Survival of the densest accounts for the expansion of mitochondrial mutations in ageing

The expansion of deleted mitochondrial DNA molecules has been associated with ageing 1,2, particularly in skeletal muscle fibres 3-5; its mechanism has remained unclear for three decades. Previous accounts have assigned a replicative advantage to the deletions 6-8, but there is evidence that cells can, instead, selectively remove defective mitochondrial DNA 9. Here we present a spatial model that, without a replicative advantage, but instead through a combination of enhanced density for mutants and noise, produces a wave of expanding mutations with speeds consistent with experimental data 10. A standard model based on replicative advantage yields waves that are too fast. We provide a formula that predicts that wave-speed drops with copy number, consonant with experimental data. Crucially, our model yields travelling waves of mutants even if mutants are preferentially eliminated. Additionally, we predict that experimentally observed mutant loads can be produced by de novo mutation rates that are drastically lower than previously thought for neutral models 11. Given this exemplar of how noise, density and spatial structure affect muscle age-ing, we introduce the mechanism of stochastic survival of the densest, an alternative to replicative advantage, that may underpin other evolutionary phenomena.