Why do mutant allele frequencies in oncogenes peak around .40 and rapidly decrease?

The mutant allele frequencies in oncogenes peak around .40 and rapidly decrease. In this article, we explain why this is the case. Invoking a key result from mathematical analysis in our model, namely, the inverse function theorem, we estimate the selection coefficients of the mutant alleles as a function of germline allele frequencies. Under complete dominance of oncogenic mutations, this selection function is expected to be linearly correlated with the distribution of the mutant alleles. We demonstrate that this is the case by investigating the allele frequencies of mutations in oncogenes across various cancer types, validating our model for mean effective selection. Consistent with the population genetics model of fitness, the selection function fits a gamma-distribution curve that accurately describes the trend of the mutant allele frequencies. While existing equations for selection explain evolution at low allele frequencies, our equations are general formulas for natural selection under complete dominance operating at all frequencies. We show that selection exhibits linear behaviour at all times, favouring dominant alleles with respect to the change in recessive allele frequencies. Also, these equations show, selection behaves like power law against the recessive alleles at low dominant allele frequencies.