The amplification model for adaptive mutation: simulations and analysis.

It has been proposed that the lac revertants arising under selective conditions in the Cairns experiment do not arise by stress-induced mutagenesis of stationary phase cells as has been previously assumed. Instead, these revertants may arise within growing clones initiated by cells with a preexisting duplication of the weakly functional lac allele used in this experiment. It is proposed that spontaneous stepwise increases in lac copy number (amplification) allow a progressive improvement in growth. Reversion is made more likely primarily by the resultant increase in the number of mutational targets--more cells with more lac copies. The gene amplification model requires no stress-induced variation in the rate or target specificity of mutation and thus does not violate neo-Darwinian theory. However, it does require that a multistep process of amplification, reversion, and amplification segregation be completed within approximately 20 generations of growth. This work examines the proposed amplification model from a theoretical point of view, formalizing it into a mathematical framework and using this to determine what would be required for the process to occur within the specified period. The analysis assumes no stress-induced change in mutation rate and describes only the growth improvement occurring during the process of amplification and subsequent elimination of excess mutant lac copies. The dynamics of the system are described using Monte Carlo simulations and numerical integration of the deterministic equations governing the system. The results imply that the amplification model can account for the behavior of the system using biologically reasonable parameter values and thus can, in principle, explain Cairnsian adaptive mutation.