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Estimating the reliability of a tree

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.

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Estimating the reliability of a tree

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  1. Estimating the reliability of a tree Reconstructedphylogenetictrees are almostcertainlywrong. They are estimates of the truetree. But how reliable are they?

  2. 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

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

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

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

  6. Bootstrapping bootstrapping uses randomsamplingwith replacement to obtainproperties of an estimator 1000-10000 times f x x x x x x

  7. Bootstrapping in phylogeneticbootstrapping, the alignmentisresampled 1 1 2 2 3 3 4 4 4 5 5 6 6 7 8 8 9 0 0 9 A A A A T T G G G G G G G A T T T T T T C C C C C C G G G G G G G G C C C G G C A A A A T T G G G G G A A G A A T T T T T T A A T T G G G G G C C G G G T T T T T T G G T T G G G G G G G C A A T T T T pseudoalignment originalalignment

  8. Bootstrapping E F C B E F B C D A D A +1 +1 +1 +1 +1 +0 +1 +1 +1 +1 bootstrapped tree original tree

  9. Bootstrapping E E E E E F F F F F C C C C C B B B B B E F B C D D D D D A A A A A D A 0.23 0.45 0.75 0.81 0.5 0.47 0.80 0.90 0.87 0.95 bootstrapped trees original tree

  10. Jackknifemethods the Jackknifeprocedure uses randomsamplingwithout replacement to obtainproperties of an estimator

  11. Jackknifemethods the Jackknifeprocedure uses randomsamplingwithout replacement to obtainproperties of an estimator

  12. Permutation methods Permutation tests are standard in non-parametricstatistics. Theyreorder the data to obtain a null distribution.

  13. Permutation methods Permutation tests are standard in non-parametricstatistics. Theyreorder the data to obtain a null distribution. N=18, x=20 N=10, x=25 Dif=5

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

  15. Permutation methods f 5% smallestdifferences 5% largestdifferences difference actualdifference

  16. Permutation methods in phylogenetics, speciescanbepermutedwithincharacters 1 1 2 3 4 5 6 7 8 9 0 A species 1 A A T G G G A T T T species 2 C C C G G G G C C G T A species 3 A A T G G A G A T T species 4 T A T G G C G G T T T species 5 T G T G G G C A T T C 1 A C reshuffle A T T

  17. Permutation methods in phylogenetics, speciescanbepermutedwithincharacters 2 1 1 2 2 3 4 5 6 7 8 9 0 G A species 1 A A A T G G G A T T T A species 2 C C C C G G G G C C G T C A species 3 A A A T G G A G A T T A species 4 T A A T G G C G G T T T species 5 A T G G T G G G C A T T C reshuffle

  18. Permutation methods in phylogenetics, speciescanbepermutedwithincharacters 3 4 5 6 7 8 9 0 2 1 1 2 3 4 5 6 7 8 9 0 A G C G G A C T T T species 1 A A T G G G A T T T T A T G G G G C T T species 2 C C C G G G G C C G A C T G G C A A T T species 3 A A T G G A G A T T T A T G G G G A T T species 4 T A T G G C G G T T species 5 C A T G G G G G C G T G T G G G C A T T

  19. Likelihood ratio tests K L H I E F B C J G D A X (ABCDEF) Y (GHI) W (J) Z (KL)

  20. Likelihood ratio tests standard likelihood tests compare trees with and without the branch X Y X (ABCDEF) Y (GHI) W Z Likelihood = L0 Likelihood = L1 W (J) Z (KL) probabilitythatbranchexists = 2 * [ln L1 – ln L0]

  21. Approximatelikelihood ratio test aLRT is fast, accurate and powerful Likelihood = L2 X X X Z Z Y Likelihood = L1 W Y W W Y Z Likelihood = L3 approximateprobabilitythatbranchexists = 2 * [ln L1 – ln L2]

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