small. Thus the intensity of selection approximates to . Comparing to the above, we have that , if we say that is the quotient of deaths for the selected locus and is again the quotient of deaths for the entire population. The problem statement is therefore that the alleles in question are not particularly beneficial under the previous circumstances; but a change in environment favors these genes by natural selection. The individuals without the genes are therefore disfavored, and the favorable genes spread in the population by the death (or lowered fertility) of the individuals without the genes. Note that Haldane's model as stated here allows for more than one gene to move towards fixation at a time; but each such will add to the cost of substitution. The total cost of substitution of the gene is the sum of all values of over all generations of selection; that is, until fixation of the gene. Haldane states that he will show that depends mainly on , the small frequency of the gene in question, as selection begins – that is, at the time that the environmental change occurs (or begins to occur). A mathematical model of the cost of diploids Let A and a be two alleles with frequencies and in the generation. Their relative fitness is given by where 0 ≤ ≤ 1, and 0 ≤ λ ≤ 1. If λ = 0, then Aa has the same fitness as AA, e.g. if Aa is phenotypically equivalent with AA (A dominant), and if λ = 1, then Aa has the same fitness as aa, e.g. if Aa is phenotypically equivalent with aa (A recessive). In general λ indicates how close in fitness Aa is to aa. The fraction of selective deaths in the generation then is and the total number of deaths is the population size multiplied by Important number 300 Haldane approximates the above equation by taking the continuum limit of the above equation. This is done by multiplying and dividing it by dq so that it is in integral form substituting q=1-p, the cost (given by the total number of deaths, 'D', required to make a substitution) is given by Assuming λ < 1, this gives where the last approximation assumes to be small. If λ = 1, then we have In his discussion Haldane writes that the substitution cost, if it is paid by juvenile deaths,