Can we harness digital technologies and physiology to hasten genetic gain in US maize breeding?

Abstract

Plant physiology can offer invaluable insights to accelerate genetic gain. However, translating physiological understanding into breeding decisions has been an ongoing and complex endeavor. Here we demonstrate an approach to leverage physiology and genomics to hasten crop improvement. A half-diallel maize (Zea mays) experiment resulting from crossing 9 elite inbreds was conducted at 17 locations in the USA corn belt and 6 locations at managed stress environments between 2017 and 2019 covering a range of water environments from 377 to 760 mm of evapotranspiration and family mean yields from 542 to 1,874 g m⁻². Results from analyses of 35 families and 2,367 hybrids using crop growth models linked to whole-genome prediction (CGM–WGP) demonstrated that CGM–WGP offered a predictive accuracy advantage compared to BayesA for untested genotypes evaluated in untested environments (r = 0.43 versus r = 0.27). In contrast to WGP, CGMs can deal effectively with time-dependent interactions between a physiological process and the environment. To facilitate the selection/identification of traits for modeling yield, an algorithmic approach was introduced. The method was able to identify 4 out of 12 candidate traits known to explain yield variation in maize. The estimation of allelic and physiological values for each genotype using the CGM created in silico phenotypes (e.g. root elongation) and physiological hypotheses that could be tested within the breeding program in an iterative manner. Overall, the approach and results suggest a promising future to fully harness digital technologies, gap analysis, and physiological knowledge to hasten genetic gain by improving predictive skill and definition of breeding goals.

Big breeding data demonstrate that linking genomics and physiology through crop modeling-genomic prediction can hasten genetic gain and reduce the yield and water productivity gaps.

Introduction

The combination of molecular technologies and digital prediction methodologies has transformed crop improvement over the last decade (Cooper et al., 2014b; Poland, 2015; Ramirez-Villegas et al., 2020) and increasingly enabled farmers to produce enough food, feed, fuel, and fiber for society. However, future agriculture is unlikely to balance supply and demand for food (Ray et al., 2013; Fischer et al., 2014), even in the absence of any considerations to reduce greenhouse gas emissions (NASEM, 2019). Novel systems frameworks are required for society to accelerate genetic gain to deliver on food, nutritional, and economic security as target environments change. Methods to effectively deal with genotype × environment interactions (G×E), which are a major factor limiting realization of the required increases in the rate of genetic gain in all major crops (Cooper et al., 1995, 2014a; Chapman et al., 2000; de la Vega and Chapman, 2001; Mwiinga et al., 2020), have been developed (Heslot et al., 2014; Li et al., 2018; Millet et al., 2019; van Eeuwijk et al., 2019; Robert et al., 2020). However, methods to predict long-term consequences of co-selection of genotypes (G) and optimal agronomic management practices (M), which underpinned the historical high rates of genetic gain for maize (Zea mays) yield in the US corn-belt (Duvick, 2005), are only just emerging (Messina et al., 2018; Cooper et al. 2020a). This is a super wicked problem (Udall, 2014) because the information needed to train data-driven models is only routinely available for few genotypes and creating training sets for many genotypes could be prohibitively expensive (Figure 1). The integration of physiology-based and data-driven approaches has been proposed as a workable solution, whereby scientific understanding can effectively deal with model underdetermination and data gaps for model training (Messina et al., 2018, 2021; Hammer et al., 2019; McCormick et al., 2021).

Figure 1.

Diagram of order of magnitude for hybrids advancing through product development along with processes to improve breeding efficiencies, gap analyses, and CGM–WGP.

Crop growth models (CGMs) are cognitive constructs that capture in mathematical form physiological knowledge with various degrees of detail (Figure 2). They embody quantitative relationships between physiological states, processes, and environmental inputs. These models are dynamic and capture the quantitative dependencies of the crop system on both its history during the growing season and the time-varying stochasticity of the environmental inputs and interactions with the crop. Typically, on a daily timescale the CGM simulates mass for a crop from the mass present the previous day plus the growth for the current day based on subprocesses relating to photosynthesis, respiration, leaf expansion, and their dependencies on leaf area index and water availability, among others. This process is repeated for each day between planting and harvest. The amount and timing of available resources dictate patterns of growth, water use, and stress during critical periods for the determination of reproductive sinks and yield. Table 1 lists a set of physiological traits often included in CGMs structured around the concepts of plant development, resource use, resource conversion efficiencies, and allocation to reproductive sinks (e.g. Holzworth et al., 2014; Wallach et al., 2019). This type of CGM has proven to be a useful quantitative framework in establishing a transparent mapping between genes, quantitative trait loci, and biological processes (Yin et al., 2000; Hoogenboom et al., 2004; Messina et al., 2006; Chenu et al., 2009; Hammer et al., 2019).

Figure 2.

Diagram of a crop growth model used for genome to phenome modeling. A genotype → phenotype mapping example is shown for maximum photosynthesis (Pmax), canopy photosynthesis (Pcan) and radiation use efficiency (RUE). The crop model schematic is adapted from Cooper et al. (2014b). Genotype marker (z) and effects (u) at genome positions (i), QE, quantum efficiency; LAI, leaf area index; I_int, light interception; _Iinc, incident light; R, respiration relative to Pcan; Cf, coefficient dependent on tissue composition used to express RUE in dry matter DM MJ^-1 (Yin et al., 2021).

Table 1.

Mean, variance, and definitions for physiological traits comprised within the crop growth model

Trait	Abbr.	Description	Value			References
			$\mu$	${\sigma }^2$	Hyb
1. Leaf appearance rate	LAR	Determines duration of vegetative phase (leaf °C-1)	0.00275	1.62×10-8	0.0023	Muchow et al. (1990); Messina et al. (2011)
2. Grain fill duration	GFD	Determines duration of reproductive phase (°C−1)	1300	2603	1300	Gambín et al. (2006)
3. Area of largest leaf	AMAX	Determines size of canopy, light capture, and water use (cm2)	850	650	850	Soltani and Sinclair (2012); Messina et al. (2018)
4. Leaf senescence	SENS	Determines light capture and water use Reduction in leaf area in response to decreasing water supply/demand.	0.05	0.0001	0.05	Holsworth et al. (2014)
5. Root elongation rate	RER	Determines capture of water (mm d−1)	25	6.5	22	Dardanelli et al. (1997); Hammer et al. (2009); Singh et al. (2010); van Oosterom et al. (2016); Ordóñez et al. (2018)
6. Radiation use efficiency	RUE	Conversion efficiency of light into mass (g MJ−1)	1.85	0.16	1.85	Messina et al. (2018); Lindquist et al. (2005); Sinclair and Muchow (1999); Muchow et al. (1990)
7. Transpiration response to VPD	LT_slope	Affects conversion efficiency of water into mass Slope of the response above a breakpoint (0–1; 1 = no response)	0.5	0.0026	0.7	Choudhary et al. (2014); Shekoofa et al. (2015); Messina et al. (2015)
8. Transpiration response to VPD	LT_bkp	Breakpoint (kPa)	2	0.065	2
9. Number of kernel rings per ear	NRINGS	Determines sink size	45	6.5	45	Messina et al. (2011)
10. Maximum silk elongation rate	SER	Determines sink size (cm h−1)	1.5	0.065	1.5	Turc et al. (2016); Messina et al. (2017)
11. SER response to water deficit	SERD	Fraction of total soil water when silk elongation rate was reduced to 50% of maximum	0.5	0.01	0.56	Turc et al. (2016); Messina et al. (2017)
12. Husk length	HLENGTH	Determines sink size (mm)	200	104	190	Messina et al. (2019)

Values used for simulating water supply to demand ratios are shown for the reference hybrid (Hyb).

