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

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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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 ]

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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