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

Abstract The superior Fisher–Kopeliovich closure is applied to the hierarchy of master equations for spatial moments in population dynamics for the first time. As a consequence, the density, pair and triplet distribution functions of entities 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.