The chromosomes of cancer cells are unstable, because of aneuploidy. Despite chromosomal instability, however, cancer karyotypes are individual and quasi-stable, as is evident especially from clonal chromosome copy numbers and marker chromosomes. This paradox would be resolved if the karyotypes in cancers represent chromosomal equilibria between destabilizing aneuploidy and stabilizing selection for oncogenic function. To test this hypothesis, we analyzed the initial and long-term karyotypes of seven clones of newly transformed human epithelial, mammary, and muscle cells. Approximately 1 in 100,000 such cells generates transformed clones at 2-3 months after introduction of retrovirus-activated cellular genes or the tumor virus SV40. These frequencies are too low for direct transformation, so we postulated that virus-activated genes initiate transformation indirectly, via specific karyotypes. Using multicolor fluorescence in situ hybridization with chromosome-specific DNA probes, we found individual clonal karyotypes that were stable for at least 34 cell generations-within limits, as follows. Depending on the karyotype, average clonal chromosome numbers were stable within +/- 3%, and chromosome-specific copy numbers were stable in 70-100% cells. At any one time, however, relative to clonal means, per-cell chromosome numbers varied +/-18% and chromosome-specific copy numbers varied +/-1 in 0-30% of cells; unstable nonclonal markers were found within karyotype-specific quotas of <1% to 20% of the total chromosome number. For two clones, karyotypic ploidies also varied. With these rates of variation, the karyotypes of transformed clones would randomize in a few generations unless selection occurs. We conclude that individual aneuploid karyotypes initiate and maintain cancers, much like new species. These cancer-causing karyotypes are in flexible equilibrium between destabilizing aneuploidy and stabilizing selection for transforming function. Karyotypes as a whole, rather than specific mutations, explain the individuality, fluidity, and phenotypic complexity of cancers.