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Spatial population dynamics: Beyond the Kirkwood superposition approximation by advancing to the Fisher–Kopeliovich ansatz

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  • Omelyan, Igor

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.

Suggested Citation

  • Omelyan, Igor, 2020. "Spatial population dynamics: Beyond the Kirkwood superposition approximation by advancing to the Fisher–Kopeliovich ansatz," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    • Handle: RePEc:eee:phsmap:v:544:y:2020:i:c:s0378437119319764
    DOI: 10.1016/j.physa.2019.123546
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    References listed on IDEAS

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    1. W. R. Young & A. J. Roberts & G. Stuhne, 2001. "Reproductive pair correlations and the clustering of organisms," Nature, Nature, vol. 412(6844), pages 328-331, July.
    2. Sharkey, Kieran J., 2011. "Deterministic epidemic models on contact networks: Correlations and unbiological terms," Theoretical Population Biology, Elsevier, vol. 79(4), pages 115-129.
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