Abstract
Honey bees (Apis mellifera) are increasingly in demand as pollinators for various key agricultural food crops, but globally honey bee populations are in decline, and honey bee colony failure rates have increased. This scenario highlights a need to understand the conditions in which colonies flourish and in which colonies fail. To aid this investigation we present a compartment model of bee population dynamics to explore how food availability and bee death rates interact to determine colony growth and development. Our model uses simple differential equations to represent the transitions of eggs laid by the queen to brood, then hive bees and finally forager bees, and the process of social inhibition that regulates the rate at which hive bees begin to forage. We assume that food availability can influence both the number of brood successfully reared to adulthood and the rate at which bees transition from hive duties to foraging. The model predicts complex interactions between food availability and forager death rates in shaping colony fate. Low death rates and high food availability results in stable bee populations at equilibrium (with population size strongly determined by forager death rate) but consistently increasing food reserves. At higher death rates food stores in a colony settle at a finite equilibrium reflecting the balance of food collection and food use. When forager death rates exceed a critical threshold the colony fails but residual food remains. Our model presents a simple mathematical framework for exploring the interactions of food and forager mortality on colony fate, and provides the mathematical basis for more involved simulation models of hive performance.
Highlights
A honey bee colony gathers dispersed floral resources from the environment to a central place, and processes them to provide food to support the current population and rearing of the cycles of brood
We proposed a simple mathematical model of honey bee population dynamics to explore the impact of varying forager death rate on colony growth and development [1]
For death rates above the critical death rate, m* the bee population goes extinct but stored food remains in the hive, even after all bees have died (Figure 2d). This is probably because the hive bee population and the brood rearing effort are so compromised that the population declines faster than residual food stores can be consumed
Summary
A honey bee colony gathers dispersed floral resources (pollen and nectar) from the environment to a central place, and processes them to provide food to support the current population and rearing of the cycles of brood. We proposed a simple mathematical model of honey bee population dynamics to explore the impact of varying forager death rate on colony growth and development [1] This model was a deliberate simplification to consider how interactions between adult foragers and hive bees and brood might influence colony growth. We present a new model to explore how changes in food availability might interact with behavioural and social processes in the colony to influence colony growth This issue is pertinent because the amount of honey that can be extracted from commercial bee hives for human use depends on bees collecting nectar in excess of what is needed to support their population, and storing the excess as honey. Recent concerns about the sustainability of bee populations [2] have highlighted a need to better understand how healthy colonies function, and why they may sometimes fail
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