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. 2024 Oct 16;48(4):2727–2738. doi: 10.1111/pce.15213

Genetic and Environmental Patterns Underlying Phenotypic Plasticity in Flowering Time and Plant Height in Sorghum

Jialu Wei 1, Tingting Guo 1, Qi Mu 1, Boris ME Alladassi 1, Ravi V Mural 2, Richard E Boyles 3, Leo Hoffmann 4, Chad M Hayes 5, Brandi Sigmon 6, Addie M Thompson 7, Maria G Salas‐Fernandez 1, William L Rooney 4, Stephen Kresovich 8, James C Schnable 9, Xianran Li 10, Jianming Yu 1,✉
PMCID: PMC11893930  PMID: 39415476

ABSTRACT

Phenotypic plasticity is the property of a genotype to produce different phenotypes under different environmental conditions. Understanding genetic and environmental factors behind phenotypic plasticity helps answer some longstanding biology questions and improve phenotype prediction. In this study, we investigated the phenotypic plasticity of flowering time and plant height with a set of diverse sorghum lines evaluated across 14 natural field environments. An environmental index was identified to quantitatively connect the environments. Reaction norms were then obtained with the identified indices for genetic dissection of phenotypic plasticity and performance prediction. Genome‐wide association studies (GWAS) detected different sets of loci for reaction‐norm parameters (intercept and slope), including 10 new genomic regions in addition to known maturity (Ma1) and dwarfing genes (Dw1, Dw2, Dw3, Dw4 and qHT7.1). Cross‐validations under multiple scenarios showed promising results in predicting diverse germplasm in dynamic environments. Additional experiments conducted at four new environments, including one from a site outside of the geographical region of the initial environments, further validated the predictions. Our findings indicate that identifying the environmental index enriches our understanding of gene‐environmental interplay underlying phenotypic plasticity, and that genomic prediction with the environmental dimension facilitates prediction‐guided breeding for future environments.

Keywords: flowering time, genome‐wide association study, genomic selection, phenotypic plasticity, plant height, reaction norm, sorghum

Summary statement

Flowering time and plant height are two complex traits highly relevant for adaptation, selection, and agricultural production. This comprehensive study uncovered patterns in genetics and environments to enrich our understanding of gene‐environmental interplay and facilitate performance prediction.

1. Introduction

Phenotypic plasticity describes the ability of a genotype to express phenotypic variation when it is exposed to different environments (Schlichting and Smith 2002; Sommer 2020). Phenotypic plasticity has been a focus of study in biology to shed light on gene–environment interactions (Pigliucci 2005). Advances in genomic and molecular research and availability of environmental profile information have enabled such studies to be conducted at larger scales and finer resolutions (Kusmec et al. 2017; Li et al. 2018, 2021; Millet et al. 2019; Guo et al. 2020). Explaining the genetic mechanisms of phenotypic plasticity and identifying the environmental cues regulating it will advance our understanding of domestication and adaptation (Via and Lande 1985; Ceccarelli 1989). This effort can further promote the development and production of climate‐resilient crops for global food security in the face of climate change (Fox et al. 2019).

Sorghum is a widely cultivated crop whose natural genetic diversity and phenotypic plasticity have enabled it to adapt to growing in many environments and being employed for diverse end uses (Boyles, Brenton, and Kresovich 2019). The Sorghum Association Panel (SAP) was assembled to represent the global genetic diversity of sorghum and facilitate studies in the temperate regions (Casa et al. 2008). The majority of the SAP is composed of converted tropical sorghum lines from the sorghum conversion program (Stephens, Miller, and Rosenow 1967). They were developed by introgressing photoperiod‐insensitivity and dwarf alleles from a common parent into exotic germplasm through backcrossing and selection for early maturity and short stature. The remainder of the panel are breeding lines consisting of diverse grain, sweet, and forage lines and lines with historical importance in breeding, all adapted to successfully complete their lifecycle in temperate regions. The SAP provides rich genetic resources for sorghum breeding programs in the United States and has been widely employed for genomic studies on different agronomic traits (Brown et al. 2008; Morris et al. 2013; Thurber et al. 2013).

Flowering time and plant height are two important traits that have been extensively studied in multiple plant species (Blackman 2016; Wallace et al. 2016). These two traits are closely related to evolution and adaptation of plants to different environments (Fournier‐Level et al. 2022). In sorghum, six major maturity loci, Ma1‐Ma6, have been described, with the dominant alleles repressing early flowering in long‐day environments (Quinby 1967; Childs et al. 1997; Rooney and Aydin 1999; Murphy et al. 2011, 2014). Four major dwarfing loci controlling sorghum plant height include Dw1–Dw4 (Quinby and Karper 1954; Multani et al. 2003; Hilley et al. 2016, 2017; Yamaguchi et al. 2016). Another locus, qHT7.1, was found to be in high frequency of repulsion phase with Dw3 on Chromosome 7 (Li et al. 2015). Besides the endogenous genetic components, environmental factors play a vital role in shaping the flowering time and plant height of organisms, among which temperature and day length (DL) are the two most dominating factors (Bernier and Périlleux 2005; Des Marais et al. 2013).

