• density effects;
  • growth equations;
  • individual-based models;
  • Richards model;
  • sequential measurements


  • 1
    We modelled the growth in estimated biomass of individuals in experimental populations of Chenopodium album grown at two densities and measured sequentially nine times over 128 days. Competition is modelled by coupling individual growth equations and, within the population, the growth rate of a plant at any point in time is a function of its size to the power a, a measure of the degree of size-asymmetry of competition.
  • 2
    The growth of individuals in these crowded populations was significantly better fit by a Richards growth model than by models with one fewer parameter (e.g. logistic or Gompertz growth models). The additional parameter determines the location of the inflection point and provides great flexibility in fitting growth curves. Density had a significant effect on this parameter.
  • 3
    At the higher density, the maximum size that plants achieved was decreased and the exponential phase of growth was reduced. The estimate of the size-asymmetry parameter a was always greater than 1 and it increased significantly at the higher density. Growth was reduced and the number of very small individuals increased at the higher density, although a few plants still achieved a large size.
  • 4
    Our approach combines several recent innovations in the modelling of stand development, including (a) modelling of individual growth with biologically meaningful growth models and (b) modelling the relationship between size and growth of individuals within the population. Sequential, non-destructive data on the growth of individuals over time, in combination with modern statistical computing techniques, can lead to major advances in the modelling of plant population development, providing powerful tools for exploring variation in individual growth and for testing a wide range of hypotheses.