Expanding comparative-advantage biological market models: contingency of mutualism on partners' resource requirements and acquisition trade-offs

We expand the comparative-advantage biological market-modelling framework to show how differences between partners, both in their abilities to acquire two resources and in their requirements for those resources, can affect the net benefit of participating in interspecific resource exchange. In addition, the benefits derived from resource trading depend strongly on the nature of the trade-off between the acquisition of one resource and the acquisition of another, described here by the shape (linear, convex or concave) of the resource acquisition constraints of the individuals involved. Combined with previous results, these analyses provide a suite of predictions about whether or not resource exchange is beneficial for two heterospecific individuals relative to a strategy of non-interaction. The benefit derived from resource exchange depends on three factors: (i) relative differences between the partners in their resource acquisition abilities; (ii) relative differences between the partners in their resource requirements; and (iii) variation in the shape of resource acquisition trade-offs. We find that such an explicit consideration of resource requirements and acquisition abilities can provide useful and sometimes non-intuitive predictions about the benefits of resource exchange, and also which resources should be traded by which species.