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The interaction of genes is more and more recognized as one of the great evolutionary factors. The longer a genotype is maintained in evolution, the stronger will its developmental homeostasis, its canalizations, its system of internal feed backs become. . . . one of the real puzzles of evolution is how to break up such a perfectly co-adapted system in such a way so as not to induce extinction . . . |
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Mayr in Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution,ed. Moorhead & Kaplan (p. 53) |
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The other and I think more interesting problem, which we have hardly begun to solve, is the question: How many changes of information are necessary to explain evolution ? |
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Waddington in Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution, ed. Moorhead & Kaplan (p. 96) |
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And, even though the centennial for the Origin of Species has passed, speciation still lacks a general mathematical explanation. Moreover, the question of "enough time" plagues the neo-Darwinian almost as much as it did his predecessors. It is a question which weighs heavily if it is assumed that coadapted sets of alleles occur only by the spread of mutant alleles to the point that relevant combinations are likely (see Eden's [1967] comments). |
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In the present context each of these questions can be rephrased in terms of the processing of schemata by genetic operators. This allows us to probe the origin and development of coadapted sets of alleles much more deeply, particularly the way in which different genetic mechanisms enable exploitation of useful epistatic effects. In the next chapter, we will be able to extend Corollary 6.4.1 to demonstrate the simultaneous rapid spread of sets of alleles, as sets, whenever they are associated with above-average performance (because of epistasis or otherwise). Theorem 7.4 establishes the efficiency of this process for epistatic interactions of arbitrary complexity (i.e., for any fitness function  , however complex). Section 7.4 gives a specific example of the process in genetic terms and exhibits a version of Fisher's (1930) theorem applicable to arbitrary coadapted sets. Finally, in section 9.3, the formalism is extended to give an approach to speciation. This extension suggests reasons for competitive exclusion within a niche, coupled with a proliferation of (hierarchically organized) species when there are many niches. |
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For the nongeneticist, the illustration at the end of section 6.2 should convey some of the flavor of algorithms of type  as optimization procedures. It is easy enough to extend that illustration to cover inversion and mutation. For example, under the revised representation of section 6.3 each bit d is paired with a number j designating its significance (i.e. (j, d) designates the bit d·2-i). Thus bits |
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