. This exercise illustrates an important principle in calculating likelihoods on trees. Equation XXXXXXXXXXgives the probability of observing particular bases at the leaves of a tree with n = 3...

.
This exercise illustrates an important principle in calculating

likelihoods on trees. Equation (12.17) gives the probability of observing particular

bases at the leaves of a tree with n = 3 species as

πaqai3 (t2)qab(t2 − t1)qbi2 (t1)qbi1 (t1).

This can also be written in the form

qab(t2 − t1)qbi2 (t1)qbi1 (t1).

Evaluate carefully how many addition and multiplication operations are performed

in these two formulae, and deduce that the first form is less efficient

than the second.