Genomewide association and prediction of phenotypic stability in barley

Abstract

Climate change threatens crop production through an increase in the occurrence of extreme abiotic stress. Breeding and growing crop cultivars that are more tolerant of these stresses may be accomplished by selecting for phenotypic stability (opposite of plasticity), which may be aided by understanding the genetic architecture and marker‐based predictive ability of plasticity. Using data from a multi‐environment experiment in barley (Hordeum vulgare L.), our objectives were to (1) identify genomic regions associated with the mean per se and linear plasticity for five agronomic and malting quality traits, (2) determine the genomewide prediction accuracy of plasticity, and (3) assess the impact of subsampling environments on estimates and predictions of plasticity. We calculated trait genotype means and linear plasticity (slope) for 233 lines (both founders and offspring) grown in 42 environments. We identified 87 marker‐trait associations and nearly all significant single nucleotide polymorphisms for the slope overlapped with previously discovered mean per se QTL for the same trait. Genomewide prediction accuracy of slope was moderate as measured using cross‐validation (r _MP = 0.32–0.69) and when predicting the slope of an unobserved offspring test population (r _MP = 0.26–0.61). Increasing the number of sampled environments from which to use phenotypic data led to more precise estimates of the slope, greater rates of marker‐trait association discovery, and greater genomewide prediction accuracy; however, a modest number of environments was sufficient for obtaining accurate predictions. Our results suggest more shared genetic control of the plasticity and mean per se of traits, but genomewide prediction may be used to select for plasticity without resource‐intensive multi‐environment trials.

Core Ideas

• Trait genotype means per se and trait phenotypic stability were used as inputs for genomewide association analysis.

• Marker‐trait associations indicated similar genetic architecture of genotype means and linear plasticity.

• Accurate genomewide predictions of linear plasticity were obtained for an observed offspring population.

• A modest number of environments may be sufficient for training genomewide prediction models for plasticity.

Plain Language Summary

Climate change threatens crop production by increasing abiotic stresses like drought and extreme temperatures. Developing crop varieties tolerant to these extremes requires selecting for yield or quality stability across environments, which demands extensive field trials. Breeding for more stable crop varieties could be aided by understanding the genetics of phenotypic stability and using genomic information to predict stability in new crop varieties. To address this, we analyzed barley data from 42 environments for five traits, calculating trait stability and identifying 87 significant molecular marker associations with stability. Overlapping genomic regions suggest shared genetic control of trait variation and stability. Genomewide prediction showed moderate‐to‐high accuracy, even with a subset of environments, offering breeders a resource‐efficient way to develop stable crop varieties.

Abbreviations

FP

founder population

GBLUP

genomic best linear unbiased prediction

GBS

genotyping‐by‐sequencing

GEI

genotype–environment interactions

GO

gene ontology

GP

grain protein

GWA

genomewide association

GY

grain yield

HD

heading date

LD

linkage disequilibrium

MTA

marker‐trait association

OP

offspring population

PH

plant height

QTL

quantitative trait loci

TW

test weight

1. INTRODUCTION

Climate change poses a challenge for crop production systems through the increased incidence and magnitude of extreme weather (Stocker, 2014). Breeding and deploying crop cultivars that are tolerant of such abiotic stresses may be one component of a strategy to mitigate the impact of climate change. Identifying these cultivars in plant breeding programs will depend on understanding the differential response of plant genotypes to environments, or genotype–environment interactions (GEIs), a common phenomenon in the study of quantitative traits (Bernardo, 2010).

One method of analyzing GEIs is through reaction norms, or the change in phenotype over an environmental gradient (Lynch & Walsh, 1998); genotypic differences in reaction norms are a form of GEI. Reaction norms can be used to study the phenotypic plasticity of genotypes (Bernardo, 2010; Eberhart & Russell, 1966; Finlay & Wilkinson, 1963). Stable genotypes will exhibit a consistent phenotype across environments, while unstable (or plastic) genotypes will display greater sensitivity to changes in environment. Stability may be more favorable when choosing cultivars that are tolerant of abiotic stresses, as phenotypic expression will remain more constant and predictable. Alternatively, plastic lines may be desirable if the environmental conditions most conducive to favorable phenotypes can be guaranteed (e.g., high‐fertility soils to promote greater yield). The phenotypic plasticity of a quantitative trait may also be considered a trait itself and incorporated as a breeding target; selections could be made in a breeding program for genotypes with both favorable mean and plasticity (Bradshaw, 2006; Eberhart & Russell, 1966). While it is well‐established that reaction norms have a genetic basis and respond to selection (Scheiner, 1993), the mean and plasticity of a genotype are often unfavorably correlated (Bernardo, 2010; Rosielle & Hamblin, 1981; Scheiner, 1993), suggesting that trade‐offs may be necessary in breeding.

Genetic improvement of plasticity in plants would be aided by knowledge of its genetic architecture. Two primary gene models of phenotypic plasticity have been proposed (El‐Soda et al., 2014; Kusmec et al., 2017; Scheiner, 1993). First, the pleiotropic (or allelic sensitivity) model suggests that quantitative trait loci (QTL) that influence the per se mean of a trait also influence plasticity; alleles at these QTLs may be differentially sensitive to environmental conditions (Via & Lande, 1985). Second, the epistatic (or regulatory) model hypothesizes that environmentally sensitive regulatory genes influence the expression of other genes (Scheiner & Lyman, 1989). These alternative models of genetic architecture have competing implications for breeding strategies and effectiveness. Pleiotropy would impose more constraints to selection gain if the per se mean and plasticity of a trait were unfavorably correlated, while the independent genetic control suggested by the regulatory model would allow breeders to simultaneously select for the trait mean per se and plasticity.

