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Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

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  • Cabella, Brenno Caetano Troca
  • Ribeiro, Fabiano
  • Martinez, Alexandre Souto

Abstract

We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics.

Suggested Citation

  • Cabella, Brenno Caetano Troca & Ribeiro, Fabiano & Martinez, Alexandre Souto, 2012. "Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1281-1286.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1281-1286
    DOI: 10.1016/j.physa.2011.11.018
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    References listed on IDEAS

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    1. Martinez, Alexandre Souto & González, Rodrigo Silva & Terçariol, César Augusto Sangaletti, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5679-5687.
    2. Strzałka, Dominik & Grabowski, Franciszek, 2008. "Towards possible q-generalizations of the Malthus and Verhulst growth models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2511-2518.
    3. Souto Martinez, Alexandre & Silva González, Rodrigo & Lauri Espíndola, Aquino, 2009. "Generalized exponential function and discrete growth models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2922-2930.
    4. Alexandre Souto Martinez & Rodrigo Silva Gonzalez & Cesar Augusto Sangaletti Tercariol, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Papers 0803.2635, arXiv.org, revised May 2008.
    5. Grabowski, Franciszek, 2010. "Logistic equation of arbitrary order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3081-3093.
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    Cited by:

    1. Ribeiro, Fabiano L. & Ribeiro, Kayo N., 2015. "A one dimensional model of population growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 201-210.
    2. Ribeiro, Fabiano L. & Li, Yunfei & Born, Stefan & Rybski, Diego, 2024. "Analytical solution for the long- and short-range every-pair-interactions system," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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