Extremal events dictate population growth rate inference

TL;DR

This paper investigates the systematic errors in estimating population growth rates from single-cell lineage data, revealing how finite data and sampling biases affect accuracy and proposing methods to correct these biases for reliable long-term growth inference.

Contribution

It introduces a comprehensive bias-variance analysis of growth rate estimators, identifies phase transition behavior, and develops bias correction techniques applicable to experimental data.

Findings

Finite-time bias can be mitigated by fitting its monotonic behavior.

Nonlinear averaging bias dominates at long times, causing a phase transition.

Corrected estimators produce consistent long-term growth rates across methods.

Abstract

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.