I have spent the last 8 months attempting to infer the phylogenetic relationships of H. influenzae strains. All methods and datasets used have converged on one answer: if there is a phylogeny it is not resolvable by our current methods. It is possible that recombination between strains has obliterated phylogenetic signal. But it is also possible that there is a tree-like structure underlying the relationships of strains but there are not enough informative sites for phylogenetic inference. I find the latter possibility very unlikely given the average pairwise difference in nucleotide sequence between strains is 3%. Furthermore, the independent evidence I have for recombination between strains is consistent with recombination preventing resolution of the tree.
What does this tell us about the evolution of competence in particular, and the evolution of H. influenzae in general? Certainly the alleles of competence genes are mixed between strains (I also have evidence supporting this), an observation consistent with the phenotypic variation we observe in DNA uptake and transformation. This tells us that the ability to take up DNA and recombine it changes relatively quickly during the evolution of strains. This also tells us that strains of H. influenzae are not diverging from one another but that they form a cohesive group, linked by the sharing of alleles.
But even though my inability to infer a resolved tree tells us interesting things about the evolution of competence and H. influenzae, it is still unsatisfying. And I keep asking myself what other methods or datasets could be used. But I have to stop somewhere and move on from here.