From subtle to substantial: a stage-structured matrix population model for predicting combined roles of nutrition and pesticides on honey bee colony health

In a healthy honey bee colony, individuals act as cooperative vehicles for colony growth and development and their actions often rely on a network of self-organizing behaviors via a series of highly elastic feedbacks to achieve stability and optimal fitness. This system is driven by the initial population size, queen fertility, demographic structure of workers, space availability, and nutrition status (Seeley, 1995). A Worker-based, Birth-pulse, Stage-structured Matrix Population Model is developed to examine how subtle changes at the individual level by negative stressors from nutrition and/ or pesticide singly or simultaneously results in substantial outcomes at the colony level. Parameter estimates. The model is formulated by the delayed differential equations consisting of six discrete stages based on the within-nest temporal polytheism: egg, larva, pupa, nurse bee, house bee, forager. The individual demographic parameters, such as individual-stage survival rate, queen egg-laying rate and the transition matrix for each stage, are derived from experimental observations and life tables of honey bee populations in the published literatures (Sakagami, 1968; Winston, 1981). Numerical solutions of the model demonstrate how inadequate nutrition in both quality and quantity can progressively destabilize one or more stages of this system, eventually altering colony dynamics.