Mutant scaling laws reveal that accelerated evolution via gene amplification requires spatially structured population growth

Principles of evolution in spatially structured expanding populations have recently received much attention, but more work remains to be performed, especially for complex, multi-step evolutionary processes, where mutations are accumulated in an expanding population. A key limitation is that the simulation of spatially explicit stochastic computational models is essential, but not feasible for larger population sizes characteristic of prokaryotic and eukaryotic cell populations. We describe a methodological advance by deriving scaling laws that allow the straightforward prediction of the number of single-hit, double-hit and multi-hit mutants as a function of wild-type population size in spatially expanding populations. While this is a versatile tool to address a range of cutting-edge evolutionary questions, here we apply this methodology to reconcile apparently contradicting data from experimental evolution studies regarding the role of gene amplifications for the emergence of point mutations in bacteria. Applying the scaling laws, we demonstrate that in populations that expand in a 2D or a 3D spatial setting, gene amplifications can significantly promote mutant emergence, and that this is not possible in well-mixed populations. In support of the predictions, experiments that do show accelerated mutant evolution through gene amplifications grew bacteria in spatially restricted lawns, while those that failed to show an effect grew bacteria in non-spatial liquid media.