Despite the growing research interest in phenotypic plasticity and its genetic basis (Mathews et al. 2008; Des Marais et al. 2013; Kusmec et al. 2017; Lőrincz et al. 2017; Arnold, Kruuk, and Nicotra 2019), studies with diverse populations under a large environmental context are still limited. Here, we investigated the phenotypic plasticity of flowering time and plant height using a diversity panel evaluated across 14 natural environments. First, growing degree days (GDD) and diurnal temperature range (DTR) during the early growing stage were identified as the environmental indices that shape flowering time and plant height observed across environments, respectively. Next, with reaction‐norm parameters obtained by regressing observations on the environmental index, genome‐wide association studies (GWAS) detected separate sets of genetic loci for intercept (genotypic mean) and slope (plasticity). Finally, we showed that by integrating environmental index and genomic prediction, the performance of this diversity panel in a large range of environments could be well predicted via cross validation and empirical validation with additional field experiments.

2. Materials and Methods

2.1. Germplasm and Phenotype

The SAP was grown and evaluated in Iowa, Nebraska, South Carolina, and Texas from 2010 to 2019, resulting in a total of 14 environments (i.e., location‐year combination) (Supporting Information S2: Table S1). Datasets from South Carolina and 2010 Iowa have been used in previous publications (Zhao et al. 2016; Mural et al. 2021), whereas the remaining datasets are yet to be published. Accessions (n = 306) with recorded phenotype values in at least five of the 14 environments were employed for subsequent analyses (Supporting Information S2: Table S2).

Flowering time was measured as the number of days between the date of planting and the date at which 50% of the plants in a plot reached anthesis. Flowering time in GDD was then calculated using the daily maximum and minimum air temperatures adjusted by base temperature of 50°F (10°C) and maximum temperature of 100°F (37.8°C) (Li et al. 2018). Plant height was measured at maturity from the soil surface to the panicle apex. Among the 14 environments, NE18 and NE19 had only flowering time record, whereas IA18 and IA19 had only plant height record. For each environment, BLUE value of each accession was calculated based on randomized complete block design for downstream analyses. Analysis of variance and variance component estimation were conducted with ‘aov’ function and ‘anovaVCA’ function in R, respectively.

Empirical validation was conducted in four additional field experiments: Lincoln, NE in 2020 (NE20), East Lansing, Michigan in 2020 (MI20), and Ames, IA in 2021 with two planting dates (IA21_1 and IA21_2). The whole panel was evaluated for flowering time and plant height with the same protocol in NE20 and MI20. For IA21, a set of 80 representative lines capturing the genetic diversity of the panel were selected for evaluation.

2.2. Identifying Environmental Indices

Daily maximum and minimum air temperature (T max and T min) were retrieved from the database of National Oceanic and Atmospheric Administration (NOAA,http://www.ncdc.noaa.gov). The average value from three closest weather stations within 50 miles was used for each field. DL was calculated using the ‘daylength()’ function in the ‘geosphere’ package (Hijmans 2024) in R. GDD was calculated as (T max + T min)/2–T base, where T max surpassing 100°F (37.8°C) was truncated to 100°F (37.8°C), T min below 50°F (10°C) was adjusted to 50°F (10°C), and T base was set to 50°F (10°C). The daily DTR was calculated as T max–T min, without temperature adjustment. The photothermal time (PTT) was calculated as GDD × DL. The photothermal ratio (PTR) was calculated as GDD/DL (Supporting Information S2: Table S3).

The Critical Environmental Regressor through Informed Search (CERIS) algorithm was implemented with R for environmental index identification (Li et al. 2021). First, an environmental mean was obtained as the average performance of the evaluated genotypes at each environment. Second, the average value of each environmental variable (GDD, DTR, PTT, and PTR) was calculated for a window of ith to jth days after planting (DAP i to DAP j ) at each environment. The window size was restricted to be between 7 and 30 days. Then, we searched through all these windows throughout the growing season before the trait was fully developed. Finally, the correlation between the environmental mean vector and each variable‐window value vector was calculated. The variable‐window combination exhibiting the strongest correlation and reasonable biological relevance was chosen as the environmental index.

2.3. Genetic Dissection of Flowering Time and Plant Height Through GWAS

We conducted GWAS for flowering time and plant height at each environment, and for the phenotypic plasticity parameters obtained across the environments. Phenotypic plasticity parameters (intercept and slope), also known as reaction‐norm parameters, were calculated for each genotype by regressing the observed trait values on the environmental index values. Environmental index was centred with the average point as zero to obtain the intercept, the average performance of a genotype (i.e., genotypic mean), and the slope, the change of performance per unit change of environmental index (i.e., plasticity). The two parameters were then treated as derived traits for GWAS.

