Modeling inter-individual variability in plant populations is a key issue to understand crop heterogeneity and its variations in response to the environment. Being able to describe the interactions among plants and explain the variability observed in the population could provide useful information on how to control it and improve global plant growth. We propose here a method to model plant variability within a field, by extending the so-called GreenLab functional-structural plant model from the individual to the population scale via nonlinear mixed-effects modeling. Parameter estimation of the population model is achieved using the stochastic approximation expectation maximization algorithm, implemented in the platform for plant growth modeling and analysis PyGMAlion. The method is first applied on a set of simulated data and then on a real dataset from a population of 34 winter oilseed rape plants at the rosette stage. Results show that our method allows for a good characterization of the variability in the population with only a limited number of parameters, which is a key point for plant models. Results on simulated data show that parameters associated with a low sensitivity index are inaccurately estimated by the algorithm when considered as random effects, but a good stability of the results can be obtained by considering them as fixed effects. These results open new ways for the analysis of inter-plant variability within a population and the study of plant–plant competition.Supplementary materials accompanying this paper appear online.
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The authors would like to thank the technical team of UMR ECOSYS 1402 (Julie Rodrigues, Marc Bidon, Alain Fortineau and Fabrice Duhamel) at INRA Grignon for their help on real data experimentation, Jean-Louis Foulley for his useful advices on model comparison using AIC and BIC in mixed models, and Benoît Bayol at CentraleSupelec for his help on producing an executable of the code.
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Baey, C., Mathieu, A., Jullien, A. et al. Mixed-Effects Estimation in Dynamic Models of Plant Growth for the Assessment of Inter-individual Variability. JABES 23, 208–232 (2018). https://doi.org/10.1007/s13253-017-0307-4
- Brassica napus
- GreenLab model
- Inter-individual variability
- Nonlinear mixed model
- Population model
- SAEM algorithm
- Winter oilseed rape