As the size of phylogenetic trees and comparative data continue to grow and more complex models are developed to investigate the processes that gave rise to them, macroevolutionary analyses are becoming increasingly limited by computational requirements. Here we introduce a novel algorithm, based on the "flow" of the differential equations that describe likelihoods along tree edges in backward time, to reduce redundancy in calculations and efficiently compute the likelihood of various macroevolutionary models. Our algorithm applies to several diversification models, including birth-death models and models that account for state- or time-dependent rates, as well as many commonly used models of discrete-trait evolution, and provides an alternative way to describe macroevolutionary model likelihoods. As a demonstration of our algorithm's utility, we implemented it for a popular class of state-dependent diversification models - BiSSE, MuSSE, and their extensions to hidden-states. Our implementation is available through the R package castor. We show that, for these models, our algorithm is one or more orders of magnitude faster than existing implementations when applied to large phylogenies. Our algorithm thus enables the fitting of state-dependent diversification models to modern massive phylogenies with millions of tips, and may lead to potentially similar computational improvements for many other macroevolutionary models.

中文翻译：

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多样化和离散特征进化模型的可能性的通用有效算法

随着系统发育树和比较数据的规模不断增长，并且开发了更复杂的模型来研究产生它们的过程，宏观进化分析越来越受到计算要求的限制。在这里，我们引入了一种新的算法，基于微分方程的“流动”，描述了逆向时间沿树边缘的可能性，以减少计算中的冗余并有效地计算各种宏观进化模型的可能性。我们的算法适用于多种多样化模型，包括出生-死亡模型和解释状态或时间相关速率的模型，以及许多常用的离散特征进化模型，并提供了一种描述宏观进化模型可能性的替代方法。作为我们算法的演示' s 实用程序，我们为一类流行的状态相关多样化模型实现了它 - BiSSE、MuSSE 及其对隐藏状态的扩展。我们的实现可通过 R 包 castor 获得。我们表明，对于这些模型，当应用于大型系统发育时，我们的算法比现有实现快一个或多个数量级。因此，我们的算法能够将依赖状态的多样化模型拟合到具有数百万个提示的现代大规模系统发育，并可能导致许多其他宏观进化模型的潜在类似计算改进。当应用于大型系统发育时，我们的算法比现有实现快一个或多个数量级。因此，我们的算法能够将依赖状态的多样化模型拟合到具有数百万个提示的现代大规模系统发育，并可能导致许多其他宏观进化模型的潜在类似计算改进。当应用于大型系统发育时，我们的算法比现有实现快一个或多个数量级。因此，我们的算法能够将依赖状态的多样化模型拟合到具有数百万个提示的现代大规模系统发育，并可能导致许多其他宏观进化模型的潜在类似计算改进。