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follow in a single generationvariants chosen completely at random are almost certain to be sterile. |
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In attempting to see how this "dilemma" is resolved, we begin to encounter some of the deeper questions about adaptation. We can only hint at the dilemma's resolution in this preliminary survey. Even a clear statement of the resolution requires a considerable formal structure, and proof that it is in fact a resolution requires still more effort. Much of the understanding hinges on posing and answering two questions closely related to the questions generated by the concept of fitness. How can an adaptive plan t (specifically, here a plan for genetic systems) retain useful portions of its (rapidly growing) history along with advances already made? How is the adaptive plan t to access and use its history (the portion stored) to increase the likelihood of fit variants ( such that µE(A) is above average)? Once again these are questions relevant to the whole spectrum of fields mentioned at the outset. |
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The resolution of the dilemma lies in the action of the genetic operators W within the reproductive plan t. The best-known genetic operators exhibit two properties strongly affecting this action: (1) The operators do not directly affect the size of the populationtheir main effect is to alter and redistribute alleles within the population. (The alleles in an individual typically come from more than one source in the previous generation, the result, for example, of the mating of parents in the case of vertebrates, or of transduction in the case of bacteria.) (2) The operators infrequently separate alleles which are close together on a chromosome. That is, alleles close together typically remain close together after the operators have acted. |
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Useful clues to the dilemma's resolution emerge when we look at the effect of these operators in a simple reproductive plan, t1. This plan can be thought of as unfolding through repeated application of a two-phase procedure: During phase one, additional copies of (some) individuals exhibiting above-average performance are added to the population while (some) individuals of subaverage performance are deleted. More carefully, each individual has an expected number of offspring, or rate of reproduction, proportional to its performance. (If the population is to be constant in size, the rates of reproduction must be "normalized" so that their average over the population at any time is 1.) During phase two, the genetic operators in W are applied, interchanging and modifying sets of alleles in the chromosomes of different individuals, so that the offspring are no longer identical to their progenitors. The result is a new, modified population. The process is iterated to produce successive generations of variants. |
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More formally, in an environment which assigns an observable performance |
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