP in HvMKK3 in the SD2 region that is likely responsible for loss of primary dormancy. The population was monomorphic for MKK3_E165Q. The AlaAT_L214F assay tags the likely causative mutation within the HvAlaAT1, leading to more rapid loss of dormancy (Sweeney et al., 2021; Vetch et al., 2020). Lightning and Flavia contained the dormant HvAlaAT1 allele, and the other three DH parents (Wintmalt, KWS Scala, and SY Tepee) carried the nondormant HvAlaAT1 allele, and the offspring within those families were segregating for this locus. Any heterozygous calls for Qsd1 were corrected if possible, or lines containing heterozygotes were filtered out of all analyses if not possible (removing 10 lines). In genome‐wide association the Qsd1 marker and region in linkage with it were highly associated with the germination traits and the only large‐effect locus (explaining >10% of the variance) (K. H. Kunze, unpublished data).

2.4. Statistical analysis

2.4.1. Data processing

All data analysis was conducted with the R statistical language (R Core Team, 2020) version 4.0.3 within the R studio (RStudio Team, 2021) environment, version 1.4.1106.

2.4.2. Heritability and line estimates for prediction in a two‐step method

For the germination traits per time point, separate linear models were fit of the form

$$y_{ikr}=g_i+L_k+R_r+e_{ikr}$$ (1)

where y_ikr is the phenotype of the ith line from the kth location in the rth replication, g_i is the random or fixed effect of genotype i, L_k is the fixed effect of environment (location‐year combination) k, R is the fixed effect of the replicate r, and e_ikr is the error associated with each measurement. Genotype was fit as a random effect to estimate heritability or as a fixed effect to extract best linear unbiased estimators (BLUEs). When genotype was fit as random effect, g ∼ N(0, σ_g ²), where σ_g ² is the genetic variance. Broad‐sense heritability was estimated according to Cullis et al. (2006) as

$$H^2=1-\mathrm{avg}\left(V_{\mathrm{blup}}\right)/\left(2\ast {\mathrm{\sigma }}_g^2\right)$$ (2)

where avg(V _blup) is the average of the variance of the best linear unbiased predictor (BLUP) estimates for genotype, and σ_g ² is as stated from the model. Heritability and BLUEs were calculated for each time point, year, and trait combination such that for the timepoints measured across both years there were estimates including only the 2020 data, only the 2021 data, and the combined 2020–2021 data. Modeling spatial variation did not significantly improve model fit. A broad‐sense heritability was estimated after accounting for Qsd1 allele by adding a fixed effect for Qsd1 in Model 1.

The narrow‐sense heritability before and after accounting for Qsd1 was calculated within ASReml R (Butler et al., 2018). A covariance structure specified as the genomic relationship matrix (G) according to Endelman and Jannink (2012), calculated within the rrBLUP package (Endelman, 2011), was used in Model 1 by assuming g ∼ N(0, Gσ_a ²), where σ_a ² was the additive genetic variance. Narrow‐sense heritability was estimated as Endelman & Jannink (2012):

$$h^2={\mathrm{\sigma }}_a^2/\left({\mathrm{\sigma }}_a^2+{\mathrm{\sigma }}_e^2\right)$$ (3)

To estimate a per Qsd1 allele group additive genetic variance, g ∼ N(0, diag(G_Qsd1D σ_aD ², G_Qsd2N σ_aN ²), where G_Qsd1D and G_Qsd1N are the additive genetic relationship matrices of only the dormant or only the nondormant lines, respectively, and σ_aD ² and σ_aN ² are the additive genetic variances of each group. A fixed effect for Qsd1 was also included.