Combining a CGM with whole-genome prediction (CGM–WGP) is the extension of the WGP framework (Meuwissen et al., 2001; Lorenz et al., 2011; Heslot et al., 2012; Poland et al., 2012) to integrate plant physiology and genomics encapsulated within crop models (Figure 2). CGMs introduce the capacity to deal with temporally varying trait–environment interactions into otherwise static mathematical formulations used in WGP to model genome-to-phenotype relations. The CGM–WGP framework is unique in its conception to leverage fundamental physiological understanding to connect genotypes and phenotypes. Previous demonstration through simulation and empirical studies (Technow et al., 2015; Cooper et al., 2016; Messina et al., 2018), albeit limited in scope, produced encouraging results. These examples used a maize CGM that has been refined over decades of experimentation and contains modules to simulate yield potentials and reductions due to intensity and timing of water stress (Hammer et al., 2009; Messina et al., 2015, 2019). CGM–WGP can be viewed as a physiological and quantitative genetics integrated framework (Cooper et al., 2020a) that could be useful for germplasm characterization and prediction, with dynamic consideration of the main and interaction effects of G, E, and M on crop performance.

In CGM–WGP, through many iterations of CGM runs housed inside of a Metropolis–Hastings-within-Gibbs algorithm, the trait estimates with the highest posterior probability for each genotype in a training set (i.e. the set of tested genotypes used in the estimation step) are determined through sampling, for a limited set of physiological traits specified by the practitioner (Messina et al., 2018). These traits should express genetic variation in the target breeding populations and be highly heritable—largely insensitive to the effects of environment and management. Model parameters in the photosynthesis response to CO₂ and light (Figure 2) are examples of processes for which there is reasonable evidence for biophysical and genetic regulation and therefore suitable targets for estimation (Leakey et al., 2006; Wu et al., 2019). Yield predictions can then be generated for field tested or untested individuals, through a final set of runs of the CGM over the distribution of samples obtained in the previous step for each tested or untested environment and agronomic management of interest (Figure 1). In this final prediction step, marker-based estimates are used to calculate the appropriate value to be used for the physiological trait(s) that were estimated in the training step. Figure 2 shows an example based on the estimation of marker effects for light saturated photosynthesis. Simulation for the target population of environment (TPE) and a set of agronomic practices can be used to assess the merit of any genotype for which the CGM assumptions are appropriate.

Breeders conduct field trials to make inferences regarding the performance of genotypes of interest in certain E and M combinations within the TPEs (Comstock, 1977, Cooper and DeLacy, 1995). However, even with careful experimental design, any given multienvironment trial (MET) samples a relatively small and often inadequate fraction of the TPE (Cooper et al., 1995, 2014b; van Eeuwijk et al., 2019). That is, several testing sites that are selected for their potential to represent distinct environment types in the TPE could experience highly similar conditions in a given year, leaving other environment types under-represented (Cooper et al., 2014a). Weighting selection decisions by the frequency of occurrence of environment type was advocated to overcome this problem (Podlich et al., 1999). Other approaches utilize managed stress environments (MSEs) designed to emulate the timing and severity of a stressor (e.g. drought in the flowering stage of development), and/or to elicit a physiological response that separates germplasm for adaptation to the target environmental conditions encountered in the TPE with a high enough frequency (Cooper et al., 1995, 2014a, 2014b). By generating contrasting environment types through use of MSEs to discriminate germplasm, it is possible to estimate physiological trait values and marker effects that give rise to the manifested norms of reactions characteristic of each genotype for the target environments of the TPE.

The gap analysis methodology seeks to quantify the difference between realized crop yields and what could be achieved given the availability of limiting natural resources (van Ittersum et al., 2013). Productivity gaps could be reduced by implementing agronomic practices that may include the choice of genotype. Cooper et al. (2020b) developed a methodology so that breeders can be deliberate about selecting combinations of agronomic practices and genotype that can reduce the yield gap faster than any combination alone. This approach has the largest impact when environmental variability is high and in drought prone environments (Cooper et al., 2020b).

Applications of the CGM–WGP methodology have thus far focused for the most part on field evaluations of a smaller number of populations from maize drought programs (Cooper et al., 2016; Messina et al., 2018). Methodologies that span the scale of the breeding program have been mentioned to be important (Cooper et al., 2016). Complementarily, gap analysis methodologies have been demonstrated in long-term studies for genetic gain but have not been linked to WGP (Cooper et al., 2020b). We propose herein an integrated approach that links the digital tools of CGM–WGP and gap analysis with MSEs to increase the number of opportunities to realize faster rates of genetic gain in the TPE (Figure 1). Specific objectives of the study were to: (1) introduce a strategy for the use of MSEs and MET data in CGM–WGP training and assess CGM–WGP predictive abilities, (2) introduce the concept of in silico germplasm characterization, and (3) connect the gap analysis and CGM–WGP methodologies to create a procedure through which breeders could select the best combinations of genotype and management to close productivity gaps in the TPE.

Results

Training strategy: simulating average performance of genotypes and environment types in MSEs and MET

A first evaluation of the CGM consisted of using parameters for a check hybrid representative of the maturity of the breeding population to check for simulation accuracy across environment types (Table 1). Baseline simulations of yield (Y_s, g m⁻²) in each environment (Table 2) resulted in reasonable approximations of mean yield of the population (Y_o) ($Y_o=93\left(\pm 122\right)+0.95\left(\pm 0.08\right)\times Y_s;df=21;\mathrm{ }{r}^2=0.86$). The relative simulation error (1−Y_s/Y_o) was within 15% for a wide range of production environments (500 to >1,500 g m⁻²). Using CGM outputs such as the soil water supply that depends on determinants of water balance and root exploration, and the plant demand for water that depends on potential growth and vapor pressure deficit (VPD), it was possible to calculate a daily water supply/demand ratio (S/D) to characterize environmental drought status given the patterns of irrigation and/or precipitation. Based on the simulated daily S/D dynamics for each environment (reduction of S/D) and the timing relative to the critical developmental period for kernel set determination in maize, it was plausible to identify three water-deficit (WD) environments with low S/D values around flowering time at MSE sites, three well-watered (WW) environments at MSE sites, and 17 TPE sites (Figure 3). The WD environments experienced a decrease in the water S/D ratio around flowering that was not observed in the WW environment and TPE, with the exception of environment E9. The multienvironment testing in the TPE under sampled drought environments (Cooper et al., 2021) and the irrigation management strategies implemented at MSEs were effective at imposing WD to the desired timing and intensity.

Table 2.

