Rethinking the logistic approach for population dynamics of mutualistic interactions

TL;DR

This paper introduces a new, simpler population dynamics model for mutualistic interactions that avoids singularities and offers clearer ecological interpretations, providing insights into community resilience and stability.

Contribution

The authors propose a novel logistic-inspired model for mutualism that is mathematically simpler, avoids divergence issues, and enhances ecological interpretability compared to existing models.

Findings

Model avoids singularities present in traditional logistic models.

Analytical and numerical analysis reveal complex stability behaviors.

Model demonstrates robustness under external perturbations.

Abstract

Mutualistic communities have an internal structure that makes them resilient to external per- turbations. 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 modifi- cations of the 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 of logistic equation diverges under some conditions. In this work, we introduce a model for population dynamics under mutualism inspired by the logistic equation but avoiding singularities. The model 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. Furthermore, each term of our model has a more direct ecological interpretation, which can facilitate the measurement of the rates involved in field campaigns. We perform an analytical stability analysis and numerical simulations to study the model behavior in more 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.