Genetic mapping studies in crops have sought to provide empirical support to either of these models. In large studies of maize (Zea mays L.), distinct QTL and candidate genes for trait per se mean and plasticity were identified, with an enrichment of gene‐proximal QTL for plasticity, both supporting the regulatory gene model (Gage et al., 2017; Kusmec et al., 2017). Conversely, high overlap between per se mean and plasticity QTL for flowering time was discovered in a biparental mapping experiment in sorghum (Sorghum bicolor L.), suggesting a greater role of pleiotropy. This pattern of coincident QTL was also prominent in barley (Hordeum vulgare L.) mapping studies (Emebiri & Moody, 2006; Kraakman et al., 2004; Lacaze et al., 2009), though these experiments were more limited in their scope of genotypes or environments.

Although understanding the genetic architecture of plasticity would be useful, measuring this parameter in selection candidates is still resource‐intensive, involving phenotyping across an appropriate range of environments (Bernardo, 2010). Marker‐based predictive tools, such as genomewide selection (Bernardo, 1994; Meuwissen et al., 2001), could aid in early‐stage selection of more stable or plastic genotypes prior to their entry into field trials. Predictions of plasticity would thereby be treated as those of any other trait and could be included in a multi‐trait index. Several studies have suggested that genomewide prediction of plasticity may have utility, reporting moderate to high estimates of prediction accuracy for the plasticity of both agronomic and quality traits in wheat (Triticum aestivum L.) and rye (Secale cereale L.) (Y. Huang et al., 2016; Lozada & Carter, 2020; Wang et al., 2015). These studies, however, addressed predictions within a common panel or set of biparental families, and the persistence of favorable prediction accuracies when genomewide selection is applied between generations, a more relevant breeding scenario, remains to be demonstrated.

To better understand GEIs and the genetic architecture of phenotypic plasticity, we conducted a barley (Hordeum vulgare L.) multi‐environment experiment under natural field conditions. Barley is cultivated worldwide, making it ideal for studying phenotypic plasticity (Dawson et al., 2015). Additionally, barley is grown in many low‐ and middle‐income regions of the world, which may be more adversely affected by climate change (International Monetary Fund, 2017). Knowledge of the genetic underpinnings of GEIs and their breeding implications would be useful for other crops and practical for improving food security. The objectives of this study were to use genomewide association (GWA) to compare the genetic architectures of trait means per se and phenotypic plasticity (both linear and nonlinear) and assess the accuracy of genomewide prediction for these characters.

2. METHODS AND MATERIALS

2.1. Plant material, marker genotyping, and phenotyping

This study used data from the spring two‐row multi‐environment trial, a coordinated effort to phenotype a common panel of elite barley breeding germplasm for training genomewide selection models (Neyhart et al., 2019a). The panel consisted of 182 founder population (FP) lines from five North American breeding programs and 50 offspring population (OP) lines that were selected from crosses made between FP lines. A more thorough description of phenotypic data collection and genomewide marker genotyping is presented elsewhere (Neyhart et al., 2019a); however, we provide salient details for the purpose of this paper.

Core Ideas

• Trait genotype means per se and trait phenotypic stability were used as inputs for genomewide association analysis.

• Marker‐trait associations indicated similar genetic architecture of genotype means and linear plasticity.

• Accurate genomewide predictions of linear plasticity were obtained for an observed offspring population.

• A modest number of environments may be sufficient for training genomewide prediction models for plasticity.

The 233‐line panel (183 FP + 50 OP) was phenotyped in 42 location–year environments from 2014 to 2017. These environments spanned longitudes of the northern United States and southern Canada, ranging from Montana, Idaho, and Oregon in the west; North Dakota, Minnesota, and Wisconsin in the US Midwest; and New York, Quebec, and Prince Edwards Island in the east. A full map is available in previous papers (Neyhart et al., 2019a). The FP was phenotyped solely in four environments, the OP solely in five environments, and the panel together in 33 environments. Many traits were measured in each of the environments, but we consider five important agronomic and malting quality characters for this study: grain protein (GP) (% w/w), grain yield (GY) (kg ha⁻¹), heading date (HD) (days after planting), plant height (PH) (cm), and test weight (TW) (g L⁻¹). A more detailed description of the methods of measuring these traits is provided in a previous paper (Neyhart et al., 2019a) and from the Triticeae Toolbox (T3; https://barley.triticeaetoolbox.org/tools/onto/). Traits were not measured in all environments; the total number of environments was 15 for GP, 40 for GY, 37 for HD, 39 for PH, and 20 for TW.

Genomewide marker data were obtained using genotyping‐by‐sequencing (GBS) (Elshire et al., 2011). We used a custom pipeline to perform quality control, clean and align reads, and call variants, which is described in detail in Neyhart et al. (2019a). We filtered variants to retain only bi‐allelic single nucleotide polymorphisms (SNPs) with mapping quality score ≥ 40, genotype quality score ≥ 40, and genotype read depth ≥ 5. The 235,216 SNPs that were initially discovered were reduced to 6,361 based on a minor allele frequency ≥ 0.05, missing data ≤ 0.8, and maximum adjacent marker correlation of r ² = 0.95. Missing marker genotypes were imputed using a combination of fastPHASE (Scheet & Stephens, 2006) and the expectation maximization algorithm implemented in the R package rrBLUP (Endelman, 2011). After these steps, 174 FP lines and 48 OP lines remained in the GBS marker dataset, which was used to construct a realized additive relationship matrix (K) using rrBLUP.

For association mapping, we obtained additional marker data for the entire 182‐line FP from the T3 (Blake et al., 2016). We downloaded marker genotypes for these lines based on the iSelect 9k barley SNP array (Comadran et al., 2012). The 8,288 SNP genotypes in this set were combined with the 6,361 obtained using GBS. Genome positions for most markers were available relative to the Morex v1 physical reference genome (Mascher et al., 2017). We removed SNPs with unknown physical genome position, and among pairs of SNPs with identical positions, we retained the SNP with the larger minor allele frequency. We then filtered the combined set of SNPs based on a minor allele frequency ≥0.054 (10/182 = 0.054) and missingness ≤0.80. Among pairs of markers in high linkage disequilibrium (LD) (r ²  > 0.95), we retained the marker with the higher minor allele frequency. This resulted in a marker dataset of 5,223 SNPs for 179 lines in the FP.