Soil properties and management practices by environment (Figure  3)

		Soil properties			Management
Name	Stress Type	Depth (m)	SWHC (cm3/cm3)	Drainage	Planting date	Density (pL m−2)	Irrigation (mm)
E1 (MSE)	WD	1.5	0.10	0.8	October 31, 2017	8	506
E2 (MSE)	WD	2.0	0.15	0.5	May 22, 2017	8	165
E3 (MSE)	WD	1.0	0.10	0.8	October 11, 2018	8	589
E4	TPE	2.0	0.10	0.5	May 8, 2017	8	449
E5	TPE	2.0	0.16	0.5	May 9, 2017	6
E6	TPE	2.0	0.15	0.5	April 12, 2017	8
E7	TPE	2.0	0.16	0.6	April 22, 2017	8
E8	TPE	2.0	0.14	0.5	April 22, 2017	8
E9	WD	2.0	0.14	0.5	April 21, 2017	7
E10	TPE	2.0	0.15	0.5	April 18, 2017	8
E11	TPE	2.0	0.14	0.5	May 17, 2017	7
E12	TPE	2.0	0.14	0.5	May 16, 2018	8
E13	TPE	2.0	0.14	0.6	April 25, 2018	7
E14	TPE	2.0	0.17	0.1	April 28, 2018	8
E15	TPE	2.0	0.14	0.5	April 25, 2018	8
E16	TPE	2.0	0.14	0.1	April 25, 2019	8
E17	TPE	2.0	0.14	0.5	May 5, 2018	8
E18	TPE	2.0	0.14	0.6	April 29, 2019	7
E19	TPE	2.0	0.15	0.3	April 21, 2019	8
E20	TPE	2.0	0.13	0.1	May 17, 2019	8
E21 (MSE)	WW	1.5	0.10	0.8	October 30, 2017	8	677
E22 (MSE)	WW	2.0	0.15	0.5	May 2, 2017	8	567
E23 (MSE)	WW	2.0	0.15	0.5	May 9, 2018	8	699

SWHC, soil water holding capacity.

Figure 3.

Environmental characterization for the multienvironment experiment. A, Daily sequences of water S/D, 1 = no stress centered at flowering by environment (E1–E23). Dashed lines indicate flowering. Because S/D was equal to 1 throughout the season, E6, E11, E12, E15, E18, E19, and E20 were grouped together. B, Corn-belt testing locations. Testing locations in managed stress environments were in California and Chile.

Training strategy: harnessing MSEs, physiological knowledge, and digital tools to train CGM–WGP

An algorithmic procedure to make physiological knowledge revealed through CGM–WGP accessible to decision makers, including to inform selection decisions by plant breeders, was herein proposed. Similar to forward variable selection in linear regression or sensitivity analyses (Wallach et al., 2019), a scan of physiological traits was conducted and followed by the combination of these until a parsimonious and physiologically plausible set of traits that minimize the prediction error was identified, and a clear advantage in predictive skill was demonstrated. The selection of candidate traits was informed by observed genotypic variation, as characterized by prior probability distributions. From an initial scan of 12 model parameters representing physiological traits involved in phenology, resource use, conversion efficiency and allocation (Table 1), a minimal set was identified that exhibited high correlations between fitted and observed values for yield across environments. This minimum set comprised number of kernel rings per ear (NRINGS; high values indicating more kernel rings and sink potential), husk length (HLENGTH; high values indicating long husks), senescence response to WD (SENS; low values indicating staygreen), and root elongation rate (RER; high values indicating rapid root elongation). This four-trait CGM–WGP model exhibited correlations between model-generated and observed values that were greater than or at parity with those of WGP (Figure 4); the latter is representative of the WGP model BayesA. Predictive skill advantage was calculated as the difference between Pearson correlation coefficients, r(predicted, observed), for each of CGM–WGP and WGP in each environment. The predictive skill measure clearly demonstrates that for specific population and environment combinations, integrating plant physiology into the prediction algorithm contributed to the enhanced modeling of G×E by CGM–WGP in this large experiment.

Figure 4.

Prediction accuracies estimated by the Pearson correlation coefficient (r) for WGP and CGM–WGP. Results shown for across family (A) and within family (B) evaluations and by environment type: WD, TPE, and WW. Mean and standard errors were estimated using bootstrapping (n = 50).

Training assessment: predictive skill advantage increased with increasing WD

Expressed trait phenotypes resulting from the differential management realized in the MSEs (Figure 3A) enables the estimation of CGM parameters that encapsulate the mechanisms underpinning germplasm performance in the TPE, which include environments with various types of WD (Figure 3B). Predictive ability advantage of the four-trait CGM–WGP model relative to WGP (r_CGM–WGP – r_WGP) was the highest when both tested genotypes and environments were included as part of the subset of data used for training the algorithms (Table 3). It decreased for any combination involving untested genotypes, environments, or their combination. For tested environments, both CGM–WGP and WGP predict yield equally well for untested genotypes. In contrast, in the presence of G×E, CGM–WGP can virtually maintain the level of prediction accuracy (0.61 versus 0.58) while WGP does not (0.62 versus 0.42). Similarly, for untested environments and genotypes, the differences in the correlation coefficients varied between 0.17 and 0.16 when training the model using data from both WD and irrigated experiments at MSEs (Table 3). Excluding WD data from the training data set increased the predictive ability of WGP. Removing this form of G×E from the training set reverts the difference in accuracy back to virtually zero (0.34 versus 0.38; Table 3). Overall, the results could be explained by the contrasting genetic correlations (r_G) between irrigated and TPE (r_G=0.68) and WD and TPE experiments (r_G=0.0003), and the under sampling of WD environments in the TPE (Figure 3A).

Table 3.

Average predictive skill and standard errors for across family prediction of CGM–WGP and WGP algorithms for cases resulting from the combination of: tested (T) and untested (U; not included in the training of the model) genotypes and tested and untested environments

	WW data				WW and WD data
Environment	CGM–WGP		WGP		CGM–WGP		WGP
	Genotype		Genotype		Genotype		Genotype
	T	U	T	U	T	U	T	U
T	0.79±0.002	0.61±0.001	0.74±0.002	0.62±0.001	0.80±0.002	0.58±0.001	0.49±0.002	0.42±0.001
U	0.39±0.003	0.34±0.002	0.41±0.003	0.38±0.002	0.47±0.003	0.43±0.002	0.30±0.004	0.27±0.003

Mean and standard errors were estimated using bootstrapping (n = 50).

Training the model with data from all 23 environments, both across and within family predictive abilities were also high with the four-trait CGM–WGP model and tended to be either at parity with those of WGP or greater—with the latter particularly being the case in WD environments (Figure 4). Taken together, the results show that for this large MET the predictive skill advantage of CGM–WGP over WGP increased with increasing severity of WD (Figure 5). Whole-season total evapotranspiration (ET) was used as a measure of the severity of WD for each environment. Analyses over 35 families and 23 environments demonstrated that CGM–WGP offered a predictive advantage for the across family prediction (defined as $r_{\mathrm{CGM}-\mathrm{WGP}}-r_{\mathrm{WGP}}$) compared to WGP that increased with decreasing ET ($\log \left(r_{\mathrm{CGM}-\mathrm{WGP}}-r_{\mathrm{WGP}}\right)=1.77(\pm 0.8)-0.008(\pm 0.002)\times \mathrm{ET};\mathrm{ }{r}^2=0.59;\mathrm{d}f=21).$

Figure 5.

