Non-linear regression models for time to flowering in wild chickpea combine genetic and climatic factors

Accurate prediction of crop flowering time is required for reaching maximal farm efficiency. Several models developed to accomplish this goal are based on deep knowledge of plant phenology, requiring large investment for every individual crop or new variety. Mathematical modeling can be used to make better use of more shallow data and to extract information from it with higher efficiency. Cultivars of chickpea, Cicer arietanum, are currently being improved by introgressing wild C. reticulatum biodiversity with very different flowering time requirements. More understanding is required for how flowering time will depend on environmental conditions in these cultivars developed by introgression of wild alleles.

We built a novel model for flowering time of wild chickpeas collected at 21 different sites in Turkey and grown in 4 distinct environmental conditions over several different years and seasons. We propose a general approach, in which the analytic forms of dependence of flowering time on climatic parameters, their regression coefficients, and a set of predictors are inferred automatically by stochastic minimization of the deviation of the model output from data. By using a combination of Grammatical Evolution and Differential Evolution Entirely Parallel method, we have identified a model that reflects the influence of effects of day length, temperature, humidity and precipitation and has a coefficient of determination of R²=0.97.

We used our model to test two important hypotheses. We propose that chickpea phenology may be strongly predicted by accession geographic origin, as well as local environmental conditions at the site of growth. Indeed, the site of origin-by-growth environment interaction accounts for about 14.7% of variation in time period from sowing to flowering. Secondly, as the adaptation to specific environments is blueprinted in genomes, the effects of genes on flowering time may be conditioned on environmental factors. Genotype-by-environment interaction accounts for about 17.2% of overall variation in flowering time. We also identified several genomic markers associated with different reactions to climatic factor changes. Our methodology is general and can be further applied to extend existing crop models, especially when phenological information is limited.