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J Math Biol. 2015 Feb;70(3):533-47. doi: 10.1007/s00285-014-0763-1. Epub 2014 Mar 13.

Modeling spatial competition for light in plant populations with the porous medium equation.

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Laboratory of Applied Mathematics and Systems (MAS), École Centrale Paris, 92295 , Chatenay Malabry, France,


We consider a plant's local leaf area index as a spatially continuous variable, subject to particular reaction-diffusion dynamics of allocation, senescence and spatial propagation. The latter notably incorporates the plant's tendency to form new leaves in bright rather than shaded locations. Applying a generalized Beer-Lambert law allows to link existing foliage to production dynamics. The approach allows for inter-individual variability and competition for light while maintaining robustness-a key weakness of comparable existing models. The analysis of the single plant case leads to a significant simplification of the system's key equation when transforming it into the well studied porous medium equation. Confronting the theoretical model to experimental data of sugar beet populations, differing in configuration density, demonstrates its accuracy.

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