Predictive accuracy difference in an across family context estimated by the difference in Pearson correlation coefficients (r, observed versus predicted yield) for each of CGM–WGP and WGP methodologies (i.e. r_CGM–WGP – r_WGP) as a function of ET. Each point represents the mean difference in prediction accuracy across families in a single environment. All environments were included for training and prediction. Mean and standard errors were estimated using bootstrapping (n = 50). Error bars are 3 × standard error (P < 0.001).

Training assessment: predictive skill in CGM–WGP correlates with robustness of trait estimates

Two of the four estimated traits, NRINGS and SENS, were further examined for determining the extent of trait stability when varying the environment types included in the training set, and when estimating one or multiple traits simultaneously. Both methodological points are important in the training and application of CGM–WGP. When estimating only one of NRINGS or SENS at a time, inclusion of all data generated in MSEs (WW + WD) in the training set versus only WW environments in the training set produced similar NRINGS estimates (r = 0.99) but vastly different SENS estimates (r = 0.26). In the opposite scenario, use of all MSEs (WW + WD) versus only WD environments in the training set produced similar SENS estimates (r∼1.0) but vastly different NRINGS estimates (r = 0.49), when estimating only one of these traits at a time. A similar pattern in stability of trait estimates within and across environment types was observed when estimating both NRINGS and SENS simultaneously. To examine from the perspective of number of estimated traits when including only WW environments in the training set, NRINGS estimates were stable whether estimating only NRINGS or both NRINGS and SENS (r = 0.99). The same was found for WD environments and the stability of SENS estimates, whether estimating only SENS or both NRINGS and SENS (r = 0.99). When using only the TPE environments as the training set, estimates of NRINGS in the 2017 versus 2018 TPE environments were moderately to highly stable (r = 0.90).

In silico germplasm characterization: relating genetic with functional diversity as determinants of yield

Estimated physiological traits were weakly correlated with each other in pairwise examinations (Table 4) and principal component analysis (PCA) biplots (Figure 6). NRINGS was positively correlated with SENS and HLENGTH, indicating that a stronger sink was associated with higher senescence and longer husks. RER was positively correlated with SENS, suggesting rapid root elongation was associated with reduced staygreen, and negatively correlated with HLENGTH, suggesting rapid root elongation was associated with improved synchrony of silk exertion and pollen release in WD. Yield under WW conditions in both MSEs and the TPE was strongly correlated with NRINGS (Figure 3A and Table 4), a determinant of sink potential in the CGM, but not under WD. Yield under WD in MSEs was strongly correlated with SENS when severe stress occurred prior to flowering or grain filling, indicating a limitation in source (Figure 3A and Table 4). In contrast, SENS and yield in the TPE were positively correlated, suggesting that SENS captured the remobilization due to the establishment of a strong sink rather than a source limitation. When WD occurred around flowering time (Figure 3A, E2), yield under WD was negatively correlated with HLENGTH due to the relationship between silk elongation rate under WD and the distance required for silk exposure to pollen (HLENGTH). Timing of WD in the MSE around silking (Figure 3A, E2) likely exposed genetic variation in husk length affecting the timing and synchrony of pollination akin to the negative relationship between the anthesis-silking interval and grain yield.

Table 4.

Genetic variance (upper diagonal) and Pearson correlation coefficients (upper off-diagonals and lower grid) for estimated physiological traits—NRINGS, SENS, RER, and HLENGTH—and yield under WD, WW conditions, and in the MET conducted in the TPE

		NRINGS	SENS	RER	HLENGTH
NRINGS		10.6	0.24	0.10	0.28
SENS			5.1 × 10−5	0.32	−0.07
RER				0.25	−0.27
HLENGTH					56.6
Yield WD	Chile	−0.05	−0.80	−0.07	0.06
	USA	−0.02	−0.05	0.04	−0.66
Yield WW	USA and Chile	0.72	−0.07	−0.03	0.11
Yield MET	USA TPE	0.96	0.20	0.03	0.35

Figure 6.

Biplots for PCs 1, 2, and 3. All hybrids included in the study are represented by gray dots. Selected crosses are shown as red dots and visualized in different panels. Vectors are for yield under WW conditions, WD at flowering time, and in the TPE, and for estimated physiological traits: NRINGS, leaf senescence response to water deficit (SENS; negative values indicate staygreen), RER, and husk length (HLENGTH).

PCA biplots were used to visualize the relationship among traits with yield in four contrasting populations resulting from crossing high yielding (non-stiff stalk [NSS]8 and NSS5) and drought-tolerant parents (NSS7 and NSS9) in three environment types (Figure 6). The first, second, and third components explained 39.9%, 26.8%, and 16.7% of total G+G×E variance, respectively. Principal component (PC) 1 discriminated hybrids for yield under WW, yield in the TPE, and NRINGS. PC 2 discriminated hybrids for yield under WD and SENS. PC 3 discriminated hybrids for RER and HLENGTH. Most hybrids from the cross NSS8/NSS5 were high yielding under TPE and WW but low yielding under WD (Figure 6, A and B). Most hybrids from the NSS8/NSS5 cross had average to low principal component scores on PC 3 for RER, and average to high scores on PC 2 for SENS. The latter trait was negatively correlated with yield under WD (Figure 6B). Crossing NSS8 with drought-tolerant parent NSS7 generated a population of hybrids with high scores for yield in the TPE, ∼50% of hybrids with high scores for yield under WD (Figure 6C), RER, and HLENGTH; and most hybrids having low scores for SENS, which corresponds to maintenance of a green canopy under WD (Figure 6D). The population NSS8/NSS9, another cross of NSS8 with a drought-tolerant parent, produced a high frequency of hybrids with high scores for yield in both the TPE and WD (Figure 6E), and consistently low scores for SENS (Figure 6F). In comparing NSS8/NSS9 with the other crosses with NSS8, the scores for HLENGTH were not changed relative to NSS8/NSS5 but decreased relative to NSS8/NSS7 (Figure 6, B and F). Hybrids resulting from crossing two drought-tolerant parents (NSS9/NSS7) had consistently high scores for yield under WD (Figure 6G) and RER (Figure 6H) and low scores for SENS and HLENGTH (Figure 6H).

Overall, different traits contribute to germplasm adaptation to WD and WW conditions in MSEs and the TPE, and the germplasm sampled in this study exposed genetic variation for these traits. The examples presented showed the possibility to improve yield under WD by improving simultaneously at least two traits related to capture of water (RER), maintenance of the canopy (SENS), and synchronous timely pollinations, in this case expressed by low HLENGTH. It appears as well that improvement of yield potential via NRINGS could indeed incur benefits for yield in the TPE. Adaptation and expression of G×E for yield emerge from different physiological pathways.

