New Approach to Modeling Symbiosis in Biological and Social Systems

TL;DR

This paper introduces a nonlinear framework for modeling symbiosis in biological and social systems, capturing various interaction types and analyzing complex dynamical behaviors including coexistence, oscillations, and regime shifts.

Contribution

It presents a unified nonlinear approach to model different symbiosis types, extending beyond traditional linear models, and analyzes their dynamical regimes and bifurcations.

Findings

Multiple dynamical regimes identified, including coexistence and oscillations.

Bifurcation analysis reveals how parameter changes affect system behavior.

Unified scheme encompasses mutualism, commensalism, and parasitism.

Abstract

We suggest a novel approach to treating symbiotic relations between biological species or social entities. The main idea is the characterisation of symbiotic relations of coexisting species through their mutual influence on their respective carrying capacities, taking into account that this influence can be quite strong and requires a nonlinear functional framework. We distinguish three variants of mutual influence, representing the main types of relations between species: (i) passive symbiosis, when the mutual carrying capacities are influenced by other species without their direct interactions; (ii) active symbiosis, when the carrying capacities are transformed by interacting species; and (iii) mixed symbiosis, when the carrying capacity of one species is influenced by direct interactions, while that of the other species is not. The approach allows us to describe all kinds of symbiosis, mutualism, commensalism, and parasitism within a unified scheme. The case of two symbiotic species is analysed in detail, demonstrating several dynamical regimes of coexistence, unbounded growth of both populations, growth of one and elimination of the other population, convergence to evolutionary stable states, and everlasting population oscillations. The change of the dynamical regimes occurs by varying the system parameters characterising the destruction or creation of the mutual carrying capacities. The regime changes are associated with several dynamical system bifurcations.