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Invasions, Species' Borders, Range Limits, Critical Phenomena, Allee Effects

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Subject-Keyword: Invasions Species' Borders Range Limits Critical Phenomena Allee Effects

Type of item: Journal Article Published

Language: English

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Description: All species’ ranges are the result of successful past invasions. Thus, models of species’ invasions and their failure can provide insight into the formation of a species’ geographic range. Here, we study the properties of invasion models when a species cannot persist below a critical population density known as an -Allee threshold.- In both spatially continuous reaction-diffusion models and spatially discrete coupled ordinary-differential equation models, the Allee effect can cause an invasion to fail. In patchy landscapes with dynamics described by the spatially discrete model, range limits caused by propagation failure pinning are stable over a wide range of parameters, whereas, in an uninterrupted habitat with dynamics described by a spatially continuous model, the zero velocity solution is structurally unstable and thus unlikely to persist in nature. We derive conditions under which invasion waves are pinned in the discrete space model and discuss their implications for spatially complex dynamics, including critical phenomena, in ecological landscapes. Our results suggest caution when interpreting abrupt range limits as stemming either from competition between species or a hard environmental limit that cannot be crossed: under a wide range of plausible ecological conditions, species’ ranges may be limited by an Allee effect. Several example systems appear to fit our general model.

Date created: 2001

DOI: doi:10.7939-R3WP9T97K

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Rights: © 2001 University of Chicago. This version of this article is open access and can be downloaded and shared. The original authors and source must be cited.





Author: Keitt, T. H. Lewis, M. A. Holt, R. D.

Source: https://era.library.ualberta.ca/


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vol.
157, no.
2 the american naturalist february 2001 Allee Effects, Invasion Pinning, and Species’ Borders Timothy H.
Keitt,1,* Mark A.
Lewis,2,† and Robert D.
Holt3,‡ 1.
National Center for Ecological Analysis and Synthesis, 735 State Street, Suite 300, Santa Barbara, California 93101; 2.
Department of Mathematics, University of Utah, Salt Lake, Utah 84112; 3.
Department of Biology, University of Kansas, Lawrence, Kansas 66045 Submitted August 18, 1999; Accepted September 21, 2000 abstract: All species’ ranges are the result of successful past invasions.
Thus, models of species’ invasions and their failure can provide insight into the formation of a species’ geographic range. Here, we study the properties of invasion models when a species cannot persist below a critical population density known as an “Allee threshold.” In both spatially continuous reaction-diffusion models and spatially discrete coupled ordinary-differential-equation models, the Allee effect can cause an invasion to fail.
In patchy landscapes (with dynamics described by the spatially discrete model), range limits caused by propagation failure (pinning) are stable over a wide range of parameters, whereas, in an uninterrupted habitat (with dynamics described by a spatially continuous model), the zero velocity solution is structurally unstable and thus unlikely to persist in nature. We derive conditions under which invasion waves are pinned in the discrete space model and discuss their implications for spatially complex dynamics, including critical phenomena, in ecological landscapes.
Our results suggest caution when interpreting abrupt range limits as stemming either from competition between species or a hard environmental limit that cannot be crossed: under a wide range of plausible ecological conditions, species’ ranges may be limited by an Allee effect.
Several example systems appear to fit our general model. Keywords: Allee effects, critical phenomena, invasions, range li...





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