Integrated framework: gap analysis and CGM–WGP methodologies can help breeders to reduce the productivity gap

Grain yields in the TPE and the two MSE WW environments were all near the 80% quantile front used to define the realistic bound for efficient production agriculture. Average ET was between 492 and 649 mm in the TPE environments, while it increased to 700–800 mm in the MSE WW environments (Figure 7A). This sample of environments is highly biased when considering the types and frequency of environments expected in the TPE (Figure 3; Cooper et al., 2020b). Deviations of the average yields relative to the 80% quantile front indicated gaps in yield productivity across all environments but were more evident under low ET (Figure 7A). Cross-over G×E interactions for yield performance were observed across ET levels among the families. For example, the NSS8/NSS5 family had low mean yield at low ET levels (806 g m⁻² for ET <480 mm) and higher mean yield at high ET levels (1,635 g m⁻²) relative to other crosses of NSS8 with drought-tolerant parents; yield at low and high ET levels were in the ranges of 892–978 g m⁻² and 1,575–1,607 g m⁻², respectively (Figure 7). Under low ET, the yield advantage (291 g m⁻²) of crosses with drought-tolerant parents relative to NSS8/NSS5 was the highest in E3 (Figure 3) when severe WD occurred prior to flowering. In contrast, because WD occurred around flowering time in E2 (Figure 3), yield advantage varied among crosses: −68, 3, and 14 g m⁻² for NSS8/NSS7, NSS8/NSS9, and NSS9/NSS7, respectively. The full expression of drought tolerance related to high RER scores in NSS8/NSS7 (Figure 6D) did not occur until it was combined with a reduced HLENGTH (Figure 6H) that enabled a timely pollination (NSS9/NSS7) and with consistent low SENS values (Figure 6G). Note that the yield advantage for NSS9/NSS7 was greater than those of the NSS8/NSS7 and NSS8/NSS9 crosses (Figure 6). This result demonstrates the opportunity to be purposeful about closing productivity gaps with respect to limited natural/production resources by means of crop improvement. Because hybrids were characterized genetically and physiologically, it is possible to use the predictors from CGM–WGP to simulate the performance of each hybrid under different managements to identify opportunities to further close the production gap (Figure 1).

Figure 7.

Linking physiology and genomics can reduce productivity gaps across a range of water availability to the crop. Gap analyses demonstrated for average yields across families in each environment (A), and for four contrasting crosses along an ET gradient: NSS8/NSS7 (B), NSS8/NSS9 (C), NSS9/NSS7 (D) and NSS8/NSS5 (B–D; open symbol). The solid line corresponds to 80th percentile from Cooper et al. (2020b).

Discussion

Here, we demonstrated an integrated approach that links digital and field experimental approaches using the combination of CGM–WGP, gap analysis, and MSEs to hasten genetic gain (Figure 1). Using a large dataset comprising 23 locations that exposed 2,367 maize hybrids to a range of WD and WW environments, we estimated that the average out-of-sample predictive skill, both genotype and environment, for WGP and CGM–WGP were 0.27 and 0.43, respectively (Table 3). Presented herein is empirical evidence for the robustness of the predictive ability of CGM–WGP with changing environments, in contrast to WGP, that is consistent with results from simulation (Messina et al., 2018). Considering the genomic breeder’s equation as a valid framework to quantify the value of the information and the prediction approach (Voss-Fels et al., 2019), the gain in predictive skill due to the use of physiological knowledge to model G×E translates into an average differential response to selection $\overline{\left(\Delta \frac{\partial g}{\partial s}\right)}=\frac{\mathrm{ }{i\times \sigma }_A\times (\overline{r_{\mathrm{CGM}-\mathrm{WGP}}}-\overline{r_{\mathrm{WGP}}})}{\partial t}$, where $\overline{\Delta \frac{\partial g}{\partial s}}$ is the average differential genetic gain per unit cycle of selection, i is the standardized selection differential, ${\sigma }_A$ is the square root of the additive genetic variance in the training population, and $\overline{r_k}$ are the average correlations between the predicted yields for method k and the corresponding values in the TPE. A positive difference in the correlations implies a gain in skill due to modeling main effects and G×E interactions, which are in part the result of dynamic interactions among physiological traits. Because predictive skill advantage of CGM–WGP relative to WGP increased with increasing WD (Figure 5), the gains from use of CGM–WGP technologies for a given breeding program will depend on the frequency of drought occurrence and magnitude of G×E in the respective TPE. Considering these and previous results (Cooper et al., 2016; Messina et al., 2018), we propose that with access to a suitable CGM, linking genomics and physiology should lead to $\overline{\left(\Delta \frac{\partial g}{\partial s}\right)}$≥0. The introduction of a method for model selection, akin to forward variable selection in statistics or sensitivity analyses in modeling (Wallach et al., 2019), enables practitioners other than physiologists to apply CGM–WGP in breeding programs thus increasing the opportunities to expand the application of the method to other germplasm, crops, and geographies. The CGM–WGP framework enables the integration of phenomic data that will contribute to overcoming limitations to translate advanced phenomics into genetic gain (Araus et al., 2018). The use of MSEs to generate appropriate environmental conditions to elicit physiological responses is a core requirement to generate stable parameters for the selected model and the associated estimation of allelic effects, and to generate environments that expose productivity gaps to inform selection decisions. Over 3 years of experimentation (Figure 7A), most of the MET results sampled WW environmental conditions conducive to high yields (Figure 3A; Cooper et al., 2021). While these experiments are useful for selection, ignoring the biased sampling of the TPE is conducive to missing opportunities to accelerate genetic gain either due to overestimating G, underestimating G×E, and/or underestimating the predictive ability of methods such as CGM–WGP. The integration of gap analysis with a simulation step, using allelic effects estimated for each G, and using E and M intensively sampled from the TPE (e.g. 10⁸ G × E × M combinations; Cooper et al., 2020b), enables implementation of a weighted selection methodology to account for the sampling bias, as advocated by Podlich et al. (1999). Current computing capabilities should be adequate to implement digital phenotyping as proposed here on millions of G, E, and M combinations for any crop for which only genetic information on relatedness to tested genotypes is available. Finally, the CGM–WGP approach can assist in starting to answer questions regarding the adaptation of any G or G×M combination to current and/or future climates and production systems, which is not possible using conventional empirical sampling approaches but requires connecting genomics and physiology as demonstrated herein.

Strategy for the use of MSEs and MET data in CGM–WGP training for prediction

This study tested the empirical application of CGM–WGP in a large maize breeding population, with yield as the observed emergent property to be used in model training. The approach is generalizable to the use of a combination of complex traits such as grain yield across diverse environments, moderately complex traits such as leaf area, and directly measured constants for simple traits such as parameters for light response curves (Figure 2). Estimation of model parameter vectors in the G, E, and M scenarios of interest was key to implementation of the predictions for physiological traits segregating in the breeding populations. The feasibility of identifying a minimum parsimonious set of parameters for genetic modeling greatly facilitates the routine application of the approach when compared with previous efforts (Cooper et al., 2016; Messina et al., 2018). The use of MSEs provided critical information to improve the estimation of CGM parameters, in agreement with previous results (Messina et al., 2018). Estimation of yield in METs can also help with trait parameterization and model identifiability (Technow et al. 2015), which could be particularly pertinent in instances where influences of emergent phenotypes (Roeder et al., 2021) other than yield cannot be observed, e.g. enhanced rate of silk elongation and kernel set in low ET drought affected environments contained within the MET.

