An approach to the modeling of honey bee colonies

In this work, populations of adult and immature honeybees and their honey production are studied through mathematical and statistical modeling approaches. Those models are complementary and are presented in disjunct form. They were used to show different modeling methods for honey bee population dynamics. The statistical approach consisted of a generalized linear model using data from the Department of Agriculture of the United States of America (USDA), which showed that the relationship between the number of colonies and the rate of honey production is not constant in time but decrease over the years. These models showed that when a bee population is subjected to a stress factor (i.e., habitat destruction, Varroa mite, climate variability, season, neonicotinoids, among others), the abundance of individuals decreases over time as well as the honey produced by the colonies. Finally, the mathematical approach consisted of two models: (1) a smooth model, in which conditions of existence and stability of the equilibrium solutions are determined by an ecological threshold value, and (2) a non-smooth model where the mortality rate of bees is included as a function of the number of adult bees in the population.