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is the probability that the mutant allele is not transmitted to the next generation in any of the progeny. As you would expect, the probability that no mutant alleles are transmitted to the next generation declines as the number of progeny produced increases.

In a population that is constant in size over time, each pair of parents produces two progeny on average that take their places in the next generation. A key phrase here is "on average," meaning that not every pair of parents will produce two progeny: some parents will produce more progeny and some parents will produce fewer. As shown in the context of the variance effective population size in Chapter 3, the Poisson distribution is commonly used to model variation in reproductive success. Here too, we can use a Poisson distribution to determine the expected frequencies of each family size when the average family size is two progeny (Table 5.3). The reason we need to know the expected proportion of the parental pairs that produce a given number of progeny is that each family size has a different probability of not transmitting the mutant allele. For a given family size k, the probability that a mutant allele is not transmitted to the next generation is the product of the expected frequency of parental pairs and the chance of not transmitting the mutant allele:

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