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Since traversing a tree *T*(*S*) in circular order counts each edge
in the tree exactly twice, we can derive a function for
determining the score of an evolutionary tree using this order.
First, we reorder the sequences in *S* according to the circular
order *C*(*S*). If we now add the PAM distances of the pairwise alignments
in this order and divide this sum by two, we score each edge of
the tree once. So the function for scoring a tree *T*(*S*) is
simple:

where
*s*_{n+1} = *s*_{1}, *n* is the number of sequences, and
*PAM* is the PAM distance of the optimal pairwise alignment (see
Definition 1.3). We abbreviate this function with

*Chantal Korostensky*

*1999-07-14*