Modelling the interindividual variability of organogenesis in sugar beet populations using a hierarchical segmented model

Modelling the interindividual variability in plant populations is a key issue to enhance the predictive capacity of plant growth models at the field scale. In the case of sugar beet, this variability is well illustrated by rate of leaf appearance, or by its inverse the phyllochron. Indeed, if the mean phyllochron remains stable among seasons, there is a strong variability between individuals, which is not taken into account when using models based only on mean population values.In this paper, we proposed a nonlinear mixed model to assess the variability of the dynamics of leaf appearance in sugar beet crops. As two linear phases can be observed in the development of new leaves, we used a piecewise-linear mixed model. Four parameters were considered: thermal time of initiation, rate of leaf appearance in the first phase, rupture thermal time, and difference in leaf appearance rates between the two phases. The mean population values as well as the interindividual variabilities (IIV) of the parameters were estimated by the model for a standard population of sugar beet, and we showed that the IIV of the four parameters were significant. Also, the rupture thermal time was found to be non significantly correlated to the other three parameters. We compared our piecewise-linear formulation with other formulations such as sigmoïd or Gompertz models, but they provided higher AIC and BIC.A method to assess the effects of environmental factors on model parameters was also studied and applied to the comparison of three levels of Nitrogen (control, standard and high dose). Taking into account the IIV, our model showed that plants receiving Nitrogen tended to have a later time of initiation, a higher rate of leaf appearance, and an earlier rupture time, but these differences were not dose-dependent (no differences between standard and high dose of Nitrogen). No differences were found on the leaf appearance rate of the second phase between the three treatments.