2.2. Phenotypic analysis

A two‐stage approach was used for phenotype data analysis (Piepho et al., 2012). In the first stage, adjusted genotype means were calculated for each trait in each environment using a model that was most appropriate for the particular experimental design (most experiments were arranged using augmented designs; see Neyhart et al. [2019a] for more detail). For data quality control, broad‐sense heritability (H) was estimated in each environment using the approach of Cullis et al. (2006) and data from trait‐environment combinations with H < 0.10 were removed.

In the second stage, we calculated linear and nonlinear plasticity using the approaches of Finlay and Wilkinson (1963) and Eberhart and Russell (1966) via the joint regression model:

$$y_{ij}=\mathrm{\mu }+g_i+\left(1+b_i\right)t_j+{\mathrm{\delta }}_{ij}+{\mathrm{\epsilon }}_{ij},$$ (1)

where y_ij is the adjusted mean of the ith genotype in the jth environment, μ is the grand mean, g_i is the effect of the ith genotype, t_j is the effect of the jth environment, b_i is the regression coefficient of y_ij on t_j , δ_ij is the residual genotype–environment interaction effect, and ε_ij is the error. All effects except for t_j were treated as random with distributions $g_i\sim N(0,{\mathrm{\sigma }}_g^2)$, $b_i\sim N(0,{\mathrm{\sigma }}_b^2)$, and ${\mathrm{\delta }}_{ij}\sim N(0,{\mathrm{\sigma }}_{\mathrm{\delta }}^2)$. The random error was modelled as ${\mathrm{\epsilon }}_{ij}\sim N(0,\mathbf{R}{\mathrm{\sigma }}_{\mathrm{\epsilon }}^2)$, where $\mathbf{R}$ is a diagonal matrix with elements equal to the variances of the genotype means estimated in the first stage (Mohring & Piepho, 2009). The genotype mean was calculated as (μ + g_i ), linear plasticity as (1 + b_i ) (Finlay & Wilkinson, 1963), and the nonlinear plasticity as (${\mathrm{\sigma }}_{\mathrm{\delta }(i)}^2=\frac{1}{t}{\sum }_{j=1}^t{\mathrm{\delta }}_{ij}^2$). Equation (1) was fitted using the blme R package (Chung et al., 2013). We refer to these parameters for the remainder of the paper as genotype mean, slope (linear plasticity), and deviation (nonlinear plasticity).

We estimated heritability and genetic correlations for the genotype mean, slope, and deviation by partitioning the total phenotypic variance using genomewide markers. We fitted the mixed‐model as follows:

$$y_i=\mathrm{\mu }+g_i+{\mathrm{\epsilon }}_i,$$ (2)

where y_i is the response (genotype mean, slope, and deviation), g_i the random effect of the ith genotype, and ε_i the associated error. The random effect of genotype was modeled as $g_i\sim N(0,\mathbf{K}{\mathrm{\sigma }}_A^2)$, where K is a realized additive relationship matrix described above and ${\mathrm{\sigma }}_A^2$ is the additive genetic variance; residual error was modeled as ${\mathrm{\epsilon }}_i\sim N(0,{\mathrm{\sigma }}_{\mathrm{\epsilon }}^2)$, where ${\mathrm{\sigma }}_{\mathrm{\epsilon }}^2$ is the residual variance. Genomic narrow‐sense heritability (H _SNP) was calculated as $H_{\mathrm{SNP}}={\mathrm{\sigma }}_A^2/({\mathrm{\sigma }}_A^2+{\mathrm{\sigma }}_{\mathrm{\epsilon }}^2)$. Genetic correlations between the genotype mean, slope, and deviation were measured by modifying Equation (2) to fit a bivariate mixed model:

$$y_{ic}={\mathrm{\mu }}_c+g_{ic}+{\mathrm{\epsilon }}_{ic},$$ (3)

where y_ic is the measurement for the ith genotype of the cth trait (one of the genotype mean, slope, and deviation), μ_c is the mean of the cth trait, g_ic is the random effect of the ith genotype, and ε_ic is the associated error. The genotypic effect was modeled as $g_{ic}\sim N(0,\mathbf{G})$, where $\mathbf{G}=\mathbf{K}[\begin{array}{cc}{\mathrm{\sigma }}_{A(1)}^2& {\mathrm{\sigma }}_{A(1,2)}\\ {\mathrm{\sigma }}_{A(1,2)}& {\mathrm{\sigma }}_{A(2)}^2\end{array}]$. Here, ${\mathrm{\sigma }}_{A(1)}^2$, ${\mathrm{\sigma }}_{A(2)}^2$, and ${\mathrm{\sigma }}_{A(1,2)}$ are the additive genetic variance of the first trait, additive genetic variance of the second trait, and the additive genetic covariance between traits, respectively; the genetic correlation was estimated as $r_{A(1,2)}=\frac{{\mathrm{\sigma }}_{A(1,2)}}{{\mathrm{\sigma }}_{A(1)}{\mathrm{\sigma }}_{A(2)}}$. Similarly, the residual errors were modeled as ${\mathrm{\epsilon }}_{ic}\sim N(0,\mathrm{\Omega })$, where $\mathrm{\Omega }=[\begin{array}{cc}{\mathrm{\sigma }}_{\mathrm{\epsilon }(1)}^2& {\mathrm{\sigma }}_{\mathrm{\epsilon }(1,2)}\\ {\mathrm{\sigma }}_{\mathrm{\epsilon }(1,2)}& {\mathrm{\sigma }}_{\mathrm{\epsilon }(2)}^2\end{array}]$. ${\mathrm{\sigma }}_{\mathrm{\epsilon }(1)}^2$, ${\mathrm{\sigma }}_{\mathrm{\epsilon }(2)}^2$, and ${\mathrm{\sigma }}_{\mathrm{\epsilon }(1,2)}$ are analogous to their genetic counterparts defined above, and the residual correlation, $r_{\mathrm{\epsilon }(1,2)}$, was similarly calculated. The delta method was used to estimate the standard errors of heritability and genetic correlations (Lynch & Walsh, 1998). Models (2) and (3) were fitted using the R package sommer (Covarrubias‐Pazaran, 2016).