The genetic marker data employed was a set of 265 K SNPs described previously (Li et al. 2015), which were generated from the previously published genotyping‐by‐sequencing data (Morris et al. 2013) with imputation using Beagle 4.0 (Browning and Browning 2016). The GWAS analyses were carried out using the GAPIT R package (Wang and Zhang 2021) using the multi‐locus mixed model method with the first three principal components. SimpleM method (Gao, Starmer, and Martin 2008) was used to obtain the significance threshold at α = 0.05 level. The Sorghum QTL Atlas database (Mace et al. 2019) was used to search for the reported QTL regions covering the significant SNPs.

Allelic effects from the GWAS results of individual environments were obtained. Genetic effect continua were then plotted as the fitted lines of these effects on the environmental index (Guo et al. 2020; Li et al. 2021). This was conducted for all loci detected in GWAS of phenotypic plasticity parameters (intercept and slope). Because the change of genetic effect in direction and degree along the environmental index can be seen in the plot of genetic effect continuum, this approach is a generalization of different types of genetic effect by environment interaction from two environments: antagonistic pleiotropy (change of effect direction), conditional neutrality (effect detected only in one environment), differential sensitivity (change of effect size but not direction), or no genotype by environmental interaction (Des Marais et al. 2013; Guo et al. 2020; Li et al. 2018, 2021).

With the significant loci detected for the reaction‐norm parameters for each trait, we examined the performance pattern of different groups of genotypes based on the haplotype combinations across these multiple loci. For flowering time, seven haplotypes were found among all possible combinations at three loci. Mean and standard deviation of intercept and slope were calculated for each haplotype. Mean intercept and slope were also used to plot haplotype‐level reaction norms. For plant height, 69 haplotypes were found among all possible combinations of 15 significant loci. To make the visualization easier, only haplotypes found in more than two genotypes were considered.

2.4. Performance Prediction Combining Environmental Index and Genomic Prediction

Besides genetic dissection, the identified environmental indices and reaction‐norm parameters also enabled us performance prediction for different scenarios. Cross‐validations were conducted with the initial 14 environments (12 environments for each trait) for performance prediction. Three scenarios were considered: (1) predicting tested genotypes in untested environments; (2) predicting untested genotypes in tested environments; (3) predicting untested genotypes in untested environments. All predictions were carried out with the CERIS‐Joint Genomic Regression Analysis (CERIS‐JGRA) framework (Li et al. 2018). Environmental index was centred at the overall mean value to obtain the intercept for each genotype, and the overall mean value was added back for plotting.

Leave‐one‐environment‐out scheme was applied for the first scenario. Reaction norms of genotypes were obtained by regressing observed trait values across 11 environments on the environmental index values. The environmental index value was calculated for the single remaining environment. Individual performance in the untested environment was then predicted by fitting the reaction‐norm parameters and environmental index value into the regression model. The above steps were repeated until each environment was predicted.

Leave‐one‐half‐of‐genotypes‐out scheme was applied for the second scenario. The whole panel was equally split into tested and untested genotypes. Reaction‐norm parameters were obtained for each tested genotype by regressing observed trait values on the environmental index values across all environments. Genomic prediction was conducted to predict the intercept and slope for untested genotypes using genome‐wise SNPs taking advantage of the genomic relationship between genotypes via ‘rrBLUP’ package (Endelman 2011) in R. Individual performance of untested genotypes was then predicted by fitting the predicted reaction‐norm parameters and environmental index value into the regression model. To evaluate the effect of different genomic prediction methods on the prediction accuracy, we switched ‘rrBLUP’ with five Bayesian methods individually under the same cross‐validation scheme. The five Bayesian methods included BayesA, BayesB, BayesC, Bayesian LASSO (BL), and Bayesian Ridge Regression (BRR) from ‘BGLR’ package in R.

The joint leave‐one‐environment‐out and leave‐one‐half‐of‐genotypes‐out scheme was applied to the third scenario. Reaction‐norm parameters were obtained for tested genotypes from tested environments. Genomic prediction was then conducted to predict the intercept and slope of untested genotypes. The predicted reaction‐norm parameters and environmental index value for the untested environment were fitted into the regression model to get the predicted performance for untested genotypes in the untested environment.

Correlation coefficient between observed and predicted values was used as the prediction accuracy. For the first scenario, prediction accuracy was calculated after predictions were completed for every environment. For the last two scenarios where untested genotypes were involved, each procedure was repeated for 50 runs, and the average prediction accuracy value across 50 runs was reported. A representative run was plotted for illustration.

Empirical validation was conducted in a similar manner as the first scenario of cross‐validation. Reaction‐norm parameters of each genotype were obtained from the initial environments. Specific environmental index values were calculated for the four new environments. Performance prediction was done by fitting the reaction‐norm parameters and environmental index values into the regression model.

