生存之争：达尔文选择与非达尔文选择的模型
Struggle for Existence: the models for Darwinian and non-Darwinian selection
摘要：
对生存斗争结果的经典理解导致了达尔文的适者生存。在这里，我们表明，情况可能是不同的，更复杂，可以说更有趣。具体来说，我们表明，不同版本的非齐次的Logistic模型与分布马尔萨斯参数意味着非达尔文的生存每个人。与此相反，非齐次逻辑斯谛方程的分布承载力显示达尔文优胜劣汰。我们还考虑了一个非齐次的生灭方程，并给出了一个简单的证明，证明了这个方程的结果是适者生存。除了这个已知的结果，我们发现这个方程的参数的一个精确的极限分布。我们还考虑了频率依赖的非齐次模型，并表明，虽然这些模型中的一些达尔文适者生存，有没有足够的时间来选择最适合的物种。我们讨论著名的纱布竞争排除原则，指出完全竞争者不能共存。虽然这一原则通常被认为是达尔文适者生存的直接后果，我们表明，从发达的数学理论的角度来看，完整的竞争对手实际上可以无限期地共存。
英文摘要：
Classical understanding of the outcome of the struggle for existence results in the Darwinian survival of the fittest. Here we show that the situation may be different, more complex and arguably more interesting. Specifically, we show that different versions of non-homogeneous logistic-like models with a distributed Malthusian parameter imply non-Darwinian survival of everybody. In contrast, the non-homogeneous logistic equation with distributed carrying capacity shows Darwinian survival of the fittest. We also consider an non-homogeneous birth-and-death equation and give a simple proof that this equation results in the survival of the fittest. In addition to this known result, we find an exact limit distribution of the parameters of this equation. We also consider frequency-dependent non-homogeneous models and show that although some of these models show Darwinian survival of the fittest, there is not enough time for selection of the fittest species. We discuss the well-known Gauze Competitive exclusion principle that states that Complete competitors cannot coexist. While this principle is often considered as a direct consequence of the Darwinian survival of the fittest, we show that from the point of view of developed mathematical theory complete competitors can in fact coexist indefinitely.
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