Background/Question/Methods   Mutualisms are ubiquitous, yet our understanding of their functioning is hindered by the complexities introduced by their context dependence. Many terrestrial plants engage in a symbiosis with mycorrhizal fungi, but the degree of benefit gained by symbionts is variable. Plant and fungal gain from trade appears to depend on the traits of the partners, such as the inherent resource uptake efficiencies or resource demands of the participating species. Environmental characteristics, such as relative abundance of plants and fungi and the availability of the resources traded, are also known to be important in determining the mutualistic, commensal, or parasitic outcome of trade. We model trade with relative advantage between plants and mycorrhizal fungi, allowing partners to adjust their allocation to direct uptake of carbon or a soil nutrient to maximize fitness. Plants and fungi negotiate the price at which they should exchange the two resources to maximize joint benefit using a Nash Bargaining Solution. We then examine how the price and degree of benefit gained through trade by the two partners depends on the traits of the participating species and on environmental characteristics.

Results/Conclusions   We find that one partner or the other limits trade, depending on the species traits and environmental characteristics. The partner limiting trade allocates completely towards taking up the resource it trades away, becoming a specialist on that resource. The other partner is a generalist, directly taking up both carbon and the soil nutrient. When the fungus limits trade, it maximizes uptake of nutrient and eliminates direct carbon uptake, specializing on nutrient uptake and depending on trade for carbon. Fungi tend to limit trade when both partners have low carbon:nutrient ratios, when fungal nutrient uptake is slow, or when fungi are less abundant than plants. Plants limit trade in other contexts. Given this dependence of the limiting, specialist partner on traits and the environment, we see that species with more efficient resource use and uptake generally gain less from trade. We also see familiar patterns of plant and fungal gain from trade across environmental gradients when we mimic the relative abundance of carbon and nutrient. The negotiated exchange rate also responds to species traits and the environment. This model of trade clarifies some of the drivers of context dependency in the plant-mycorrhizal symbiosis and suggests new empirical work.