Aneuploidy theory explains tumor formation, the absence of immune surveillance, and the failure of chemotherapy.

The autocatalyzed progression of aneuploidy accounts for all cancer-specific phenotypes, the Hayflick limit of cultured cells, carcinogen-induced tumors in mice, the age distribution of human cancer, and multidrug-resistance. Here aneuploidy theory addresses tumor formation. The logistic equation, phi(n)(+1) = rphi(n) (1 - phi(n)), models the autocatalyzed progression of aneuploidy in vivo and in vitro. The variable phi(n)(+1) is the average aneuploid fraction of a population of cells at the n+1 cell division and is determined by the value at the nth cell division. The value r is the growth control parameter. The logistic equation was used to compute the probability distribution for values of phi after numerous divisions of aneuploid cells. The autocatalyzed progression of aneuploidy follows the laws of deterministic chaos, which means that certain values of phi are more probable than others. The probability map of the logistic equation shows that: 1) an aneuploid fraction of at least 0.30 is necessary to sustain a population of cancer cells; and 2) the most likely aneuploid fraction after many population doublings is 0.70, which is equivalent to a DNA(index)=1.7, the point of maximum disorder of the genome that still sustains life. Aneuploidy theory also explains the lack of immune surveillance and the failure of chemotherapy.