Modelling risk of competitive effects from honeybees on wild bees

Abstract This paper suggest an area model to assess the risk of negative effects on wild bees due to food competition from honeybees. The model includes four factors: (1) the total number of foraging visits by honeybees per day; (2) the foraging range of the honeybees, typically measured as a mean or median value; (3) the area covered by floral resources in the landscape; (4) the tolerable competitive pressure posed by honeybees, i.e. the no effect intensity of foraging honeybees per flowering area below which adverse effects on wild bees due to competition will not occur. However, the need of knowing the foraging range (factor 2) is eliminated in the final model using a worst-case approach. As the honeybees from an apiary disperse into the landscape, the distance between the honeybees increases, leading to a decrease in the competitive pressure. Close to the apiary, the competition may exceed the no effect level, leading to the risk of negative effects on wild pollinators, while the competition will decrease below the no effect level further away from the apiary. The model predicts the distance from the apiary needed to keep the density of foraging honeybees below no effect level to avoid competition with wild bees. In spite of rather high spatial complexity, the final model becomes simple and defines a load factor as a ratio between the number of foraging trips and the carrying capacity of the landscape.