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Separation of
scales in an integrodifference equation model of
metapopulation dispersal and homing predicts changes in
equilibria
Jacob P. Duncan, Roger Janusiak and Laura Kloepper |
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Vol. 17 (2024), No. 3, 481–502
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Abstract |
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We develop an integrodifference equation (IDE) model of a metapopulation in a system of point-patch habitats wherein movement between patches (roosts) is characterized by a two-stage dispersal process transpiring at discrete time steps, e.g., diurnally. In the first stage (dispersal), individuals disperse out of their current patch onto the landscape to forage or find mates according to an implicitly climate-sensitive dispersal kernel. In the second stage (homing), individuals use olfactory chemotaxis via odor cue concentration gradients to find new patches for the next time-step. The model is appropriate for a variety of organisms whose habitats may be considered isolated points on a landscape such as bat caves, bee hives, or ant colonies. Since organism dispersal and odor cue diffusion processes typically occur on spatial scales that differ by several orders of magnitude, we employ a separation of scales method to enable the derivation of analytic predictions of equilibria in terms of parameters that depend on local climate conditions. |
Keywords
integrodifference equations, Mexican free-tailed bat,
spatiotemporal population dynamics
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Mathematical Subject Classification
Primary: 92-10, 92B99
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Milestones
Received: 30 November 2022
Revised: 24 March 2023
Accepted: 17 April 2023
Published: 17 July 2024
Communicated by Suzanne Lenhart
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Authors |
| Jacob P. Duncan | |
| Department of Mathematics and
Statistics Winona State University Winona, MN United States |
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| Roger Janusiak | |
| Department of Physics University of Washington Seattle, WA United States |
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| Laura Kloepper | |
| Department of Biological
Sciences University of New Hampshire Durham, NH United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
