RESUMEN
Consider a population of cells, such
as bacteria, consisting of nonmutant cells and $k$
types of mutants. Recognizing that the mutation-birth-death process can be
modeled as a (k + 1)-dimensional multivariate branching process, in this paper
the probability distribution of the number of mutant cells whenthe
cell population is subjected to mutation and stochastic birth and death is
derived. The probability generating functions, the cumulants,
and an iterative formula for computing probabilities are obtained; a
representation formula for the number of mutants is also derived. The results
obtained in this paper will be useful for stochastic modeling of many mutagenicity and carcinogenesis assays.