2.4.3. Variance partitioning across families and to Qsd1

Several models were fit to the raw germination phenotypes on a per‐timepoint/trait basis to attribute genetic or additive genetic variance to Qsd1 (Butler et al., 2018). Finding different variances is a key piece of evidence in establishing differences in marker effects across groups. A likelihood ratio test between two models of the form

$$y_{krfi}=L_k+R_r+F_f+g_i+e_{krfi}$$ (4)

was compared with

$$y_{krfi}=L_k+R_r+F_f+g_{(i|f)}+e_{krfi}$$ (5)

where L_k , R_r , and F_f are the fixed effects for location k, replicate r, and family f. In Model 4, g_i is a random effect for line ∼N(0, σ_g ²), where σ_g ² is the overall genetic variance. In Model 5 g _{( i|f )} was a random effect for line ∼N(0, σ_g ² ) where a separate genetic variance was estimated for each family [i.e., σ_g ²  = diag(σ_gf ²), where σ_gf ² is the genetic variance for each family f]. A significant likelihood ratio test indicated that fitting specific variances per family improved model fit. Once total family genetic variance was assessed with Model 5, attribution of variance to Qsd1 was determined by fitting the model

$$y_{krsfi}=L_k+R_r+F_f+Q_{(s|f)}+g_{(i|f)}+e_{krsfi}$$ (6)

where Q _{( s | f )} was a fixed effect for Qsd1 allele status by family interaction, and all other variables are as described for Model 5. The variance attributable to Qsd1 per family was then estimated as

(7)

where σ_gf ² _{Model 5} is the per‐family genetic variance from Model 5, and σ_gf ² _{Model 6} is the per‐family genetic variance from Model 6. Another model was fit of the form

$$y_{krsfi}=L_k+R_r+F_f+Q_{(s|f)}+g_{(i\left|s\right|f)}+e_{krsfi}$$ (8)

All variables are equivalent to Model 6 except g _{( i | s | f )}, which was a random effect with a unique genetic variance per family:qsd1 grouping [i.e., σ_g ²  = diag(σ_gsf ²), where σ_gsf ² is the genetic variance of family f with Qsd1 allele called s]. To determine if each allele group per family was better modeled with a unique genetic variance, Model 8 was compared with Model 6 with a likelihood ratio test.

2.4.4. Correlation of marker effects within the Qsd1 allele group

Low correlation of marker effects between groups is also evidence of heterogeneous marker effects between them. To ensure balance between the datasets, only families segregating for Qsd1 were used to examine the correlation between marker effects. Within group, a ridge regression BLUP on markers was performed to estimate marker effects. The Pearson correlation of marker effects between the groups was calculated. This correlation was compared with a null distribution obtained by grouping the population with randomly selected SNPs at intermediate allele frequency (0.3–0.7) not on Chr5H. Significant decreases in correlation were determined using the null distribution.

2.4.5. Genomic prediction of germination within and across allele groups

Low cross‐group prediction accuracy should be expected if marker effects are not transferable across groups and is evidence of marker effect heterogeneity. Combined 2020–2021 BLUEs calculated with Model 1 from families segregating for Qsd1 (all families except for the Flavia/Lightning family) were used in cross‐allele group genomic prediction tests. This was done to ensure balanced representation of each allele by family. The rrBLUP genomic prediction method within the rrBLUP package (Endelman, 2011) was used in three ways: (a) the genomic prediction model was trained on a random sample of lines in the three families segregating for Qsd1, and the remaining lines were predicted; (b) only lines containing the dormant allele were used for model training, dormant lines not used for model training, and all nondormant lines were predicted; and (c) only lines containing the nondormant allele were used in model training, and nondormant lines not used for model training and all dormant lines were predicted. In each of these cases, the prediction accuracy was assessed in two ways: (a) an overall prediction accuracy (including all predicted lines) and (b) a within‐allele group prediction accuracy (i.e., a prediction accuracy for the dormant Qsd1 and a prediction accuracy for the nondormant Qsd1). Training population size was varied from 40 lines to no more than ∼85% of a group's size to ensure adequate numbers of lines for testing accuracy. Every prediction model was replicated 100‐fold with randomly generated training populations.

2.5. Strategies to increase prediction accuracy within allele groups and structured GBLUP

Multiple model frameworks were evaluated from BayesB, BayesC, and LASSO, including fixed effects for allele groups or not. None of the models increased prediction accuracy substantially over Bayesian ridge regression (equivalent to rrBLUP and GBLUP). The GBLUP parametrization was used exclusively in the remaining tests. This was done with the Reproducing Kernel Hilbert Space method in the BGLR R package (Perez and de los Campos, 2014 ). As phenotypes, BLUEs from the combined 2020–2021 analysis were used.

