Axiomatic Community Ecology, Topology, and Dynamic Distance

The super-organismal view of ecosystems has largely been superseded by the individualistic view. One consequence of the dominance of the individualistic view is that many modern ecologists treat ecosystems as nothing more than vectors of relative abundances, ignoring the potentially important idea that an understanding of ecosystems should be based on dynamics rather than abundances or species identities. We develop a mathematical framework in which we compare dynamical properties of ecosystems with different sets of species, using ideas from functional analysis, metric spaces, and topology. We give two proof-of-principle applications of our framework to marine sessile communities and to a large database of ecosystem models. We show that under a set of biologically-motivated axioms designed to capture the properties of predator-prey systems, there is only one natural kind of ecosystem.