Modeling bumble bee population dynamics with delay differential equations

H. T. Banks, John E Banks, Riccardo Bommarco, A. N. Laubmeier, N. J. Myers, Maj Rundlöf, Kristen Tillman

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)14-23
Number of pages10
JournalEcological Modelling
Volume351
DOIs
Publication statusPublished - 2017 May 10

Subject classification (UKÄ)

  • Ecology

Free keywords

  • Bombus terrestris
  • Delay differential equations
  • Non-autonomous
  • Non-linear
  • Population models
  • Reproduction
  • Spline approximations

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