Two statistical problems in bioinformatics

The human gut is the home for bacterial cells more numerous than the human cells themselves. The existing methods provide numerical estimates of the species abundance in a given individual. The number of species clearly depends on the coverage (the number of counted cells), as they are approximately distributed by the power law, but at the first approximation, the number of prevalent species is in the low tens. The communities of individuals may differ, although the prevalent species are more or less the same (while their abundance may differ by orders of magnitude). An open question, discussed in the literature, is whether there exist “typical” communities or, in other words, whether there exist natural groups of individuals such that the communities of individuals from the same group are more similar than communities of individuals from different groups.
Microevolution of bacteria includes two processes. (1) At each division random errors may happen and be inherited by daughter cells (mutation). (2) Bacteria may exchange fragments of their genomes (recombination) so that a random fragment of one genomes substitutes the matching fragment of another genome. Hence different regions of genomes may have different histories. We know tens of genomes that constitute a tiny minority of all genomes. The problem is to identify recombining regions, estimate their average size and the recombination rate (compared to the mutation rate).