  The mutant allele frequencies in oncogenes peak around 0.40 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 pressures of the mutations 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 behavior at all times, favoring dominant alleles with
respect to the change in recessive allele frequency. Also, these equations
show, selection behaves like power-law against the recessive alleles at low
dominant allele frequency.
