summary from pp. 516 - 517 of Haldane's "The Cost of Natural Selection"

Let p_n be the frequency of an allele A in any generation n, and q_n be the frequency of an alternative allele a at the same locus for a diploid organism.

Such an organism would have three different genotypes for this locus : AA, Aa, and aa. The expected frequencies of these genotypes, based upon the frequency of the two alleles (A and a) are:
  AA - p_n²
   Aa  - 2p_nq_n
  aa   - q_n²

Using the usual relative fitnesses,  (1 - s) of individuals with the aa genotype survive for every one with the AA, and (1 - s*h) individuals having the Aa genotype survive for each AA individual. In the second case, the factor h is >= 0 and <= 1. This is the dominance factor. If h = 1, the a allele is dominant; if h = 0, the A allele is dominant; and for intermediate values of h, we have incomplete dominance. If the frequencies of the three genotypes (AA, Aa, and aa) and the relative fitness of each genotype is 1, 1 - hs, and 1 - s, then after a round of selection, the relative frequencies of the three genotypes will be:
 AA -  1 * p_n² / [ 1 - 2shp_nq_n - sq_n² ]
 Aa  -  (1 - sh) * 2p_nq_n / [ 1 - 2shp_nq_n - sq_n² ]
  aa   -  (1 - s) * q_n² / [ 1 - 2shp_nq_n - sq_n² ]
In his calculations of the substitution cost, Haldane chose to ignore the denominator (1 - 2shp_nq_n - sq_n² ) for small s.  It can be shown that ignoring the denominator introduces a maximal error of s  in one generation. If the selection coefficient is 0.01, the error will be less than 1% per generation when q is large (nearly 1.0), and it will go down as q is reduced. Haldane felt this could be ignored, but others have disagreed with Haldane on this point.

Under these conditions, the  fraction of selective deaths due to natural selection for a single generation is given approximately as follows:
    d_n = 2shp_nq_n + sq_n²
This becaue (ignoring the denominator) the frequency of the Aa genotype will be reduced by 2shp_nq_n and the frequency of the aa genotype will be reduced by sq_n² . These reductions are the fraction of selective deaths required for the change.

If q _n+1 is defined as the frequency of the a allele after a round of selection,
   q_n+1  = 1/2 * (1 - sh) *2 p_nq_n / [ 1 - 2shp_nq_n - sq_n² ] + (1 - s) * q_n² / [ 1 - 2shp_nq_n - sq_n² ]
            = [(1 - sh) * p_nq_n + (1 - s) * q_n² ]/ [ 1 - 2shp_nq_n - sq_n² ]

The change in q due to a single generation of selection (Dq_n) is given by:
   Dq_n =q_n+1  - q_n
   Dq_n =[-p_nq_n/(sh(p_n - q_n)]/[1 - 2shp_nq_n - q_n²]
   Dq_n =-sp_nq_n[(h(1 - 2h)q_n)] approximately (ignoring the denominator). Follow this link for details: Derivation of Dq_n for a Diploid
 

Therefor, D, the total of the deaths (as a fraction of the population size) over the course of a substitution is given by:
   D = S^¥_n=0 [2hsq_n + sq_n²]     (This is the summation from n=1 to infinity of 2shsq_n + sq_n².)
 After placing the constant s term outside the summation, we have:
   D = s*S^¥_n=0 [2hq_n + q_n²]