A simple and bounded model of population dynamics in mutualistic networks

Juan Manuel Pastor1,2, Javier García-Algarra1, Javier Galeano1,2, 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.

(March 2015)

Dynamic population models are based on the Verhulst's equation (logisitic equation), where the classic Malthusian growth rate is damped by intraspecific competition terms. Mainstream population models for mutualism are modifications of the logistic equation with additional terms to account for the benefits produced by the interspecies interactions. These models have shortcomings as the population divergence under some conditions (May's equations) or a mathematical complexity that difficults their analytical treatment (Wright's type II models). In this work, we introduce a model for the population dynamics in mutualism inspired by the logistic equation but cured of divergences. The model is also mathematically more simple than the type II. We use numerical simulations to study the model stability in more general interaction scenarios. Despite its simplicity, our results suggest that the model dynamics are rich and may be used to gain further insights in the dynamics of mutualistic interactions.