The number of environments sampled in our dataset is much larger than the scope of routine testing in breeding programs. We therefore performed a subsampling experiment to determine the impact of environment number on parameter estimates. For each trait, we sampled 10%–90% of the total available environments (in steps of 10%) and used phenotypic data from those environments to estimate the genotype mean, slope, and deviation for each genotype. At each percentage, 25 random samples of environments were drawn. In each of the 1125 samples (nine percentages × 25 replicates × five traits), we calculated the mean absolute error as $mae({\widehat{x}}_m)=\frac{1}{n}{\sum }_{i=1}^n|{\widehat{x}}_{im}-x_i|$, where ${\widehat{x}}_{im}$ is the parameter estimate of the ith genotype in the mth sample and $x_i$ is the parameter estimate of the ith genotype when using data from all available environments. In addition to random samples of all environments, we conducted a similar analysis using targeted samples of environments. We defined four environment targets based on the distribution of environmental effects, t_j : the upper tail (t_j above the 0.5 quantile), lower tail (t_j below the 0.5 quantile), middle (t_j above the 0.25 quantile and below the 0.75 quantile), and tails (t_j below the 0.25 quantile and above the 0.75 quantile). For each target (which represents at most 50% of all environments), we sampled 20%–100% of the environments within that target (in steps of 20%) and again used phenotypic data from those environments to estimate the genotype mean, slope, and deviation for each genotype.

2.3. Genomewide association analysis

We conducted GWA scans for associations between genomic regions and the genotype mean, slope, and deviation. The g_i , b_i , and σ_{δ ( i )} parameters estimated from Equation (1) were used as response variables in univariate mixed‐effect models. Only data from the 179 lines in the FP that were present in the 5223‐SNP marker set were included in the GWA. Population structure was controlled using principal components (PCs) of the 5223 SNP genotypes. We performed separate scans using zero and the first one, two, and three PCs, which explained 65%, 7.0%, and 3.7% of the variance, respectively.

GWA analyses were performed using the multi‐locus mixed model approach implemented in FarmCPU (Liu et al., 2016). The routine was executed with the optimum bin selection method, default bin size and selection options, and a maximum of 10 iterations. The ideal number of PCs for the association analysis of each trait and parameter [g_i , b_i , or σ_{δ ( i )}] was allowed to vary and was determined by visual inspection of Q–Q plots (Figure S1) and the estimated p‐value inflation factor (where factors closer to 1 indicate superior model fit). A false discovery rate cutoff of 0.10 was used to identify significant marker‐trait associations (MTAs).

We explored the genomic regions harboring significant GWA markers by defining a 4.5 Mb window on either side of each SNP. This corresponds to a roughly 3 cM window, the distance in this germplasm at which LD decays to r ² = 0.2 (Hamblin et al., 2010). Within these windows, we compared our results with three sources of information: first, we made qualitative comparisons with previous barley genetic mapping studies of the trait genotype mean, slope, and deviation (Emebiri & Moody, 2006; Kraakman et al., 2004; Lacaze et al., 2009); second, we examined the results of GWA analyses for per se trait means in the same germplasm (H. Pauli et al., 2014; Wang et al., 2012), along with the catalog of MTAs identified across all germplasm in the T3 database (Blake et al., 2016); third, we used genome annotation information and associated gene ontology (GO) terms for the v1 barley physical reference genome (Mascher et al., 2017) to identify nearby predicted genes.

To determine the impact of the number of environments on the rate of detection of MTA, we used the parameters estimated in the sampling experiment described above as inputs in GWA models. We calculated the discovery rate as the proportion of replicates (n = 25) at each environment sampling level (10%, 20%, …, 90%) in which we detected the same markers identified in the analysis of the full dataset.

2.4. Genomewide prediction

A genomic best linear unbiased prediction (GBLUP) model (Equation 3) was used to evaluate the accuracy of genomewide prediction for the genotype mean, slope, and deviation. We used two validation methods to calculate prediction accuracy: first, 25 replicates of fivefold cross‐validation were conducted using only the FP; second, between‐generation validation was performed by using the FP as a training population and the OP as a testing population. Prediction accuracy (r _MP) was defined as the correlation between the predicted and observed values of the genotype mean, slope, and deviation. Finally, we used the FP parameter estimates from the 25 replicates at each environmental sample level to train genomewide prediction models, with those parameters estimated in the OP using the full dataset serving as model testing data.

2.5. Data availability

The phenotypic and genotypic data used in this study are available on T3 (https://triticeaetoolbox.org/barley/) database under the experiment name “UMN Spring 2‐row MET.” Code used to perform the analysis and generate the figures in this manuscript is available in the GitHub repository: https://github.com/UMN‐BarleyOatSilphium/S2MET_StabilityMapping.

3. RESULTS

3.1. Phenotypic plasticity

Considerable phenotypic variation among genotype‐environment means was observed for each trait, pointing to the breadth of environments—and genotypic responses to those environments—captured by our dataset (Figure 1A). There was significant variation in the slope and deviation parameters for all traits. Likelihood ratio tests indicated that the variance components ${\mathrm{\sigma }}_b^2$ and ${\mathrm{\sigma }}_{\mathrm{\delta }}^2$ estimated in Equation (1) were all highly significant (p < 1 × 10⁻¹⁶). The distribution of slope estimates was generally similar across traits, ranging from about 0.60 to 1.3. The traits GP and TW had notably wider ranges in b_i , from about 0.40 to 1.5. Genotypes with lower values of the slope parameter are considered more stable, while those with higher values are considered more plastic. We observed more crossovers in the reaction norm patterns for GP and GY than for other traits (Figure 1A). Of all pairwise comparisons between the reaction norms of lines within the FP, 68% were crossovers for GP, 44% for GY, 20% for HD, 34% for PH, and 38% for TW. The phenotypic correlations between the genotype mean and slope parameters ranged from −0.18 to 0.37 (Figure 1B), while the genotype mean and deviation parameters were not correlated (Figure 1C).

