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Consider, now, how such a prediction would differ from one made under the assumption of independent substitution of alleles, using the earlier example (the tables of section 7.3). In the present case the elements of W play the role of indices: w1 at position 1 indicates the allele 1 for position 1 is present; the same w1 at position 2 indicates the presence of allele 1 for position 2, an allele which may be quite different from the former one. Under independent selection |
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Thus, under independent selection, combinations of alleles have a rate of change which is the sum of their average excesses. |
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Reinterpreting Table 4 in terms of average excesses (noting that  ), we see that the rate of change of the favorable  (Table 3) is |
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while that of the less favorable  is  under independent selection. Thus independent selection leads to maladaptation here. |
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As mentioned earlier, adaptation under independent selection amounts to adaptation under the operator equilibrium of section 6.2, |
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This is a common assumption in mathematical genetics, but it clearly leads to maladaptations whenever |
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The above equation for a(x) in terms of  shows this to be the case whenever  , which occurs whenever the fitness is a nonlinear function of the alleles present, i.e., whenever there is epistasis. |
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