Graph and circuit theory connectivity models of conservation biological control agents.

The control of agricultural pests is an important ecosystem service provided by predacious insects. In Midwestern USA, areas of remnant tallgrass prairie and prairie restorations may serve as relatively undisturbed sources of natural predators, and smaller areas of non-crop habitats such as seminatural areas and conservation plantings (CP) may serve as stepping stones across landscapes dominated by intensive agriculture. However, little is known about the flow of beneficial insects across large habitat networks. We measured abundance of soybean aphids and predators in 15 CP and adjacent soybean fields. We tested two hypotheses: (1) landscape connectivity enhances the flow of beneficial insects; and (2) prairies act as a source of sustaining populations of beneficial insects in well-connected habitats, by using adaptations of graph and circuit theory, respectively. For graph connectivity, incoming fluxes to the 15 CP from connected habitats were measured using an area- and distance-weighted flux metric with a range of negative exponential dispersal kernels. Distance was weighted by the percentage of seminatural area within ellipse-shaped landscapes, the shape of which was determined with correlated random walks. For circuit connectivity, effective conductance from the prairie to the individual 15 CP was measured by regarding the flux as conductance in a circuit. We used these two connectivity measures to predict the abundance of natural enemies in the selected sites. The most abundant predators were Anthocoridae, followed by exotic Coccinellidae, and native Coccinellidae. Predator abundances were explained well by aphid abundance. However, only native Coccinellidae were influenced by the flux and conductance. Interestingly, exotic Coccinellidae were negatively related to the flux, and native Coccinellidae were highly influenced by the interaction between exotic Coccinellidae and aphids. Our area- and distance-weighted flux and the conductance variables showed better fit to field data than area-weighted flux or Euclidean distance from the prairie. These results indicate that the network of seminatural areas has greater influence on the flow of native predators than that of exotic predators, and that the prairie acts as a source for native Coccinellidae. Managers can enhance conservation biocontrol and sustain the diversity of natural enemies by optimizing habitat networks.