FIGURE 1.

We observed considerable phenotypic variation among lines and across environments, visualized by (A) histograms of phenotypic values in each location (colors, shaded by year). (B) Phenotypic plasticity was measured by regressing phenotypic values on the mean in each environment (colored points corresponding to locations) and calculating the slope of the regression line (b_i , linear plasticity) and deviations from that line (σ_{δ ( i )}, nonlinear plasticity). Different patterns of genotypic response were observed for each trait, including more stable (red) or plastic (blue) genotypes. (C) Correlations between the genotype mean (g_i ) and the slope were often positive, but (D) no correlation was observed between the genotype mean and the deviation.

Whole‐genome regression models indicated that the genotype mean and slope parameters were moderately heritable. Estimates of H _SNP for the genotype mean ranged from 0.57 (PH) to 0.82 (HD), while those for the slope ranged from 0.35 (TW) to 0.66 (GP); the deviation parameter, however, was not heritable (Table 1). Bivariate mixed models yielded estimates of the genetic correlation between the genotype mean and slope parameters that were roughly equal to the phenotypic correlation (Table 1; Figure 1B). The genetic correlation between the genotype mean and slope was more strongly positive for GP and GY, while more strongly negative for TW, though these estimates had a much larger standard error. Two models did not converge, and estimates of the genetic correlation were unavailable (Table 1).

TABLE 1.

Genomic narrow‐sense heritability (H _SNP) estimates for the per se genotype mean (g_i ), slope (linear plasticity; b_i ), and deviation [nonlinear stability; σ_{δ ( i )}], and their pairwise additive genetic correlations (r_A ) with standard errors in parentheses.

	H SNP			Genetic correlation a
Trait	gi	bi	σδ ( i )	rA ( g , b )	rA ( g , σ )	rA ( b , σ )
Grain protein	0.64 (0.11)	0.66 (0.10)	0.050 (0.058)	0.31 (0.17)	0.47 (0.43)	−0.17 (0.41)
Grain yield	0.60 (0.11)	0.46 (0.12)	0.0052 (0.032)	0.23 (0.17)	0.17 (0.93)	−0.30 (0.62)
Heading date	0.82 (0.082)	0.62 (0.11)	0 (0.027)	0.078 (0.15)
Plant height	0.57 (0.11)	0.39 (0.11)	0 (0.027)	0.40 (0.18)
Test weight	0.60 (0.11)	0.35 (0.11)	0.052 (0.060)	−0.13 (0.20)	−0.012 (0.42)	0.32 (0.45)

Abbreviation: SNP, single nucleotide polymorphism.

^a In some cases, bivariate models failed to converge, leading to missing estimates of r_G .

3.2. Marker‐trait associations

In our initial genomewide scan, we identified 87 significant MTAs for the genotype mean, slope, and deviation (Table 2; Figure 2; Table S1). For nearly all traits, significant associations were identified for the genotype mean and slope parameter, while no associations were detected for the deviation parameter. The exception to this was TW, where zero markers were significantly associated with the slope and two markers were identified for the deviation. We did not observe any pattern of enrichment within lines (or within the originating breeding program of those lines) for favorable stability alleles at the identified MTAs (data not shown).

TABLE 2.

Summary of marker‐trait associations (MTAs) for five traits and three parameters, including the number of principal components (PCs) used as fixed effects, the percentage variance explained (PVE), and the number of MTAs coincident (overlapping) with previously identified QTL or predicted genes.

Trait	Parameter	PCs	MTAs	PVE K a	PVEMTA b	PVEMTA range c	MTA‐QTL overlaps	MTA‐gene overlaps
Grain protein	Mean	3	8	0.1	0.47	0.0012–0.29	8	8
	Slope	2	7	0.093	0.35	0.030–0.21	5	7
	Deviation	3	0				0	0
Grain yield	Mean	0	13	0.11	0.65	0.000020–0.19	13	13
	Slope	0	9	0.092	0.6	0.0034–0.29	9	9
	Deviation	2	0				0	0
Heading date	Mean	1	6	0.059	0.59	0.0000041–0.65	6	6
	Slope	2	10	0.19	0.41	0.000063–0.084	10	10
	Deviation	3	0				0	0
Plant height	Mean	2	9	0.12	0.54	0.00069–0.19	9	9
	Slope	0	11	0.27	0.48	0.0023–0.20	11	11
	Deviation	2	0				0	0
Test weight	Mean	0	12	0.056	0.65	0.0046–0.20	12	12
	Slope	1	0				0	0
	Deviation	1	2			0.10–0.11	2	2

Abbreviation: QTL, quantitative trait loci.

^a Percent variance explained attributed to kinship.

^b Percent variance explained attributed to all significant MTAs.

^c Range in percent variance explained attributed to each significant MTA.

FIGURE 2.

Genomewide association analyses conducted using estimates of the genotype mean or slope (linear plasticity) parameters discovered multiple significant associations at a false discovery rate of 0.10 (black horizontal line). Nearly all associations were coincident with previously identified quantitative trait loci (QTL) (black ticks) cataloged in the Triticeae Toolbox (T3) database and many coincided with known genes. Three traits are highlighted here (GP, grain protein; GY, grain yield; HD, heading date), and results for all traits and all parameters are available in Figure S2.

