We apologize that we made a few minor mistakes in the equations. The fixes are minor and the results would still hold with these fixes:
In Equation (1), the normalization by the denominator should be removed, as ρ(t,g) should be the number, not proportion, of rooted triples.
In Equations (2) and (5): The use of |G| is correct when a single individual (allele) is sampled per species. However, when that is not the case (i.e., more than a single allele/individual is sampled), the |G| term should be replaced by ρ(t1,g)+ρ(t2,g)+ρ(t3,g). Notice that this replacement can also take place when a single allele per species is sampled, as in that case, |G| = ρ(t1,g)+ρ(t2,g)+ρ(t3,g).
Mistakes in the equations.
5 October 2015
We apologize that we made a few minor mistakes in the equations. The fixes are minor and the results would still hold with these fixes:
We sincerely apologize for these mistakes.
Luay Nakhleh
Competing interests
I have no competing interests.