Hundreds or thousands of loci are now routinely used in modern phylogenomic studies. Concatenation approaches to tree inference assume that there is a single topology for the entire dataset, but different loci may have different evolutionary histories due to incomplete lineage sorting (ILS), introgression, and/or horizontal gene transfer; even single loci may not be treelike due to recombination. To overcome this shortcoming, we introduce an implementation of a multi-tree mixture model that we call mixtures across sites and trees (MAST). This model extends a prior implementation by Boussau et al. (2009) by allowing users to estimate the weight of each of a set of pre-specified bifurcating trees in a single alignment. The MAST model allows each tree to have its own weight, topology, branch lengths, substitution model, nucleotide or amino acid frequencies, and model of rate heterogeneity across sites. We implemented the MAST model in a maximum-likelihood framework in the popular phylogenetic software, IQ-TREE. Simulations show that we can accurately recover the true model parameters, including branch lengths and tree weights for a given set of tree topologies, under a wide range of biologically realistic scenarios. We also show that we can use standard statistical inference approaches to reject a single-tree model when data are simulated under multiple trees (and vice versa). We applied the MAST model to multiple primate datasets and found that it can recover the signal of ILS in the Great Apes, as well as the asymmetry in minor trees caused by introgression among several macaque species. When applied to a dataset of 4 Platyrrhine species for which standard concatenated maximum likelihood (ML) and gene tree approaches disagree, we observe that MAST gives the highest weight (i.e., the largest proportion of sites) to the tree also supported by gene tree approaches. These results suggest that the MAST model is able to analyze a concatenated alignment using ML while avoiding some of the biases that come with assuming there is only a single tree. We discuss how the MAST model can be extended in the future.

中文翻译：

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MAST：跨站点和树的混合物的系统发育推理


成百上千个基因座现在通常用于现代系统发育研究。树推理的串联方法假设整个数据集只有一个拓扑，但由于不完全谱系排序 （ILS）、渗入和/或水平基因转移，不同的基因座可能具有不同的进化历史;由于重组，即使是单个基因座也可能不是树状的。为了克服这个缺点，我们引入了一个多树混合模型的实现，我们称之为跨站点和树木的混合 （MAST）。该模型扩展了 Boussau 等人 （2009） 的先前实现，允许用户在单个对齐中估计一组预先指定的分叉树中每棵树的权重。MAST 模型允许每棵树都有自己的权重、拓扑、分支长度、替代模型、核苷酸或氨基酸频率以及跨位点速率异质性模型。我们在流行的系统发育软件 IQ-TREE 中的最大似然框架中实现了 MAST 模型。模拟表明，我们可以在各种生物学现实情景下准确恢复真实的模型参数，包括一组给定树木拓扑的树枝长度和树木权重。我们还表明，当在多个树下模拟数据时，我们可以使用标准的统计推理方法来拒绝单树模型（反之亦然）。我们将 MAST 模型应用于多个灵长类动物数据集，发现它可以恢复类人猿体内 ILS 的信号，以及几种猕猴物种之间因渗入而导致的小树不对称性。 当应用于标准级联最大似然 （ML） 和基因树方法不一致的 4 个 Platyrrhine 物种的数据集时，我们观察到 MAST 为基因树方法也支持的树赋予了最高权重（即最大比例的位点）。这些结果表明，MAST 模型能够使用 ML 分析串联的对齐，同时避免假设只有一棵树所带来的一些偏差。我们将讨论将来如何扩展 MAST 模型。