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Nonlocal pattern formation effects in evolutionary population dynamics

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  • Aranda, Orestes Tumbarell
  • Penna, André L.A.
  • Oliveira, Fernando A.

Abstract

In this work, we derive a deterministic equation for a generalized nonlocal population dynamics that depends fundamentally on two lengths parameters (α,β). We associate these parameters to the reproduction, competition, and pattern formation in bacterial dynamics. We propose that each set of parameters defines a state, and based on that, we formulate a stochastic cellular automaton for describing the evolutionary dynamics of a bacterial colony. It results in a selection of the bacteria more able to share space. In this way, we show that the evolution of the colony towards a maximum population allowed, in a given niche, defines the final pattern.

Suggested Citation

  • Aranda, Orestes Tumbarell & Penna, André L.A. & Oliveira, Fernando A., 2021. "Nonlocal pattern formation effects in evolutionary population dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    • Handle: RePEc:eee:phsmap:v:572:y:2021:i:c:s0378437121001370
    DOI: 10.1016/j.physa.2021.125865
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    References listed on IDEAS

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    1. Benjamin Allen & Gabor Lippner & Yu-Ting Chen & Babak Fotouhi & Naghmeh Momeni & Shing-Tung Yau & Martin A. Nowak, 2017. "Evolutionary dynamics on any population structure," Nature, Nature, vol. 544(7649), pages 227-230, April.
    2. Benedict Borer & Robin Tecon & Dani Or, 2018. "Spatial organization of bacterial populations in response to oxygen and carbon counter-gradients in pore networks," Nature Communications, Nature, vol. 9(1), pages 1-11, December.
    3. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    4. Kenkre, V.M., 2004. "Results from variants of the Fisher equation in the study of epidemics and bacteria," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 242-248.
    5. Barbosa, Fernando V. & Penna, André A.L. & Ferreira, Rogelma M.S. & Novais, Keila L.V. & da Cunha, Jefferson A.R. & Oliveira, Fernando A., 2017. "Pattern transitions and complexity for a nonlocal logistic map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 301-312.
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