Abstract: In mutualism studies, we often fail to acknowledge how the complexity of multispecies networks influences the outcomes of symbiosis. When a mutualism is external to the ‘host’ organism, it opens the door to both partners interacting with numerous alternative sources for the resources they seek. For example, in the symbiosis between ectomycorrhizal fungi and woody plants, trees can host multiple species of fungi which may provide variable benefits in different conditions. The fungi, in turn, may associate with multiple trees or tree species. This presents a series of challenging coexistence questions. What ecological and evolutionary pressures stabilize or destabilize these mutualism networks? Which conditions allow participants in mutualism networks to cheat off of their neighbors or be cheated themselves? How stingy should members be with their resources if maintaining multiple partners is safer in the face of environmental change? In this study, we develop and analyze a mathematical model consisting of a system of ordinary differential equations describing the exchange of resources between tree and fungi. This framework allows us to quantify the benefits (or costs) of shared partners and determine how fungal partner traits can impact the stability of the mutualism. First, we test the hypothesis that trees in a shared network, where fungi distribute resources to multiple host trees, will support a greater number of fungal partners. We find that two trees with shared fungal partners reach a critical nutrient threshold at levels up to 50% lower and will always increase their number of symbionts more quickly as a function of resource need. Second, we test how partner allocation strategies influence network stability. We find that when fungi allocate resources indiscriminately, trees with different photosynthetic capacities may coexist but that as the flow of nutrients becomes more responsive to a fungus’s experienced return on investment, lower-productivity trees will collapse as their productivity rate approaches 1.5 times their maintenance cost. These types of imperfect partner control may be important for susceptibility of the system to environmental perturbations or rapid change. Thus, our mathematical framework leads to testable predictions of the environmental circumstances and partner traits that may allow for the evolution of partner sharing in multispecies mutualisms.
