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Modeling bumble bee population dynamics with delay differential equations

Banks, H. T.; Banks, John E; Bommarco, Riccardo LU ; Laubmeier, A. N.; Myers, N. J.; Rundlöf, Maj LU and Tillman, Kristen (2017) In Ecological Modelling 351. p.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... (More)

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.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Bombus terrestris, Delay differential equations, Non-autonomous, Non-linear, Population models, Reproduction, Spline approximations
in
Ecological Modelling
volume
351
pages
10 pages
publisher
Elsevier
external identifiers
  • scopus:85014234759
ISSN
0304-3800
DOI
10.1016/j.ecolmodel.2017.02.011
language
English
LU publication?
yes
id
0acc7333-b24a-4fc8-81a3-27304ca6ebd4
date added to LUP
2017-03-14 10:41:06
date last changed
2017-05-24 15:02:13
@article{0acc7333-b24a-4fc8-81a3-27304ca6ebd4,
  abstract     = {<p>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.</p>},
  author       = {Banks, H. T. and Banks, John E and Bommarco, Riccardo and Laubmeier, A. N. and Myers, N. J. and Rundlöf, Maj and Tillman, Kristen},
  issn         = {0304-3800},
  keyword      = {Bombus terrestris,Delay differential equations,Non-autonomous,Non-linear,Population models,Reproduction,Spline approximations},
  language     = {eng},
  month        = {05},
  pages        = {14--23},
  publisher    = {Elsevier},
  series       = {Ecological Modelling},
  title        = {Modeling bumble bee population dynamics with delay differential equations},
  url          = {http://dx.doi.org/10.1016/j.ecolmodel.2017.02.011},
  volume       = {351},
  year         = {2017},
}