How many paraphyletic groups can theoretically be created from this phylogeny?

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I found (2n)-2. Is this correct? This is not homework nor exam, just a question about paraphyletic groups.


1 Answer 1


If we define a paraphyletic group as any group on a phylogeny that is not monophyletic, I count there to be 2^n - 2*n paraphyletic groups for a fully ladderized tree with n tips.

There are 2^n possible groups of n species. Of these groups, 2*n of them are monophyletic: n groups containing a single species, and n groups containing multiple species.

  • $\begingroup$ I cant find a good explanation for paraphyletic group, what are all possible para. Groups if n=3? $\endgroup$
    – Nemexia
    Commented Mar 29, 2016 at 2:29
  • $\begingroup$ @Nemexia The term "paraphyletic" doesn't really have a hard definition, but the way I defined it, a tree with 3 tips will have 2^3 - 2*3 = 2 paraphyletic groups: {1,3} and {2,3}. $\endgroup$
    – C_Z_
    Commented Mar 29, 2016 at 2:48
  • $\begingroup$ Why arent these paraphyltic? {1,2} with common ancestor( first and secound node)? $\endgroup$
    – Nemexia
    Commented Mar 31, 2016 at 10:53
  • $\begingroup$ {1,2} is a monophyletic group because it contains all descendants of the MRCA of {1,2} (the ancestor of {1,2} only has 1 and 2 as descendants, so the {1,2} group is monophyletic. $\endgroup$
    – C_Z_
    Commented Mar 31, 2016 at 13:20

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