Patterns of nestedness and specialization asymmetry, where specialist speciesinteract mainly with generalists while generalists interact with bothgeneralists and specialists, are often observed in mutualistic and antagonisticbi-partite ecological networks. These have been explained in terms of therelative abundance of species, using a null model that assigns links inproportion to abundance, but doubts have been raised as to whether this offersa complete explanation. In particular, host-parasite networks offer a varietyof examples in which the reverse patterns are observed. We propose that the link between specificity and species-richness may also bedriven by the co-evolution of hosts and parasites, as hosts allocate resourcesto optimize defence against parasites, and parasites to optimize attack onhosts. In this hypothesis, species interactions are a result of resourceallocations. This novel concept, linking together many different arguments fornetwork structures, is introduced through the adaptive dynamics of a simpleecological toy system of two hosts and two parasites. We analyse the toy model and its functionality, demonstrating thatco-evolution leads to specialization asymmetry in networks with closely relatedparasites or fast host mutation rates, but not in networks with more distantlyrelated species. Having constructed the toy model and tested its applicability,our model can now be expanded to the full problem of a larger system.
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