2.5.1. Structured GBLUP

A structured GBLUP approach was used in an attempt to increase the prediction accuracy. The method implemented is described in more detail elsewhere (Berro et al., 2019; Lehermeier et al., 2015). The structured GBLUP model estimates a common main marker effect and group‐specific deviations from the main marker effect. The main stratifying factor was Qsd1, and the second was family structure. In this test, all four families were used, with a training size of 325 out of 424. All kinship matrices were calculated using the rrBLUP package function A.mat(). All models used the standard formula

$$y=\mathrm{\mu }+\mathrm{\beta }\mathbf{X}+{\mathbf{Z}}_0{\mathrm{\mu }}_0+{\mathbf{Z}}_1{\mathrm{\mu }}_1+\mathrm{error}$$ (9)

where μ is the model intercept; X is design matrix relating fixed effects to lines with effects β; Z ₀ is a design matrix for μ₀; μ₀ is a random vector of genotypic predictors ∼N(0,Kσ_μo), where K_{( nxn)} is the realized additive genetic relationship matrix as in GBLUP and σ_μo is the genetic variance; Z ₁ is a design matrix for μ₁; and μ₁ is a second random vector of genotypic predictors incorporating the group‐specific effects ∼N(0, K₁σ_μ1 ), where K_{1 (nxn)} is a block diagonal matrix with each block being the realized additive genetic matrix within each group and σ_μ1 is a vector of group‐specific genetic variances such that each group (block) in the block diagonal matrix has a unique variance.

All results were compared with a standard GBLUP model. There were four different ways of stratifying the population to establish groups (Table 1): stratification by Qsd1 allele (two groups), by family (four groups), by family:Qsd1 allele interaction (seven groups), and by Qsd1 allele and family (two deviation terms, two groups and four groups). For each stratification, the prediction model (as in Model 9) was varied in five different ways by setting different components of Model 9 to zero (Table 1). In each of these cases, K₁ was determined by these groups. In the Qsd1 and family case, a third random effect (Z ₂μ₂) was incorporated following similar rules as μ₁, Z ₂ was a design matrix for μ₂, μ₂ ∼N(0, K₂σ_μ2 ), where K_{2 (nxn)} is another block diagonal matrix and σ_μ2 as described for σ_μ1 with groups from K₂ . In this model K₁ was a block diagonal matrix with groups according to Qsd1, and K₂ was a block diagonal matrix with groups according to family.

TABLE 1.

Each case and variation for the structured genomic best linear unbiased predictor used

			Variation
Case	Stratifying factor	Effects	Full	Base_fixef	JC	JC_Fix	NoFix
Base	none	fixed	none	n/a	n/a	n/a	n/a
	no groups	random	μ0 effect: standard GBLUP
Family	family	fixed	family	family	none	family	none
	4 groups	random	μ0 effect, μ1 by family	μ0 effect	μ1 by family	μ1 by family	μ0 effect, μ1 by family
Qsd1	Qsd1	fixed	Qsd1 allele	Qsd1 allele	none	Qsd1 allele	none
	2 groups	random	μ0 effect, μ1 by Qsd1	μ0 effect	μ1 by Qsd1	μ1 by Qsd1	μ0 effect, μ1 by Qsd1
Qsd1:Family interaction	Qsd1:family	fixed	Qsd1:family interaction	Qsd1:family interaction	none	Qsd1:family interaction	none
	7 groups	random	μ0 effect, μ1 by Qsd1:family	μ0 effect	μ1 by Qsd1:family	μ1 by Qsd1:family	μ0 effect, μ1 by Qsd1:family
Qsd1 and Family	Qsd1, family	fixed	Qsd1 allele and family	Qsd1 allele and family	none	Qsd1 allele and family	none
	2 groups/4 groups	random	μ0 effect, μ1 by Qsd1, μ2 by family	μ0 effect	μ1 by Qsd1, μ2 by family	μ1 by Qsd1, μ2 by family	μ0 effect, μ1 by Qsd1, μ2 by family
	$y=\mathrm{\mu }+\mathrm{\beta }\mathbf{X}+{\mathbf{Z}}_0{\mathrm{\mu }}_0+{\mathbf{Z}}_1{\mathrm{\mu }}_1+{\mathbf{Z}}_2{\mathrm{\mu }}_2+\mathrm{error}$

3. RESULTS

3.1. Phenotypes and heritability of germination traits

Phenotypes (BLUEs) calculated on a per‐year or combined basis are shown in Figure 1 and Supplemental Figure S2, separated by Qsd1 status and the family structure. The year effect was substantial; however, the within‐year location effect was often small. Crop year 2021 exhibited substantially more dormancy.

