Fluctuation tests: how reliable are the estimates of mutation rates?

Fifty one years ago, Luria and Delbrück published in Genetics a paper that was to become a classic. In it they proved, beyond all reasonable doubt, that bacteria were mutating to phage resistance long before they could have encountered any bacteriophage. Luria and Delbrück also showed how the same experimental data could be used to estimate bacterial mutation rates. Since that time and in many different contexts the methods that they introduced have been used to estimate mutation rates. However, little seems to be known about the errors to be expected in such estimates. In what follows I examine how much uncertainty in the estimates is to be expected merely on the basis of the stochastic variability inherent in the sampling process. On the basis of this examination I question a few traditional ideas and conclude with some practical suggestions. The results were obtained by stimulation. It is my hope that they may inspire others to provide a rigorous theoretical basis for such calculations.