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The existence of beyond mean field quasi-cycle oscillations in a simplespatial model of predator prey interactions is derived from a path integralformalism. The results agree substantially with those obtained from analysis ofsimilar models using system size expansions of the master equation. In all ofthese analyses, the discrete nature of predator prey populations and finitesize effects lead to persistent oscillations in time, but spatial patterns failto form. The path integral formalism goes beyond mean field theory and providesa focus on individual realizations of the stochastic time evolution ofpopulation not captured in the standard master equation approach.

Predator-Prey Quasi-cycles from a Path Integral Formalism