# JC and GTR Model

JC and GTR Model

Discussion 7                                Systematics 112

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• Convert the following character matrix into a distance half matrix (total # of changes only). (2 point)

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 A A T G G T A C C C A T C G G A C T T A C B A T T C T A G C C G T T A G C C T T G C C A T G T T A C C C A T G G G A C T T A C D A T C A T T T C G T C A C G T C T T T A

 A B C D A – B – C – D –

• Does this matrix show metric distances? Ultrametric distances? Why or why not? Show all four 3-taxon statements (triangles). (1 point)

• Does the distance matrix show additive distances? Use Buneman’s four point metric and show work. (1 point)

• Use UPGMA to build a tree from the distance matrix. Show all steps. (12point)

• Convert the raw distance half matrix to a percentage distance half matrix (total # changes converted to percent difference). Use this matrix to calculate the corrected Jukes-Cantor distances using the equation (2 point):

dxy = -(3/4) ln (1 – 4/3D)

 A B C D A – B – C – D –

dAB =___________________

dAC =___________________

dBC =___________________

dBD =___________________

dCD =___________________

EXTRA CREDIT!

• Which evolutionary model is more complex: GTR or JC? Explain how each model treats the two parameters and how that affects complexity. (1 point)

• Why are ultrametric distances rarely found in real data? Why doesn’t UPGMA work with non-ultrametric distances? (1 point)