Extremal events dictate population growth rate inference

Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite data, which introduces systematic errors. A comprehensive understanding of these errors in the context of finite data remains elusive. To address this gap, we study the error in growth rate estimates across different models. We show that under the usual bias-variance decomposition, the bias can be decomposed into a finite-time bias and nonlinear averaging bias. We demonstrate that finite-time bias, which dominates at short times, can be mitigated by fitting its monotonic behavior. In contrast, at longer times, nonlinear averaging bias becomes the predominant source of error, leading to a phase transition. This transition can be understood through the Random Energy Model, a mean-field model of disordered systems, where a few lineages dominate the estimator. Applying these methods to experimental data demonstrates that correcting for biases in lineage-based approaches yields consistent results for the long-term growth rate across multiple methods and enables the reverse-engineering of dynamic models. This new framework provides a quantitative understanding of growth rate estimators, clarifies the conditions under which they can be effectively applied to finite data, and introduces model-free approaches for studying the connections between physiology and cell growth.Author summary: Understanding how quickly a microbial population grows is a central question in biology, intimately linked to evolutionary fitness. While recent advances have made it possible to estimate growth rates from single-cell data, these estimates often vary widely in practice. In this work, we demonstrate that such inconsistencies arise from fundamental limitations imposed by the fact exponential growth selects for exponentially rare phenotypes, which dictate the growth rate. Here, we show that two widely used “model-free” approaches both suffer from tradeoffs between two sources of bias: at short timescales, limited observation windows lead to underestimation, while at longer timescales, a small number of exceptionally fast-growing cells disproportionately influence the growth rate. We present a unified framework that disentangles and corrects both sources of error, enabling robust growth rate estimates even from modest datasets. Our results clarify when lineage-based methods can be trusted and what kinds of data are required to accurately infer population growth from single-cell measurements.