Say you have a genotype A that produces x offspring and another genotype B that produces y offspring, where x>y. These x offspring are of genotype A but with modest differences in fitness due to mutation and these y offspring are of genotype B but with modest differences in fitness due to mutation. How would you model how many offspring these x offspring can themselves produce and how many offspring these y offspring can themselves produce as a function of the quantity their original parents produced?
Obviously, you could say that each descendant of genotype A produces x and each descendant of genotype B produces y, but that would unrealistically benefit genotype A, since realistically, one of B’s offspring could have a chance to be fitter than A’s by developing a favorable mutation or one of A’s offspring could have a chance to be less fit than B’s by developing an unfavorable mutation.
You could say that each descendant of genotype A and B produce (x+y)/2, but this would not be fair to genotype A, since it is fitter, so its offspring would probably be fitter than B’s offspring.
You could use the breeder’s equation and say that each of A’s offspring produce xh+m(1-h), where h is the heritability of fitness and m is the population mean, and that each of B’s offspring produce yh+m(1-h). But this is also unfair to genotype B because all of its offspring are less fit than all of A’s offspring, since x>y. So, what’s a way of modeling how resultant mutations might occur, such that B has a chance of producing some offspring that are fitter than A’s offspring?