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Stated another way, allele v0 is only expressed or tested when it occurs in the pair (v0, v0). Let us assume that, on the average, the adaptive plan is to provide at least one occurrence of each allele in every T generations. That is, P(v0, t) > 1/MT must be assured. In the absence of dominance (using the earlier single l-tuple representation), let the reproduction rate of v0 (corrected for operator losses) be  exclusive of additions resulting from mutation. Then |
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To keep P(v0, t) ³ 1/MT for all t, 1 PM must be at least large enough to maintain the steady state P(v0, t) = P(v0, t + 1) = 1/MT. That is, |
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If MT is at all large (as it will be for all cases of interest) this reduces to |
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as a close approximation to the mutation rate required without dominance. (In the extreme case that alleles v0 are deleted whenever they are tested, 1PM = 1/MT.) With dominance, the allele v0 is subject to selection only when the pair (v0, v0) occurs. Under crossover, as extended to homologous pairs, the pair (v0, v0) occurs with probability P2(v0, t). The loss from selection then is |
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the factor 2 occurring because 2 copies of v0 are lost each time the pair (v0, v0) is deleted. Again the gains from mutation are |
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where the factor 2 occurs because the M homologous pairs are 2M l-tuples. Thus |
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for the homologous pairs with dominance. Setting P(v0, t) = P(v0, t + 1) = 1/MT as before, and solving, we get |
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