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the fitness of any set of alleles {s1, . . . , sm} is taken to be the sum of the fitnesses of the alleles in the set, |
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However, in general, the fitness of an allele depends critically upon the influence of other alleles (epistasis). The replacement of any single allele in a coadapted set may completely destroy the complex of phenotypic characteristics necessary for adaptation to a particular environmental niche. The genetic operators provide for the preservation of coadapted sets by inducing a "linkage" between adjacent allelesthe closer together a set of alleles is on a chromosome, the more immune it is to separation by the genetic operators. Thus a more realistic set of adaptive plans provides for emphasis of coadapted sets through reproduction, combined with application of the genetic operators to provide new candidates and test established coadapted sets in new combinations and contexts. |
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More formally, an interesting set of plans can be defined in terms of a two-phase procedure: First the number of offspring of each individual A in a finite population  is determined probabilistically, so that the expected number of offspring of A is proportional to A's observed fitness µE(A). The result is a population  '(t) with certain chromosomes emphasized, along with the coadapted sets they contain. Then, in the second phase, the genetic operators from W are applied (in some predetermined order) to yield the new population  . One class of plans of considerable practical relevance can be defined by assuming that operator wi from W is applied to an individual  with probability pi (constant over time). It is easy to see that the efficiency of such a plan will depend upon the values of the pi; it is perhaps less clear that once each of the pi has a value within a certain critical range, the plan remains efficient, relative to other possible plans, over a very broad range of fitness functions  . In particular, if chromosomes containing a given linked set of alleles repeatedly exhibit above-average fitness, the set will spread throughout the population. On the other hand, if a linked set occurs by happenstance in a chromosome of above-average fitness, later tests will eliminate it (see chapters 6 and 7). It is this mode of operation (and others similar) which gives such plans robustnessthe ability to discover complex combinations of coadapted sets appropriate to a wide variety of environmental niches. |
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Because of the central role of fitness, it is natural to discuss the efficiency and robustness of a plan t in terms of the average fitnesses of the populations it produces. Formally, the average fitness in E of a finite population of genotypes  produced by t at time t is given by |
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