Long term-low dose mutation assays offer a means to study the genetic effects of environmental mutagens at concentrations relevant to human exposure. These assays involve continuous induction of mutants, serial dilution of cultures and sampling to determine the mutant fraction as a function of time and mutagen concentration. An arithmetic model for the expected variance among identically treated cultures is presented. This model provides means to calculate a predicted variance of the mutant fractions and mutation rates in typical long term-low dose experiments. We have calculated the expected variances of the mutant fraction with this model and compared them to the observed variances among 4 independent experiments in which human lymphoblastoid cells were treated for 5, 10, 15 and 20 days with a non-toxic concentration of the mutagen 4-aminobiphenyl. Mutations at the HPRT locus were measured by determining the 6-thioguanine-resistant mutant fraction. The expected and observed variances of the mutant fractions are in close agreement. This model is adequate to predict the variance of the mutant fraction and should be useful in experimental design and objective evaluation of long term-low dose mutation assays.