用于系统发育树标度的简单模型
Simple models for scaling in phylogenetic trees
摘要：
许多过程和模型--在生物、物理、社会和其他背景下--产生的树的深度与叶子的数量成比例关系。描述生物物种之间进化关系的系统发育树是没有观察到这种尺度的树的例子。有了这个动机，我们数值分析两个分支模型，导致非对数缩放的深度与叶数。对于福特的阿尔法模型，虽然幂律缩放的深度与树的大小建立解析，我们的数值结果表明，渐近制度接近只有在非常大的树的大小。我们在这里介绍一个新的模型，活动模型，显示分析和数值，它也显示了幂律缩放的深度与树的大小在一个关键的参数值。
英文摘要：
Many processes and models --in biological, physical, social, and other contexts-- produce trees whose depth scales logarithmically with the number of leaves. Phylogenetic trees, describing the evolutionary relationships between biological species, are examples of trees for which such scaling is not observed. With this motivation, we analyze numerically two branching models leading to non-logarithmic scaling of the depth with the number of leaves. For Ford's alpha model, although a power-law scaling of the depth with tree size was established analytically, our numerical results illustrate that the asymptotic regime is approached only at very large tree sizes. We introduce here a new model, the activity model, showing analytically and numerically that it also displays a power-law scaling of the depth with tree size at a critical parameter value.
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