Thermoregulation in honey bee colonies during winter is thought to be
self-organised. We added mortality of individual honey bees to an existing
model of thermoregulation to account for elevated losses of bees that are
reported worldwide. The aim of analysis is to obtain a better fundamental
understanding of the consequences of individual mortality during winter. This
model resembles the well-known Keller-Segel model. In contrast to the often
studied Keller-Segel models, our model includes a chemotactic coefficient of
which the sign can change as honey bees have a preferred temperature: when the
local temperature is too low, they move towards higher temperatures, whereas
the opposite is true for too high temperatures. Our study shows that we can
distinguish two states of the colony: one in which the colony size is above a
certain critical number of bees in which the bees can keep the core temperature
of the colony above the threshold temperature, and one in which the core
temperature drops below the critical threshold and the mortality of the bees
increases dramatically, leading to a sudden death of the colony. This model
behaviour may explain the globally observed honey bee colony losses during
winter.Comment: 20 pages, 12 figure