Diversification models describe the random growth of evolutionary trees, modeling the historical relationships of species through speciation and extinction events. One class of such models allows for independently changing traits, or types, of the species within the tree, upon which speciation and extinction rates depend. Although identifiability of parameters is necessary to justify parameter estimation with a model, it has not been formally established for these models, despite their adoption for inference. This work establishes generic identifiability up to label swapping for the parameters of one of the simpler forms of such a model, a multitype pure birth model of speciation, from an asymptotic distribution derived from a single tree observation as its depth goes to infinity. Crucially for applications to available data, no observation of types is needed at any internal points in the tree, nor even at the leaves.
翻译:多样化模式描述进化树木的随机增长,通过物种特征和灭绝事件来模拟物种的历史关系。一类此类模式允许树内物种的特性或类型独立变化,而物种特征和灭绝率取决于树内物种的特征或类型。虽然参数的可识别性对于用模型来证明参数估计是合理的是必要的,但尚未对这些模型正式确立,尽管采用了这些模型的推理。这项工作确立了通用的可识别性,以标签转换这种模型的一种简单形式的参数,一种多型纯种的物种生成模型,从从一个树的深度到无限的单一观测得出的无症状分布。对于现有数据的应用来说,至关重要的是,在树内的任何点,甚至叶叶上,都不需要对种类进行观测。