Progress of a half century in the study of the Luria-Delbruck distribution

The Luria-Delbruck mutation model has been mathematically formulated in a n umber of ways. This review article examines four most important formulation s, focusing on important practical issues closely linked with the distribut ion of the number of mutants. These issues include the probability generati ng functions, moments (cumulants), computational methods and asymptotics. T his review emphasizes basic principles which not only help to unify existin g results but also allow for a few useful extensions. In addition, the revi ew offers a historical perspective and some new explanations of divergent m oments. (C) 1999 Published by Elsevier Science Inc. All rights reserved.