Deleterious alleles maintained by recurrent mutation.
          stable equilibrium(read as "q hat," where $q$= 0) reached
                when rate of replacement (by mutation)
                balances rate of removal (by selection).

       µ = frequency of new mutant alleles per locus per generation
           µ = 10^-6 : 1 in 1,000,000 gametes has new mutant 

            then  =  $\sqrt{⋯}$    [see derivation below]

        Ex.: For recessive lethal allele (s  = 1) with mutation rate of µ = 10^-6
               then  =   $\sqrt{⋯}$   =    $\sqrt{⋯}$ =  0.001
 

Mutational Genetic Load
    Lowered selection against deleterious allele increases frequency
        Medical intervention increases frequency of heritable conditions
            in Homo (e.g., diabetes, myopia)
    Eugenics: 1920s ~ 1960s social policy
            Modification of human condition by selective breeding
            'positive eugenics': encouraging people with "good genes" to breed
            'negative eugenics': discouraging people with "bad genes'' from breeding
                   e.g., immigration control, compulsory sterilization, and worse
                   [See: SJ Gould, "The Mismeasure of Man"]

       Is eugenics effective at reducing frequency of deleterious alleles?
            What proportion of 'deleterious alleles' occur in heterozygous carriers?

       (2pq) / 2q² = p/q  1/q    (if  q << 1)

             for s = 1, ratio 1000 / 1 : most variant alleles in heterozygotes,
                                                    not subject to selection

^{Conclusion: if most mutations are rare (u < 0.001) & selectively disadvantageous ( s > 0.01)
                      mutation will not maintain population variation at high levels observed:}

                                      for paired values of s & µ by approximation
 

HOMEWORK: Suppose myopia due to recessive allele b at a single locus, with mutation rate µ = 10^-5 from B b.
                               Suppose myopia historically associated with selection coefficient s = 0.3,
                                   & vision correction has reduced selection by 90%.
                          1) What is former vs new equilibrium frequency of b allele?
                         2) What is former vs new equilibrium frequency of persons with myopia ?

Derivation of Mutation / Selection equilibrium 

    f(a) = q << 1   &   f(A) = p ~ 1
    f(Aa) =  µ  mutation rate (# new mutant alleles / gamete)

: equilibrium between loss of a due to selection
                                     & replacement of a by new mutation

        change in f(a) due to selection: q_s = -spq² / (1 - sq²)     [complete dominance model]
        change in f(a) due to mutation: q_µ  = µp

Then   q_µ  +  q_s  =  µp -  spq² / (1 - sq²)
                                 µp  -  spq²                     [ (1 - sq²)    1   if   q << p ]
                              =  (p) (µ - sq²)

At equilibrium,  q = 0 = (p) (

µ - s²)

- s²  

       [if p  1 ]

                              s² =  µ
                                ² =  µ / s

                           =$($