Quadratic transformations: a model for population growth. II

In this last part the F n ( i ) and M n ( i ) are considered as random variables whose distributions are described by the model and various mating rules of Section 2. Several convergence results will be proved for those specific mating rules, but we begin with the more general convergence theorem 6.1. The proof of this theorem brings out the basic idea of this section, namely that when F n and M n are large, F n + 1 ( i ) and M n + 1 ( i ) will, with high probability, be close to a certain function of F n (·) and M n (·) (roughly the conditional expectation of F n+1 ( i ) and M n + 1 ( i ) given F n (·) and M n (·)).

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