Multiple classes of interactions may exist affecting one another in a given system. For the mutualistic networks of plants and pollinating animals, it has been known that the degree distribution is broad but often deviates from power-law form more significantly for plants than animals. To illuminate the origin of such asymmetry, we study a model network in which links are assigned under generalized preferential-selection rules between two groups of nodes and find the sensitive dependence of the resulting connectivity pattern on the model parameters. The nonlinearity of preferential selection can come from interspecific interactions among animals and among plants. The model-based analysis of real-world mutualistic networks suggests that a new animal determines its partners not only by their abundance but also under the competition with existing animal species, which leads to the stretched-exponential degree distributions of plants.

Nutrients from a flowering plant are shared by its pollinators, giving rise to competition in the latter. Such exploitative competition of pollinators can limit their abundance and affect the global organization of the mutualistic partnership in the plant-pollinator mutualistic community. Here we investigate the effects of the exploitative competition between pollinators on the structure and the species abundance of the mutualistic networks which evolve by changing mutualistic partnership towards higher abundance of species. Simulations show different emergent network characteristics between plants and animals; hub plants connected to many pollinators are very rare while a few super-hub pollinators appear with the exploitative competition included, in contrast to equally many hubs of both types without the exploitative competition. More interestingly, the abundance of plant species increases with increasing the exploitative competition strength. We analyze the inverse of the generalized interaction matrix in the weak-interaction limit to identify the leading structural factors relevant to the species abundance, which are shown to be instrumental in optimizing the network structure to increase the mutualistic benefit and lower the cost of exploitative competition.