Improved modeling of grain number in winter wheat

Four models were compared for estimating grain number per square meter (GPSM) of winter wheat (Triticum aestivum L.). As a data-base for model comparison, values of GPSM were determined in a field trial in northern Germany ranging from 8.3 to 25 thousand grains per square meter under the influence of three years (2003/04 to 2005/06), five cultivars, and varying N supply (0–320kg/ha). The comparison was repeated using a published independent dataset collected in the Netherlands in 1983 and 1984 (Wageningen dataset) with a cultivar differing from the German trial grown across sites and N treatments. Both datasets included several measurements of shoot dry weight (DM), shoot N concentration (cN) and stage of development (BBCH) during a vegetation period. Simulations of phenological development (BBCH scale) were performed with a separate model and used for all four models. Input values of all models were obtained from experimental data, using fitted logistic growth curves to estimate DM, whereas cN was linearly interpolated. Three of the four models (M1–3) had been published before: M1 uses shoot dry weight at flowering (DM65), M2 uses shoot dry weight increase between end of leaf growth and flowering (ΔDM39–65), whereas M3 is a multiple regression with log transformed nitrogen nutrition index at anthesis (NNI60) and average photothermal quotient from 45 days preceding anthesis (Q45) as explanatory variables. The fourth model (M4) was developed in this study based on the data observed in the German trial and considers the product of DM65, NNI60 and Q45. The relation between explanatory variables and GPSM did not vary greatly between the modern bread wheat cultivars of the German dataset, but there were considerable differences to the cultivar used in the Netherlands dataset. Thus, a genotype specific fit parameter (G) was added to the models and calibrated over each dataset. The Wageningen dataset was used for a ceteris paribus comparison between models and as validation of the new model. M4 shows best results for both datasets (n=45), whereas the relative root mean square error (rRMSE) of simulated GPSM over all crops of the ceteris paribus comparison (n=9) could be reduced to 8%, compared to 12–17% obtained from the existing approaches. The number of grains per unit shoot weight is influenced by NNI60 and Q45. This relation is considered by M4 and founded its improvement.