Many of the significant MTAs were coincident with (≤4.6 Mbp/∼3 cM away from) predicted or known genes or previously identified QTL (Table 2; Figure 2; Table S1). Coincident markers were often proximal to known QTL, with the median distance to the nearest QTL ranging from 13 to 2300 kb. These markers were very close to predicted genes (Mascher et al., 2017), and the median distance from coincident markers to the nearest gene ranged from 0 to 35 kb. Despite this, there were few MTAs that were coincident for at least two of the genotype mean, slope, and deviation within each of the traits (Figure 2).

The results of the environmental sampling experiment are visualized in Figure 3. Sampling an increasing proportion of the total available environments had the expected effect of reducing the mean absolute error between parameters (genotype mean, slope, and deviation) estimated at each environment proportion level and those estimated using the full dataset (Figure 3A). While increasing the proportion of total sampled environments continued this trend, decreasing marginal reductions in the error were observed after sampling about 30%–40% of total environments. This pattern was consistent when the samples of environments were targeted to certain quantiles of the distribution of environmental means (i.e., upper 50%, lower 50%, middle 50%, upper/lower 25%), though we noted that the mean absolute error was lowest for the slope parameter when environments were sampled from the upper 50% or lower 50% (Figure S3).

FIGURE 3.

Sampling phenotypic data from an increasing proportion of the total environments led to (A) decreasing mean squared error between the genotype mean (blue), slope (linear plasticity, orange), and deviation (nonlinear plasticity, green) estimated using the sampled environments and those parameters estimated using the full dataset. (B) The individual (thin lines) and mean (thick lines) discovery rate of marker‐trait associations detected using the full dataset (Figure 2) generally increased as data from a greater proportion of environments were used.

Correspondingly, the discovery rate of full‐dataset significant MTAs consistently increased as a greater proportion of environments were sampled (Figure 3B). The discovery rate of associations for the genotype mean was generally greater than that for linear or nonlinear plasticity. For all parameters, there were two apparent patterns. First, the discovery rate of some associations increased sharply when sampling few environments, while for others the rate remained low or increased slowly. Some of these markers were coincident with major QTL or genes; for example, the association with the most sharply increasing rate for GP genotype mean was that coinciding with the HvNAM‐1 gene, while that for HD genotype mean coincided with Vrn‐H3. Second, discovery rates remained low, even after sampling a high proportion of environments. For example, when using data from 90% of the total environments, the average discovery rate ranged from only about 0.3 (GY, PH, and TW) to 0.5 (GP and HD).

3.3. Genomewide prediction

Prediction accuracies using GBLUP models were moderate to high for the genotype mean and slope parameters of all traits (Figure 4). Cross‐validation within the FP led to average prediction accuracies ranging from about 0.46 (TW) to 0.84 (HD) for the genotype mean and 0.32 (TW) to 0.69 (GP) for the slope (Figure 4A). The deviation parameter was not accurately predicted. These high prediction accuracies were consistent even when using the OP as a separate test population (Figure 4B). Predictions remained highly accurate for the genotype mean, ranging from 0.56 (GP) to 0.63 (GY, PH, and TW), but were slightly less accurate for slope, ranging from 0.26 (PH) to 0.61 (GP). Again, predictions of the deviation parameter remained inaccurate.

FIGURE 4.

Genomewide predictions of the genotype mean (blue), slope (linear plasticity, orange), and deviation (nonlinear plasticity, green) were generally accurate (except for nonlinear stability). This was apparent (A) using within‐generation cross‐validation of the founder population (FP) and (B) between‐generation prediction using the FP to predict an offspring population (OP). (C) When using phenotypic data from an increasing proportion of the total environments to estimate mean and slope parameters, it led to moderately high between‐generation prediction accuracy, even at a modest number of environments.

We used parameter estimates from the environmental sampling experiment to further test genomewide predictions. For each sample, parameter estimates of the FP were used to train the GBLUP model; predictions were tested using the full‐dataset parameter estimates of the OP. Along with decreasing mean absolute error estimated and increasing MTA discovery rates, sampling a greater proportion of the total environments led to increasing r _MP of the genotype mean and slope (Figure 4C). Yet, fewer environments were required to achieve high prediction accuracies; for example, a mere 10% (HD and PH) to 30% (TW) of the total environments led to predictions of the genotype mean that were at least 80% as accurate as those when using the whole dataset, and 20% (PH) to 60% (HD, TW) of environments were needed for similarly accurate predictions of the slope parameter (Figure 4C). A similar pattern was observed when targeted samples of environments were generated from different quantiles of the distribution of environmental means. We did note that for HD, sampling environments with the lowest 50% of means led to the highest prediction accuracy, while sampling from the middle 50%, upper 50%, or lower/upper 25% led to accuracies much lower than randomly sampling an equivalent number of environments (Figure S4).

4. DISCUSSION

4.1. Complexity and overlap of genetic architecture between per se means and plasticity

Our results suggest that, for the traits in this study, the genetic architecture of phenotypic stability/plasticity is as complex as that for the trait per se. The genomic narrow‐sense heritabilities of the genotype mean and slope (linear plasticity) parameters were moderate to high and appeared to be correlated (Table 1). These estimates are consistent with previous knowledge of these traits (Hockett & Nilan, 1985; Neyhart et al., 2021). The deviation parameter (nonlinear plasticity) exhibited very low heritability estimates and few MTAs. This may be the result of (i) limited genetic basis of nonlinear plasticity, (ii) a greater role of linear plasticity in explaining GEI (Lin et al., 1986), or (iii) the statistical reality that nonlinear plasticity, as defined, is the residual deviation from the regression line (Eberhart & Russell, 1966).

The similarities in genetic complexity of the genotype mean and slope parameters are also apparent in the results of association mapping. Though we detected several loci that together explained a sizable proportion of the variance (Table 2), many of these individually explained only a small proportion and were only of modest effect (Table S1). These results are consistent with previous genetic analyses of phenotypic plasticity in barley and other crops. In barley, previous studies have typically identified only a handful of loci associated with the phenotypic plasticity of different traits, including GY, GP, HD, and 1000‐kernel weight (Emebiri & Moody, 2006; Kraakman et al., 2004; Lacaze et al., 2009). Recent, larger analyses in maize and soybean also suggested complex genetic architectures for phenotypic plasticity (Kusmec et al., 2017; Xavier et al., 2018).

