Integrating Crop Growth Models and Genomic Prediction to Improve Flowering Time Forecasting Across Novel Environments and Breeding Lines

Technical Summary: Integrating Crop Growth Models and Genomic Prediction to Improve Flowering Time Forecasting

Problem Statement
Genomic selection (GS) has accelerated genetic gain in plant breeding but faces limitations when predicting performance in novel environments characterized by strong genotype-by-environment-by-management (GxExM) interactions not represented in training data. While process-based crop growth models (CGMs) can extrapolate to unobserved conditions by encoding physiological relationships, they traditionally lack the ability to leverage genomic information directly. Conversely, standard statistical genomic models (e.g., GBLUP) often fail to generalize beyond the specific environmental conditions of the training set. The challenge lies in developing a framework that unites the mechanistic extrapolation of CGMs with the predictive power of whole-genome prediction (WGP) to accurately forecast phenotypes, specifically flowering time, across diverse horticultural crops and novel environments.

Methodology
The study applied the Crop Growth Model–Whole Genome Prediction (CGM-WGP) framework to two horticultural species with contrasting physiological responses: broccoli (Brassica oleracea var. italica) and common bean (Phaseolus vulgaris L.).

• Data Sources:
  • Broccoli: A doubled haploid (DH) biparental population (200 lines) evaluated across six planting dates in North Florida to span a natural temperature gradient.
  • Common Bean: A recombinant inbred line (RIL) population (187 lines) evaluated across five environments in the US, Colombia, and Puerto Rico.
• The CGM-WGP Framework:
  • Mechanistic Component: Flowering time was modeled as a thermal time-driven process governed by a cardinal temperature beta function and a photoperiod function. The model calculates daily development rates based on temperature and daylength, accumulating until a genotype-specific physiological time requirement ($\Theta_g$) is met.
  • Genomic Component: The genotype-specific parameters ($\Theta_g$, photoperiod sensitivity $S_g$, and critical photoperiod $P_{c,g}$) were treated as random effects following a multivariate normal distribution with a genomic relationship matrix ($G$) as the covariance structure.
  • Estimation: An Expectation-Maximization (EM) algorithm was used to jointly estimate population-level hyperparameters and genotype-specific parameters. This "joint approach" allows genomic priors to regularize parameter estimates for genotypes with sparse phenotypic data, shrinking them toward genetically similar neighbors.
• Comparative Benchmarks:
  • Reaction Norm GBLUP (RN-GBLUP): A statistical model incorporating environmental covariance kernels (temperature and daylength) interacting with genomic kernels.
  • Standard GBLUP: A model using only genomic relationships and fixed environmental effects.
  • Pure CGM: A mechanistic model using only population-mean parameters without genomic differentiation.
• Validation: Four cross-validation schemes were employed to test predictive ability under increasing difficulty: sparse testing (CV2), new genotypes (CV1), new environments (CV0), and new genotypes in new environments (CV00).

Key Results

• Performance in Novel Environments: The CGM-WGP framework significantly outperformed the RN-GBLUP benchmark when predicting untested environments and untested genotype-environment combinations.
  • Common Bean: In the new environment scenario (CV0), CGM-WGP achieved a Pearson correlation ($r$) of 0.86 with an RMSE of 5.2 days, compared to lower accuracy for RN-GBLUP, particularly at the high-latitude North Dakota site where photoperiod regimes differed from the training set.
  • Broccoli: In the new environment scenario, CGM-WGP achieved $r = 0.66$ and RMSE = 9.4 days, outperforming RN-GBLUP which struggled with the thermal gradients of late-season plantings.
• Performance in Sparse Testing: When training data covered all target environments (CV2 and CV1), RN-GBLUP achieved the highest accuracy (e.g., bean CV2 $r = 0.93$), with CGM-WGP performing as a close second.
• Parameter Estimation: The thermal time requirement ($\Theta_g$) captured the majority of genotype-specific variation. Photoperiod parameters ($S_g$ and $P_{c,g}$) collapsed to population-mean values in both species, attributed to limited daylength contrast in the training environments.
• Heritability: Narrow-sense heritability of the estimated physiological time requirement ($\Theta_g$) was moderate in beans ($h^2 = 0.47$) and low in broccoli ($h^2 = 0.08$), reflecting the complexity of the trait and the experimental design.

Significance and Claims
The authors claim that this study demonstrates the generalizability of the CGM-WGP framework from major row crops (like maize) to horticultural species. The primary significance lies in the framework's ability to:

1. Generalize Across Physiology: Successfully model crops with contrasting strategies (e.g., temperature sensitivity in broccoli vs. photoperiod sensitivity in beans) using a unified modular architecture.
2. Extrapolate to Novel Conditions: Provide accurate predictions for environments and genotypes not present in the training data by structurally encoding GxExM interactions through physiological mechanisms rather than relying solely on statistical similarity.
3. Operate Without Prior QTL Identification: Utilize genome-wide marker data directly to predict flowering time, removing the requirement for prior identification of quantitative trait loci (QTL) or the restriction to specific mapping populations.
4. Inform Breeding Strategy: The results suggest that breeding programs operating across diverse environments should consider maintaining both CGM-WGP (for extrapolation to novel climates/geographies) and RN-GBLUP (for dense testing within known environments) in their prediction pipelines.

The paper concludes that while standard genomic selection benefits from increasing genotype numbers within target environments, CGM-WGP requires experimental designs that deliberately span sufficient environmental contrast (thermal, photoperiodic) to allow the model to calibrate transferable parameters. This approach enables selection for target environments not yet represented in a breeding program's trial network.