Competition landscapes: scaling up local biotic and abiotic processes in heterogeneous environments.

I present a model based on benthic populations by first defining a competition landscape where competitive interactions are confined to small areas, defined by the distribution of resource renewal from a global pool. Using truncated kernels and results from 1-dimensional percolation theory, I then derive an approximation allowing the scaling up of local interactions among individuals to patch and landscape levels. This approximation is used to explore how spatially structured habitats can affect competition intensity. The competition landscape is then compared to a simulation of mussel colonization under various flow velocity patterns, and is shown to predict the qualitative effect of the scale of patchiness in habitat quality on total competition intensity. The interaction between large scale hydrodynamic forcing and local competition is also shown to provide an alternate hypothesis explaining the observed among-year reversal of the relationship between topographic scale and mussel abundance in some intertidal communities. The model more generally highlights the nonlinear scaling up of competitive interactions in competition landscapes, and provides a framework for the study of self-organization in heterogeneous ecosystems.