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We assess the degree to which adaptation to a uniform environment among independently evolving asexual populations is associated with increasing divergence of those populations. In addition, we are concerned with the pattern of adaptation itself, particularly whether the rate of increase in mean fitness tends to decline with the number of generations of selection in a constant environment. The correspondence between the rate of increase in mean fitness and the within-population genetic variance of fitness, as expected from Fisher's fundamental theorem, is also addressed. Twelve Escherichia coli populations were founded from a single clonal ancestor and allowed to evolve for 2,000 generations. Mean fitness increased by about 37%. However, the rate of increase in mean fitness was slower in later generations. There was no statistically significant within-population genetic variance of fitness, but there was significant between-population variance. Although the estimated genetic variation in fitness within populations was not statistically significant, it was consistent in magnitude with theoretical expectations. Similarly, the variance of mean fitness between populations was consistent with a model that incorporated stochastic variation in the timing and order of substitutions at a finite number of nonepistatic loci, coupled with substitutional delays and interference between substitutions arising from clonality. These results, taken as a whole, are consistent with theoretical expectations that do not invoke divergence due to multiple fitness peaks in a Wrightian evolutionary landscape.