3. Results

3.1. Flowering Time and Plant Height Variations Under Natural Field Environments

The SAP was grown under 14 natural environments in the United States (Figure 1A). During the growing season, all environments experienced DL longer than 12 h. The DL curves varied for different environments, influenced by both the latitudes and the planting dates. A large amount of variation was recorded for temperature within and across environments during the growing season (Supporting Information S1: Figure S1).

Figure 1.

Figure 1

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Phenotypic variations of the Sorghum Association Panel across 14 natural environments. (A) Fourteen environments under study. NE18 and NE19 (yellow dot) had flowering time data only. IA18 and IA19 (blue dot) had plant height data only. (B) Correlation between the flowering time and plant height for the 10 common environments. Plotted is the correlation between environmental means of FT and PH with the correlation coefficient labelled at the top centre. Within‐environment correlation coefficients and significance levels are labelled in parentheses. *p < 0.01; **p < 0.001. (C) Reaction norms for flowering time with environments ordered by ascending average day length. Grey dots are observed values with lines connecting the values between adjacent environments for each genotype. Coloured dots are environmental means. (D) Reaction norms for plant height with environments ordered by ascending average day length. (E) Reaction norms for flowering time with environments ordered by ascending environmental mean. A regression‐fitted reaction norm is plotted for each genotype. (F) Reaction norms for plant height with environments ordered by ascending environmental mean.

Phenotypic variations were observed for flowering time and plant height across the 14 environments (Supporting Information S1: Figure S2). Flowering time expressed as GDD was used in all analyses since flowering time expressed as days after planting (DAP) did not show a clearer pattern (Supporting Information S1: Figure S3). The average flowering time of the whole panel in each environment (i.e., environmental mean) varied from 1552.49 to 2295.46 GDD (Figure 1C, Supporting Information S2: Table S4). Variance component analysis (Supporting Information S2: Table S5) revealed that more than half of the flowering time variation (51.5%) was due to environment (E), followed by genotype (G, 26.9%) and the interaction between them (G × E, 13.4%). The environmental mean of plant height varied from 105.72 to 158.14 cm across the environments (Figure 1D, Supporting Information S2: Table S4). Genotype accounted for the most phenotypic variation (74.5%) of plant height, followed by E (11.1%) and G × E (9.0%) (Supporting Information S2: Table S6). For both traits, G × E had a significant effect on the phenotypic variation, though to different degrees. The correlation between flowering time and plant height was not significant in terms of environmental means (r = −0.60, p = 0.0667), whereas significant positive correlations were observed within some environments (Figure 1B and Supporting Information S1: Figure S4).

To elucidate the patterns of phenotypic variations, we characterized each environment by its environmental mean and implemented the traditional joint regression analysis (Figure 1E,F) (Finlay and Wilkinson 1963; Eberhart and Russell 1966). A reaction norm was obtained for each genotype by regressing its observed phenotype values on the environmental mean. The regression‐based reaction norms displayed clear patterns of phenotypic plasticity across environments. For a genotype with known reaction‐norm parameters (intercept and slope), we can predict its performance at environments with a known environmental mean. To circumvent the issue of unavailable environmental means before testing trials, a recently proposed algorithm, CERIS provided a solution by replacing the environmental mean with an environmental index.

3.2. Early‐Season Temperature Shaping Flowering Time and Plant Height

Environmental index is defined as the combination of environmental variable and growth window. Once established, the value for a new environment without testing trials can be directly obtained from the environmental data. We focused on four derived environmental variables from temperature and photoperiod, namely GDD, DTR, PTT and PTR.

For flowering time, the average PTR from 28 to 37 DAP (denoted as PTR28–37) showed the strongest correlation (r = 0.88) with the environmental mean, among all considered combinations of environmental variable and growth window (Supporting Information S1: Figure S5). PTR is the ratio of GDD over DL. However, having the additional environmental factor (DL) in PTR28–37 didn't lead to a substantial correlation coefficient increment compared with the best searching result of GDD, GDD32–59 (r = 0.85, p = 0.0005). In addition, the surrounding windows of PTR28–37 with strong correlations had small sizes, which could be unreliable under climate fluctuation. As a contrast, the surrounding windows of GDD32–59 showed consistent high correlations with the environmental mean and had reasonable sizes. Therefore, GDD32–59 was eventually chosen as the environmental index to characterize the environments as regards to flowering time (Figure 2A). Following the same rationale for plant height, DTR25–31 was identified as the environmental index strongly and negatively correlated (r = −0.85, p = 0.0005) with the environmental mean of plant height (Figure 2B, Supporting Information S1: Figure S6). These two environmental variable and growth window combinations indicate the effects of early‐season environmental inputs on sorghum growth and development.

