"Spontaneous symmetry breaking between species in large Lotka-Volterra communities"Baron, Joseph WilliamOne criticism that was levelled at Robert May's seminal ecological work, which posited random interactions to describe the stability of many-species ecological communities, was that such interactions may not arise naturally in any reasonable model of the ecosystem dynamics. In this talk, I discuss the kinds of interactions that arise between species in communities modelled by generalised Lotka-Volterra dynamics. Far from being iid random variables, there is an intricate structure of correlations between different species' interactions. These arise due to constraints on the species abundances that are imposed by the dynamics. I show that in order to correctly predict stability, one can no longer think of species as being statistically equivalent -- a hierarchy amongst the species naturally emerges, even when the initial pool of species are statistically interchangeable. In a similar vein, I also show how the initial interaction network between species is warped by the Lotka-Volterra dynamics, changing the degree distribution, and introducing correlations between a species' connectivity and its interaction statistics. In the end, we see that the interactions in coexisting communities have non-trivial statistical interdependencies, and understanding this statistical structure can help us to understand which species are able to persist in a particular community. |
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