We study a size--structured population model of proliferating cells in which biomass accumulation and binary division occur at rates modulated by fluctuating internal phenotypes. We quantify how fluctuations in internal variables that influence both growth and division shape the distribution of population phenotypes. We derive conditions under which the distributions of size and internal state decouple. Under this decoupling, population--level expectations are obtained from lineage-level expectations by an exponen…

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,…

Single-cell microfluidic experiments have shown that upon abrupt exposures to antibiotics, genetically homogeneous microbial populations undergo divergent cell fates. The mechanism underlying this divergence is not clear and in particular, the emergence of a range of distinct slow-growing phenotypes cannot be explained by models relying on bistability alone. Here, we propose a model for gene expression and growth dynamics during antibiotic exposures, which is informed by well-known scaling relations connecting pro…

Abstract The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman’s coalescent process, which produces a binary tree, emerges universally from many microscopic models in which the variance in the number of offspring is finite. It is understood that power-law offsprings distributions with infinite variance can result in a very different type of coalescent structure with merging of more than two lineages. Here, we investigate the regime where the va…

The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman's coalescent process, which produces a binary tree, universally emerges from many microscopic models in which the variance in the number of offspring is finite. It is understood that power-law offspring distributions with infinite variance can result in a very different type of coalescent structure with merging of more than two lineages. Here we investigate the regime where the variance of t…