Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON K1N 6N5, Canada.
Bull Math Biol. 2010 Nov;72(8):2089-112. doi: 10.1007/s11538-010-9529-0. Epub 2010 Mar 16.
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.
物种间的竞争在自然界中普遍存在，因此在生态学中通过实验和理论广泛研究。其中一个核心问题是在什么条件下，（稀有）入侵者可以在承载能力下由居民物种主导的景观中建立自己的地位。将相同的问题应用于入侵者和居民角色反转，就会得出“相互入侵意味着共存”的原则。一个相关但不同的问题是，在有或没有竞争居民的情况下，一个本地引入的入侵者在景观中传播的速度有多快，前提是它可以入侵。我们在一个确定的、空间明确的模型中探索了这些问题的一些方面，该模型适用于具有离散非重叠世代的两种竞争物种，在斑块状周期性环境中。我们获得了允许相互入侵和共存的碎片水平和扩散距离的阈值，即使非空间竞争模型预测竞争排斥。当扩散受拉普拉斯核控制时，我们获得了确切的结果。使用平均扩散成功率，我们开发了一个数学框架来获得独立于精确扩散模式的近似结果，并通过数值显示这些近似值非常准确。
