A large deviation principle linking lineage statistics to fitness*

In exponentially proliferating populations of bacteria, a population may double at a rate greater than or less than the average doubling time of a single-cell, depending on the variability and heritability of generation times at the single-cell level. Previous studies have shown that the distribution of generation times obtained from an isolated lineage is, in general, insufficient to determine the population’s doubling time or growth rate, both of which are proxies for fitness. This poses a fundamental challenge for experimentalists who wish to probe the fitness effects of physiological perturbations using single-cell tracking data. Using a large deviation approach, we present a procedure for inferring a population’s fitness from lineage statistics that is independent of the model specifics. Interestingly, the Large deviation structure underlying the population dynamics imposes a fundamental constraint on the accuracy to which one can infer a population’s fitness from finite lineage data.