FIGURE 1.

Best linear unbiased estimators of the phenotypes of the lines used within this study for the combined 2020–2021 dataset separated by family (top facets), Qsd1 (color) status, and trait (side facets)

Broad‐sense heritability of the germination traits remained high (>.75) over time, although a substantial portion of the genetic variance can be explained by Qsd1, as demonstrated by the 20–40% drop in broad‐sense heritability when Qsd1 is accounted for with a fixed effect in the model framework (Figure 2a; Supplemental Figure S3). The narrow‐sense heritability ranged from about .5–.9, except for later timepoints of germination percent, when variation declined as most lines had reached 100% germination at that timepoint, and also commonly decreased moderately to substantially upon including Qsd1 as a fixed effect in the model. Narrow‐sense heritability was typically not substantially different from the broad‐sense heritability both when Qsd1 was and was not a fixed effect in the model. The additive genetic variance of each Qsd1 allele group often differed substantially, depending on the time point/year combination.

FIGURE 2.

Results of variance breakdown for germination rate using the 2020 and 2021 data. Timepoint is on the x axis. See the Supplemental Information for per‐year and germination percentage traits. (a) Different heritability estimates combining families, Cullis H ², Cullis heritability overall individuals; Cullis H ² Qsd1 Fixed, Cullis heritability after Qsd1 was accounted for as a fixed effect; h ² additive genetic heritability over all lines; h ² Qsd1 Fixed, additive genetic heritability over all lines with Qsd1 fixed; h ² Qsd1_D and h ² Qsd1_D additive genetic heritability in the Qsd1 dormant and Qsd1 nondormant lines, respectively. (b) Genetic variance in each family. The height of the bar gives the total genetic variance in the family. The darker portion of the bar gives the portion of genetic variance attributable to Qsd1; the lighter is the genetic variance unexplained by Qsd1. (c) Genetic variance per family per Qsd1 allele group over time

3.2. Attribution of variance to family and Qsd1 groupings

Fitting unique family genetic variances always improved model fit by a likelihood ratio test (p < .05) except in two cases at later timepoints of the germination percentage trait. Qsd1 explained 40–90% of the genetic variance in families segregating it (Figure 2b; Supplemental Figure S4). There was a substantial difference between years for when the genetic variance peaked. The heritability of the non‐Qsd1–attributable variance (using the error variance from Model 6) varied from quite low (H ² <.2) to >.6) (Supplemental Figure S5), repeating the broad‐sense heritability found in Figure 2a when Qsd1 was included as a fixed effect.

Family:Qsd1 groups were assigned unique genetic variances between the allele calls by a likelihood ratio test between Models 6 and 8 (Figure 2C; Supplemental Figure S6). The genetic variances of the dormant and nondormant alleles peaked at different times. In most cases, one Qsd1 allele had a heritability of moderate magnitude at a single timepoint (Supplemental Figure S7). In some cases, the variance/heritability of one of the allele groups was high, whereas the other was closer to zero, especially in the 2021 crop year (Supplemental Figures S6 and S7), where initially the nondormant Qsd1 allele group started with a high variance, which then declined over time, whereas the dormant Qsd1 allele group started with a low variance, which increased over time before it too began to decline.

3.3. Correlation of marker effects between dormant and nondormant allele groups

Marker effects calculated within an allele group were highly correlated across time. Closer timepoints were more highly correlated than temporally distant timepoints. Between the dormant and nondormant groups, marker effects were generally lowly correlated, with the main exception being the early timepoints of the nondormant group and the later timepoints of the dormant group (e.g., non‐dormant PM₅ and PM₁₂ to and dormant PM₆₈ and PM₉₆; Figure 3). On a per‐TP basis, for example comparing TP1 D and ND marker effects, effects are significantly less correlated (p < .05) than the marker effect correlations found by grouping the population be random SNPs.

