进化下的代数$α$ -Ford树
The algebraic $α$-Ford tree under evolution
摘要：
二元系统发生树的遗传模型对于检验真实世界的系统发生假说是有用的。在本文中，我们考虑的二叉树没有边的长度加上一个抽样措施，并编码为代数测度树。这允许通过关注子树的样本形状及其子树质量来描述实际和模拟的相似性程度。我们更详细地描述了零模型，即分支树，合并树和梳状树的子树质量统计的退火规律。最后，我们使用鞅问题的方法来描述扩散极限下进化系统树的特征。
英文摘要：
Null models of binary phylogenetic trees are useful for testing hypotheses on real world phylogenies. In this paper we consider phylogenies as binary trees without edge lengths together with a sampling measure and encode them as algebraic measure trees. This allows to describe the degree of similarity between actual and simulated phylogenies by focusing on the sample shape of subtrees and their subtree masses. We describe the annealed law of the statistics of subtree masses of null models, namely the branching tree, the coalescent tree, and the comb tree in more detail. Finally, we use methods from martingale problems to characterize evolving phylogenetic trees in the diffusion limit.
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