A number of different measures of goodness of fit between distance data and metric trees have been proposed. Let di j denote the distance between taxa i and j obtained from experimental data, and let...

A number of different measures of goodness of fit between distance data and metric trees have been proposed. Let
di j
denote the distance between taxa
i
and
j
obtained from experimental data, and let
ei j
denote the distance from
i
to
j
along the tree. A few of the measures

that have been proposed are:

.

In all these measures, the sums include terms for each distinct pair of taxa,
i
and
j
.

a. Compute these measures for the tree constructed in the text using the FM algorithm, as well as the tree constructed from the same data using UPGMA in Problem 5.2.3. According to each of these measures, which of the two trees is a better fit to the data?

b. Explain why these formulas are reasonable ones to use to measure goodness of fit. Explain how the differences between the formulas make them more or less sensitive to different types of

errors.