The dynamics of market mutualisms.
Umbanhowar, James*,1, Hoeksema, Jason2, Schwartz, Marc3, 1 University of Guelph, Guelph, ON, Canada2 University of California, Santa Cruz, Santa Cruz, CA, USA3 University of California, Davis, Davis, CA, USA
ABSTRACT- We synthesize two previously studied models of mutualism: the economic theory of resource trading and the resource based population dynamics of mutualism. This synthesis fills in gaps in both theory. The economic theory assumed that environment and densities of the mutualists remained static, while the resource based dynamics assumed either a static trade price or that one mutualist has full control of the interaction. The model we develop assumes that trade and specialization occurs on a short timescale compared to growth and resource depletion in the environment. Our approach generates predictions about resource trading mutualisms that neither framework did, alone. The purely economic approach predicts specialization and trade will occur even when one of the mutualists is inferior in uptake of both nutrients, while adding dynamics reveals that such associations will not last as the superior nutrient forager will outcompete the poorer. Dynamically, the pure trading behavior of the mutualists prevents parasitism arising in situations of high availability of one nutrient, in contrast to the situation with fixed costs. However, such changes in nutrient availability do have significant effects on the amount of trade, suggesting what the strength of mutualisms are likely to be in nature. Finally, we demonstrate how to incorporate a form of cheating into the economic framework and how to calculate the cost of policing for cheaters in this framework.
Key words: mutualism, resource trade, population dynamics, cheating
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