Rethinking the logistic approach for population dynamics of mutualistic interactions

Javier García-Algarra1, Javier Galeano1,2, Juan Manuel Pastor1,2, José María Iriondo3 and José J. Ramasco4

1Complex System Group, Universidad Politécnica de Madrid, 20040 Madrid, Spain.
2Dep. Ciencia y Tecnología Aplicadas a la I.T. Agrícola, E.U.I.T. Agrícola, Universidad Politécnica de Madrid, 20040 Madrid, Spain.
3 Área de Biodiversidad y Conservación, Dept. Biología y Geología, Universidad Rey Juan Carlos, 28933 Móstoles, Spain.
4Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca, Spain.

(May 2013)

Mutualistic communities have an internal structure that makes them resilient to external perturbations. Late research has focused on their stability and the topology of the relations between the different organisms to explain the reasons of the system robustness. Much less attention has been invested in analyzing the systems dynamics. The main population models in use are modifications of the r-K formulation of logistic equation with additional terms to account for the benefits produced by the interspecific interactions. These models have shortcomings as the so-called r-K formulation diverges under some conditions. In this work, we introduce a model for population dynamics under mutualism that preserves the original logistic formulation. It is mathematically simpler than the widely used type II models, although it shows similar complexity in terms of fixed points and stability of the dynamics. We perform an analytical stability analysis and numerical simulations to study the model behavior in general interaction scenarios including tests of the resilience of its dynamics under external perturbations. Despite its simplicity, our results indicate that the model dynamics shows an important richness that can be used to gain further insights in the dynamics of mutualistic communities.