With the incorporation of WGP and a sampling component, attributes of plant growth that were not measured in the field but that were influential to yield can be approximated in a genotype-specific fashion by integrating over time the rates of growth, development, and biomass partitioning. The refinement of priors for physiological traits can be conducted on a small subsample of individuals that are representative of the breeding population. The parameterization of variation for physiological traits through CGM–WGP is contrasted with more intensive approaches in which all individuals in a breeding population are directly phenotyped for the physiological traits of interest (Yin et al., 2000; Reymond et al., 2003; Messina et al., 2006, 2011; Chenu et al., 2009). The CGM–WGP framework can thus be used to introduce—following initial experimentation to refine priors—a physiological component into the analysis of field trials in one or multiple stages of breeding programs (Figure 1), where in a typical season it may only be economical and/or logistically feasible to quantify yield for a majority of the tested genotypes. Further, advancements in high throughput phenotyping for canopy (Rutkoski et al., 2016; Crain et al., 2017), photosynthesis (Yendrek et al., 2017; Cotrozzi et al., 2020), roots (Atkinson et al., 2019; Messina et al., 2021), reproductive traits (Gage et al., 2017; Berghoefer et al., 2020), and grain/seed quality (Tillman et al., 2006) can create opportunities for a hybrid approach between direct phenotyping at the field level (Messina et al., 2011) and digital characterization of germplasm as demonstrated in the present study (Figure 6). This integration can address what was recognized as a problem of translating phenomics into decisions in breeding (Araus et al., 2018). We hypothesize that such an approach can increase predictive skill by reducing the underspecification of data-driven models and facilitating a deeper understanding of the physiological determinants of adaptation in the germplasm, and genetic determinants of physiological processes.

Algorithmic approach to parameter selection for modeling genome-to-phenotype relations

Translating physiological understanding into breeding decisions has been an ongoing and complex endeavor. The successful application of physiological knowledge underpinning drought adaptation in AQUAmax maize (Cooper et al., 2014b, Gaffney et al., 2015) required substantial investment in crop physiology and genetics to select predefined sets of traits within crop models to enable prediction and selection (Messina et al., 2011, 2018; Cooper et al., 2020a). Trait identification that requires a priori field research may constitute a bottleneck and a barrier for breeders to embed physiological knowledge and use CGMs to improve selection decisions, including due to underfunding of research pertaining to areas such as sink strength and root biology as defined by Reynolds et al. (2021). An iterative model building approach was previously suggested to lower the barrier to adoption (Messina et al., 2011). The present study introduces an approach to move from a priori selection of target physiological traits to enable CGM–WGP, to a formal algorithm approach for selection of the most parsimonious physiological genetic hypothesis that could be tested within the breeding program. Akin to parameter selection in multiple regression and sensitivity analysis (Pathak et al., 2007; Wallach et al., 2019), we show that an algorithmic approach can be effective in selecting parameter sets, which generate hypotheses for empirical evaluation, to improve predictive abilities compared to a contemporary WGP methodology. The use of global optimization and artificial intelligence to improve trait selection and parameter estimation is an active and promising area of research (Wallach et al, 2019; Washburn et al., 2020; McCormick et al., 2021). With appropriate parameterization, scoping, and updating, decision support systems that enable automated selection of traits for a given set of experiments could further enable the use of biological understanding in crop improvement in breeding programs of various sizes, in a manner that becomes routine and not an exception.

Evaluating CGM–WGP accuracy using a large breeding half-diallel G×E experiment

The WGP approach used herein represents a reasonable benchmark for CGM–WGP, in that it reflects contemporary, purely statistical methods for prediction of yield from marker effects (Meuwissen et al., 2001; Lorenz et al., 2011; Voss-Fels et al., 2019) as they are applied in commercial maize breeding (Cooper et al., 2014b). The choice of 2,935 markers thus guaranteed that marker density was not a limiting factor in this study. Numerous studies have shown that 200–300 informative markers distributed across the genome are sufficient for WGP applications in biparental maize populations (Guo et al., 2012; Combs and Bernardo, 2013; Hickey et al., 2014; Technow and Totir, 2015). Other approaches such as genotyping by sequencing (Elshire et al., 2011; Poland and Rife, 2012) could have been used for genotyping the DH lines. The results presented in this study are applied to a substantially larger set of G and E scenarios for the TPE than previous studies that used MSE data for at most four populations (Cooper et al., 2016; Messina et al., 2018). For an experiment comprising 23 locations and 2,367 maize hybrids, representing 35 populations, we demonstrated a decrease in the accuracy difference between BayesA, a widely used method, and CGM–WGP with decreasing WD (Figure 5). However, in agreement with previous studies (Cooper et al., 2016; Messina et al., 2018), whenever G×E was small, CGM–WGP still performed at parity with linear models (Figure 4 and Table 3). Therefore, in agreement with a previous study (Messina et al., 2018), it was possible to obtain a robust estimation of physiological traits with the use of multiple environment types, ranging from drought to WW, in the training set. Together, these findings suggest that CGM–WGP offers utility in incorporating signals from multiple environment types, and that the difference between benchmark methods and a form of CGM–WGP (Messina et al., 2018; Millet et al., 2019; van Eeuwijk et al., 2019) will increase with the increasing importance of G×E, G×M, and G×E×M interactions in the determination of yield.

Germplasm characterization in silico for hastened genetic gain

Understanding physiology at the level of individual genotypes offers utility both in germplasm characterization and in making selections that maintain physiological diversity, for risk management in the short, medium, and long term (Hammer et al., 2020). However, physiological experiments often focus on few genotypes, due to the intensiveness of the phenotyping methods and/or the systems-level of detail that is required to build a comprehensive mechanistic understanding. Linking genomics and physiology through CGM–WGP brings opportunities to generate hypotheses regarding the mechanisms of adaptation for millions of untested individuals for which only marker information is available (Figure 1). Here we focused on four traits for estimation using the CGM–WGP model: NRINGS, HLENGTH, SENS, and RER, and estimated values for 2,367 hybrids at 23 locations (Figure 6). A PCA showed that estimated parameters using the CGM–WGP are physiologically sound, and exposed genotypic variation within the germplasm (Figure 6 and Table 4).

Because NRINGS affects the potential number of silks, it is an important trait in defining yield potential (Messina et al., 2019). Results conform to the expected positive relationship between NRINGS and yield when WD is low (Figures 3 and 6). Because silks must extend beyond the husk, for a given elongation rate husk length can determine protandry, failure in pollination, and low yields (Hall et al., 1982; Messina et al., 2019) as exposed by the trait relationships depicted in PCA biplots (Figure 6). HLENGTH can also determine susceptibility to ear diseases by exposing kernels to the environment, which was not considered in the model. This trait could thus be somewhat informative for differential yield performance in TPEs, and a weak positive correlation was indeed observed (Figure 6). SENS models the response of leaf area loss to water S/D, and contributes to maintenance of photosynthetic rates, grain growth, and yield under certain WD environments (Borrell et al., 2000; Duvick, 2005; Messina et al., 2021). RER can impact the timing and volume of soil water available to the plant (Hammer et al., 2009, Lynch, 2013). Since the introduction of the hypothesis that deep roots contribute to long-term genetic gain for yield of maize in the US corn-belt, two studies (Reyes et al., 2015; Messina et al., 2021) have shown that total water extraction itself was not found to have changed over 100 years of maize breeding despite substantial genetic gain for yield, such that other mechanisms of yield optimization were likely exploited by breeding (Reyes et al., 2015; Messina et al., 2021).

