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as schemata (pp. 100-102), being continually modified by operators at lower levels. Thus certain hierarchies will be favored because of their stability, the corresponding punctuations and operators becoming common features of the overall population. Chapter 4 of Simon's book, The Sciences of the Artificial (1969), gives a good qualitative discussion of this and related topics. |
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It is natural to ask whether these operator-induced hierarchies can account for important features of such observed hierarchies as the organelle, cell, organ, organism, species, . . . hierarchy of biology, or the hierarchical organization of the CNS or a computer program. There would seem to be a strong relation between operator-induced hierarchies and the sequences of developmental biology (embryogenesis and morphogenesis) whereby, for example, a fertilized egg develops into a mature multicellular organism. |
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As a final problem area we can look to situations wherein payoff to a given structure varies in time and space. For example, in the case of limited resources, the resource renewal rates Qx may be both temporally and spatially inhomogeneous, being described by a function Qx(x1, . . ., xk, t). In such cases we would also expect the population at time t to be distributed spatially, yielding  (x1, . . ., xk, t) as the component at coordinate (x1, . . ., xk).After some adaptation any one component of the population, in response to the spatial variations in payoff, will generally exhibit different proportions of schemata than its neighbors. |
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In ecological situations, as well as in certain control situations, it is appropriate to consider the migration of structures from one component of the population to another (one coordinate to another). That is, under the direction of the adaptive plan, the jth structure Aj(x1, . . ., xk, t)in the population component (x1, . .., xk, t) may be transferred to a neighboring coordinate (x'1, . . . , x'k), becoming an element of (x'1, . . ., x'k, t + 1). (Such systems can be usefully described with the help of cellular automata; see R. F. Brender's A Programming System for Cellular Spaces 1969 and Essays on Cellular Automata edited by A. W. Burks 1970.) Under these conditions we would expect to observe a spatial diffusion of schemata. Thus schemata having a large number of instances in (x1, . . . xk, t)would be expected to appear in fair numbers in neighboring components of the population, even if their performance there is poor. At the "boundaries" between different niches the genetic operators will produce unusual "hybrids" of schemata common in each of the niches. That is, where there are sharp changes in the Qx(x1, . . . , xk, t),crossover will yield a wide range of new schemata, which would otherwise occur with low probability. Many of these schemata will be unfit or fit only in the boundary region, but some may exhibit exceptional performance on one or both niches. The relation to Mayr's (1963) description of speciation as the |
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