Richards-like two species population dynamics model

• DOI: 10.1007/s12064-014-0205-z
• Publication Date: 2014-08-12T02:27:27Z
• Authors: Fabiano Ribeiro; Brenno Caetano Tr...; Alexandre Souto M...
• Keywords: 0301 basic medicine; 0303 health sciences; Pattern formation ecological; Models, Statistical; Population dynamics; Dinâmica populacional; Extinction, Biological; Biological Evolution; Models, Biological; Population growth models; 6. Clean water; Food Supply; Formação de padrões ecológicos; 03 medical and health sciences; Predatory Behavior; Animals; Humans; Computer Simulation; Population Growth; Modelos de crescimento populacional; Ecosystem

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.