Mathematical Modeling of Multispecies Mutualism: From Particular Models Toward a Generalization of the Concept

Mutualism refers to any species interaction in which the presence of one species benefits the others. While many specific models of two-species mutualism have been developed and analyzed, comparatively, more attention has been devoted to antagonistic interactions among species (i.e., predation and competition). However, recent work revisited the problem of modeling mutualistic interactions with a focus on two basic objectives: an attempt at unifying existing particular models into a smaller set of general models and at providing a qualitative analysis of their solutions in order to reveal the fundamental role of mutualism in the dynamics of the population under consideration. In this chapter we provide an overview on the most important results concerning general models of mutualism. In particular, we place the development of these models in the general context of establishing realistic “building blocks” in ecological models. To this end, particular attention is paid on the mathematical conditions necessary to separate bounded solutions from unbounded ones and, whenever possible, on the conditions leading to a unique, globally stable, coexistence equilibrium. We show how these results can be extended to an unspecified number of mutualistic species and how one can identify a subset of these species most likely to cause unbounded solutions. Last but not least, we argue for the importance of developing general models with carefully selected assumptions that are not too restrictive but, at the same time, still useful in potential experimental research.