Four species A, B, C and D have these differences in a gene: A and B 4; A and C 10; B and C 10; A…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Four species A, B, C and D have these differences in a gene: A and B 4; A and C 10; B and C 10; A and D 16; B and D 16; C and D 16. Build the tree by the UPGMA method, joining the closest pair each time, with each height half of the distance.
- What is the height of the first join, of A and B?
- What is the height when C joins the group AB?
- What is the height when D joins the group ABC?
Need a reminder? The key ideaShow
UPGMA joins the closest pair at half their distance, and averages the distances to the new group. The molecular clock gives , because both lines change. Closer relatives share a more recent common ancestor.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. The table of differences.
Plan. Join the closest pair, average the distances, and repeat.
Step 1. (a) The closest pair is A and B, at . Height: .
Step 2. (b) The distance from AB to C is the average of and , which is . It is the smallest distance left, since AB to D is and C to D is . Height: .
Step 3. (c) The distance from ABC to D is the average of , and , which is . Height: .
Answer: ; ; .
Check. The heights rise as the joins go back in time, so the last join, D, is the oldest split.
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