Size hierarchy and stability in competitive plant populations.

A neighbourhood-based competition model for plant individuals is studied to evaluate how a hierarchical structure related to size may emerge in plant communities. It is shown by numerical simulations and linear stability analysis that many stable states exist in the hierarchical structure when both the total number of individuals and the degree of asymmetry of competition are high. When the hierarchical structures are self-organized by the dynamic instability of the homogeneous state due to non-linearity of competition, it is proved that these states are always locally stable. The relevance of the results to size structures in real plant communities (boreal forests vs tropical and temperate forests) is discussed. This is suggested to be the mechanism responsible for the coexistence of species in plant communities.