We observed moderate additive genetic correlations between the genotype mean and the slope for most traits (Table 1), though low or negative correlations were apparent for HD and TW. The former suggests the presence of shared genetic architecture, either due to pleiotropy or LD. Genetic correlations between the trait mean and slope parameter have been observed previously (Kusmec et al., 2017; Rosielle & Hamblin, 1981; Scheiner, 1993), yet have not implicated an allelic sensitivity model or otherwise shared genetic control. Conversely, a lack of genetic correlation does not preclude common genetic control, as factors such as LD and effect sizes can mask genetic correlation when pleiotropy is present.

The results from the GWA analysis showed that, while few overlapping associations were detected for the genotype mean and slope, all of those for the latter were coincident with per se QTL detected in similar germplasm (Table 2; Figure 2). Further, many of the MTAs detected in our study were localized to regions identified in previous QTL mapping studies of linear plasticity (Emebiri & Moody, 2006; Kraakman et al., 2004; Lacaze et al., 2009). There are several associations that are coincident with well‐described barley genes (Figure 2; Figure S2) that are worth further discussion. First, associations on chromosomes 3 and 5 for GP slope overlapped with the genes denso and HvDEP1, respectively. While the semidwarf gene denso is associated primarily with PH (Jia et al., 2009), it has also been linked to variation GY and quality (Thomas et al., 1991). The HvDEP1 gene impacts GY and grain size, though this effect is notably environmentally dependent (Wendt et al., 2016). Grain size may influence GP content by a concentration of the same absolute protein level in a smaller kernel. Interestingly, we did not observe any significant MTAs near this gene for the genotype mean or slope for GY or 1000‐kernel weight. Second, the MTA on chromosome 4 for the genotype mean and slope of GY was coincident with the flowering time gene Vrn‐H2, which, although not associated with HD in our study, has been shown to impact GY and yield stability (Rollins et al., 2013). Third, several MTAs, including those for GP mean, GY mean and slope, HD mean, and PH mean and slope, localized to a region on chromosome 7. This region contains Vrn‐H3 (Pauli et al., 2014; H. Wang et al., 2012; Yan et al., 2006), another known flowering time gene and one purported to influence shoot development (Arifuzzaman et al., 2016), suggesting a role in governing PH. Additionally, variation at this gene has been associated with agroecological adaptation (Casas et al., 2011), which may help explain its apparent influence on overall productivity (GY) and GP in this study. These specific examples, as well as the extensive overlap of significant slope parameter associations with previously identified QTL, suggest that genes influencing the trait mean are also contributing to phenotypic plasticity.

It is interesting that few markers in our study were significantly associated with both the genotype mean per se and plasticity of a trait. This points to the broader strengths and limitations of our study. First, while our study covered the largest number of environments yet in an investigation of phenotypic plasticity, it is limited by small population size. The resulting reduction in statistical power may have prevented the detection of additional QTL; however, other association mapping studies and simulations using similar germplasm suggest that our population size may be adequate to detect QTL (Bradbury et al., 2011; Gutiérrez et al., 2011), particularly for more highly heritable traits. Second, other properties of our population, namely, the non‐random selection imposed on the FP for starting a breeding program, may have fixed alleles at relevant QTL. Third, the relative contribution of QTL to the per se mean versus plasticity may be a factor. Even if the genetic control of these traits is shared, a QTL may influence the mean with a small effect, but is highly sensitive to environment and would thus influence the plasticity with a larger effect. Fourth, as in other GWA studies, the detection of particular MTAs depends on the sample of environments from which phenotypic data were collected. The differential rates of MTA discovery in our environmental resampling test (Figure 3B) suggested both a degree of randomness in the probability of MTA detection and the presence of potentially undiscovered loci when using data from a particular set of environments.

Our results suggest a greater role for the pleiotropic or allelic sensitivity model for phenotypic plasticity, consistent with the conclusions of several previous studies in barley (Emebiri & Moody, 2006; Kraakman et al., 2004; Lacaze et al., 2009). In contrast, recent studies in maize have suggested that the genes influencing trait means per se are separate from those influencing plasticity (Gage et al., 2017; Kusmec et al., 2017). These conclusions were based on analyzing candidate genes and enrichment of MTAs in gene‐proximal or genic regions, made possible in part by the rapid decay of LD in maize. The pattern found in those analyses could be present in our species of study, but it is challenging to confidently assign genomic annotation classification to MTAs in barley given the long‐range extent of LD and small population size. However, we did note that, among the annotated genes most proximal to the MTAs detected in this study, we did not observe any pattern of elevated enrichment of GO terms with MTAs for the genotype mean or slope parameters. If a regulatory gene model played a more important role in defining the genetic architecture of phenotypic plasticity, we would expect to find an enrichment of GO terms associated with gene regulation (e.g., DNA binding). While this was not the case (Table S1), our results do not rule out the possibility of a combination of allelic sensitivity and regulatory models in the genetic architecture of plasticity (Tibbs‐Cortes et al., 2024).

4.2. Accurate genomewide predictions of phenotypic plasticity

As with many complex traits, we found that prediction using all genomewide markers could attain reasonably high accuracy within and between populations (Figure 4). Cross‐validation within the FP returned r _MP estimates that were consistent with the genomic narrow‐sense heritability of the genotype mean and slope (Figure 4A; Table 1) and suggested that genomewide prediction would be effective for identifying stable genotypes, consistent with previous investigations (Y. Huang et al., 2016; Wang et al., 2015).

