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A conceptual model is proposed for the genetic evolution of many human solid tumors that is based on the observations that cancer cells may spontaneously double their chromosome number; that cells with excessive chromosome numbers may be cytogenetically unstable, both losing chromosomes randomly during subsequent cell divisions, and often developing structural abnormalities in the chromosomes that are retained; and that some structural chromosome abnormalities may activate growth-promoting genes. The sequence of tetraploidization with chromosome loss can occur repeatedly in a given tumor. The available evidence supporting the model is reviewed. A computer simulation system that embodies these concepts is described and the model is used to generate distributions of chromosome number/cell under various simulated conditions and in a variety of simulated biological settings. A simulation of the time course of changes in chromosome number per cell that accompany the spontaneous neoplastic transformation of mouse fibroblasts in vitro is described. The best fit to the data was obtained when provision was made for the activation of at least two growth-promoting genes. The conditions for generating discrete aneuploid peaks in cytogenetic and flow cytometric studies were explored; our modeling studies suggest that the activation of a growth promoting gene is required in order to produce a discrete aneuploid peak. Our modeling studies suggest that the overrepresentation of individual oncogene-bearing chromosomes in aneuploid cell lines may require the activation of gene dose-dependent growth-promoting genes and is not likely to occur in cell lines in which at least two copies of each normal chromosome are required for cell survival. Overall, the results obtained using the model are consistent with a wide variety of flow cytometric and cytogenetic studies in human solid tumors.