Modeling the Interaction Dynamics between Honeybees and Food Availability

Abstract

The success of honeybee (Apis mellifera) colonies is critical to the United States agriculture with 35% of American diets dependent on honeybee pollination. There are various complex factors that can contribute to a colony’s failure, such as nutritional stress. Nutritional stressors primarily pertain to food scarcity, lack in diversity of food, and the availability of food with low nutritional value. In this work, we use a mathematical model to investigate the impact of food scarcity and limited storage space on honeybee viability, early recruitment rates of workers into foragers, and the influence of these rates on the growth of a colony. Social inhibition of honeybee pollination is described through the role change between foragers and workers. A threshold was found for conditions when a colony persists or collapses. We obtained conditions for the coexistence of a honeybee population and food supply as well as coexistence conditions in fluctuation fashion. Our sensitivity analysis showed that a honeybee colony is most sensitive to changes in the rate at which a worker bee encounters food and the rate food is entering the food supply.