Modeling bumble bee population dynamics with delay differential equations

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

Ecological Modelling, 2017, vol. 351, issue C, 14-23

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.

Keywords: Population models; Delay differential equations; Non-linear; Non-autonomous; Spline approximations; Bombus terrestris; Reproduction (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecomod:v:351:y:2017:i:c:p:14-23

DOI: 10.1016/j.ecolmodel.2017.02.011

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