Compositional heterogeneity among lineages can compromise phylogenetic analyses, because models in common use assume compositionally homogeneous data. Models that can accommodate compositional heterogeneity with few extra parameters are described here, and used in two examples where the true tree is known with confidence. It is shown using likelihood ratio tests that adequate modeling of compositional heterogeneity can be achieved with few composition parameters, that the data may not need to be modelled with separate composition parameters for each branch in the tree. Tree searching and placement of composition vectors on the tree are done in a Bayesian framework using Markov chain Monte Carlo (MCMC) methods. Assessment of fit of the model to the data is made in both maximum likelihood (ML) and Bayesian frameworks. In an ML framework, overall model fit is assessed using the Goldman-Cox test, and the fit of the composition implied by a (possibly heterogeneous) model to the composition of the data is assessed using a novel tree-and model-based composition fit test. In a Bayesian framework, overall model fit and composition fit are assessed using posterior predictive simulation. It is shown that when composition is not accommodated, then the model does not fit, and incorrect trees are found; but when composition is accommodated, the model then fits, and the known correct phylogenies are obtained.

中文翻译：

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建模成分异质性

谱系之间的成分异质性可能会影响系统发育分析，因为常用的模型假设成分均一的数据。此处描述了可以以很少的额外参数适应成分异质性的模型，并在两个示例中使用，其中真实的树是可信的。使用似然比检验表明，可以用很少的成分参数实现对成分异质性的充分建模，数据可能不需要用树中每个分支的单独成分参数建模。使用马尔可夫链蒙特卡罗 (MCMC) 方法在贝叶斯框架中进行树搜索和在树上放置组合向量。模型与数据的拟合评估在最大似然 (ML) 和贝叶斯框架中进行。在 ML 框架中，使用 Goldman-Cox 检验评估整体模型拟合，并使用新的基于树和模型的组合拟合测试评估（可能是异质的）模型暗示的组合对数据组合的拟合。在贝叶斯框架中，使用后验预测模拟评估整体模型拟合和组合拟合。结果表明，当组合不适应时，则模型不适合，并且发现不正确的树；但是当成分被适应时，模型就会拟合，并获得已知的正确系统发育。使用后验预测模拟评估整体模型拟合和组合拟合。结果表明，当组合不适应时，则模型不适合，并且发现不正确的树；但是当成分被适应时，模型就会拟合，并获得已知的正确系统发育。使用后验预测模拟评估整体模型拟合和组合拟合。结果表明，当组合不适应时，则模型不适合，并且发现不正确的树；但是当成分被适应时，模型就会拟合，并获得已知的正确系统发育。