Search for: All records

In this paper, we use an adaptive modeling framework to model and study how nutritional status (measured by the protein to car- bohydrate ratio) may regulate population dynamics and foraging task allocation of social insect colonies. Mathematical analysis of our model shows that both investment to brood rearing and brood nutri- tion are important for colony survival and dynamics. When division of labour and/or nutrition are in an intermediate value range, the model undergoes a backward bifurcation and creates multiple attrac- tors due to bistability. This bistability implies that there is a threshold population size required for colony survival. When the investment in brood is large enough or nutritional requirements are less strict, the colony tends to survive, otherwise the colony faces collapse. Our model suggests that the needs of colony survival are shaped by the brood survival probability, which requires good nutritional status. As a consequence, better nutritional status can lead to a better survival rate of larvae and thus a larger worker population. 

Western honeybees (Apis Mellifera) serve extremely important roles in our ecosystem and economics as  they are responsible for pollinating $ 215 billion dollars annually over the world.  Unfortunately,  honeybee population and their colonies have been declined dramatically. The purpose of this article is to explore how we should model honeybee population with age structure and validate the model using empirical data so that we can identify different factors that lead to the survival and healthy of the honeybee colony.  Our theoretical study combined with simulations and data validation suggests that the proper age structure incorporated in the model  and seasonality are important for modeling honeybee population.  Specifically, our work implies that the model assuming that (1) the adult bees are survived from the egg population rather than the brood population; and (2) seasonality in the queen egg laying rate, give the better fit than other honeybee models. The related theoretical and numerical analysis of the most fit model indicate that (a) the survival of honeybee colonies requires a large queen egg-laying rate and smaller values of the other life history parameter values in addition to proper initial condition; (b) both brood and adult bee populations are increasing with respect to the increase in the egg-laying rate and the decreasing in other parameter values; and (c) seasonality may promote/suppress the survival of the honeybee colony.