Here we will calculate the fitness advantage of a genotype with
mutation rate 
over a genotype with a very low (or 0)
mutation rate. Under the assumptions of appendix 1, it is clear that
the growth rate for a whole cycle of 2n generations will be 
for a mutation rate 
.
To calculate the selection for 
we use
equation 22. This gives us
where we used 
. For big enough
n, when 
, and this gives:
Which means that the growths rate is of the form 
, K is
a function which depends only on s, and not on n. If we compare
this with the growths rate of for a mutation rate of 0, we see
that the relative growth rate of a genotype with vs. a
genotype with will be 
for 2n
generations, or 
per generation. When n is large enough, this gives 
. Thus the selection in favor of the ``right'' mutation
rate will be at least of strength 
.