Theory in Biosciences

, Volume 133, Issue 3–4, pp 135–143 | Cite as

Richards-like two species population dynamics model

  • Fabiano Ribeiro
  • Brenno Caetano Troca Cabella
  • Alexandre Souto Martinez
Original Paper
First Online:
Received:
Accepted:

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.

Keywords

Complex systems Population dynamics (ecology) Pattern formation ecological  
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Notes

Acknowledgments

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Fabiano Ribeiro
    • 1
  • Brenno Caetano Troca Cabella
    • 2
  • Alexandre Souto Martinez
    • 3
    • 4
  1. 1.Departamento de Ciências Exatas (DEX)Universidade Federal de Lavras (UFLA)LavrasBrazil
  2. 2.Sapra AssessoriaSão CarlosBrazil
  3. 3.Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP)Universidade de São Paulo (USP)Ribeirão PretoBrazil
  4. 4.Instituto Nacional de Ciência e Tecnologia em Sistemas Complexos (INCT-SC)Rio de Janeiro Brazil

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