Though cross‐validation within the FP provided encouraging results for the usefulness of genomewide prediction of phenotypic plasticity, in practice a breeder would seek to predict the phenotypes of lines in subsequent generations. Our evaluation of genomewide prediction between parent and offspring generations, using the FP to train and the OP to test the models, more closely reflected this objective. This concept has hitherto remained untested in the context of predicting phenotypic plasticity, and our results showed that predictions of both the trait mean per se and slope could remain accurate, even for a separate breeding population (Figure 4B). While we observed a decrease in r _MP from within‐generation to between‐generation prediction, this result is not unexpected and is likely due to a decrease in relatedness or change in patterns of LD due to recombination (Habier et al., 2007).

One of the important advantages of genomewide prediction is in the ability to impose selection on candidates prior to obtaining phenotypic information (Lorenz et al., 2011). This is particularly relevant for traits that are expensive or resource‐intensive to measure, such as postharvest quality or pathogen toxin content. Given the large number of environments in which phenotypic data were collected for this study (N_E  = 15–40), measuring phenotypic plasticity for any trait will involve substantial investment of resources. This makes the high r _MP observed for between‐generation predictions all the more encouraging, as it indicates that selection candidates could be screened on the basis of both trait genotype mean and slope prior to their entry into expensive multi‐environment trials. Of course, most breeding programs do not have the resources to phenotype a common panel of lines in upward of 40 environments for training genomewide prediction models. Fortunately, the results of our environmental sampling analysis showed that for many traits, a more modest number of environments is sufficient to achieve useful r _MP for both the genotype mean and slope (Figure 4C).

4.3. Implications for breeding crops for climate change resiliency

Developing crop cultivars that are tolerant of more extreme environmental conditions and also more predictable in increasingly variable climates will be important for addressing agricultural productivity. Meeting this objective will depend on understanding the genetic basis of how genotypes interact with the environment (GEI). Phenotypic plasticity is one way to measure GEI that provides a useful metric for characterizing the ability of genotypes to maintain a consistent phenotypic expression across varying environmental conditions. The consensus that plasticity is heritable (Scheiner, 1993), made more concrete by our study and recent research using genomic information (Y. Diouf et al., 2020; Gage et al., 2017; Huang et al., 2016; Kusmec et al., 2017; Wang et al., 2015; Xavier et al., 2018), indicates that breeding programs should be able to make gain toward improving plasticity in their populations.

The classic Finlay–Wilkinson approach to measuring plasticity regresses phenotypic values to the phenotypic mean of each environment (Finlay & Wilkinson, 1963). Using this as a selection target implicitly assumes that overall plasticity will correspond to plasticity for specific abiotic stresses such as excessive heat or drought. Absent explicit environmental information (i.e., temperature, rainfall, and soil data), this may be a necessary assumption; however, informatics resources are becoming increasingly available to link breeding trial data to climate or environmental information (Costa‐Neto et al., 2021; Westhues et al., 2022). Though some studies have addressed the use of explicit weather and soil data to understand the genetic basis of phenotypic plasticity (Diouf et al., 2020), disaggregating plasticity into reactions to specific environmental conditions should improve breeding for relevant abiotic stress tolerance. Additionally, with advancements in high‐throughput phenotyping and sensing technologies, the ability to evaluate the phenotypic plasticity of genotypes within growing seasons will become practicable, permitting the selection of genotypes that are more tolerant of acute, extreme abiotic stresses (Moreira et al., 2020). Previously, we have used this same dataset to investigate the use of environmental covariates to improve genomewide prediction (Neyhart et al., 2021, 2022); however, these covariates were not necessarily chosen to reflect specific abiotic stresses, and future research may address the use of such covariates in understanding and selecting for phenotypic plasticity.

The results of our study suggested greater overlap between the genetic architectures of trait genotype mean and phenotypic plasticity and that allelic sensitivity is likely contributing more to plasticity and GEI (Via & Lande, 1985). While this implies extensive pleiotropy and thus some biological limitation to selecting for both the genotype mean and plasticity, genetic gain can still be made by exploiting favorable correlations and LD and breaking up unfavorable linkages between loci influencing trait means per se and plasticity. Our results suggest that this task may be easier for many traits when meeting the specific objectives for barley cultivar development. Assuming that lower plasticity (higher stability) is ideal for all traits, the genetic correlations we observed (Table 1) would be favorable for GP, HD, and PH (where lower per se mean values are preferred) and for TW (where higher per se mean values are preferred); the correlation observed for GY, however, is unfavorable. Regardless, the same practical tools that are applied when breeding for multiple traits, such as appropriately weighed selection indices (Smith & Cullis, 2018) or selecting crosses based on predicted variances and covariances (Mohammadi et al., 2015; Neyhart et al., 2019b), can be used for jointly improving trait means and plasticity.

AUTHOR CONTRIBUTIONS

Jeffrey L. Neyhart: Conceptualization; formal analysis; writing—original draft; writing—review and editing. Lucia Gutierrez: Formal analysis; writing—original draft; writing—review and editing. Kevin P. Smith: Formal analysis; writing—original draft; writing—review and editing; writing—review and editing.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

Supporting information

Figure S1. Q–Q plots for marker‐trait association p‐values.

Figure S2. Manhattan plot of the genomewide association analyses for the genotype mean (Mean), linear plasticity (Slope), and nonlinear plasticity (Deviation) of five traits.

Figure S3. Mean absolute error of estimates of the slope (linear plasticity) and genotype mean when using phenotypic data sampled from environments in four different quantiles of the distribution of environmental means. Twenty‐five random samples of environments from each of 20% to 100% of environments in the lower 50% of environmental means, middle 50%, upper 25% and lower 25%, and upper 50% were generated. The mean absolute error was calculated as the difference between parameters (i.e., slope and mean) estimated using a sample of data and those estimated using all phenotypic data. The gray ribbons denotes a 90% sampling interval for each parameter.

Table S1. Complete table of marker‐trait associations (MTAs) detected using genomewide association analysis.

Supporting Information

Neyhart, J. L. , Gutierrez, L. , & Smith, K. P. (2025). Genomewide association and prediction of phenotypic stability in barley. The Plant Genome, 18, e70121. 10.1002/tpg2.70121