The competitive exclusion principle in stochastic environments
The competitive exclusion principle in stochastic environments
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DOI：
10.1007/s00285-019-01464-y
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发表时间：
2018-10
影响因子：
1.9
通讯作者：
Alexandru Hening;D. Nguyen
中科院分区：
文献类型：
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作者：
Alexandru Hening;D. Nguyen
以其最简单的形式，竞争排斥原理指出，许多物种竞争较少数量的资源不能共存。然而，根据经验观察，在某些情况下，共存是可能的。哈钦森的“浮游生物悖论”就是一个例子。这是一个大量浮游植物物种共存的例子，同时竞争非常有限的资源。实验和理论研究都表明，环境的时间波动可以促进竞争物种的共存。哈钦森推测，人们可以共存，因为非平衡条件会使不同的物种在不同的时间受到环境的青睐。在本文中，我们展示了可变（随机）环境如何使一组受较少资源或其他密度相关因素限制的竞争物种共存。如果环境波动采用白噪声模型，并且竞争者的人均增长率与资源呈线性关系，则证明存在竞争排斥。然而，如果增长率与资源之间的依赖关系不是线性的，或者白噪声项是非线性的，我们表明在比物种少的资源上共存是可能的。更令人惊讶的是，如果时间环境变化来自于在有限数量的可能状态之间随机切换环境，那么即使增长率线性依赖于资源，所有物种也有可能共存。我们用一个例子（其变体首次出现在Benaim和Lobry ' 16）表明，与Hutchinson的解释相反，一个人可以在两个环境之间切换，其中同一物种受到青睐，仍然可以共存。
In its simplest form, the competitive exclusion principle states that a number of species competing for a smaller number of resources cannot coexist. However, it has been observed empirically that in some settings it is possible to have coexistence. One example is Hutchinson’s ‘paradox of the plankton’. This is an instance where a large number of phytoplankton species coexist while competing for a very limited number of resources. Both experimental and theoretical studies have shown that temporal fluctuations of the environment can facilitate coexistence for competing species. Hutchinson conjectured that one can get coexistence because nonequilibrium conditions would make it possible for different species to be favored by the environment at different times. In this paper we show in various settings how a variable (stochastic) environment enables a set of competing species limited by a smaller number of resources or other density dependent factors to coexist. If the environmental fluctuations are modeled by white noise, and the per-capita growth rates of the competitors depend linearly on the resources, we prove that there is competitive exclusion. However, if either the dependence between the growth rates and the resources is not linear or the white noise term is nonlinear we show that coexistence on fewer resources than species is possible. Even more surprisingly, if the temporal environmental variation comes from switching the environment at random times between a finite number of possible states, it is possible for all species to coexist even if the growth rates depend linearly on the resources. We show in an example (a variant of which first appeared in Benaim and Lobry ’16) that, contrary to Hutchinson’s explanation, one can switch between two environments in which the same species is favored and still get coexistence.