Figure 2.

Figure 2

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Identifying environmental indices for flowering time and plant height. (A) Average growing degree days (GDD) from 32 to 59 days after planting (GDD32–59, highlighted by the black circle) was identified as the environmental index for flowering time. (B) Average diurnal temperature range (DTR) from 25 to 31 days after planting (DTR25–31, highlighted by the black circle) was identified as the environmental index for plant height. (C) Regression‐fitted reaction norms with GDD32–59 as the regressor for flowering time. (D) Regression‐fitted reaction norms with DTR25–31 as the regressor for plant height. In (C and D), the thick black line is the population‐level regression line. Grey lines are regression‐fitted reaction norms of genotypes. [Color figure can be viewed at wileyonlinelibrary.com]

Collectively, two temperature‐related environmental indices were able to capture the major pattern in flowering time and plant height variation across environments. The overall responses of the SAP to the environmental gradients were depicted with population‐level reaction norms (Figure 2C,D). On average, the flowering time was delayed by 63.75 GDD per unit increment of GDD32–59; the plant height decreased by 3.87 cm per unit increment of DTR25–31.

3.3. Phenotypic Plasticity Varying Among Individuals

For the purposes of identifying environmental indices, the entire population was initially treated as a single mega‐genotype. To investigate the patterns of phenotypic plasticity among genotypes, we obtained individual reaction norms by regressing the observed phenotypic values of each genotype on the environmental index values across environments (Figure 2C,D). This process generated the reaction‐norm parameters (intercept and slope) for each genotype to quantify average trait value (genotypic mean) and sensitivity to environmental change (plasticity) along the gradient defined by the environmental index (Supporting Information S1: Figure S7).

The SAP comprises two groups of sorghum lines, diverse breeding lines and conversion lines. The reaction norm of conversion‐line set was below that of breeding‐line set for both traits (Supporting Information S1: Figure S8A,C), indicating conversion lines as a group flowered earlier and developed shorter stature than breeding lines. This could be a result from the stringent selection for early flowering and short stature of the sorghum conversion program. In terms of trait plasticity, the flowering time of these two groups responded to GDD32–59 change in a similar manner, which was reflected by their parallel reaction norms (Supporting Information S1: Figure S8A,B). However, the breeding‐line set appeared to be more plastic than the conversion‐line set for plant height (Supporting Information S1: Figure S8C,D).

3.4. Genetic Dissection of Phenotypic Plasticity Through GWAS

We conducted GWAS using the reaction‐norm parameters obtained from all genotypes to identify the genetic mechanisms underlying the observed variation in phenotypic plasticity. For flowering time, no significant SNP was found for intercept besides some suggestive genomic regions. A SNP on chromosome 6 that was detected for slope fell nearby the Ma1 (Figure 3A) region with ~2 Mb. Ma1 was reported to have the largest impact on flowering time in sorghum among the four classic maturity genes (Ma1–Ma4) (Murphy et al. 2011). Two other slope associations on chromosome 1 and 5 were located in previously reported flowering‐time QTLs (Mace, Hunt, and Jordan 2013; Guindo et al. 2019) (Supporting Information S2: Table S7).

Figure 3.

Figure 3

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Genetic dissection of phenotypic plasticity through GWAS. (A) Manhattan plot from GWAS of intercept and slope derived for flowering time. (B) Manhattan plot from GWAS of intercept and slope derived for plant height. (C) Scatter plot of –log(p) values from the GWAS of intercept and slope for flowering time. (D) Genetic effect continua of phenotypic plasticity loci for flowering time. (E) Scatter plot of –log(p) values from the GWAS of intercept and slope for plant height. (F) Genetic effect continua of phenotypic plasticity loci for plant height. In (D and F), the grey vertical dash line represents the centre of the environmental range; the grey horizonal dash line represents where the allelic effect is zero; coloured solid lines represent significant loci for intercept; and coloured dash lines represent significant loci for slope. [Color figure can be viewed at wileyonlinelibrary.com]

For plant height, dwarfing genes, Dw1, Dw2, Dw3 and Dw4, together with qHT7.1 were revealed to be underlying the intercept variation (Figure 3B). The associations of these known genes with plant height were also detectable in a few (n = 2) to all (n = 12) single‐environment GWAS results (Supporting Information S1: Figure S9, Supporting Information S2: Table S8). Among these five intercept loci, Dw1 and Dw3 were also significantly associated with the slope of plant height, although distinct SNPs (~4 kb away from each other) within each locus were detected for the two parameters. Reported plant height QTLs (Hart et al. 2001; Liu et al. 2019) have been found at the same genomic regions of the other intercept loci (S1_43350473 and S10_43486183), however, the closest genes were 90–200 kb away from the detected SNP peaks. A novel locus (S6_5702897) with slope association was detected for plant height in single‐environment GWAS of IA10_C, SC13 and SC14 (Supporting Information S1: Figure S9, Supporting Information S2: Table S8).

