ON THE PERSISTENCE AND PERVASIVENESS OF A NEW MUTATION

It has frequently been assumed that the persistence of a deleterious mutation (the average number of generations before its loss) and its pervasiveness (the average number of individuals carrying the gene before its loss) are equal. This is true for a particular simple, widely used infinite model, but this agreement is not general. If hs >> 1/(4N(e)), where hs is the selective disadvantage of mutant heterozygotes and N(e) is the effective population number, the contribution of homozygous mutants can be neglected and the simple approximate formula 1/hs gives the mean pervasiveness. But the expected persistence is usually much smaller, 2(log(e)(1/2hs) + 1 - gamma) where gamma = 0.5772. For neutral mutations, the total number of heterozygotes until fixation or loss is often the quantity of interest, and its expected value is 2N(e), with remarkable generality for various population structures. In contrast, the number of generations until fixation or loss, 2(N(e)/N)(1 + log(e)2N), is much smaller than the total number of heterozygotes. In general the number of generations is less than the number of individuals.