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Coevolution, between a population of candidate solutions and a population of test cases, has received increasing attention as a promising biologically inspired method for improving the performance of evolutionary computation techniques. However, the results of studies of coevolution have been mixed. One of the seemingly more impressive results to date was the improvement via coevolution demonstrated by Juille and Pollack (1998) on evolving cellular automata to perform a classification task. Their study, however, like most other studies on coevolution, did not investigate the mechanisms giving rise to the observed improvements. In this paper, we probe more deeply into the reasons for these observed improvements and present empirical evidence that, in contrast to what was claimed by Juille and Pollack, much of the improvement seen was due to their "resource sharing" technique rather than to coevolution. We also present empirical evidence that resource sharing works, at least in part, by preserving diversity in the population.