Genetic effect continua along the environmental indices were examined to quantify the gene‐environment interplay (Figure 3D,F). This additional analysis allowed us to connect findings from the phenotypic plasticity analysis with findings from individual environment analysis. In addition, obtaining genetic effect continuum generalized the types of genetic effect by environment interaction into changes of genetic effects along the environmental index. For flowering time, the three SNPs associated with slope showed substantial allelic effect increment along the environmental gradient. Their effects changed not only in degree but also in direction (negative effects for environments on the left side and positive effects for environments on the right side), which is called antagonistic pleiotropy (Des Marais et al. 2013; Li et al. 2018). In contrast, the majority of plant height SNPs showed the differential sensitivity pattern, that is, genetic effect changing in degree but not in direction, with a few of them falling into the antagonistic pleiotropy category. As expected, significant SNPs for the intercept of plant height had a relatively large effect size at the average point of the environmental index values, and significant SNPs for the slope of plant height had relatively large effect size changes across the DTR25–31 range.

No overlapping SNPs were detected to be associated with both flowering time and plant height, which agreed with the weak phenotypic correlation between the two traits. Subsequently, haplotype analysis was conducted for reaction‐norm parameters of each trait based on significant loci (Supporting Information S2: Tables S9 and S10). For flowering time, the majority of this panel (91.9%) was fixed for major alleles at the three loci. Using this most frequent haplotype (Hap2) as baseline, the effects of three loci were illustrated, S1_60476246 being the loci with the largest effect (Supporting Information S1: Figure S10A). Similar to allelic effect continua, reaction norms of the seven haplotypes also had crossovers located close to the average point of the environmental index values (Supporting Information S1: Figure S10B). For plant height, contrasts between haplotypes indicated that most minor alleles tended to increase both intercept and plasticity (Supporting Information S1: Figure S11A). qHT7.1 was the exception whose minor allele decreased plant height intercept as well as plasticity. Such correlation between intercept and slope was also demonstrated in reaction norms of the 21 haplotypes. Short plants (with low intercept or low average height across environments) tended to be more stable (with low slope or less responsive to the change in environmental inputs), while tall plants (with high intercept) being more plastic (with high slope) (Supporting Information S1: Figure S11B).

3.5. Performance Prediction Enabled by Identified Environmental Index and Genomic Prediction

Coupled with the CERIS algorithm, a CERIS‐JGRA framework was proposed, which enabled the genomic prediction of complex traits in multienvironment trials with the identified environmental index (Li et al. 2018, 2021; Guo et al. 2020; Mu et al. 2022). In this study, we implemented both cross‐validations and empirical validations with this framework.

For leave‐one‐environment‐out cross‐validation (Figure 4A,D), the overall prediction accuracy for flowering time and plant height was 0.74 and 0.91, with the within‐environment prediction accuracy varying from 0.61 to 0.86 and 0.82 to 0.97, respectively. The predicted performance was in high correlation with the observed performance with precision.

Figure 4.

Figure 4

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Cross‐validation with the initial 14 environments. (A) Leave‐one‐environment‐out performance prediction for flowering time (FT). (B) Leave‐one‐half‐of‐the‐genotype‐out performance prediction for FT. (C) Joint leave‐one‐environment‐out and leave‐one‐half‐of‐the‐genotype‐out performance prediction for FT. (D) Leave‐one‐environment‐out performance prediction for plant height (PH). (E) Leave‐one‐half‐of‐the‐genotype‐out performance prediction for PH. (F) Joint leave‐one‐environment‐out and leave‐one‐half‐of‐the‐genotype‐out performance prediction for PH. [Color figure can be viewed at wileyonlinelibrary.com]

When the prediction scope was expanded to include untested genotypes in both tested and untested environments (Figure 4B,C,E,F), it was unsurprising to see some decline in accuracy for performance prediction due to the level of prediction accuracy for two reaction‐norm parameters (Supporting Information S1: Figures S12 and S13). For flowering time, the within‐environment prediction accuracy for untested genotypes in tested environments ranged from 0.30 to 0.58, and the across‐environment prediction accuracy was 0.69 (Figure 4B). For untested genotypes in untested environments, the within‐environment and across‐environment prediction accuracies remained at similar levels (0.28–0.56, 0.69) (Figure 4C). The same trend applied to plant height as well. Different prediction methods and training set ratios were compared to explore the possibility of improving the prediction accuracy. rrBLUP was shown to be a robust method with the best prediction results in most environments compared to other Bayesian methods (Supporting Information S1: Figure S14). The prediction accuracy of untested genotypes could be improved slightly by increasing the training set ratio (Supporting Information S2: Tables S11 and S12).

