Mutant evolution in spatially structured and fragmented populations

Understanding mutant evolution in spatially structured systems is crucially important for a range of biological systems, including bacterial populations and cancer. While previous work has shown that the mutation load is higher in spatially structured compared to well-mixed systems for neutral mutants in the absence of cell death, we demonstrate a significantly higher degree of complexity, using a comprehensive computational modeling approach that takes into account different mutant fitness, cell death, and different population structures. While an agent-based model assuming nearest neighbor interactions predicts a higher abundance of neutral or advantageous mutants compared to well-mixed systems of the same size, we show that for disadvantageous mutants, results depend on the nature of the disadvantage. In particular, if the disadvantage occurs through higher death rates, as opposed to lower reproduction rates, the result is the opposite, and a lower mutation load occurs in spatial compared to mixed systems. Interestingly, we show that in all cases, the same results are observed in fragmented patch models, where individuals can migrate to randomly chosen patches, thus lacking a strict spatial component. Hence, the results reported for spatial models are the consequence of population fragmentation, and not spatial restrictions per se. We further derive growth laws that characterize the expansion of wild type and mutant populations in different dimensionalities. For example, we find that while disadvantageous mutant abundance scales with the total population size, N, neutral mutants grow faster (as N2 for 1D, as N3/2 in 2D, and as N4/3 in 3D). Advantageous mutants scale with the cube of N in 1D and with the square of N in higher dimensions. These laws are universal (as long as mutants remain a minority) and independent of \"microscopic\" modeling details.