A reference collection of 71 natural isolates of Escherichia coli (the ECOR collection) has been studied with respect to the distribution and abundance of transposable insertion sequences using DNA hybridization. The data include 1173 occurrences of six unrelated insertion sequences (IS1, IS2, IS3, IS4, IS5 and IS30). The number of insertion elements per strain, and the sizes of DNA restriction fragments containing them, is highly variable and can be used to discriminate even among closely related strains. The occurrence and abundance of pairs of unrelated insertion sequences are apparently statistically independent, but significant correlations result from stratifications in the reference collection. However, there is a highly significant positive association among the insertion sequences considered in the aggregate. Nine branching process models, which differ in assumptions regarding the regulation of transposition and the effect of copy number on fitness, have been evaluated with regard to their fit of the observed distributions. No single model fits all copy number distributions. The best models incorporate no regulation of transposition and a moderate to strong decrease in fitness with increasing copy number for IS1 and IS5, strong regulation of transposition and a negligible to weak decrease in fitness with increasing copy number for IS3, and less than strong regulation of transposition for IS2, IS4 and IS30.