Empirical experiments were conducted in four new environments to further evaluate the prediction ability of this framework (Supporting Information S2: Table S13, Supporting Information S1: Figure S15). At each trial, specific environmental index values were obtained (Figure 5A,B) to predict the performance for each genotype. The prediction accuracies were between 0.70 and 0.74 for flowering time, and between 0.84 and 0.96 for plant height (Figure 5C,D, Supporting Information S1: Figure S16). Even though the location of MI20 fell outside the geographical area of the 14 initial environments, its environmental index values were close to the centres of the environmental ranges and prediction accuracies for this trial were high. The observed environmental means of two Iowa environments (IA21_1 and IA21_2) were similar, agreeing with what was expected from their close environmental index values. Although in all four environments, the observed environmental means were slightly lower than predictions, their deviations from the regression lines were of a similar magnitude as those of the initial environments. These deviations could be caused by local environmental factors that were not accounted for by the environmental indices.

Figure 5.

Figure 5

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Empirical validation with four new environments. (A) Environmental index values of the four empirical experiments for flowering time (FT) were calculated and positioned as coloured vertical lines. Coloured dots represent the environmental means of the four new environments. The dash vertical line represents the centre of the environmental range. (B) Environmental index values and environmental means of the four empirical experiments for plant height (PH). (C) Prediction results for FT. The correlation coefficient between observed and predicted values is labelled for each environment in parentheses. (D) Prediction results for PH. [Color figure can be viewed at wileyonlinelibrary.com]

4. Discussion

With climate change, understanding phenotypic plasticity in crops is paramount for sustainable agriculture and global food security (McCouch et al. 2013, 2020; Fox et al. 2019). Although there is increasing research interest in the study of phenotypic plasticity, expanding the genetic diversity of tested materials and the environmental range would still be desirable.

Plants detect and assess environmental cues to adjust growth and make developmental transition (Scheres and van der Putten 2017). Identifying an environmental index can help us quantitatively connect multiple environments and further investigate the mechanisms of gene‐environment interplays (Li et al. 2018, 2021; Guo et al. 2020; Mu et al. 2022). In this study, temperature was shown as the most critical environmental factor for both traits, with two variables derived from temperature (GDD32–59 and DTR25–31) chosen as the environmental indices for flowering time and plant height, respectively. The strength of correlation between environmental index and environmental mean depended on the environmental range, genetic diversity, and the target trait. In previous studies with biparental populations of sorghum and rice, environmental indices were identified that had nearly perfect correlations with environmental means for flowering time and plant height (Li et al. 2018; Guo et al. 2020; Mu et al. 2022). The strength of the correlation was lower in diversity panels of maize, wheat and oat (Li et al. 2021) as in this sorghum study. Although temperature was the most relevant environmental factor in all these studies, the critical growth windows varied among different target populations of environments and target populations of genotypes.

GWAS conducted using reaction‐norm parameters identified both previously known and new genetic loci. Ma1 is a known maturity gene with a major effect on flowering time (Murphy et al. 2011). However, no significant association was found for the intercept of flowering time. This could be partially explained by the fact that the sorghum accessions in the SAP have been adapted to temperate regions by the introgression of early‐flowering alleles and that no SNP captured adequately the linkage disequilibrium among multiple alleles. In addition, the value of intercept, defined as the expected performance of a genotype at the average point of the environmental index values, depended on the studied set of environments. The reaction norms of genotypes can have a pattern where the separation of intercepts (genotypic means) at this point of environmental index does not permit the detection of individual locus. Therefore, it was not surprising to detect Ma1 associated with flowering time only at one individual environment, SC13, which had a high environmental index value (Supporting Information S1: Figure S9). For plant height, distinct sets of SNPs were associated with the intercept and slope, although gene colocalization was observed from Dw1 and Dw3. These two genes were significantly associated with both reaction‐norm parameters. Regulatory gene theory, a proposed genetic model behind phenotypic plasticity, assumes that trait mean and trait plasticity are controlled by separate genes (Scheiner 1993). The GWAS results suggested regulatory gene theory to be behind the plasticity of plant height in this study. In contrast, the same set of genes were detected for the two reaction‐norm parameters of plant height in a sorghum biparental population (Mu et al. 2022), supporting the allelic sensitivity theory. The trait plasticity is explained as a result of differential expression of the same genes in allelic sensitivity theory. Evidences have been shown for both theories from phenotypic plasticity studies (Kusmec et al. 2017; Li et al. 2018, 2021; Guo et al. 2020). Collectively, the phenotypic plasticity of different traits under the same environments can be explained by the two theories individually. Moreover, the regulatory gene and allelic sensitivity theories are not mutually exclusive even for the same trait in the same species, depending on the genetic and environmental context.

