Modelling Food and Population Dynamics in Honey Bee Colonies

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.

Rapid behavioral maturation accelerates failure of stressed honey bee colonies

“…Several earlier models of honey bee colony population dynamics have been developed (34,35,(43)(44)(45)(46). Of these, the most relevant studies are those of Schmickl and Crailsheim (46), Makela et al (45), and Khoury et al (35), which have all modeled how changes in food and mortality can influence colony growth.…”

Resistance to nutritional stress in ants: when being fat is advantageous

“…Under natural conditions, this behaviour might translate to reduced brood care, less defence or poorer hygiene. Some recent theoretical papers (Khoury et al, 2011(Khoury et al, , 2013Russell et al, 2013) investigating colony collapse disorder (CCD), strongly suggest that high mortality rate in honeybee foragers increases the pressure on colony population, affecting its growth and, by extension, could be responsible for colony decline. Their model predicts that above a certain forager death rate, colony population would decrease dramatically and colony failure would become inevitable.…”

How to know which food is good for you: bumblebees use taste to discriminate between different concentrations of food differing in nutrient content

“…Like all other animals, bees need the right amount and composition of resources to raise their brood (Keller et al, 2005;Khoury et al, 2013) and to maintain colony health (Brodschneider and Crailsheim, 2010). Proteins and carbohydrates, and to a lesser extent lipids, represent important macronutrients for all herbivorous and pollinivorous insects, including bees (Friend, 1958).…”