Banks, H.T., J.E. Banks, Riccardo Bommarco, Maj Rundlof, and Kristen Tillman. 2016. Modeling Bumble Bee Center for Research in Scientific Computation, North Carolina State University Raleigh, NC USA
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 ower 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 over ordinary differential equations, particularly for bumble bee modeling. We then describe 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, neonicotinoids
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