How Many Colonies a Landscape Carries: A Stocking-Rate Bound from Seasonal Sugar Production and Colony Demand

This paper computes an upper stocking-rate bound for honey bee colonies from the seasonal sugar production of three named forage types, a stated harvestable fraction, and a stated seasonal demand per colony. The study is simulated, not measured. Assuming that 20% of produced sugar is actually collected, that a colony consumes 60 kg of sugar in a season, and that one colony can collect at most 110 kg of sugar so that its surplus above its own demand is capped at 50 kg, the density at which per-colony surplus falls to half of its single-colony value is 35.3 colonies per square kilometre on oilseed rape, 18.8 on clover and 7.1 on wildflower meadow. The density at which colonies merely break even, collecting exactly what they consume, is 50.0 colonies per square kilometre on oilseed rape, 26.7 on clover and 10.0 on wildflower meadow. These are energetic ceilings for landscapes composed entirely of the named forage, not recommended stocking rates: mixed landscapes, disease, weather and competition from other pollinators all push the supportable density below them, and on meadow the ceiling is low enough that a modest apiary can approach it.