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Estimating the reliability of a tree Reconstructed phylogenetic trees are almost certainly wrong. They are estimates of the true tree. But how reliable are they?

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Reliability most of the time, ‘reliability’ refers to the topology, not to branch lengths. reliability = probability that the members of a given clade are always members of that clade

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Methods phylogeneticists use different methods to test the reliability of trees Bootstrapping Jackknife Permutation tests Likelihood ratio tests (a)LRT

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Bootstrapping bootstrapping uses random sampling with replacement to obtain properties of an estimator

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Bootstrapping bootstrapping uses random sampling with replacement to obtain properties of an estimator

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x Bootstrapping bootstrapping uses random sampling with replacement to obtain properties of an estimator x x x x 1000-10000 times x f

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Bootstrapping in phylogenetic bootstrapping, the alignment is resampled AAT CGC AGT TGT TCT 1 A C A A G 2 T C T T T 3 G G G G G 4 G G G G G 5 G G A C G 67 T C A G A 89 T G T T T 0 A C A T T 1 G G G G G 4 T C A G A 8 T C T T T 3 G G A C G 6 T G T T T 0 A C A A G 2 G G G G G 4 T C T T T 9 G G G G G 5 original alignment pseudo alignment

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Bootstrapping A BC D EF A CB D EF original tree bootstrapped tree +1 +0 +1

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A CB D EF A CB D EF A CB D EF A CB D EF Bootstrapping A BC D EF A CB D EF original tree bootstrapped trees 0.810.75 0.87 0.95 0.80 0.90 0.5 0.47 0.450.23

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Jackknife methods the Jackknife procedure uses random sampling without replacement to obtain properties of an estimator

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Jackknife methods the Jackknife procedure uses random sampling without replacement to obtain properties of an estimator

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Permutation methods Permutation tests are standard in non- parametric statistics. They reorder the data to obtain a null distribution.

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Permutation methods Permutation tests are standard in non- parametric statistics. They reorder the data to obtain a null distribution. N=18, x=20 N=10, x=25Dif=5

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Permutation methods N=18, x=23 N=10, x=19.6Dif=3.4

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Permutation methods difference f 5% largest differences 5% smallest differences actual difference

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Permutation methods in phylogenetics, species can be permuted within characters AAT CGC AGT TGT TCT 1 A C A A G 2 T C T T T 3 G G G G G 4 G G G G G 5 G G A C G 67 T C A G A 89 T G T T T 0 species 1 species 2 species 3 species 4 species 5 A C A T T 1 A C A T T 1 reshuffle

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Permutation methods in phylogenetics, species can be permuted within characters AAT CGC AGT TGT TCT 1 A C A A G 2 T C T T T 3 G G G G G 4 G G G G G 5 G G A C G 67 T C A G A 89 T G T T T 0 species 1 species 2 species 3 species 4 species 5 A C A T T 1 A C A A G 2 A C A A G 2 reshuffle

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Permutation methods in phylogenetics, species can be permuted within characters AAT CGC AGT TGT TCT 1 A C A A G 2 T C T T T 3 G G G G G 4 G G G G G 5 G G A C G 67 T C A G A 89 T G T T T 0 species 1 species 2 species 3 species 4 species 5 A C A T T 1 A C A A G 2 A T G CG T GT C T T C T T T 3 G G G G G 4 G G G G G 5 G G A C G 67 T C A G A 89 T G T T T 0

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Likelihood ratio tests A BC D EF G HI J KL X (ABCDEF) Y (GHI) W (J) Z (KL)

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Likelihood ratio tests standard likelihood tests compare trees with and without the branch X (ABCDEF) Y (GHI) W (J) Z (KL) X Y W Z Likelihood = L 1 Likelihood = L 0 probability that branch exists = 2 * [ln L 1 – ln L 0 ]

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Approximate likelihood ratio test aLRT is fast, accurate and powerful X Y W Z Likelihood = L 1 Likelihood = L 2 approximate probability that branch exists = 2 * [ln L 1 – ln L 2 ] X Z W Y Likelihood = L 3 X Z Y W

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