  Patterns of nestedness and specialization asymmetry, where specialist species
interact mainly with generalists while generalists interact with both
generalists and specialists, are often observed in mutualistic and antagonistic
bi-partite ecological networks. These have been explained in terms of the
relative abundance of species, using a null model that assigns links in
proportion to abundance, but doubts have been raised as to whether this offers
a complete explanation. In particular, host-parasite networks offer a variety
of examples in which the reverse patterns are observed.
  We propose that the link between specificity and species-richness may also be
driven by the co-evolution of hosts and parasites, as hosts allocate resources
to optimize defence against parasites, and parasites to optimize attack on
hosts. In this hypothesis, species interactions are a result of resource
allocations. This novel concept, linking together many different arguments for
network structures, is introduced through the adaptive dynamics of a simple
ecological toy system of two hosts and two parasites.
  We analyse the toy model and its functionality, demonstrating that
co-evolution leads to specialization asymmetry in networks with closely related
parasites or fast host mutation rates, but not in networks with more distantly
related species. Having constructed the toy model and tested its applicability,
our model can now be expanded to the full problem of a larger system.
