Many social and biological systems are characterized by enduring hierarchies, including those organized around prestige in academia, dominance in animal groups, and desirability in online dating. Despite their ubiquity, the general mechanisms that explain the creation and endurance of such hierarchies are not well understood. We introduce a generative model for the dynamics of hierarchies using time-varying networks, in which new links are formed based on the preferences of nodes in the current network and old links are forgotten over time. The model produces a range of hierarchical structures, ranging from egalitarianism to bistable hierarchies, and we derive critical points that separate these regimes in the limit of long system memory. Importantly, our model supports statistical inference, allowing for a principled comparison of generative mechanisms using data. We apply the model to study hierarchical structures in empirical data on hiring patterns among mathematicians, dominance relations among parakeets, and friendships among members of a fraternity, observing several persistent patterns as well as interpretable differences in the generative mechanisms favored by each. Our work contributes to the growing literature on statistically grounded models of time-varying networks.

许多社会和生物系统都以持久的等级制度为特征，包括围绕学术界的声望、动物群体的主导地位以及在线约会的吸引力而组织的等级制度。尽管它们无处不在，但解释这种等级制度的产生和持久的一般机制尚不清楚。我们引入了一种使用时变网络的层次结构动态生成模型，其中新链接是根据当前网络中节点的偏好形成的，而旧链接会随着时间的推移而被遗忘。该模型产生了一系列层次结构，从平等主义到双稳态层次结构，我们得出了在长系统记忆的限制下区分这些政权的关键点。重要的是，我们的模型支持统计推断，允许使用数据对生成机制进行原则性比较。我们应用该模型来研究数学家雇用模式、长尾小鹦鹉之间的支配关系以及兄弟会成员之间的友谊等经验数据中的层次结构，观察几种持久的模式以及每种模式所偏爱的生成机制中可解释的差异。我们的工作为越来越多的关于时变网络的统计模型的文献做出了贡献。