A time-tree is a rooted phylogenetic tree with all internal and leaf nodes equipped with absolute divergence and sampling dates, respectively. Although these time-trees have emerged as a major focus of phylogenetics research, little is known about their parameter space. From a graphtheoretic and algorithmic point of view, we present and investigate a hierarchy of discrete time-tree space approximations in this article. The NNI graph, one of the most fundamental and widely used phylogenetic graphs, is our hierarchy's lowest level and roughest approximation. The sampling dates and relative timing of evolutionary divergence are discretized by more refined approximations.
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