Given that some initial linkage disequilibrium is necessary before recombination can act as an evolutionary force in a random-mating population, it is important to understand what factors can create an initial disequilibrium. Many factors can create linkage disequilibrium, including:
• Nonrandom mating
• Finite population size
• Natural selection
Note that this list of factors that can generate linkage disequilibrium corresponds to the very same factors that are assumed not to occur in the simple Hardy-Weinberg model (Table 2.1).
All of these factors will be considered in this book, but for now we focus only upon the first: mutation. The impact of mutation is most easily seen by considering another measure of linkage disequilibrium known as the normalized linkage disequilibrium D', which is the linkage disequilibrium divided by its theoretical maximum absolute value. Because two-locus gamete frequencies cannot be negative or greater than the corresponding single-locus allele frequencies (equation 2.7), we have that
Solving equation 2.9 for gAB and substituting the result into inequality 2.12 yield
= min (Pa(1 - Pb), Pb(1 - Pa)) or - PaPb < D < min (pAPb, PaPB)
As noted above, equations similar to 2.9 can be derived with respect to the other gamete frequencies, such as gab, so D also satisfies the inequality
Thus we have
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