Because (1) RER varied among populations (Table 4), (2) WD was imposed during the critical window for yield determination in the Woodland MSE (Figure 3A, E2), and (3) the depth of water extraction in Woodland can occur to depths >2.5 m (Table 2; Reyes et al., 2015), results from this experiment allowed testing of the hypothesis that RER is correlated with yield under WD in deep soils. On average, the yield difference between NSS8/NSS7 and NSS8/NSS5, which have contrasting scores for yield under WD and RER, was negative (−67 g m⁻²) and consistent with prior results (Reyes et al., 2015). However, the yield advantage due in part to high scores in RER (Figure 6D) was not fully expressed except in a population (NSS9/NSS7) that also had low scores for HLENGTH and SENS (Figure 6, G and H). HLENGTH and other traits are determinants of a timely pollination (Messina et al., 2019) contributing to reproductive resilience. These results suggest the hypothesis that in the absence of limitations to root growth in the soil profile (Fan et al., 2016; Ordóñez et al., 2018; Osborne et al., 2020), and considering that reproductive resilience underpins long-term genetic gain (Messina et al., 2021), the maintenance of gains in reproductive resilience will hasten genetic gain for yield when combined with positive selection for RER. This approach can hasten the identification of germplasm to both accelerate genetic gain and improve understanding of root traits underpinning crop improvement.

On the future of gap analysis and CGM–WGP digital methodologies

The CGM–WGP framework unifies the extent of physiological detail developed regarding crop growth and development on a daily timescale, with the germplasm testing and selection strategies that already take place within plant breeding pipelines (Messina et al., 2011; Technow et al., 2015). Here, we extended the system to consider the gap between attained and potential yield for a given availability of a yield limiting resource, in this case water. We demonstrated that gap analysis was useful in examining levels of yield performance in the various environments analyzed in this study, and in identifying families that tended to display more or less stability in yield performance across water availability levels measured by crop ET. These findings related to yield performance and stability can also be examined in light of the characterizations provided by the CGM–WGP model. For example, certain combinations of parents may tend to alleviate or exacerbate one or more trait vulnerabilities (e.g. for NSS8/NSS5, in the case of SENS) or bolster or weaken certain strengths. Continued integration of gap analysis methodologies with CGM–WGP could thus provide insight into specific targets for improvement of yield and yield stability across environmental gradients in the TPE. Considering the farming system context can provide a productive next methodological step to realize crop improvement gains through changes in root systems (Thorup-Kristensen and Kirkegaard, 2016; Bančič et al., 2021), which so far have been elusive in maize (Reyes et al., 2015; Messina et al., 2021).

Robust predictive abilities of the CGM–WGP methodology were observed both across and within families (Figure 4), and predictive abilities and physiological trait estimates were stable upon inclusion of data from multiple environment types in the model training data set. The outputs of the CGM–WGP framework additionally enabled germplasm characterization and gap analysis, which provided insight into opportunities for further improvement of yield and yield stability through breeding and/or agronomy. These findings suggest the multifaceted utility of CGM–WGP in large breeding populations and early stages of the breeding process and later stages of product placement (Figure 1) for the continued improvement—with potential increases in efficiency and genetic gain, as is enabled by predictive skill—of yield and yield stability in the TPE.

Conclusion

Leveraging physiological understanding to accelerate genetic gain and close productivity gaps has proven more difficult to materialize within breeding programs than anticipated. Based on our results, it is possible to generalize that biological understanding embodied within CGMs can increase prediction accuracy of WGP algorithms and that improvement increases with increasing contributions of G×E, G×M, or G×E×M to the total phenotypic variance. By introducing an algorithmic approach to trait selection, and the companion method for in silico phenotyping of populations, we have identified a promising opportunity for research to eliminate a major bottleneck to the broad use of physiological genetics knowledge to inform selection decisions in breeding programs of any size. Because CGMs embody physiology and its dependencies on the environment, among other dependencies, it is feasible to use CGM–WGP to assess germplasm and make deliberate selections to close the productivity gaps conditional to a TPE.

Materials and methods

Data

A maize (Zea mays) breeding and genetics experiment was conducted by crossing nine NSS inbred parents, denoted as NSS1, NSS2, …, NSS9, in a half-diallel mating design. From each of the resulting 35 families, 75 doubled haploids (DHs) were produced in vivo following standard protocols (Chaikam et al. 2019). Those DHs were then crossed to a common stiff stalk inbred tester resulting in 2,367 hybrids in total. These hybrids were evaluated in 23 environments (herein E1–E23) from 2017 to 2019. Six environments were from MSEs located at Corteva research stations in Woodland, CA and Viluco, Chile. Planting density, planting date, and crop husbandry followed best local practices (Table 2). Row spacing was 0.76 m for all environments. Irrigation was managed to impose water stress at different times of development including flowering (E1–E3; Figure 3). WW irrigated controls were included. Irrigation was applied using drip tape buried at 20-cm deep (E21–E23; Figure 3 and Table 2). The remaining 17 environments were in the US corn-belt states. Yield was measured at each location using mechanical combines and adjusted to 150 g kg⁻¹ grain moisture.

Soil data required to run simulations using the CGM were from in-field measurements. Daily weather data (solar radiation, maximum and minimum temperature, and precipitation) were from nearby weather stations from the National Oceanic and Atmospheric Administration (Bell et al., 2013; Table 2). Environment and management parameters such as plant population (plants per square meter) and planting date were also included (Table 2).

Experimental design and statistical analyses

The experimental design in each environment was a row–column design with diagonal checks. The grain yield data were analyzed using the ASREML mixed model software (Gilmour et al. 2009) for each environment with genotype as a fixed effect, row/column as random effects, and a 2D, first-order autoregressive (AR1×AR1) residual structure,

$$y_{\mathit{ijk}}=\mu +g_i+\underset{\_}{r_j}+\underset{\_}{c_k}+\underset{\_}{{ϵ}_{\mathit{ijk}}}$$

where $y_{\mathit{ijk}}$ is the yield for genotype i in row j and column k, $\mu$ is the overall mean, $g_i$ is effect of genotype i, $r_j\mathrm{ }$is the effect of row j, $c_k$ is the effect of column k, and ${ϵ}_{\mathit{ijk}}$ are the residual effects. $\mu$ and $g_i$ are fixed effects, $r_j$ and $c_k$ are assumed to be randomly normally distributed variables with mean 0 while ${ϵ}_{\mathit{ijk}}$ are assumed to be randomly normally distributed variables with mean 0 and variance matrix $R=\mathrm{ }{\sigma }_e^2\left[AR1\left({\rho }_r\right)\otimes AR1\left({\rho }_c\right)\right]$, representing the Kronecker product of first-order autoregressive processes across rows and columns, respectively, with the spatial residual variance ${\sigma }_e^2$. Best linear unbiased estimators for each genotype and for each environment were produced after adjusting for spatial effects and were used for subsequent analyses. Linear regressions were conducted using R (R Core Team, 2020). PCAs were used to characterize physiological parameters estimated for the 35 families and 2,367 hybrids and yields under different environment types. Analyses were conducted using the prcomp function in R package stats (R Core Team, 2020).

Genotyping

Each DH was genotyped with approximately 2,935 single-nucleotide polymorphism (SNP) markers. Missing SNP allele calls were imputed based on parent–progeny relationships (Technow and Gerke, 2017).

