On the inference of complex phylogenetic networks by Markov Chain Monte-Carlo
Fig 2
Illustration of the concepts and notation employed to describe likelihood computations.
The species network topology is the same as that in Fig 1, but branches (populations) are now represented as grey parallelograms. A gene tree is drawn inside the species network (green and red lines). One mutation occurs in the branch above D. We focus on three branches: x, y and z. Colored horizontal bars represent the population interfaces ,
,
and
. Note that
(blue) is a vector of incomparable population interfaces, while
(orange) is not, as
is a descendant of
. Here, nA = nB = nC = nD = 2, rA = 2, rB = 1, rC = 0, rD = 2 are known, whereas the values of
and
are not observed, and depend on the gene tree generated by the MSNC process. For the gene tree shown,
and
. Since z is incident to leaf B, we have
and
. Now note
. Then,
.