..... A single mutant expands clonally and finally replaces the wild-type population of a whole cell. One proposal to explain the driving force behind this accumulation states that the reduced size leads to a shorter replication time, which provides a selection advantage. However, this idea has been questioned on the grounds that the mitochondrial half-life is much longer than the replication time, so that the latter cannot be a rate limiting step. To clarify this question, we modelled this process mathematically and performed extensive deterministic and stochastic computer simulations to study the effects of replication time, mitochondrial half-life and deletion size. Our study shows that the shorter size does in principle provide a selection advantage, which can lead to an accumulation of the deletion mutant. However, this selection advantage diminishes the shorter is the replication time of wt mtDNA in relation to its half-life. Using generally accepted literature values, the resulting time frame for the accumulation of mutant mtDNAs is only compatible with the ageing process in very long lived species like humans, but could not reasonably explain ageing in short lived species like mice and rats.