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238                                                CHAPTER 11

                                These rough guidelines and comparative predictions set a baseline
                              for expectations of variant allele frequency. When observations deviate
                              significantly from expectations, then we may turn to forces other than a
                              balance between deleterious mutation and purging by natural selection.


                              HIGH PENETRANCE AND EARLY ONSET
                                Suppose a mutation is expressed in all carriers, and those carriers
                              die before they have reproduced. In this situation, each case must arise
                              from a new mutation, and the frequency of mutated alleles, q, is roughly
                              equivalent to the mutation rate per generation, u, that is, q = u.
                                Inherited cases of retinoblastoma, Wilms’ tumor, and skin cancer in
                              xeroderma pigmentosum transmit as dominant mutations. Most indi-
                              viduals who carry a highly penetrant mutation develop the disease dur-
                              ing childhood or early life. Without treatment, carriers do not usually
                              reproduce. These diseases all occur at frequencies, q, of approximately
                              10 −5 –10 −4  (Vogelstein and Kinzler 2002).
                                The commonly quoted values for mutation rate, u, tend to be in the
                              range of 10 −6 –10 −5  per gene per generation (Drake et al. 1998), an order
                              of magnitude lower than the frequency of cases. For this type of ap-
                              proximate calculation, a match within an order of magnitude suggests
                              that we have roughly the right idea about the factors that influence allele
                              frequencies.
                                Certainly, other estimates of frequency for these diseases or other
                              early-onset cancers will not match so closely to the usual estimate of
                              the mutation rate. A mismatch implicates some force beyond the stan-
                              dard baseline mutation rate and immediate removal of all mutations by
                              natural selection. For example, the penetrance may be less than perfect,
                              some carriers may reproduce, or the gene may be unusually mutable.


                              AGE OF ONSET AND THE FORCE OF SELECTION
                                Some inherited mutations have low penetrance or cause later-onset
                              disease. Natural selection removes a mutation from the population in
                              proportion both to the probability that it causes disease and to the re-
                              duction in reproductive success of those individuals who express the
                              disease (Rose 1991; Nunney 1999, 2003; Frank 2004e). Reduction in
                              reproductive success depends on the age of onset: later onset has less
                              effect on transmission of alleles to the next generation. Figure 11.8
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