Spatial population dynamics: beyond the Kirkwood superposition approximation by advancing to the Fisher-Kopeliovich ansatz

The superior Fisher-Kopeliovich closure is applied to the hierarchy of master equations for spatial moments of population dynamics for the first time. As a consequence, the population density, pair and triplet distribution functions are calculated within this closure for a birth-death model with nonlocal dispersal and competition in continuous space. The new results are compared with those obtained by ``exact'' individual-based simulations as well as by the inferior mean-field and Kirkwood superposition approximations. It is shown that the Fisher-Kopeliovich approach significantly improves the quality of the description in a wide range of varying parameters of the model.Comment: 24 pages, 9 figure