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Three associated objects occupied the center of the preliminary survey: |
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| the environment of the system undergoing adaptation, | | t, | the adaptive plan which determines successive structural modifications in response to the environment, | | µ, | a measure of the performance of different structures in the environment. |
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Implicit in the discussion is a decomposition of the overall process into two disjoint partsthe adaptive system employing t, and its environment E. This decomposition is usually fixed or strongly suggested by the particular emphasis of each study, but occasionally it can be arbitrary and, rarely, it can be a source of difficulty. Thus, in some biological studies the epidermis naturally serves as the adaptive system-environment boundary, while in other biological studies we deal with populations which have no fixed spatial boundaries, and in ecological settings the boundary shifts with every change in emphasis. Similarly, the emphasis of the study usually determines what notion of performance is relevant and how it is to be measured to yield µ. Because E, t,and µ are central and can be regularly identified in problems of adaptation, the formal framework will be built around them. |
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In the basic formalism the adaptive plan t will be taken to act at discrete instants of time, t = 1, 2, 3,. . . , rather than continuously. The primary reason for adopting a discrete time-scale is the simpler form it confers on most of the important results. Also this formalism intersects smoothly with extant mathematical theories in several fields of interest where much of the development is based on a discrete time-scale, viz., mathematical economics, sequential sampling theory, the theory of self-reproducing automata, and major portions of population genetics. Where continuity is more appropriate, it is often straightforward to obtain continuous counterparts of definitions and theorems, though in some cases appropriate |
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