. Consider a tree with just two leaves. Suppose the branch to species 1 has length t1 and the branch to species 2 has length t2. Show that for a reversible mutation model, the probability Fij of...

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Consider a tree with just two leaves. Suppose the branch to

species 1 has length t1 and the branch to species 2 has length t2. Show that

for a reversible mutation model, the probability Fij of observing base i in

species 1 and base j in species 2 depends on t1 and t2 only through the

sum t1 + t2. This result is known as the pulley principle, which says that

we cannot tell the direction of time. (For the meaning of “pulley principle,”

imagine that two leaves are connected by a rope through a pulley mounted

at the node immediately above it. If you lengthen the rope on one side of the

pulley, the rope length on the other side must correspondingly shorten.)