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Life on the Move: Modeling the Effects of Climate-Driven Range Shifts with Integrodifference Equations

Part of the Lecture Notes in Mathematics book series (LNMBIOS,volume 2071)

Abstract

Climate change is causing many species to shift their ranges. We analyze an integrodifference equation that combines growth, dispersal, and a shifting habitat in order to assess the impact of climate change on persistence. We apply this model to butterflies and show that over-dispersal and under-dispersal can both lead to extinction. We focus on the critical range-shift speed (for extinction), survey numerical methods for determining this speed, and introduce new analytic approximations for the critical shift speed. Finally, we apply our numerical methods and analytic approximations to a variety of redistribution kernels and show that critical-speed curves shed light on the complicated effects of dispersal on persistence in a changing climatic environment.

Keywords

  • Eigenvalue Problem
  • Legendre Polynomial
  • Critical Speed
  • Integrodifference Equation
  • Laplace Distribution

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Zhou, Y., Kot, M. (2013). Life on the Move: Modeling the Effects of Climate-Driven Range Shifts with Integrodifference Equations. In: Lewis, M., Maini, P., Petrovskii, S. (eds) Dispersal, Individual Movement and Spatial Ecology. Lecture Notes in Mathematics(), vol 2071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35497-7_9

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