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Richards-like two species population dynamics model

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Abstract

The two-species population dynamics model is the simplest paradigm of inter- and intra-species interaction. Here, we present a generalized Lotka–Volterra model with intraspecific competition, which retrieves as particular cases, some well-known models. The generalization parameter is related to the species habitat dimensionality and their interaction range. Contrary to standard models, the species coupling parameters are general, not restricted to non-negative values. Therefore, they may represent different ecological regimes, which are derived from the asymptotic solution stability analysis and are represented in a phase diagram. In this diagram, we have identified a forbidden region in the mutualism regime, and a survival/extinction transition with dependence on initial conditions for the competition regime. Also, we shed light on two types of predation and competition: weak, if there are species coexistence, or strong, if at least one species is extinguished.

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Acknowledgments

The authors acknowledges support from CNPq (305738/2010-0, 476722/2010-1 and 127151/2012-5) and CAPES.

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Authors and Affiliations

  1. Departamento de Ciências Exatas (DEX), Universidade Federal de Lavras (UFLA), Caixa Postal 3037, Lavras, Minas Gerais, Brazil

    Fabiano Ribeiro

  2. Sapra Assessoria, Rua Cid Silva Cezar, 600, 13562-400, São Carlos, SP, Brazil

    Brenno Caetano Troca Cabella

  3. Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP), Universidade de São Paulo (USP), Avenida dos Bandeirantes, 3900, 14.040-901, Ribeirão Preto, SP, Brazil

    Alexandre Souto Martinez

  4. Instituto Nacional de Ciência e Tecnologia em Sistemas Complexos (INCT-SC), Rio de Janeiro , Brazil

    Alexandre Souto Martinez

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  1. Fabiano Ribeiro
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  2. Brenno Caetano Troca Cabella
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  3. Alexandre Souto Martinez
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Correspondence to Brenno Caetano Troca Cabella.

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Ribeiro, F., Cabella, B.C.T. & Martinez, A.S. Richards-like two species population dynamics model. Theory Biosci. 133, 135–143 (2014). https://doi.org/10.1007/s12064-014-0205-z

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  • DOI: https://doi.org/10.1007/s12064-014-0205-z

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