Global versus local coupling models and theoretical stability analysis of size-structure dynamics in plant populations

A local coupling model for growth dynamics of plant populations is proposed , in which each individual occupies a square lattice point and follows logi stic growth with potential maximum relative growth rate c(0) being reduced by the competitive effects from eight interacting neighbours. The competiti ve effects are given by the competition function W, which describes the deg ree of competitive asymmetry between individuals, beta and the distance-dep endent intensity of competition between individual i and j, alpha(ij), as a coupling constant. Then a global coupling model corresponding to the local coupling model is proposed, in which every individual interacts with all t he other individuals in the field. In the global coupling model, the coupli ng constant alpha as the same parameter for all the individuals was employe d instead of alpha(ij)'s in the local coupling model. alpha was given as an average of alpha(ij)'s of eight interacting neighbours in the local coupli ng model. Both the coupling constants were normalized by the number of inte racting individuals to make simulation results comparable between the model s. Numerical simulations revealed that the local coupling model can be simu lated by the corresponding global coupling model fairly well if population growth dynamics are continuous without deaths or new recruits. In both the models, multi-layered structure of size distribution was more likely to eme rge under asymmetric and/or intense competition than under symmetric and/or weak competition. This conforms to the widely known phenomenon of size-str ucture dynamics in plant populations. Since theoretical analysis is impossi ble for the local coupling model, linear stability analysis of size-structu re dynamics was made for the global coupling model. It was theoretically sh own that if alpha < c(0)/(1 + beta), mono-layered size structure is stable; if alpha > c(0)/(1 + beta), multi-layered size structure is stable. As alp ha and/or beta increases (decreases), multi-layered (mono-layered) size str ucture gets stable. As c(0) (i.e. seedlings' relative growth rate) increase s, the domain of stable mono-layered (multi-layered) size structure becomes larger (smaller). Therefore, the above simulation results were supported b y linear stability analysis of the dynamical systems. Ecological implicatio ns of these theoretical results are discussed concerning the relationship b etween the stability of stand size structure and the degree of competitive asymmetry (multi-layered versus mono-layered). (C) 1999 Elsevier Science B. V. All rights reserved.