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Integrodifference equations in the presence of climate change: persistence criterion, travelling waves and inside dynamics
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- Author(s) / Creator(s)
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To understand the efects that the climate change has on the evolution of species as well as
the genetic consequences, we analyze an integrodifference equation (IDE) models for a reproducing and
dispersing population in a spatio-temporal heterogeneous environment described by a shifting climate
envelope. Our analysis on the IDE focuses on the persistence criterion, travelling wave solutions,
and the inside dynamics. First, the persistence criterion, characterizing the global dynamics of the
IDE, is established in terms of the basic reproduction number. In the case of persistence, a unique
travelling wave is found to govern the global dynamics. The e ects of the size and the shifting speed
of the climate envelope on the basic reproduction number, and hence, on the persistence criterion, are
also investigated. In particular, the critical domain size and the critical shifting speed are found in
certain cases. Numerical simulations are performed to complement the theoretical results. In the case
of persistence, we separate the travelling wave and general solutions into spatially distinct neutral
fractions to study the inside dynamics. It is shown that each neutral genetic fraction rearranges itself
spatially so as to asymptotically achieve the profi le of the travelling wave. To measure the genetic
diversity of the population density we calculate the Shannon diversity index and related indices and
use these to illustrate how diversity changes with underlying parameters. -
- Date created
- 2018-01-01
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- Type of Item
- Article (Draft / Submitted)