Abstract
• Basic concepts of crop modelling founders are fading into oblivion since the mid-1990s. • The multi-model ensemble approach does not facilitate the models as a heuristic tool. • A bottom-up approach that assembles all biological elements is not conducive to simulating the crop. • An intermediate approach combining physiology and mathematics is recommended. • Leaf area index and radiation use efficiency are used as showcases. • Outstanding areas for further model development and caveats are outlined. 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.
Highlights
Since the pioneering work by de Wit (1959,1965,1968) and Duncan et al (1967), crop modelling research has seen exciting initial de velopments
It is recognised that these models need improving to face new challenges in crop science (Boote et al, 2013), such as predicting complex crop phenotypes (Muller and Martre, 2019) and assessing the impact of climate change on crop productivity and designing new crop types and management practices based on underlying genotype-environment-management interactions (Rotter et al, 2011; Peng et al 2020)
Discussions on how to improve crop models are rare, and where new approaches are presented, opinions differ with regard to how to improve crop modelling
Summary
Since the pioneering work by de Wit (1959,1965,1968) and Duncan et al (1967), crop modelling research has seen exciting initial de velopments (see the review of Loomis et al, 1979). We argue that crop modellers should aim to achieve real biologically improved models that predict complex crop phenotypes on the basis of underlying physiological principles. Quantum mechanics E = hυ of Max Planck) seem simple, but were derived from combining physical principles and mathematical analytics, albeit with approximations in some cases. Constants in these equations G, c and h all have physical meanings with explicit units. Cases where it is hard to develop such analytical algorithms but still possible to simplify numerical procedures are discussed We hope, these cases and discussions can catalyse the efforts towards real improvement of crop models in the future. Our discussions focus on annual crops, cereals in particular, and on processes at the field-plot scale
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