Four models were compared for estimating grain number per square meter (GPSM) of winter wheat (Triticum aestivum L.). As a data base for model validation and comparison, GPSM were determined in a field trial in northern Germany with values ranging in between 8.3 - 25 thousand grains per squaremeter under the influence of three years (2003/04 to 2005/06), five cultivars, and varying N supply (0-320 kg/ha).

The comparison was repeated using a published independent dataset collected in the Netherlands in 1983 and 1984 with a cultivar differing from the German trial grown across years, sites and N treatments.

Both data sets included several determinations for, shoot dry weight (DM), shoot N concentration (cN) and stage of development (BBCH) during a vegetation period.

The daily development progress (BBCH stages) for application of all models was simulated by a separate phenology model. Fitted logistic growth curves (DM) and linear interpolation (cN) were used to estimate explanatory crop variables.

The first three models had been published and use shoot dry weight at flowering (DM₆₅), shoot dry weight increase from the end of leaf growth to flowering (DDM_39-65), or nitrogen nutrition index at anthesis (NNI₆₀) term combined with the mean photothermal quotient (Q45) as explanatory variables. The fourth model is new, considering 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 valuable differences to the cultivar used in the Netherlands data set. Thus, modelling of GPSM required the calibration of a genotype specific parameter (G) for each model to both data sets.

Thus, the Wageningen dataset was used for a ceteris paribus comparison between models and validation of the new model using one fit parameter to each model. With the new approach the relative root mean square error (RMSE/Mean) of simulated GPSM over all plots could be reduced to 8%, compared to 12 - 17% obtained from the existing approaches. The trade-off between physiological relevance, empiricism, and accuracy is discussed.