Negotiation of mutualism: rhizobia and legumes.

The evolution and persistence of biological cooperation have been an important puzzle in evolutionary theory. Here, we suggest a new approach based on bargaining theory to tackle the question. We present a mechanistic model for negotiation of benefits between a nitrogen-fixing nodule and a legume plant. To that end, we first derive growth rates for the nodule and plant from metabolic models of each as a function of material fluxes between them. We use these growth rates as pay-off functions in the negotiation process, which is analogous to collective bargaining between a firm and a workers' union. Our model predicts that negotiations lead to the Nash bargaining solution, maximizing the product of players' pay-offs. This work introduces elements of cooperative game theory into the field of mutualistic interactions. In the discussion of the paper, we argue for the benefits of such an approach in studying the question of biological cooperation.