Branch-specific substitution models are popular for detecting evolutionary change-points, such as shifts in selective pressure. However, applying such models typically requires prior knowledge of change-point locations on the phylogeny or faces scalability issues with large data sets. To address both limitations, we integrate branch-specific substitution models with shrinkage priors to automatically identify change-points without prior knowledge, while simultaneously estimating distinct substitution parameters for each branch. To enable tractable inference under this high-dimensional model, we develop an analytical gradient algorithm for the branch-specific substitution parameters where the computational time is linear in the number of parameters. We apply this gradient algorithm to infer selection pressure dynamics in the evolution of the BRCA1 gene in primates and mutational dynamics in viral sequences from the recent mpox epidemic. Our novel algorithm enhances inference efficiency, achieving up to a 126-fold speedup per iteration in maximum likelihood optimization when compared to central difference numerical gradient method and up to a 2026-fold improvement in computational performance within a Bayesian framework using Hamiltonian Monte Carlo sampler compared to conventional univariate random walk sampler.

翻译：分支特异性替换模型广泛用于检测进化变化点（例如选择压力的转变）。然而，应用此类模型通常需要预先了解系统发育树上变化点的位置，或面临大数据集的可扩展性问题。为同时解决这两个限制，我们将分支特异性替换模型与收缩先验相结合，可在无需先验知识的情况下自动识别变化点，同时为每个分支估计不同的替换参数。为了在高维模型下实现可处理的推断，我们开发了一种基于解析梯度的分支特异性替换参数算法，其计算时间与参数数量呈线性关系。我们将该梯度算法应用于推断灵长类BRCA1基因进化中的选择压力动态，以及近期猴痘疫情中病毒序列的突变动态。实验表明，与中心差分数值梯度方法相比，我们的新算法在最大似然优化中每次迭代的推理效率提升高达126倍；在贝叶斯框架下结合哈密顿蒙特卡洛采样器时，相较于传统单变量随机游走采样器，计算性能提升高达2026倍。