Coexistence and Spread of Competitors in Heterogeneous Landscapes |
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Authors: | Yasmine Samia Frithjof Lutscher |
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Institution: | (1) Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2E1;(2) Department of Biological Sciences, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada, T2N 1N4;(3) Department of Biological Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2E1 |
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Abstract: | Competition between species is ubiquitous in nature and therefore widely studied in ecology through experiment and theory.
One of the central questions is under which conditions a (rare) invader can establish itself in a landscape dominated by a
resident species at carrying capacity. Applying the same question with the roles of the invader and resident reversed leads
to the principle that “mutual invasibility implies coexistence.” A related but different question is how fast a locally introduced
invader spreads into a landscape (with or without competing resident), provided it can invade. We explore some aspects of
these questions in a deterministic, spatially explicit model for two competing species with discrete non-overlapping generations
in a patchy periodic environment. We obtain threshold values for fragmentation levels and dispersal distances that allow for
mutual invasion and coexistence even if the non-spatial competition model predicts competitive exclusion. We obtain exact
results when dispersal is governed by a Laplace kernel. Using the average dispersal success, we develop a mathematical framework
to obtain approximate results that are independent of the exact dispersal patterns, and we show numerically that these approximations
are very accurate. |
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