Background/Question/Methods   Using the Perfect Plasticity Approximation (PPA) of height-structured light competition, we present a model that scales up the physiological and structural traits of individual trees competing for light and nitrogen across a gradient of soil nitrogen to their community-level consequences. We predict the most competitive (i.e. the Nash strategy or ESS) allocations to foliage, wood, and fine roots for canopy and understory stages. We present the allocations as analytical formulae, which, like the equations of a simple Lotka-Volterra system, provide immediate insights into the underlying ecology that do not depend on parameter values or model simulations.

Results/Conclusions   ESS allocation to fine root decreases with soil nitrogen but increases with either growing season length or maximum photosynthetic rate, providing a potential explanation for conflicting reports of fine root productivity and biomass across nitrogen gradients. For canopy individuals, ESS allocation to foliage maximizes carbon gain and growth rate (i.e. is “optimal”), whereas ESS allocations to wood and fine roots do not. This result stands in stark contrast to the optimality of allocation to all structures assumed in many earlier allocation models. We test our quantitative predictions of allocation against data from 152 stands, which support our surprising prediction that the dominant structural tradeoff is between fine roots and wood, not foliage. This suggests the “root-shoot” tradeoff is more precisely a “root-stem” tradeoff, at least for long-lived trees. Assuming other resources are abundant, we predict that forests will always be limited by both nitrogen and light, or at the brink of such dual limitation.