On the needs for combining physiological principles and mathematics to improve crop models

Major crop models were developed before the 1990s and many of their algorithms are (semi-)empirical. In the recent two decades, the number of models has grown rapidly, but the increase in their quality does not match the growth in number. Often, an ensemble of multiple models is required to make a useful prediction. This ensemble approach does not facilitate the improvement of models as a tool to understand crop physiological mechanisms. On the other hand, following a bottom-up approach that tries to assemble all elements along different scales of biological organisation may result in numerically clumsy models that are not necessarily more robust than existing models in simulating phenotypes at the crop scale. We argue that to model complex crop phenotypes in a simple yet accurate manner, crop modellers should be inspired by experiences in some fundamental sciences. For example, physicists used sound theories and solid mathematics in thought experiments, and came up with seemingly simple equations to explain the behaviour of very diverse systems, from sub-atomic particles to the largest clusters of galaxies. We review examples, where biological insights and mathematics are combined to derive simple equations that apply to different processes of crop growth. The essence of this modelling approach is a combination of simplicity, elegance and robustness. Models integrating those equations can predict crop phenotypes as well as generate hypotheses or emerging properties to assist in knowing the unknowns. Thus, crop models should not only provide practical predictions, but should especially be considered as a research tool for data interpretation, system design, and heuristic understanding.