Cell death and growth dynamics shape DNA-replication-based estimates of microbial growth

Inferring bacterial growth rates is fundamental to understanding microbial interactions and community dynamics, but remains difficult in natural settings where time points are limited or organisms are unculturable. In these cases, a widely used method is the origin-to-terminus ratio, or peak-to-trough ratio (PTR), which estimates DNA replication activity from origin and terminus copy numbers. Although PTR is theoretically related to bacterial growth rate, it is frequently benchmarked against population growth rate, which reflects the balance between cell division and loss. Understanding when and why these measures diverge is therefore important for validating PTR-based approaches. To quantify how departures from steady growth affect PTR, population growth rate, and bacterial growth rate, we developed a stochastic, cell-based model that explicitly tracks DNA replication, cell division, and cell death. We show that transient stress-induced mortality and heterogeneous survival can cause PTR to fail to reflect population growth rate while still reflecting bacterial growth rate. We experimentally validated these predictions by exposing \textit{Escherichia coli} to osmotic shock or antibiotics, and measuring population growth rate and DNA replication activity. We further show that initial physiological state, lag before replication resumes, and abrupt growth arrest can alter the relationship between PTR and population growth rate. In the presence of mortality, lag can increase PTR's correspondence with population growth rate while decreasing its correspondence with bacterial growth rate. These results provide a mechanistic and quantitative framework for interpreting PTR across changing growth states, mortality regimes, and environmental perturbations.