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Numerical responses in resource-based mutualisms: a time scale approach

In mutualisms where there is exchange of resources for resources, or resources for services, the resources are typically short lived compared with the lives of the organisms that produce and make use of them. This fact allows a separation of time scales, by which the numerical response of one species with respect to the abundance of another can be derived mechanistically. These responses can account for intra-specific competition, due to the partition of the resources provided by mutualists, in this way connecting competition theory and mutualism at a microscopic level. It is also possible to derive saturating responses in the case of species that provide resources but expect a service in return (e.g. pollination, seed dispersal) instead of food or nutrients. In both situations, competition and saturation have the same underlying cause, which is that the generation of resources occur at a finite velocity per individual of the providing species, but their depletion happens much faster due to the acceleration in growth rates that characterizes mutualism. The resulting models can display all the basic features seen in many models of facultative and obligate mutualisms, and they can be generalized from species pairs to larger communities. The parameters of the numerical responses can be related with quantities that can be in principle measured, and that can be related by trade-offs, which can be useful for studying the evolution of mutualisms. Abstract Keywords: mutualism, resources, services, steady-state, functional and numerical response

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