Background - Experimental populations of Escherichia coli have evolved for 20,000 generations in a uniform environment. Their rate of improvement, as measured in competitions with the ancestor in that environment, has declined substantially over this period. This deceleration has been interpreted as the bacteria approaching a peak or plateau in a fitness landscape. Alternatively, this deceleration might be caused by non-transitive competitive interactions, in particular such that the measured advantage of later genotypes relative to earlier ones would be greater if they competed directly. Results - To distinguish these two hypotheses, we performed a large set of competitions using one of the evolved lines. Twenty-one samples obtained at 1,000-generation intervals each competed against five genetically marked clones isolated at 5,000-generation intervals, with three-fold replication. The pattern of relative fitness values for these 315 pairwise competitions was compared with expectations under transitive and non-transitive models, the latter structured to produce the observed deceleration in fitness relative to the ancestor. In general, the relative fitness of later and earlier generations measured by direct competition agrees well with the fitness inferred from separately competing each against the ancestor. These data thus support the transitive model. Conclusion - Non-transitive competitive interactions were not a major feature of evolution in this population. Instead, the pronounced deceleration in its rate of fitness improvement indicates that the population early on incorporated most of those mutations that provided the greatest gains, and subsequently relied on beneficial mutations that were fewer in number, smaller in effect, or both.