Branching-Time Signatures of Growth Regime in Tumor Birth-Death Models

Abstract

Tumor evolution is shaped by cell division, cell death, competition, and constraints imposed by the local microenvironment. Because these dynamics are usually not observed directly, phylogenetic trees inferred from somatic variation in sampled tumor cells can provide an indirect record of the population history that produced the sample. In this paper, we examine whether the distribution of inferred internal branching times exhibits signatures that depend on the underlying tumor growth regime. Specifically, we study the distribution of internal branching times in continuous-time birth-death models of tumor evolution. Exponentially growing populations exhibit a unimodal distribution of internal branching times, with the mode located near the root. In contrast, logistic growth, which models expansion constrained by carrying capacity, yields a substantially more intricate genealogical structure: the distribution of branching times undergoes a systematic transition as the time elapsed since tumor initiation increases. Specifically, this progression shifts from an expansion-dominated phase, through an intermediate early-recent bimodal phase, to a final recent-dominated phase. Extensive simulations of reconstructed tumor genealogies support these theoretical findings.