Rethinking the logistic approach for population dynamics of mutualistic interactions

Abstract

We introduce a new population dynamics model for mutualistic communities. The new model preserves the original logistic formulation. We perform an analytical stability analysis to study the model behavior. We perform numerical simulations to test the model behavior. The model shows as much richness or even more than other mutualistic models. a r t i c l e i n f o t r a c tMutualistic 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 À 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 À 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.

The effect of multiple biotic interaction types on species persistence

“…to a population dynamics model based on the recent extensions to the logistic growth equation by García‐Algarra et al. (). Their formulation averts a known divergent behavior of the r‐k classic form of the logistic equation and is sufficiently simple while being able to reproduce the complexity of more elaborate models in terms of fixed points and stabillity of the dynamics.…”

Biological interactions and cooperative management of multiple species

“…Consequently, it was feasible to quantify management outcomes in a reasonable amount of computing time. Third, the type II functional response is sufficiently generally applicable in describing various interactions within ecosystems [8,21,22]. …”

Pattern formation induced by intraspecific interactions in a predator-prey system

“…We use a generalized model of population dynamics, based on a modified version of García-Algarra et al population dynamics model [10,11], which bounds mutualistic behavior (otherwise unlimited) by saturation Verhulst-like terms. The functionals of a two species system are described with the following equations, in dimensionless form (see A):…”