| Summary: | A principal objective in agriculture is to maximise food production; this is particularly relevant with the added demands of an ever increasing population, coupled with the unpredictability that climate change brings. Further improvements in productivity can only be achieved with an increased understanding of plant and crop processes. In this respect, mathematical modelling of plants and crops plays an important role. In this thesis we present a two-scale mathematical model of crop yield, that accounts for plant growth and canopy interactions. A system of ordinary differential equations (ODEs) has been developed for each individual plant, where equations are coupled via a term that describes plant competition. Both analytical and numerical methods have been considered to describe this competition. This model has been formulated for an underutilised African legume called bambara groundnut, a drought tolerant crop, which is currently being investigated to be used more widely as a food source in light of climate change and food security. Like many plant species, bambara groundnut exhibits physiological diversity which may affect the overall growth dynamics and crop yield. Such plant diversity is not regularly accounted for in crop scale models. Our model not only allows us to account for plant diversity, but we can investigate the effect of individual plant traits (e.g. plant canopy size and growth rates, planting distance) on the crop scale yield. The mathematical model has been formulated and validated using experimental data collected from the Tropical Crops Research Unit (TCRU) and Future Crops greenhouses at the University of Nottingham. We find that the mathematical model developed in this thesis is able to predict the growth of a population of bambara groundnut well and we go on to optimise the arrangement of individual plants for a series of scenarios. The primary aim of this is to maximise crop yield. Whilst formulated specifically for bambara groundnut, our model may also be extended to other crop species. In this thesis we demonstrate that the model is also able to simulate the growth of oil palm. We then apply the mathematical model to maximise crop yield in an intercropping environment; the planting of two or more species together in the same field area. We again investigate a series of scenarios that require optimisation and find that the optimisation techniques are able to provide plausible recommendations. This work has been undertaken in a multidisciplinary environment involving interactions with Plant Scientists at the University of Nottingham (Nottingham and Malaysia) and the Crops for the Future Research Centre, Malaysia.
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