Linking stem density, stem size and spatial arrangement: an approach to   model discriminative self-thinning in even-aged forest stands
  To model discriminative, i.e. competition induced, self-thinning in even-aged forest stands a concept has been explored that discriminative mortality alters spatial arrangement of trees which in turn alters the mortality. Function of density was suggested to be a balance of initial density minus mortality that was dependent on initial spatial arrangement and mean horizontal size in the forest stand. Assuming initial spatial arrangement to be aggregation and performing normalizations gave the self-thinning function depending on only two parameters, initial stem density and maximal horizontal size (represented by stem diameter). Normalizations included integral of probability of trees to collide to be unity and stem density at maximal size to be zero. The self-thinning function obtained has been shown to successfully capture non-linear self-thinning dynamics in Douglas-fir long-term experiments in which competition-induced mortality prevailed. 
Vladimir L. Gavrikov, Rem G. Khlebopros
q-bio.PE