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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