Exercise sheet 12: Quartet Tree Puzzling

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Exercise 1 - Quartet Tree Basics

1a)

How many possible quartet trees can you produce with six taxa of any specific topology?

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Formula

Solution

1b)

What does a set of quartet trees tell you, in a biological sense?

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Formula

• It tells you which of the quartet trees are likelier than others.

• It tells you which of the taxa are closer related than others.

• It tells you the exact distance between each set of four taxa.

Solution

• It tells you which of the quartet trees are likelier than others.

• It tells you which of the taxa are closer related than others.

• It tells you the exact distance between each set of four taxa.

Exercise 2 - Quartet Tree Reconstruction

You are given a set of quartet trees and an initial topology. You want to include a new taxa P. Where does the P belong to? (We are only using five quartet trees, but there are more possible as you determined in exercise 1 a.)

Quartet Trees:

\(N_1(P,Y|Q,W)\)
\(N_2(X,P|Z,W)\)
\(N_3(X,Z|P,W)\)
\(N_4(P,Y|Z,Q)\)
\(N_5(X,Z|Q,P)\)

Initial Topology:

The letters a-g denote the edges in the topology and represent the violation counter.

2a)

Add \(N_1(P,Y|Q,W)\) to the initial topology. How does the violation counter look after adding \(N_1\)?

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Solution

2b)

Add \(N_2(X,P|Z,W)\) to the initial topology. How does the violation counter look after adding \(N_2\)?

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Solution

2c)

Add \(N_3(X,Z|P,W)\) to the initial topology. How does the violation counter look after adding \(N_3\)?

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Solution

2d)

Add \(N_4(P,Y|Z,Q)\) to the initial topology. How does the violation counter look after adding \(N_4\)?

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Solution

2e)

Add \(N_5(X,Z|Q,P)\) to the initial topology. How does the violation counter look after adding \(N_5\)?

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Solution

2f)

To which edge will taxon \(P\) be attributed, after adding quartet trees \(N_1\) to \(N_5\). What is the closest taxon to the newly added taxon \(P\)?

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Solution

Edge - “C”
Taxon - “Y”