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LEMMA 6.5.1: To assure that, at all times, each allele a occurs with probability P(a, t)³ 1/MT, the mutation rate 1PM must be ³ 1/MT in the absence of dominance, but only ³(1/MT)2 with dominance. |
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For example, to sustain an average density of at least 10-3 for every allele, the mutation rate would have to be 10-3 without dominance, but only 10-6 with dominance. |
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It should be noted that, with dominance, P(v0, t) is no longer the expected testing rate. Although dominance allows the constant mutation load to be reduced, while maintaining a given proportion of disfavored alleles as a reserve, the testing rate of the reserved alleles is only P2(v0, t) not P(v0, t). This reservoir is only released through a change in dominance. |
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Dominance change in the general case  occurs simply through a change in context, so that dominance is directly subject to adaptation by selection of appropriate contexts. In the more restricted case  a special operator is required. The example using Vh = {1, 10, 0} will serve to illustrate the process. The basic idea will be to replace some or all occurrences of 1 by 10, and vice versa, in an l-tuple. Thus the previous recessives become dominant and vice versa, this change being transmitted to all progeny of the l-tuple. A simple way to do this is to designate a special inversion operator which not only inverts a segment but carries out the replacement in the inverted segment. (In genetics, there is a distant analogue in the effects produced by changes of context when a region is inverted, but it should not be taken literally.) Thus for the dominance-change inversion operator, step 3, p.107 of the inversion operator is followed by |
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4. In the inverted segment each occurrence of 1 is replaced by 10 and vice-versa. |
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With this operator the defining alleles of an arbitrary schema can be "put in reserve" in a single operation to be "released" later, again in a single operation. |
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Dominance provides a reserved status not only for alleles but, more importantly, for schemata. A useful schema x1 defined on many positions may be the result of an extensive search. As such it represents a considerable fragment of the adaptive plan's history, embodying important adaptations. When it is superseded by a schema x2 exhibiting better performance, it is important that x1 not be discarded until it is established that x2 is useful over the same range of contexts as x1. x2's performance advantage may be temporary or restricted in some way, or x1 may be useful again in some context engendered by x2. In any case it is useful to retain |
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