Patterns of specialization asymmetry, where specialist species interact mainly with generalists while generalists interact with both generalists and specialists, are often observed in mutualistic and antagonistic bipartite 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 coevolution of hosts and parasites, as hosts allocate resources to optimize defense 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 analyze the toy model and its functionality, demonstrating that coevolution 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.