Modeling bumble bee population dynamics with delay differential equations

Research output: Contribution to journalArticle


Bumble bees are ubiquitous creatures and crucial pollinators to a vast assortment of crops worldwide. Bumble bee populations have been decreasing in recent decades, with demise of flower resources and pesticide exposure being two of several suggested pressures causing declines. Many empirical investigations have been performed on bumble bees and their natural history is well documented, but the understanding of their population dynamics over time, causes for observed declines, and potential benefits of management actions is poor. To provide a tool for projecting and testing sensitivity of growth of populations under contrasting and combined pressures, we propose a delay differential equation model that describes multi-colony bumble bee population dynamics. We explain the usefulness of delay equations as a natural modeling formulation, particularly for bumble bee modeling. We then introduce a particular numerical method that approximates the solution of the delay model. Next, we provide simulations of seasonal population dynamics in the absence of pressures. We conclude by describing ways in which resource limitation, pesticide exposure and other pressures can be reflected in the model.


  • H. T. Banks
  • John E Banks
  • Riccardo Bommarco
  • A. N. Laubmeier
  • N. J. Myers
  • Maj Rundlöf
  • Kristen Tillman
External organisations
  • North Carolina State University
  • California State University
  • Swedish University of Agricultural Sciences
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Ecology


  • Bombus terrestris, Delay differential equations, Non-autonomous, Non-linear, Population models, Reproduction, Spline approximations
Original languageEnglish
Pages (from-to)14-23
Number of pages10
JournalEcological Modelling
Publication statusPublished - 2017 May 10
Publication categoryResearch