Efficient mathematical methodology to determine multistep mutant burden in spatially growing cell populations.

The accurate computational prediction of mutant burden in spatially structured growing cell populations is a major goal both for basic evolutionary science, such as interpreting bacterial evolution studies, and for clinical applications, such as predicting the timing of drug resistance-induced cancer relapse for individual patients. Yet, this is currently not feasible for biologically realistic parameters, due to the inefficiency of computationally simulating stochastic mutant dynamics in large populations. Here, we fill this gap by deriving universal scaling laws that allow the straightforward prediction of the number of single-hit, double-hit, and multihit mutants as a function of wild-type population size in spatially expanding populations, in different spatial geometries, without the need to perform lengthy computer simulations. We demonstrate the applicability of this approach by reconciling different results from experimental evolution studies in bacteria that examine the role of gene amplifications for the rate of evolution.