Abstract
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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Acknowledgments
We are grateful to the French Technical Industrial Sugarbeet Institute (I.T.B., Paris) for providing us with the real plant data for the model validation. This work was supported by a doctoral scholarship of the Heinrich Böll Foundation.
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Beyer, R., Etard, O., Cournède, PH. et al. Modeling spatial competition for light in plant populations with the porous medium equation. J. Math. Biol. 70, 533–547 (2015). https://doi.org/10.1007/s00285-014-0763-1
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DOI: https://doi.org/10.1007/s00285-014-0763-1
Keywords
- Local leaf area index
- Competition for light
- Beer–Lambert law
- Inter-individual variability
- Reaction–diffusion equation