恒化器中的公地悲剧
Tragedy of the Commons in the Chemostat
摘要：
我们提出了一个原则证明的公地悲剧的现象，是在许多理论的中心合作的演变。我们建立的悲剧的背景下，一般恒化器模型的两个物种，合作者和骗子。这两个物种具有相同的生长速率函数和产量常数，但合作者将一部分养分吸收分配给公共产品-悲剧中的“公地”-这是消化外部提供的养分所必需的。另一方面，作弊者不产生这种酶，并将所有营养吸收分配给自己的生长。我们证明了当作弊者最初出现时，合作者和作弊者最终都会灭绝，从而证实了悲剧的发生。我们还表明，如果没有作弊者，合作者可以无限期地生存，前提是至少有一个低水平的公共产品或加工的营养素最初是可用的。我们的研究结果提供了一个预测框架的合作者-骗子动态分析在一个强大的实验进化模型系统。
英文摘要：
We present a proof of principle for the phenomenon of the tragedy of the commons that is at the center of many theories on the evolution of cooperation. We establish the tragedy in the context of a general chemostat model with two species, the cooperator and the cheater. Both species have the same growth rate function and yield constant, but the cooperator allocates a portion of the nutrient uptake towards the production of a public good -the "Commons" in the Tragedy- which is needed to digest the externally supplied nutrient. The cheater on the other hand does not produce this enzyme, and allocates all nutrient uptake towards its own growth. We prove that when the cheater is present initially, both the cooperator and the cheater will eventually go extinct, hereby confirming the occurrence of the tragedy. We also show that without the cheater, the cooperator can survive indefinitely, provided that at least a low level of public good or processed nutrient is available initially. Our results provide a predictive framework for the analysis of cooperator-cheater dynamics in a powerful model system of experimental evolution.
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