Survival Analysis Modeling of Phylogenetic and Coalescent Trees

Both phylogenetic and coalescent trees are the recordings of evolution over time. In other words, each distinguishable node on the tree, either interior or exterior, represents an evolutionary event. Ignoring the complexity involved in evolution, these events are time-to-events, which means that they can be described with a special type of positive random variables -time-to-event random variables (also known as survival, lifetime, or failure time). There is a branch of mathematical statistics, known as survival analysis, which is advanced to study time-to-event random variables. In this paper, after a brief review of the issues in phylogenetic and coalescent data analysis and modeling, we suggest that survival analysis holds great potential in the modeling of phylogenetic and coalescent trees. To the best of our knowledge, there have been only a very small handful of applications of survival analysis in phylogenetics (we only found seven ad hoc application papers in literature). It appears that there have never been any comprehensive tutorials or reviews on the potential of survival analysis in phylogenetics and coalescent research. We hope that this concise review of state-of-the-art research in survival analysis and the perspective of its applications in phylogenetics and coalescence research will fill the gap.