The Spatial Distribution of Colonial Food Provisioners

We present spatially explicit models to predict the optimal distribution of numerous food provisioners that share a nesting aggregation. We compare predictions for solitary and social provisioners, and for three foraging currencies. When distinct food patches with identical food parameters are considered, fewer provisioners use the farther patches. The rate of decline in number of provisioners depends on the currency used. With net rate of energy intake (net energy gain over time), the rate of decline is relatively small under a wide range of realistic parameter values and distances; with efficiency (net energy gain over energy cost) and empirically derived energetic costs, the rate of decline is much higher. With lifetime fitness (lifetime food delivery under predation risk), outcomes depend on the ratio of mortality risk during flight and during food collection at the patch. With all currencies, there is a difference between the optimal spatial distribution of solitary and social provisioners, with a larger proportion of social provisioners being farther from the central place. The optimal distribution of solitary provisioners in a two dimensional field of uniformly distributed food such as a flowering meadow is such that the density of solitary provisioners (number per unit area) declines monotonically with distance, and provisioner number peaks at half the maximum area used.