Obligate mutualism in a resource-based framework

Abstract

Obligate mutualist interactions appear to be ubiquitous in nature but cannot be described by the simple models that have been so effective for developing the theory of other population interactions including competition, predation, mixotrophy, and facultative mutualism. We present a teaching framework that extends the standard Lotka--Volterra analysis of these interactions to the more complicated obligate mutualism. This provides a useful addition to applications of dynamical systems theory for mathematics students and an advanced course in population dynamics for ecology students. The theoretical framework used in this work is based on explicitly accounted resources and per capita rates of change for populations that are negative when they have no resources and positive when they have maximal resources. We extend the Lotka--Volterra models by including terms that capture the “catalytic" effect of obligation, reflecting that while one population may be necessary for survival of another, the obligated population does not necessarily consume it. A key attribute of our consumer-resource approach is that the catalytic services provided by obligate mutualists are treated as pseudoresources for the purposes of determining these rates of change. This framework allows all major ecosystem population interactions to be modeled within a single, simple consumer-resource framework, and it reveals how populations can smoothly change their trophic status through a continuum of stable coexistence states.