Accuracy of the Second Cumulant Expansion (SCE) for real lineage data

Ascertain the accuracy of the Second Cumulant Expansion (SCE) approximation when estimating the population growth rate Λ from real single-cell lineage datasets using the fixed-divisions ensemble, and determine the conditions under which SCE is valid or fails for non-Gaussian or correlated generation-time statistics.

Background

The SCE is exact when the large-deviation rate function of the lineage first-passage time $T_n$ is quadratic (i.e., Gaussian statistics), yielding a closed-form expression for Λ. However, real generation-time distributions and correlations may deviate from Gaussian assumptions.

The authors highlight that for real data the accuracy of SCE is not known a priori and provide a counterexample where SCE fails, underscoring the need to establish validity criteria for its application to experimental datasets.