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x1 for a period comparable to the time it took to establish it. Dominance makes this possible. |
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Summing up: Under dominance, a given minimal rate of occurrence of alleles can be maintained with a mutation rate which is the square of the rate required in the absence of dominance. Moreover, with the dominance-change operator the combination of alleles defining a schema can be "reserved" (as recessives) or "released" (as dominants) in a single operation. |
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When the performance function depends upon many more or less independent factors, there is another pair of operators, segregation and translocation which can make a significant contribution to efficiency. In such situations it is useful to make provision for distinct and independent sets of associations (linkages) between genes. This again calls for an extension in the method of representation. Let each element in  be represented by a set of homologous pairs of n-tuples, and let crossover be restricted to homologous n-tuples. After two elements of , A and A',are chosen for crossover and after all homologous pairs have been crossed (as detailed under the discussion of dominance change) then from each pair of resultants one is chosen at random to yield the offspring's n-tuples. Each offspring thereby consists of the same number of homologous pairs of n-tuples as its progenitors. The genetic counterpart of this random selection of resultants is known as segregation. Clearly, under segregation, there is no linkage between alleles on separate nonhomologous n-tuples, while alleles on homologous n-tuples are linked as before. With this representation it is natural to provide an operator which will shift genes from one linkage set to another (so that, for example, schemata that are useful in one context of associations can be tested in another). The easiest way to accomplish this is to introduce an exceptional crossover operator, the translocation operator, which produces crossing-over between randomly chosen nonhomologous pairs. |
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Another genetic operation provides a means of adaptively modifying the effective mutation rate for different closely linked sets of alleles. The operator involved is intrachromosomal duplication (see Britten 1968); it acts by providing multiple copies of alleles on the same n-tuple. To interpret this operation, n-tuples with multiple copies of the alleles for a given gene must be mapped into the set of original structures. This can be done most directly by extending the concept of dominance to multiple copies of alleles. With this provision, if there are kacopies of a given allele a,the probability of one or more mutations of allele a is katimes greater than if there were but one copy. That is, the probability of occurrence, via mutation, of allele a' ¹ a is increased katimes. Thus, increases and decreases in the number of copies of an allele have the effect of modifying the (local) mutation |
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