Microbial species 4a: monophyly and species
Here is a nice image that shows that even among eukaryotes, reciprocal monophyly is not always the case for species. It's from a paper in PLOS Computational Biology critical of the DNA Barcoding proposal.
Each version shows two species, X and Y. In A, X and Y are reciprocally monophyletic, which means that the coalescent (or last common shared genomic node in the tree, shown by the open stars) is different for each of them and is not nested within either. In B, Y is nested in X, and so X is paraphyletic, although Y is monophyletic. In C, X and Y are interspersed, phylogenetically, in each other, and so each species is polyphyletic and share a coalescent.
Of course in sexual species this raises the question of what makes X and Y species in the latter two cases (that is, why do we think they are different species? The usual answer is either based on mating behaviours, ecology or morphology, or some mix of these) but in asexuals this will occur when the two species cluster genomically as quasispecies in different ways despite being convergently evolved.