IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i4p1281-1286.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111008533
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2011.11.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Piva, G.G. & Colombo, E.H. & Anteneodo, C., 2021. "Interplay between scales in the nonlocal FKPP equation," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    2. Destefano, Natália & Martinez, Alexandre Souto, 2011. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1763-1772.
    3. dos Santos, Lindomar Soares & Destefano, Natália & Martinez, Alexandre Souto, 2018. "Decision making generalized by a cumulative probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 250-259.
    4. Natalia Destefano & Alexandre Souto Martinez, 2010. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Papers 1010.5648, arXiv.org, revised May 2011.
    5. Oscar García, 2019. "Estimating reducible stochastic differential equations by conversion to a least-squares problem," Computational Statistics, Springer, vol. 34(1), pages 23-46, March.
    6. Moriguchi, Kai, 2018. "An approach for deriving growth equations for quantities exhibiting cumulative growth based on stochastic interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1150-1163.
    7. Barberis, L. & Condat, C.A. & Román, P., 2011. "Vector growth universalities," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1100-1105.
    8. Rivera-Castro, Miguel A. & Miranda, José G.V. & Borges, Ernesto P. & Cajueiro, Daniel O. & Andrade, Roberto F.S., 2012. "A top–bottom price approach to understanding financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1489-1496.
    9. Takahashi, Taiki, 2010. "A social discounting model based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3600-3603.
    10. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1281-1286. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.