FIGURE 3.

Correlation of marker effects on a per group/timepoint basis. Germination percent (upper diagonal) and germination rate (lower diagonal) using the 2021 dataset; similar outcomes were observed with the combined and the 2020 datasets. ‘Sig’ is appended along the upper and lower diagonals of the matrix where the correlation between timepoints (i.e., D and ND at PM₅) were tested and significantly different (p < .05) from that obtained with a null distribution. D, dormant group; ND, nondormant group

3.4. Within‐ and across‐allele genomic prediction

The overall prediction accuracy for a model trained on both alleles of Qsd1 was generally >0.6 (Figure 4; Supplemental Figures S8 and S9). The prediction accuracy within each allele group for the model trained on both alleles was substantially lower. Models trained and predicting on the same allele (i.e., predicting dormant lines with a model trained on dormant lines) led to a higher prediction accuracy at the same training population size than the models trained on both alleles. The rank order of models remained consistent with increasing training population size. Within‐allele training and prediction always led to the highest prediction accuracy with the exception of the PM₅ time point where each of the different training methods (training on both alleles, or each Qsd1 group) performed approximately equivalently.

FIGURE 4.

Germination rate of physiological maturity at 5 and 152 d of after‐ripening genomic prediction results of using training populations derived from both alleles of Qsd1 vs. training within Qsd1 allele grouping at n_train = 100. Variation in training population does not affect results. Colors show allele or alleles that the genomic prediction model was trained on; the number indicates what is being tested according to the diagram on the right

3.5. Structured GBLUP results

A number of the structured GBLUP models used improved the prediction accuracy of the genomic prediction model overall and within allele group, depending on the timepoint (Figure 5; Supplemental Figures S10 and S11). For germination rate PM₅, no models significantly improved the prediction accuracy over the base model. For the remaining timepoints, the ‘Base_fixef’, the ‘Full’, ‘JC_fix’, and the ‘No_Fix’ variations all increased the prediction accuracy by up to 12% when information about Qsd1 was used to create groups or fixed effects. Approximately the same held true for germination percent (Supplemental Figure S10); however, at PM₅, there were improvements in prediction accuracy.

FIGURE 5.

Structured genomic best linear unbiased predictor (GBLUP) results of germination rate prediction for the 2020–2021 dataset. Cases (what determined the groups used in the structured GBLUP) are shown as the facet label. The Base model's prediction accuracy is shown numerically on the graph. Color and size of points correspond to percentage increase or decrease in the prediction accuracy of the model variation used compared with the Base GBLUP model for each timepoint. The JC variation is not shown here

4. DISCUSSION

We used four winter malting barley families segregating for the large‐effect locus HvAlaAT1, called Qsd1 here, to determine whether a single locus could affect allele substitution effects. We examined variance partitioning associated with Qsd1 and genomic prediction accuracies between and within models trained on individuals containing either both or one of the alleles. Various genomic prediction models were evaluated and found to increase the prediction accuracy both overall and within allele groups.

Qsd1 was associated with a large effect (Figure 1; Supplemental Figure S2), explaining a substantial amount of the genetic variance within families and overall (Figures 2). Although we did not perform experiments to prove causality, Sato et al. (2016) and Vetch et al. (2020) provide evidence that the mutation assayed with the AlaAT_L214F (Qsd1) marker is the causative mutation. On a per‐year basis, the remaining genetic variance assigned to each family after accounting for Qsd1 was similar (Figure 2; Supplemental Figure S5). The additive and total genetic variance was different between Qsd1 groups (either overall or per family) after the additive Qsd1 effect had been taken into account, indicating that Qsd1 was not solely additive.

Under the additive genetic model if linkage is ignored, in diploid inbred organisms (such as barley), each marker follows a Bernoulli distribution. The individual's phenotype is approximated as the sum of the Bernoulli variables times each of their respective marker effects. The genetic variance is then the sum of the variances of each Bernoulli variable [p × (1 − p), where p is the allele frequency of the major allele] times its marker effect squared. If allele frequencies do not differ significantly between groups, different genetic variances mean that allele substitution effects differ between the groups (de los Campos et al., 2015). However, similar genetic variances do not preclude different marker effects. Between the Qsd1 groups, allele frequencies did not differ except at Qsd1, where the grouping artificially created segregation distortion (Supplemental Figure S12).

