MODELING THE INTERACTION DYNAMICS BETWEEN HONEYBEES AND FOOD AVAILABILITY
Carlos Cruz1, Matthew Baca2, Armando Salinas3, Carlos Agrinsoni-Santiago4, Baojun Song5.
1Loyola Marymount University, Los Angeles, CA, 2New Mexico Institute of Mining and Technology, Socorro, NM, 3School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 4University of Puerto Rico in Cayey, Cayey, PR, 5Montclair State University, Montclair, NJ.
The success of honeybee (Apis mellifera) colonies is critical to U. S. 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. Previous mathematical models have examined the impact of nutrition and the early recruitment on honeybee population dynamics. These models do not include the impact of a food supply with a limited storage space within a single hive. 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. A threshold, Rd, was found for conditions when a colony will persist or collapse. We found conditions for the stable coexistence of a honeybee population and food supply as well as conditions for periodic behavior. Through sensitivity analysis we find 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. There are no qualitative differences between using a Holling type I or Holling type II functional response in honeybee population persistence when modeling the interaction between a honeybee colony and the availability of food.