Previous studies have shown that genetic exchange in bacteria is too rare to prevent neutral sequence divergence between ecological populations. That is, despite genetic exchange, each population should diverge into its own DNA sequence-similarity cluster. In those studies, each selective sweep was limited to acting within a single ecological population. Here we postulate the existence of globally adaptive mutations, which may confer a selective advantage to all ecological populations constituting a metapopulation. Such adaptations cause global selective sweeps, which purge the divergence both within and between populations. We found that the effect of recurrent global selective sweeps on neutral sequence divergence is highly dependent on the mechanism of genetic exchange. Global selective sweeps can prevent populations from reaching high levels of neutral sequence divergence, but they cannot cause two populations to become identical in neutral sequence characters. The model supports the earlier conclusion that each ecological population of bacteria should form its own distinct DNA sequence-similarity cluster.