title: Richards-like two species population dynamics model.
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.
authors.affiliation: Departamento de Ciências Exatas (DEX), Universidade Federal de Lavras (UFLA), Caixa Postal 3037, Lavras, Minas Gerais, Brazil, fribeiro@dex.ufla.br.
authors.forename: Fabiano
authors.initials: F
authors.lastname: Ribeiro
authors.forename: Brenno Caetano Troca
authors.initials: BC
authors.lastname: Cabella
authors.forename: Alexandre Souto
authors.initials: AS
authors.lastname: Martinez
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003198:Computer Simulation; D017753:Ecosystem; D053476:Extinction, Biological; D005523:Food Supply / Q000706:statistics & numerical data; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D011158:Population Growth; D011235:Predatory Behavior / Q000502:physiology*
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