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there are many well-established procedures for optimization, inference, mathematical learning, etc., where the relation between sampled performance and future sampling is quite different. Nevertheless reproduction in proportion to measured performance is an important concept which can be generalized to yield sampling plansreproductive plansapplicable to any adaptive problem (including the broad class of problems where there is no natural notion of reproduction). Moreover, once reproductive plans have been defined in the formal framework, it can be proved that they are efficient (in a reasonable sense) over a very broad range of conditions. |
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A part of the answer to the second question, for genetic systems, comes from the observation that future populations can only develop via reproduction of individuals in the current population. Whatever history is retained must be represented in the current population. In particular, the population must serve as a summary of observed sample values (performances). The population thereby has the same relation to an adaptive process that the notion of (complete) state has to the laws of physics or the transition functions of automata theory. Knowing the population structure or state enables one to determine the future without any additional information about the past of the system. (That is, different sampling sequences which arrive at the same population will have exactly the same influence on the future.) The state concept has been used as a foundation stone for formal models in a wide variety of fields; in the formal development to follow generalizations of population structure will have this role. |
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An understanding of the two questions just posed leads to a deeper understanding of the requirements on a genetic adaptive plan. It also leads to an apparent dilemma. On the one hand, if offspring are simple duplicates of fit members of the population, fitness is preserved but there is no provision for improvement. On the other hand, letting offspring be produced by simple random variation (a process practically identical to enumeration) yields a maximum of new variants but makes no provision for retention of advances already made. The dilemma is sharpened by two biological facts: (1) In biological populations consisting of advanced organisms (say vertebrates) no two individuals possess identical chromosomes (barring identical twins and the like). This is so even if we look over many (all) successive generations. (2) In realistic cases, the overwhelming proportion of possible variants (all possible allele combinations, not just those observed) are incapable of surviving to produce offspring in the environments encountered. Thus, by observation (1), advances in fitness are not retained by simple duplication. At the same time, by observation (2), the observed lack of identity cannot result from simple random variation because extinction would almost certainly |
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