某些进化模型的统计
Statistics of Certain Models of Evolution
摘要：
在最近的一篇论文中，纽曼调查了关于进化中幂律谱的文献，自组织临界性，并提出了一个自己的模型，得出了自组织临界性对进化来说不是必要的结论。他不仅错过了一个关键的模型（艺康），有一个明确的自组织的关键机制，但纽曼的模型也表现出相同的机制，产生幂律行为的艺康。纽曼的模型实际上是一个自组织临界系统的“平均场”近似。在本文中，我也实现了纽曼的模型使用Ecolab软件，删除的限制，物种的数量保持不变。事实证明，恒定物种数量的要求是不平凡的，导致物种之间的全局耦合，这与Ecolab中看到的物种相互作用类似。事实上，模型必须自组织到一个状态，在这个状态下，物种的长期平均值与物种的长期平均值相平衡，否则系统要么崩溃，要么爆炸。有鉴于此，纽曼的模型并没有为进化中自组织临界性的存在提供所希望的反例，但确实提供了一个简单的，几乎是分析性的模型，可以用来理解更复杂的模型，如Ecolab。
英文摘要：
In a recent paper, Newman surveys the literature on power law spectra in evolution, self-organised criticality and presents a model of his own to arrive at a conclusion that self-organised criticality is not necessary for evolution. Not only did he miss a key model (Ecolab) that has a clear self-organised critical mechanism, but also Newman's model exhibits the same mechanism that gives rise to power law behaviour as does Ecolab. Newman's model is, in fact, a ``mean field'' approximation of a self-organised critical system. In this paper, I have also implemented Newman's model using the Ecolab software, removing the restriction that the number of species remains constant. It turns out that the requirement of constant species number is non-trivial, leading to a global coupling between species that is similar in effect to the species interactions seen in Ecolab. In fact, the model must self-organise to a state where the long time average of speciations balances that of the extinctions, otherwise the system either collapses or explodes. In view of this, Newman's model does not provide the hoped-for counter example to the presence of self-organised criticality in evolution, but does provide a simple, almost analytic model that can used to understand more intricate models such as Ecolab.
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