Dragomir Dakota, Allman Elizabeth S, Rhodes John A
Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, Alaska, USA.
J Comput Biol. 2023 Mar;30(3):277-292. doi: 10.1089/cmb.2022.0330. Epub 2023 Feb 6.
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.
多样化模型描述了进化树的随机生长，通过物种形成和灭绝事件对物种的历史关系进行建模。这类模型中的一类允许树内物种的特征或类型独立变化，物种形成和灭绝速率取决于这些特征或类型。尽管模型参数的可识别性对于证明参数估计的合理性是必要的，但对于这些模型而言，尽管它们已被用于推理，但尚未正式确立其参数可识别性。这项工作从单个树观察值在其深度趋于无穷大时导出的渐近分布出发，建立了这类模型中一种较简单形式（即物种形成的多类型纯生模型）的参数在标签交换意义下的一般可识别性。对于应用于现有数据而言至关重要的是，在树的任何内部节点甚至叶子节点都无需观察类型。
