This is a term typically applied to analyses of gene tree data from two sister species. If we consider two species, A, and B, to say that they are reciprocally monophyletic means that all of the halplotypes sampled from species A are more closely related to each other than any haplotype from species B, and vice versa. Because we expect shared ancestral polymorphism to persist long after gene flow ceases, finding that two species are reciprocally monophyletic suggests that they have been isolated for a very long period of time.

I'm guessing they mean neither is paraphyletic to the other.

Dear Sergei:

I  understood the concept of reciprocal monophyly with your answer. So the reciprocal monophyly means same to monophyly as a criterion of  species delimitation? such as in the Dejaco's paper (https://academic.oup.com/sysbio/article/65/6/947/2281629/Taxonomist-s-Nightmare-Evolutionist-s-Delight-An) mentioned in fig.5, 6, though using reciprocal monoplyly as a criterion, in fact he still performed it by the concept of monoplyly?

In the same way, a species should be a monophyly, but is don't demand a monophyletic sister clade?

This is a term typically applied to analyses of gene tree data from two sister species. If we consider two species, A, and B, to say that they are reciprocally monophyletic means that all of the halplotypes sampled from species A are more closely related to each other than any haplotype from species B, and vice versa. Because we expect shared ancestral polymorphism to persist long after gene flow ceases, finding that two species are reciprocally monophyletic suggests that they have been isolated for a very long period of time.

The above discussion reflects current conventional wisdom, but according to Hennig and others (e. g., Nixon, K. C., Wheeler, Q. D. 1990. An amplification of the phylogenetic species concept. Cladistics 6, 211-223), the property of monophyly is only pertinent to groups of two or more species.  However, the concept is often applied to gene trees (e. g. mtDNA "barcodes").  Sister species often are not "recprocally monophyletic" in the latter respect, and need not be to be diagnosable as distinct (Brower, A. V. Z. 1999. Delimitation of phylogenetic species with DNA sequences: a critique of Davis and Nixon's Population Aggregation Analysis. Syst. Biol. 48, 199-213.)

Also, I disagree with Alastair Tanner's claim that birds and mammals are not reciprocally monophyletic.  If each group is a clade with respect to the other, then in my view, they are (or, in more evolutionary terms, if each group has a most recent common ancestor that is not part of the other group, then they are).

Dear Sergei Drovetski and all

Can we consider the following case as ""two reciprocally monophyletic lineages"?: two groups of species (each group consists of several species that belong to the same genous, and all have a single ancestor), and both of them share a common ancestor??