  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
