The Economic Forage Radius of a Honey Bee Colony: A Flight-Energy Bound on Net Gain per Trip

This paper computes, from a stated flight-energy budget, the distance at which a honey bee forage trip stops paying for itself. The study is simulated, not measured. A forager carrying 40 mg of nectar, flying at a cost of 12.0 J per kilometre each way and paying a fixed handling cost of 15.0 J per trip, breaks even at a one-way distance of 4.94 km when the nectar contains 20% sugar, 7.72 km at 30% sugar, 10.51 km at 40% sugar and 13.29 km at 50% sugar. Defining a working radius as the distance at which net gain per trip has fallen to half of its zero-distance value gives 3.86 km at 30% sugar and 5.25 km at 40% sugar. At three miles (4.83 km) a 30% trip returns only 37.5% of its maximum net gain. Although the land beyond three miles is 60.9% of the area inside the 30% break-even circle, it contributes only 31.6% of the area-weighted net gain. Dilute nectar therefore does not support the familiar claim that a colony uses everything within three miles in any economically equal sense: at 20% sugar a three-mile trip returns almost nothing, and at every concentration studied the far annulus contributes far less than its share of the land.