BACKGROUND: Population samples show bacterial genomes can be divided into a core of ubiquitous genes and accessory genes that are present in a fraction of isolates. The ecological significance of this variation in gene content remains unclear. However, microbiologists agree that a bacterial species should be 'genomically coherent', even though there is no consensus on how this should be determined. RESULTS: We use a parsimonious model combining diversification in both the core and accessory genome, including mutation, homologous recombination (HR) and horizontal gene transfer (HGT) introducing new loci, to produce a population of interacting clusters of strains with varying genome content. New loci introduced by HGT may then be transferred on by HR. The model fits well to a systematic population sample of 616 pneumococcal genomes, capturing the major features of the population structure with parameter values that agree well with empirical estimates. CONCLUSIONS: The model does not include explicit selection on individual genes, suggesting that crude comparisons of gene content may be a poor predictor of ecological function. We identify a clearly divergent subpopulation of pneumococci that are inconsistent with the model and may be considered genomically incoherent with the rest of the population. These strains have a distinct disease tropism and may be rationally defined as a separate species. We also find deviations from the model that may be explained by recent population bottlenecks or spatial structure.