Branching under First-Passage Resetting

TL;DR

This paper introduces a new framework for population dynamics driven by first-passage stochastic processes, revealing how timing fluctuations influence growth and optimizing lysis time in bacteriophages.

Contribution

The authors develop an exact renewal equation linking first-passage statistics to population growth, uncovering effects of timing fluctuations and yield-delay trade-offs.

Findings

Fluctuations in timing can enhance growth under fixed offspring and mean replication time.

Yield depending on first-passage time introduces a yield-delay trade-off affecting growth.

Application to bacteriophage lysis yields an optimal lysis time matching empirical data.

Abstract

Many biological processes, from cell division to viral lysis, are triggered when an internal stochastic variable reaches a threshold. Here we introduce Branching under First-Passage Resetting, a general framework in which replication events arise endogenously from first-passage dynamics rather than from externally imposed lifetime clocks. We show that the resulting population dynamics obey an exact renewal equation linking single-trajectory first-passage statistics to the population growth rate. This mapping shows that, for fixed offspring number and fixed mean replication time, stochastic timing fluctuations necessarily enhance growth relative to a deterministic clock. When offspring yield depends on the first-passage time, however, fluctuations have non-trivial effects and expose a fundamental yield-delay trade-off: waiting longer can increase the number of descendants, but delays all future lineages. Our framework allows us to address this optimization problem analytically, and upon application to bacteriophage lysis, gives an optimal lysis time and growth rate consistent with empirical data.