Strongly monomorphic limit

In this limit the mutation rate tends to zero while the population size is kept fixed, ϵ → 0 [52, 56–58]. Consider the Fourier transform of the steady-state distribution in Eq 7:

where the integral is over the (K − 1)-dimensional simplex. Using Eq 9, we can write the Fourier transform as a ratio of two generalized hypergeometric functions:

Taking the ϵ → 0 limit yields

Thus the steady-state distribution in the monomorphic limit is given by:

where Vol(ΣK-1)=K/(K-1)! is the volume of the (K − 1)-dimensional simplex and (1_m)_i = δ_mi. The population resides in one of the K monomorphic states available to it, with the probability of being in a particular state exponentially weighted by its fitness [59–61].