Size-structure is thought to be a critical feature of biological populations but its incorporation into ecological theory of competition is so far limited. Growing taller, especially for a tree, can mean access to resources otherwise blocked, and hence strategy variation related to how quickly an individual may grow, or the maximum size it may reach, has the potential to create coexistence opportunities. Existing studies of size-structured tree species competition models do suggest size structure opens coexistence opportunities. However, these studies are limited in that they are either based in simulation or numerical approaches that assessed feasibility but not stability or mutual invasion, include additional complexity such as patch-age structure that may affect results, or are based on discrete size-structure. Here we investigate a simple partial differential equation model of competition with continuous size structure to demonstrate analytically the key types of density-dependence needed for coexistence opportunities to arise under size structure alone, and the life history variation between species that allows them to coexist.
We find that density-dependence on the production of offspring (e.g. seed production in trees) from taller individuals (as would be expected under competition for light among trees), opens up the opportunity for competitive coexistence. We show analytically that under this density dependence, two species that vary along a maximum height versus seed production tradeoff can feasibly coexist and will mutually invade one another. Density-dependence in recruitment on the other hand does not open coexistence opportunities. This is perhaps not surprising, since all individuals of all sizes negatively impact recruitment and so there is no way of limiting this form of density-dependence with a different size-based life history strategy. Our results agree with prior results based on feasibility alone in more complex models and support the potential coexistence-enabling nature of a key axis of variation identified in recent work using tropical forest census data.
