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of loss when P(x, t) is near one. But as t advances ct® 0, so that |
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and the rate of change approaches [µx(t)/µ(t)] - 1. In particular, if some schema begins to occupy a large fraction of the population (through consistent above-average performance) its rate of increase will come very close to [µx(t)/µ(t)] - 1. |
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We can now go on to determine the number of trials allocated to the observed best schema as a function of the number of trials allocated to structures which are not instances of x. In this determination  designates the number of structures in  which are not instances of schema x.  and  designate the number of trials allocated from t0 to t to structures which are, respectively, instances of x and not instances of x. (That is,  , for t ³ t0.) The logarithm of the effective payoff to x or log payoff, bounded below by  , plays a direct role in |
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LEMMA 7.3: If each instance of x gives rise, on the average, to at least one new instance of x in each generation over the interval (t0, t), i.e., if   , then the trials from t0 onward satisfy |
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where  is (a lower bound on) the average log payoff over (t0, t). |
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