New spin models in ecology: Super multi-stationarity and chaos

This manuscript introduces a novel spin model that captures the dynamics of ecological systems. We assume that these ecosystems consist of species whose ecological properties are completely determined by their discrete genotypes, and these genotypes are encoded by spin strings. We demonstrate that the Hamiltonian of this spin model can be derived naturally from classical models of population dynamics. Specifically, we establish a connection between the maximization of species abundance and the minimization of the Hamiltonian. The standard mean-field analysis reveals that the proposed spin model corresponds to the well-known Hopfield system, in general, characterized by asymmetric interactions. Remarkably, the resulting Hopfield system can possess an exponential number of local attractors, which, in the case of asymmetric interactions, may be complex. We term this characteristic “super multistationarity”. We also demonstrate that super multistationarity combined with spontaneous symmetry breaking empowers populations to identify optimal genotypes. This adaptation process mirrors the search for solutions in a parallel computer.