Professor University of California, Los Angeles Los Angeles, California, United States
Abstract: Plant-mycorrhizal interactions are among the most ubiquitous of terrestrial mutualisms. Recent years have seen a steady increase in both theoretical and empirical studies of how plant-mycorrhizal relationships arise, function, and persist. While theory on plant-mycorrhizal interactions and mutualisms in general have yielded important predictions about their population dynamics, such as the existence of thresholds below which positive density-dependence leads to extinction (“Allee thresholds”), they remain difficult to test empirically. Here, we attempt to address this gap in our knowledge by developing a mechanistic model of the plant-mycorrhizal interaction, in which the dynamical behavior is determined by a suite of directly measurable parameters. We use a framework that (i) combines the facilitative (e.g., benefits conferred on the partner) and the antagonistic (e.g., benefits extracted from the partner) elements of plant-mycorrhizal interaction and (ii) includes explicit nutrient-plant interactions via a mass balance constraint. We explore our model with a combination of analytical and numerical approaches to elucidate how key parameters of the nutrient-plant-mycorrhizal community drive the emergent dynamics of the interaction.
Our model not only recovers the same qualitative behaviors characteristic of consumer-resource and mutualistic interactions (biomass oscillations and partner Allee thresholds, respectively), but also provides a basis for predicting the dynamics of real plant-mycorrhizal interactions based on a few key parameters that describe the facilitative and antagonistic aspects of the interaction. We find that the dynamical behavior and associated stability properties of a system are strictly governed by the net effect of the mycorrhizae on the plant species’ equilibrium biomass. In particular, this framework allows us to investigate an interaction’s susceptibility to both stochastic extinction (due to periodic low biomass arising from oscillatory consumer-resource dynamics) and deterministic extinction (due to positive density dependence inherent in the facilitative interaction) as a function of this equilibrium biomass effect. We examine how different parameter combinations influence these extinction pathways and demonstrate the utility of our framework as a diagnostic tool for empirical investigations of plant-mycorrhizal community dynamics. For example, our model can be applied to determine the minimum plant and mycorrhizal biomass necessary to exceed the Allee threshold of an interaction when restoring a plant community so that both species may establish successfully. Finally, we compare these properties to other mutualisms (i.e., plant-pollinator interactions), and discuss how the tension between the different constituent feedbacks within the plant-mycorrhizal interaction may resolve in the emergent structure of more speciose communities.
