Competition between early stochasticity and transient dynamics in exponentially growing populations

Exponentially growing systems, such as bacterial populations, can exhibit significant stochasticity when their population sizes are small. As these populations grow, their dynamics become increasingly deterministic. While much research has focused on steady-state exponential growth, the transient phase approaching this state can reveal additional insights into single-cell statistics. Recent studies have shown that populations originating from a single cell display oscillations in their growth rate as they approach steady exponential growth. These oscillations arise because cells sharing a common ancestor tend to divide near integer multiples of their expected division time. These oscillations encode information about variability in single-cell growth rates.

In this talk, I will explore the competition between early stochasticity and these transient oscillations. We identify a critical threshold in single-cell growth rate variability—approximately 13%—below which the oscillations become asymptotically deterministic. Above this threshold, initial stochastic fluctuations dominate, masking all information about single-cell statistics. We believe this exemplifies a generic competition between early stochasticity and transient dynamics in many systems with stochastic exponential growth.