Is it due to recombination? Probably. I tested for recombination using a parsimony based approach (Bruen et al. 2006. Genetics 172:2665) in each of the 101 alignment files (so within each alignment region, not between alignment files) and found that only 11 alignment files did NOT have evidence of recombination. The lack of recombination in all but one of these is probably due to the small size, most of the 11 were under 1 kb.
What does this all mean? Recombination was previously thought to be rare in H. influenzae, based on linkage between phenotypes and multi-locus enzyme electrophoresis types. But sequence data is changing what we know about the population structure of H. influenzae. MLST studies have already shown modest incongruence between gene trees and fancy Bayesian statistics have shown that the recombination rate is moderate. My work is now showing that recombination occurs often enough to obliterate phylogenetic signal. My next question is: is it mostly due to transformational recombination?