Random phylogenies and the distribution of branching times

•The theoretical lineages-through-time plot is computed for any time-dependent model of diversification.•A method is developed to define a prediction interval around a theoretical or observed LTT curve.•The accuracy of the prediction interval was assessed with simulations.

Phylogenetic trees reconstructed without fossils have become an important source of information to study evolutionary processes. A widely used method to describe patterns of phylogenetic diversification is known as the lineages-through-time (LTT) plot. Recently, it has been shown that it is possible to predict the distribution of the branching times of a phylogeny, thus making possible to derive a theoretical LTT curve conditioned on diversification parameters. Here, I review some aspects related to this prediction showing how to derive it for any time-dependent model of diversification, as well as calculating a prediction interval around a theoretical LTT curve. The accuracy of the prediction interval was assessed with simulations using fixed or random tree sizes under constant-rate models as well as two models of time-dependent diversification. The prediction intervals were relatively narrower and more accurate for larger trees. The features of this approach are discussed as well as its potential applications.