The Scaled Subspaces Method: A new trait-based approach to model communities of populations with largely inhomogeneous density

We present a new individual-based approach to model populations of largely inhomogeneous densities. By monitoring different populations at a spatial scale which is inversely proportional to the maximum expected concentration, the Scaled Subspaces Method solves the problem of demographic explosion of the most numerous species. It is intuitively similar to the experimental practice of changing the magnification of a microscope depending on the size-class of organisms inspected, and retains the possibility for uniform biological descriptions across scales. We use this method to simulate a pelagic microbial mixotrophic food web, where the most abundant species has population densities up to five orders of magnitude higher than the rarest species. The model generates biologically plausible and highly consistent predictions of biomass distribution across this density spectrum. Individual-based community models are affected by the possibility of artificial extinctions. We discuss theoretically and confirm experimentally this possibility, and show that this problem can be overcome through the use of large populations, genetic mutations, and periodical random reintroduction of lost species or traits. We also show that the proposed individual-based model produces the same solutions as a state-variable model of the same ecological scenario. This indicates that the predictions of the two models are independent of implementation issues, and allows using them interchangeably according to convenience. Overall, the study proves the viability of the Scaled Subspaces Method, and provides useful insights on its functioning and parameterization.