Although it is possible that the linkage and its decay surrounding Qsd1 led to the different variances estimated for each Qsd1group, it seems unlikely. The linkage of Qsd1 with surrounding markers should lead to smaller, but similar, genetic variances between alleles if Qsd1 only acted additively. We concluded Qsd1 had epistatic effects across the genome to change marker effects in a time‐dependent, and perhaps allele‐dependent, way, leading to the differences in genetic variance. For example, take the two alleles of Qsd1, dormant and non‐dormant, and another unlinked locus that responds to it (Supplemental Figure S13). The terminal effect on the phenotype may be the same, but the effect size may differ until that “terminal” time has been reached. The apparent marker effect heterogeneity observed here may be transient, only effecting prediction during dormancy break. Assessment of terminal germination (perhaps at 300 d after PM) could be used to test for persistence of the effects. The later timepoints of the dormant marker effects were most highly correlated (r = .4–.5) (Figure 5) to the earliest timepoints of the nondormant marker effect, indicating that the terminal effects of each allele apart from Qsd1 may be similar.

Different marker effects between groups should lead to low cross‐group prediction accuracy and low correlation of marker effects. The marker effects of the groups were significantly less correlated than segregation by random markers (Figure 3). Prediction models trained on individuals containing one allele predict that allele better than prediction models trained on individuals containing both alleles and with one allele (Figure 4; Supplemental Figures S8 and S9). This held true for most trait/timepoint combinations. The main exception to this was at PM₅, where the model trained on both alleles performed as well as the models trained on each allele and outperformed them as the training population size increased. Repeating this analysis on a single year of data for that time point (Supplemental Figure S14) gives the same results. This may be due to the low genetic variance of the dormant group at PM₅.

Because marker effects were heterogeneous across the groups, a prediction method allowing deviations from a main marker effect was tested to increase within‐allele group prediction accuracy. Incorporating family into the model structure did not change the prediction accuracy. The presence of family‐specific markers likely captured familial deviations. Prediction accuracies both within allele group and overall improved significantly when information pertaining to Qsd1 was used in stratification. The “Full” variation in these Qsd1‐stratified models with all random effects (μ₀ up to μ₂) and the fixed effects often had the highest prediction accuracy. The efficacy of the group‐specific marker effect deviations (μ₁ and μ₂) may be questioned because incorporating fixed effects into the base GBLUP model (“base_fixef” variation) sometimes led to approximately the same increase in prediction accuracy overall. Within‐allele prediction accuracies typically had the greatest increase when the marker‐specific deviations were included (Supplemental Figures S10 and S11). However, models with fixed effects mostly outperformed the equivalent model without fixed effects.

We also attempted to increase the prediction accuracy by using different prediction modeling frameworks. The Bayesian models (B and C) tested perform variable selection (Meuwissen et al., 2017) and are often used intentionally when large‐effect loci are present in the prediction model. These prediction models give variable performance in comparison to GBLUP, likely dependent on genetic architecture (Kaler et al., 2022; Meher et al., 2022). Here, even with the presence of a large‐effect locus, the Bayesian methods did not lead to higher prediction accuracies (Supplemental Figure S1). These methods may in theory fit the architecture of large‐effect additive loci better; however, they are still bound to estimate common marker effects for all individuals in the model. This seems to be the main assumption violated in this population for these traits. The evidence points to different allele substitution effects between the groups. These methods have been extended to incorporate group deviations from main effects similar to the structured GBLUP (Martínez et al., 2017). Because the chances of multiple large effect loci segregating in the population are rarer (and there are no others in this study; K. H. Kunze, unpublished data), the infinitesimal model likely applies to the remaining markers once the large effect locus is accounted for, and under those circumstances GBLUP seems to outperform other models (Meher et al., 2022).

