Phylogenetic and discrete-trait evolutionary inference depend heavily on an appropriate characterization of the underlying character substitution process. In this paper, we present random-effects substitution models that extend common continuous-time Markov chain models into a richer class of processes capable of capturing a wider variety of substitution dynamics. As these random-effects substitution models often require many more parameters than their usual counterparts, inference can be both statistically and computationally challenging. Thus, we also propose an efficient approach to compute an approximation to the gradient of the data likelihood with respect to all unknown substitution model parameters. We demonstrate that this approximate gradient enables scaling of sampling-based inference, namely Bayesian inference via Hamiltonian Monte Carlo, under random-effects substitution models across large trees and state-spaces. Applied to a dataset of 583 SARS-CoV-2 sequences, an HKY model with random-effects shows strong signals of nonreversibility in the substitution process, and posterior predictive model checks clearly show that it is a more adequate model than a reversible model. When analyzing the pattern of phylogeographic spread of 1441 influenza A virus (H3N2) sequences between 14 regions, a random-effects phylogeographic substitution model infers that air travel volume adequately predicts almost all dispersal rates. A random-effects state-dependent substitution model reveals no evidence for an effect of arboreality on the swimming mode in the tree frog subfamily Hylinae. Simulations reveal that random-effects substitution models can accommodate both negligible and radical departures from the underlying base substitution model. We show that our gradient-based inference approach is over an order of magnitude more time efficient than conventional approaches.

中文翻译：

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通过可扩展梯度近似进行系统发育的随机效应替换模型


系统发育和离散性状进化推断在很大程度上取决于对潜在特征替换过程的适当表征。在本文中，我们提出了随机效应替代模型，这些模型将常见的连续时间马尔可夫链模型扩展到一类更丰富的过程，能够捕获更广泛的替代动力学。由于这些随机效应替代模型通常需要比通常的对应模型多得多的参数，因此推理在统计和计算上都可能具有挑战性。因此，我们还提出了一种有效的方法来计算关于所有未知替代模型参数的数据似然梯度的近似值。我们证明，在跨大树和状态空间的随机效应替换模型下，这种近似梯度可以缩放基于采样的推理，即通过哈密顿蒙特卡洛的贝叶斯推理。应用于 583 个 SARS-CoV-2 序列的数据集，具有随机效应的 HKY 模型显示出替代过程中不可逆的强烈信号，后验预测模型检查清楚地表明它是一个比可逆模型更合适的模型。在分析 1441 个甲型流感病毒 （H3N2） 序列在 14 个区域之间的系统地理传播模式时，随机效应系统地理替代模型推断航空旅行量足以预测几乎所有的传播率。随机效应状态依赖性替换模型显示，没有证据表明树栖现实对树蛙亚科 Hylinae 的游泳模式有影响。仿真表明，随机效应替代模型可以容纳与基础碱基替代模型的可忽略不计和激进的偏离。 我们表明，我们基于梯度的推理方法比传统方法的时间效率高出一个数量级。