Modeling Honey Bee Colonies in Winter Using a Keller--Segel Model With a Sign-Changing Chemotactic Coefficient

Robbin Bastiaansen, Arjen Doelman, Frank Van Langevelde, Vivi Rottschafer

Research output: Contribution to journalArticleAcademicpeer-review


Thermoregulation in honey bee colonies during winter is thought to be self-organized.
We added mortality of individual honey bees to an existing model of thermoregulation as an approach
to model the elevated losses of bees that are reported worldwide. The aim of this 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 toward 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 behavior may help
explain the globally observed honey bee colony losses during winter.
Original languageEnglish
Pages (from-to)839-863
JournalSIAM Journal on Applied Mathematics
Issue number2
Publication statusPublished - 2020


  • thermoregulation
  • ecology
  • spatial self-organization


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