Mutualisms are ubiquitous in nature, provide important ecosystem services, and involve many species of interest for conservation. Theoretical progress on the population dynamics of mutualistic interactions, however, has comparatively lagged behind that of trophic and competitive interactions. As a result, ecologists still lack a generalized framework to investigate the population dynamics of mutualistic interactions. Previous models of mutualisms have been criticized for generating unrealistic outcomes, relying on phenomenological derivations, or being too case-specific such that they are difficult to generalize. Here, we propose a generalizable modeling framework for two-species mutualisms using systems of ordinary differential equations. We focus on nutritional, protection, and transportation mechanisms which can be applied to a variety of specific mutualistic contexts. We then investigate the dynamical consequences of increasing mechanistic detail in the models. In particular, we study the benefits and costs of mutualisms more mechanistically than has been done in previous work. Finally, for each system, we discuss the modeling assumptions (both mathematical and biological) and analyze the dynamical behavior and outcomes.
Results/Conclusions
We develop three models that highlight system-specific examples of mutualistic mechanisms. Our first model uses purely nutritional mechanisms to describe exchange of food resources between, for example, plants and mycorrhizae. Our second model uses protection mechanisms that reduce mortality via fear or direct consumption effects inspired by ant-acacia and ant-aphid interactions. Our third model uses transportation mechanisms from pollination and seed dispersal interactions to describe the dependence of seed production or recruitment on animals’ visitation rate assuming that visits are proportional to animal abundance. Despite resulting from different biological mechanisms, our models show qualitatively similar behavior in many parameter spaces, including a single stable coexistence equilibrium and threshold effects. Thresholds occur in all three of our models when both partners are obligate mutualists, and in the transportation model even when both partners are facultative. Finally, we show cases in which “costs” of mutualistic interactions can be incorporated into per-capita birth and death rates without loss of generality.