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On the other hand the nonlinearities of µx (Table 3) have no effect on  . Lemma 7.2 makes this quite clear. |
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whereas  now satisfies |
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Clearly  quickly gains the ascendancy. Thus a plan of type preserves and exploits useful interactions between the weights. Moreover Lemma 7.2, in conjunction with Theorem 7.4, makes it clear that such a plan can actually exploit local optima (false peaks) to improve its interim performance on the way to a global optimum. |
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4. Robustness Vis-À-Vis A Complex Natural Adaptive System |
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Many points made in connection with the game-playing algorithm can be translated to the much more complex situation in genetics. We shall see that these points weigh strongly against the (still widely held) view that biological adaptation proceeds by the substitution of advantageous mutant genes under natural selection. In addition, they directly contradict the closely related view (in mathematical genetics) that alleles are replaced independently of each other, increasing or decreasing according to their individual average excesses. Rather, the results of this chapter suggest that the adaptive process works largely in terms of pools of schemata (potentially coadapted sets of genes) instead of gene pools. Because the pool of schemata corresponding to a population is so much larger than the pool of genes, selection has broader scope (some multiple of 2l vs. 2l, or with k =2 alleles and just l = 100 loci, some multiple of 1030 vs. 200) with many more pathways to improvement, and the great advantage of intrinsic parallelism. |
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To translate the results on robustness to genetics, the central genetic parameter, "average excess (of fitness)," must be defined in terms of observational quantities  . First let  ; that is,  is the effective rate of increase of the schema x at time t. For adaptive plans of type  , |
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