Gene-Based Modeling of Common Bean Flowering Time (Phaseolus vulgaris L.) with Non-Linear Response to Temperature and Day Length.

Crop models that integrate genetic, environment (E) and management information to predict crop growth and development in targeted environments are needed to help plant breeders design new cultivars adapted to climate change. A challenge to building these models is the difficulty of integrating genetic components into non-linear models of environmental plant responses. The goal of this project was to develop a model to predict flowering time of common bean (Phaseolus vulgaris L.) as affected by genetics (quantitative trait loci, QTLs), environmental responses, and QTL x E interactions. The model estimates flowering time by using a well-established approach where the daily product of the maximum rate of progress (α) toward an event, temperature (Ft), and photoperiod (Fpp) functions are integrated until a threshold value is met. Here, photoperiod and temperature responses were estimated with piecewise linear functions. To convert this model into gene-based model, 12 QTLs for flowering were first identified through composite interval mapping on data from 171 recombinant inbred (RI) genotypes at five sites (Citra, FL; Palmira and Popayan, Colombia; Isabela, Puerto Rico; and Prosper, North Dakota). Then, the model parameters for Ft and Fpp were calculated as linear equations of relevant QTLs. The estimated median optimal temperature of growth for the population was 21.4 °C, while median photoperiod sensitivity was estimated to be -0.025 [hr^-1]. Model evaluation with an independent dataset of the 2 parents and 7 RILs grown in Palmira, Colombia showed reliable predictions for time to anthesis (RMSE = 3.74 days from emergence). This modelling approach demonstrates the benefits of using gene-based models as a framework for analyzing genotype to phenotype responses.