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A multiscale mathematical model describing the growth and development of bambara groundnut

Dodd, Josie; Sweby, Peter K.; Mayes, Sean; Murchie, Erik H.; Karunaratne, Asha S.; Massawe, Festo; Tindall, Marcus J.

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Josie Dodd

Peter K. Sweby

Associate Professor

Professor of Applied Plant Physiology

Asha S. Karunaratne

Festo Massawe

Marcus J. Tindall


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 paper we present a two-scale mathematical model of crop yield that accounts for plant growth and canopy interactions. A system of nonlinear ordinary differential equations (ODEs) is formulated to describe the growth of each individual plant, where equations are coupled via a term that describes plant competition via canopy–canopy interactions. A crop of greenhouse plants is then modelled via an agent based modelling approach in which the growth of each plant is described via our system of ODEs. The model is formulated for the African drought tolerant legume bambara groundnut (Vigna subterranea), which is currently being investigated as a food source in light of climate change and food insecurity challenges. Our model allows us to account for plant diversity and also investigate the effect of individual plant traits (e.g. plant canopy size and planting distance) on the yield of the overall crop. Informed with greenhouse data, model results show that plant positioning relative to other plants has a large impact on individual plant yield. Variation in physiological plant traits from genetic diversity and the environmental effects lead to experimentally observed variations in crop yield. These traits include plant height, plant carrying capacity, leaf accumulation rate and canopy spread. Of these traits plant height and ground cover growth rates are found to have the greatest impact on crop yield. We also consider a range of different planting arrangements (uniform grid, staggered grid, circular rings and random allocation) and find that the staggered grid leads to the greatest crop yield (6% more compared to uniform grid). Whilst formulated specifically for bambara groundnut, the generic formulation of our model means that with changes to certain parameter's, it may be extended to other crop species that form a canopy.


Dodd, J., Sweby, P. K., Mayes, S., Murchie, E. H., Karunaratne, A. S., Massawe, F., & Tindall, M. J. (2023). A multiscale mathematical model describing the growth and development of bambara groundnut. Journal of Theoretical Biology, 560, Article 111373.

Journal Article Type Article
Acceptance Date Nov 24, 2022
Online Publication Date Dec 9, 2022
Publication Date Mar 7, 2023
Deposit Date Jan 10, 2023
Publicly Available Date Jan 13, 2023
Journal Journal of Theoretical Biology
Print ISSN 0022-5193
Electronic ISSN 1095-8541
Publisher Elsevier BV
Peer Reviewed Peer Reviewed
Volume 560
Article Number 111373
Keywords Applied Mathematics; General Agricultural and Biological Sciences; General Immunology and Microbiology; General Biochemistry, Genetics and Molecular Biology; Modeling and Simulation; General Medicine; Statistics and Probability
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