CGM–WGP configurations

This research used the CGM–WGP methodology described by Messina et al. (2018). The CGM used in this study uses an approach similar to APSIM (Holsworth et al., 2014) and other simple mechanistic models (Wallach et al., 2019) and was previously reported (Messina et al., 2015; Cooper et al., 2016). Briefly, crop development is simulated based on accumulation of thermal units (base temperature is set to 8°C prior to silking and to 0°C for the reproductive period; Table 1). Canopy development and the resulting leaf area are determined by the simulation of leaf appearance (Figure 2) and the size of the expanded and expanding leaves (Holsworth et al., 2014; Messina et al., 2015). The size of each expanding leaf is modeled based on the allometry between consecutive leaves, which is modeled as a function of the size of the largest leaf (Table 1) and the total number of leaves for a genotype (19 for this study). Dry matter growth is simulated as the product of light interception using the Beer–Lambert’s law (k = 0.4) and radiation use efficiency (Table 1; Sinclair and Muchow, 1999). Water demand is calculated using transpiration use efficiency (Tanner and Sinclair, 1983) dry matter growth potential, and VPD. Water demand and growth are adjusted whenever growth is limited by soil water supply and conductance response to VPD (Choudhary et al., 2014; Messina et al., 2015). The maximum daily leaf senescence fraction response to WD is set to 0.05 and decreases with increasing S/D up to zero when S/D equals 1 (Holsworth et al., 2014). Yield is determined by the product of dry matter mass and a daily increase in harvest index.

The maximum harvest index was set to 0.55 and was allowed within the model to vary with the occurrence of WD. WDs can limit growth during the grain filling period, and an early termination of growth due to leaf senescence can prevent the simulation from reaching the maximum harvest index. Further reductions could be due to failure in pollination and the establishment of the reproductive sink. An algorithm was included in the CGM to simulate silk elongation and response to the S/D ratio. This algorithm is based on cohorting floret/kernel rings in the ear, and pollination after silk emergence from the tip of the husk based on pollen availability (Oury et al., 2016; Turc et al., 2016; Messina et al., 2019). Briefly, the maximum number of silks is determined by the NRINGS and the number of kernels per ring (KRINGS). Silk emergence depends on the average rate of silk elongation, its response to WD, and the average distance that the average silk needs to travel along the husk (HLENGTH). The availability of pollen at any time follows a Gaussian distribution centered shortly after the time of anthesis/shedding of the main culm (Uribelarrea et al., 2002). Changes with age in silk receptivity follow Anderson et al. (2004). The simulated total number of embryos determined the attainable harvest index as described in Cooper et al. (2016).

A Bayesian hierarchical model was used to model allelic effects for physiological traits as described in Messina et al. (2018) with the extension to model soil properties such as depth, which is estimated independently for each location but held constant for all genotypes evaluated at a given location. The rationale for modeling soil factors as a variable is that for many environments sampled in a plant breeding trial, these model inputs are either unknown or known with underdesired precision. Inaccurate environmental inputs directly impact the accuracy of crop growth model simulation and thus prevent the accurate estimation of physiological traits and their genetic determinants. Allowing important environmental inputs to be estimated jointly with physiological traits prevents the model from exploring unrealistic physiological trait space because of biased environmental inputs. Prior distributions were from Messina et al. (2018) and are listed in Table 1. The prior for soil depth was a truncated normal distribution with 0 cm as the lower bound and 200 cm as the upper bound for each location, and variance of 25 cm. The Metropolis–Hastings-within-Gibbs algorithm was used to sample all parameters, including soil depth.

Model evaluation and selection

Models, which herein refer to CGM–WGP models for which different CGM parameters were estimated using marker data, were evaluated for their capacity to simulate and predict observed trait phenotypes. The metric to compare simulations and observations was the Pearson correlation coefficient. Evaluations were conducted for the prediction of mean yield performance for all genotypes across locations, for the prediction of family means across environment types (WD, corn-belt trials/TPE, irrigated), and for the prediction of within family hybrids across environment types. Comparisons between WGP and CGM–WGP were conducted to assess advantages of using MSEs and CGM–WGP in prediction. Eight cases (Table 3) stem from the prediction of family means for the observations in the corn belt (or TPE) using data collected in MSEs (irrigated and irrigated plus WD data): the combination of tested environments and genotypes (included in the training of CGM–WGP or WGP), and untested (or out-of-sample; not included during the training process) environments and genotypes. Genotypes used to train the model were a random sample of 500 out of the total of 2,367 hybrids. The procedure was repeated 50 times to estimate standard errors for the predicted means. The model was also trained for all locations and 250 out of 2,367 individuals to make predictions for untested genotypes for within and across family at each location. The difference in predictive accuracy with respect to ET, an indicator of G×E interaction, was modeled using a negative exponential function and parameters estimated using nonlinear regression (R Core Team, 2020).

Algorithmic approach to physiological model trait selection

A trait selection scheme was designed to identify feasible sets of physiological traits that have acceptable predictive skill. This method is deemed necessary both biologically and computationally. Biologically, not all 12 traits are relevant in the present dataset. If all environments were WW, traits related to yield potential should be more informative whereas if all environments were water-limited, traits related to drought tolerance should be more informative. In the case of sets of environments comprising contrasting water conditions, both yield potential traits and drought tolerance traits should be needed to understand and model the G×E variation. Moreover, traits impacting different physiological processes in the CGM may result in similar yield variation observed and thus may have similar importance. Including multiple or all traits may result in model unidentifiability issues given that different combinations of traits could tend to result in similar model likelihoods. The trait selection scheme can be viewed as a nonlinear analog of forward variable selection in multiple linear regression or sensitivity analyses (Pathak et al., 2007; Wallach et al., 2019). Since this model evaluation procedure involved many runs of CGM–WGP, only 250 randomly chosen genotypes were used in the trait selection procedure to reduce run time. This procedure starts with only one trait in the model. To evaluate the fitness of each of the 12 one-trait models, by-location prediction accuracy was calculated as the correlation between the predicted yield and observed yield and compared with the WGP model BayesA by-location accuracy (Meuwissen et al., 2001). The results can be inspected in scatterplots with BayesA by-location accuracy on the x-axis and the one-trait model by-location accuracies on the y-axis. Upon inspection and calculation of correlations between predicted and observed values, the most predictive one-trait model is selected. Other traits are selected in an iterative manner for their potential to increase this correlation. A limited number of candidate multitrait models were evaluated, and one parsimonious set was selected for the purpose of comparing CGM–WGP with BayesA results. Table 1 depicts the 12 CGM parameters coding for rates regulating physiological processes that were tested as the candidate traits driving the yield variation and G×E.

Data

The data can be made available through https://openinnovation.corteva.com/ upon reasonable request for public research purposes and project evaluation.

 

C.D., T.T., and C.M., conceived and executed the research plan. C.D. and T.T. conducted CGM–WGP modeling. F.T. and C.M provided technical assistance on CGM–WGP, implementation of sampling algorithm and crop modeling. M.J., M.C., D.P., S.L., and C.M. designed the experiments. M.J. and C.M. supervised and executed experiments. D.P. and T.T. conducted phenotypic analyses. M.C. and C.M. conceived the project. C.D., T.T., M.C., and C.M. wrote the manuscript with contributions from all the authors.

The author responsible for distribution of materials integral to the findings presented in this article in accordance with the policy described in the Instructions for Authors (https://academic.oup.com/plphys/pages/General-Instructions) is: Charlie Messina (charlie.messina@corteva.com).

Data requests should be submitted through Corteva Open Innovation Portal (https://openinnovation.corteva.com/).