Background/Question/Methods   The question we pose here is whether and how forest tree species coexist in equilibrium, when they compete with each other for light. Based on the general competition theory, equilibrium coexistence between species that compete for a single resource is possible only when species differ in species-pair specific competitive performance. In contrast, competitive intensity of forest trees for light is naturally expressed by species-additive foliage density that suppresses life-history performance of each species. Further architectural aspects exist in forests such that competition for light is local among adjacent foliage leaves and that it is one-sided along vertical foliage profile reflecting the attenuation of light. A variety of forest models that describe dynamics of forest architecture with physiological, allometric and demographic traits successfully demonstrate the stable coexistence of tree species. In this paper. I overview findings with partial differential equation (pde) models that describe dynamics of (continuous) size structure of trees in forest patches with (continuous) age structure, where competition is localized within a patch of particular age, and is one-sided in terms of local tree size structure. To fill the gap between simulation results with pde models and general theories of competition, I approximate size-age continuous processes employing discrete two-stage models with ordinary differential equations.

Results/Conclusions   Simulation results with pde models suggest that the inter-specific trade-off between maximum tree size and fecundity is the most pronounced condition for coexistence of tree species, and that is supported by permanent forest plot censuses. Horizontal heterogeneity associated with shifting patch mosaic facilitates coexistence of species with different shade tolerance. Approximated models with two height stories (without horizontal patch structure) allows graphical nullcline analysis of coexistence stability on the coordinates of species-sum foliage density in the upper layer and that in the lower layer. The way that two nullclines intersect corresponds to the stability of coexistence. Each life-history trait of a species uniquely contributes to the shape of its nullcline. Coexistence equilibrium is always stable between canopy and understory species, whereas that between canopy and canopy species can be stable or unstable. Approximated model with two patch stages (without height stratification) is examined by nullcline diagrams on the coordinates of species-sum densities at young and aged stages. The present procedure of graphical analysis implies similarity to the ZNGI diagram of Tilman's resource-ratio theory. Forest architecture that partition a single resource of light acts somewhat like multiple resources competed among species.