Plant-soil feedback theory aims to distill a lot of ecological complexity into a few coefficients that summarize the effects of different soil microbial communities on different plant species. By emphasizing the signs and relative strengths of pairwise interactions, this simplified framework provides a straightforward way to quantify the net plant-soil feedback and is thus ideal for integrating theory and experiment. Necessarily, it omits many details, like the effect of changes in the plant community on the population dynamics of different soil functional groups. Population dynamic models, on the other hand, consider functional interactions with soil pathogens and mutualists, thus allowing theoreticians to study the mechanisms underlying plant-soil feedbacks. However, these models generally make predictions (such as how microbial populations will change through time) that are much more difficult to test experimentally. Ultimately, both theoretical approaches have the same goal and complementary pros and cons. In this study, we characterize the relationships between the parameters (demographic and interaction rates) in population dynamic models and the coefficients used in feedback theory, in order to bridge these two complementary theoretical approaches.
Results/Conclusions
By applying standard stability analyses to a general population dynamic model for two plants and two soil functional groups (pathogens and mutualists), we derive conditions expected to lead to stable coexistence of all members of the community. We likewise derive an expression for the net plant-soil feedback in this model. We then compare the criteria for stable coexistence with the criteria for a net negative (stabilizing) plant-soil feedback. While the criteria are different, they contain common motifs – functions of the parameters that appear repeatedly – that allow us to understand more rigorously which mechanisms are accounted for in the calculation of net feedback. Furthermore, the criteria for a negative feedback resemble a subset of the criteria for stable coexistence, emphasizing that current plant-soil feedback theory gives necessary but not sufficient conditions for coexistence. Finally, our work enhances the links between population dynamics modeling and experiments by identifying aspects of the stability criteria that should change in predictable ways during the training and testing phases of many plant-soil feedback experiments.