Spatial population structure can reverse the dependence of mutant burden on the death-to-birth ratio of cells

Expanding cell populations, including bacterial colonies and tumors, continuously accumulate mutations as they grow. Yet how mutant burden depends on the cellular death-to-birth ratio in spatially structured populations has not been addressed, despite clinical studies associating higher tumor turnover with both better and worse patient outcomes across cancers. This question is especially relevant for deleterious mutants, which can become advantageous if the environment changes, such as when treatment begins. Mutant accumulation has been studied extensively in well-mixed populations. Here, we derive a new closed-form approximation for the mean deleterious mutant burden at a specified population size when cell death is nonzero, serving as a baseline for comparisons to spatial structure. We show that spatial structure, a defining feature of solid tumors, can fundamentally alter how mutant burden depends on the death-to-birth ratio. Relationships that increase monotonically in well-mixed populations can become nonmonotonic or even decrease in spatially expanding populations, depending on population size and the fitness cost of mutants. These results provide a mechanistic framework for understanding why higher tumor turnover has been associated with either improved or worsened outcomes across patients and cancer types. An analysis of the probability that a colony regrows after an environmental change (such as treatment initiation) reveals a similar pattern: spatial structure can reverse or reshape this dependence. Overall, our findings establish spatial structure as a key determinant of how cellular death-to-birth ratios shape mutant accumulation, with implications for interpreting clinical data and predicting the burden of preexisting mutants during tumor evolution. Significance statementThe number of mutants present when a growing cell population reaches a given size shapes its capacity to adapt, since deleterious mutants can become advantageous once conditions change, such as when cancer treatment begins. Clinical studies report contradictory links between tumor cell turnover (death-to-birth ratio) and patient outcomes, with higher turnover linked to both better and worse prognosis. Building on established theory for well-mixed populations, we show that spatial population structure, a key feature of solid tumors, can make mutant burden increase, decrease, or vary non-monotonically with the death-to-birth ratio, depending on tumor size and mutant fitness cost, patterns absent in the well-mixed system. This resolves the contradiction and clarifies how tumor turnover shapes its potential to evolve and progress.