Given the high introgression frequency detected from most part of chromosome 6 in the SAP, there was a concern that very little functional diversity on this chromosome had been exploited for temperate sorghum breeding (Brown et al. 2008; Morris et al. 2013; Thurber et al. 2013). The detection of Dw2, Ma1, and other loci on chromosome 6 suggested the segregation of these loci in this panel, and the potential to discover other useful exotic alleles in this region for future breeding efforts. In addition, the variation not only existed for average trait value (intercept or genotypic mean) across the environments, but also for plasticity (slope). Therefore, there are two considerations for the application of this new knowledge to breeding strategies: first, there is an opportunity to adapt the high‐plasticity sorghum lines into more stable ones, which can be facilitated by manipulating the loci underlying plasticity; second, if the high‐plasticity lines are not desirable for the target trait in some environments, they can still be desirable in other environments, and this can be determined based on the environmental index.

The integration of genotype‐by‐environment interaction and genomic prediction research has shown promising results to enhance the prediction ability in varied conditions (Malosetti, Ribaut, and van Eeuwijk 2013; Heslot et al. 2014; Jarquín et al. 2014; Li et al. 2018, 2021; Guo et al. 2020; Costa‐Neto, Fritsche‐Neto, and Crossa 2021; Mu et al. 2022). With identified environmental indices, we were able to implement genomic prediction under multiple scenarios, including the most challenging one of predicting untested genotypes in untested environments. For cross‐validations, the within‐environment prediction accuracy tended to be low for untested genotypes, nevertheless, the across‐environment prediction accuracy was high for all schemes, driven by the environmental indices that well captured the environmental variation. In empirical validations, the prediction capability of the environmental‐index‐enabled framework was further demonstrated. Besides the locations that were included in the initial training set (IA for both traits and NE for flowering time), we also conducted empirical experiments in new sites (MI for both traits and NE for plant height). The prediction accuracy was high for both cases. Advances of geographic information systems scaled up the accessible environmental covariates in breeding applications (Annicchiarico, Bellah, and Chiari 2006; Resende et al. 2021). In addition to the four environmental variables considered in this study, more variables can be added to this framework for the dissection and prediction of other complex traits in diverse germplasms. While the approach implemented in the current research focused on the general pattern across environments, additional research is needed to further consider local environmental variables and their effect periods to better explain and predict the performance. This would generally require a large number of environments and better monitoring and characterization of weather, soil, and plant conditions. In addition, if the cultivar placement is the focus, a composite environmental index with multiple combinations of environmental variables and periods may be searched based on the performance of that particular cultivar, rather than environmental mean, to generate genotype‐specific findings and recommendations.

As the global climate becomes increasingly unpredictable and extreme (Wheeler and von Braun 2013), it is critical to be able to understand and predict the different phenotypes that the same genotype will exhibit in different environmental conditions (Arnold, Kruuk, and Nicotra 2019). Harnessing genetic diversity is also crucial for the improvement of crop adaptation and long‐term sustainable production (McCouch et al. 2020). With a sorghum diversity panel, this study illustrated how the environment, genotype, and phenotype can be exploited in concert to enrich our understanding of the gene‐environment interplay and adapt diverse germplasm to dynamic environments.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting information.

PCE-48-2727-s002.docx (5.1MB, docx)

Supporting information.

PCE-48-2727-s001.xlsx (380.2KB, xlsx)

Acknowledgements

The authors thank Gregory Schoenbaum, Hallie Longest, Michaela Erickson, Mackenzie Zwiener, Lou Townsend, Leighton Wheeler, Nate Pester, Alexandra Bradley, Luke Micek, Isaac Stevens, and many members from participating labs for assisting with the phenotyping and field work.

The work was supported by the Agriculture and Food Research Initiative competitive grant (2021‐67013‐33833) and the Hatch project (1021013) from the USDA National Institute of Food and Agriculture, the Iowa State University Plant Sciences Institute, and the Iowa State University Raymond F. Baker Center for Plant Breeding. The first author was partially funded by the China Scholarship Council. Open access funding provided by the Iowa State University Library.

Data Availability Statement

Data for weather information and phenotype are uploaded in the supplemental material. Raw phenotype and imputed SNP data can be accessed from Figshare: https://doi.org/10.6084/m9.figshare.20520600.v1. Codes of CERIS‐JGRA framework is available in Github (https://github.com/jmyu/CERIS_JGRA). The data that support the findings of this study are openly available in Figshare at https://figshare.com/, reference number 20520600.v1.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supporting information.

PCE-48-2727-s002.docx (5.1MB, docx)

Supporting information.

PCE-48-2727-s001.xlsx (380.2KB, xlsx)

Data Availability Statement

Data for weather information and phenotype are uploaded in the supplemental material. Raw phenotype and imputed SNP data can be accessed from Figshare: https://doi.org/10.6084/m9.figshare.20520600.v1. Codes of CERIS‐JGRA framework is available in Github (https://github.com/jmyu/CERIS_JGRA). The data that support the findings of this study are openly available in Figshare at https://figshare.com/, reference number 20520600.v1.

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