In a broad context, this is the first in‐depth analysis of the effects of a large‐effect locus on marker effects and within allele group prediction accuracy. Generally, they show that large effect loci can have epistatic effects on the rest of the genome and affect prediction models. We achieved a higher prediction accuracy by incorporating information into a structured GBLUP model. In cross‐population prediction methods there is high probability of population‐specific marker effect deviation (Guo et al., 2014; Liu et al., 2011; Rio et al., 2019, 2020). The structured GBLUP method was developed for prediction in this case (de los Campos & Sorensen, 2014; Lehermeier et al., 2015; Schulz‐Streeck et al., 2012), but the results of using it in structured populations have been variable. Schulz‐Streek et al. (2012) saw moderate gains in prediction accuracy, whereas Lehermeier et al . (2015) and Berro et al. (2019) saw variable results as compared with a standard GBLUP. More generally, in stratified prediction, models that consider group effects (without specifically using a structured GBLUP framework) led to improvements in prediction accuracy (Guillenea et al., 2022; Karaman et al., 2021; Lyra et al., 2018; Ramstein & Casler, 2019). Here we show that a model developed for highly differentiated populations can improve prediction accuracy within a highly related population due to the presence of group‐specific marker effects associated with a large‐effect locus. This seems to be the first reported case of this phenomenon. In the larger prediction sphere, however, large‐effect loci are rare, and the increase in the prediction accuracy attainable using a more complicated model may not be worth the trouble depending on the trait predicted.

In the context of malting barley there are other implications. If germination traits are highly correlated to malting quality traits then prediction models built for malting quality may benefit from a more sophisticated or informed model. Malting quality is extremely expensive to measure. Even small changes in prediction accuracy may be beneficial in that case. These results indicate that the high prediction accuracies obtained by Rooney et al. (2021) may be somewhat obscuring a relatively lower within‐haplotype prediction accuracy. Within the spring barley population they used, there were two highly significant loci affecting the germination traits. For prediction of pre‐harvest sprouting and germination traits, taking into account large‐effect loci and structuring prediction models around them leads to increased accuracy and better selection decisions. In the interest of malting and pre‐harvest sprouting resistance, prediction of close‐to‐maturity germination and germination at the putative earliest time of malting (∼12 wk after maturity) to ensure germination suitable for malting would be most useful. Ongoing work is assessing the relationships between the germination and malting quality. The extra computation expense of using a more complex model would also need to be gauged. In this dataset there were no problems with convergence or excessive computational time arising from the use of the structured GBLUP.

5. CONCLUSION

We examined the effect of Qsd1 on variance partitioning after incorporating Qsd1 as a fixed effect in several mixed models and found different variances assigned to each Qsd1 allele group. We concluded this non‐additive change in variance was due to an epistatic effect of Qsd1 on the rest of the genome and would lead to different marker effects based on the additive gene model. We showed that prediction accuracies across Qsd1 allele groups were poor and that marker effects between Qsd1 alleles were uncorrelated. A structured GBLUP with fixed effects and group‐specific marker effect deviations according to Qsd1 groups was shown to increase prediction accuracy by up to 12%. Generally, careful examination of variance partitioning according to large‐effect loci can be used inform best practices when designing a genomic prediction model; however, the cases where it may be practically useful to do this are likely few. Specifically for malting barley, if germination traits are genetically correlated to malting quality then genomic prediction of malting quality under structured models should be tested.

AUTHOR CONTRIBUTIONS

Travis E. Rooney: Conceptualization; Data curation; Formal analysis; Funding acquisition; Investigation; Methodology; Project administration; Resources; Validation; Visualization; Writing – original draft; Writing – review & editing. Karl H. Kunze: Data curation; Funding acquisition; Methodology; Writing – review & editing. Mark E. Sorrells: Funding acquisition; Investigation; Project administration; Supervision; Writing – review & editing.

CONFLICT OF INTEREST

The authors declare no conflict of interest.

Supporting information

Supplemental Figures and Supplemental Table are within the .docx file.

Rooney, T. E. , Kunze, K. H. , & Sorrells, M. E. (2022). Genome‐wide marker effect heterogeneity is associated with a large effect dormancy locus in winter malting barley. The Plant Genome, 15, e20247. 10.1002/tpg2.20247

DATA AVAILABILITY STATEMENT

All analysis scripts, data, and scripts to produce the figures in this paper have been published in a Github repository (https://github.com/ter56/WinterQsd1Effects).