Systematics - Bio 615 Confidence - Assessment of the Strength of the Phylogenetic Signal - part 3 Branch lengths and support: Farris S. J. (2001) Branch lengths do not indicate support - even in maximum likelihood. Cladistics 17: 298-299 “As a simple example, suppose that the data comprise four terminals A–D and 500 informative characters, of which half split the terminals AB/CD and the rest AC/ BD. The (undirected) consensus of most parsimonious trees is unresolved, so that the Bremer support (Bremer, 1988, 1994; cf. Farris, 1996) for either split is zero, but the internal branch of either tree has length 250 according to parsimonious optimization (Farris,1970).” [italics added] Derek S. Sikes University of Alaska Confidence - Assessment of the Strength of Confidence - Assessment of the Strength of the Phylogenetic Signal - part 3 the Phylogenetic Signal - part 3 1. Consistency Index 1. Consistency Index 2. g1 statistic, PTP - test 2. g1 statistic, PTP - test 3. Consensus trees 3. Consensus trees 4. Decay index (Bremer Support) [pp.190-193 - Text] 4. Decay index (Bremer Support) [pp.190-193 - Text] 5. Bootstrapping / Jackknifing 5. Bootstrapping / Jackknifing 6. Statistical hypothesis testing (frequentist) 6. Statistical hypothesis testing (frequentist) - Independent Dataset Congruence - Independent Dataset Congruence 7. Posterior probability - Bayesian Inference 7. Posterior probability - Bayesian Inference Comparing competing phylogenetic Comparing competing phylogenetic hypotheses - tests of two trees hypotheses - tests of two trees • Particularly useful techniques are those designed to 1. Winning sites test (MP & ML) allow evaluation of alternative phylogenetic hypotheses (frequentist, not Bayesian) 2. Templeton test (MP & ML) • Several such tests allow us to determine if one tree is statistically significantly worse than another: 3. Kishino-Hasegawa test (MP & ML) Winning sites test, Templeton test, Kishino-Hasegawa test, 4. Shimodaira-Hasegawa test (ML only) Shimodaira-Hasegawa test, parametric bootstrapping* *(we won’t cover but you can read about this method in Hillis, D. M., B. K. Mable, and C. Moritz. 1996. Applications of molecular systematics: The state of the field and a look to the future. Chapter 12 in Hillis, D. M., C. Moritz, & B. K. Mable (eds). Molecular Systematics (2nd ed). Sinaeur Associates, Inc. Massachusetts. xvi + 655 pp.) 5. Bayesian Posterior Probabilities (BI only) 1 Systematics - Bio 615 Tests of two trees The Templeton test • Test the null hypothesis that the differences between two trees (A and B) are no greater than expected from sampling error • A non-parametric Wilcoxon signed ranks test of the differences in fits of characters to two • The simplest test is the ‘winning sites’ test trees – sums the number of sites supporting tree A over tree B and vice versa (those having fewer steps on, and better fit to, one of the trees) • Like the ‘winning sites’ test but also takes into account the magnitudes of differences in the • If the null hypothesis is true: characters are equally likely to support tree A or tree B support of characters for the two trees – a binomial distribution gives the probability of the observed difference in numbers of winning sites Comparing competing phylogenetic Templeton’s test! - an example ! ! ! ! ! Recent studies of the relationships of ! ! ! hypotheses - tests of two trees 1! ! turtles using morphological data have ! ! ! produced very different results with turtles grouping either within the parareptiles (H1) or within the diapsids 1. Winning sites test (MP & ML) Seymouriadae Paleothyris Diadectomorpha Lepidosauriformes Araeoscelidia (H2) the result depending on the Archosauromorpha Parareptilia Captorhinidae Claudiosaurus Younginiformes Placodus Eosauropterygia Synapsida 2! morphologist This suggests there may be: - problems with the data 2. Templeton test (MP & ML) - special problems with turtles - weak support for turtle relationships 3. Kishino-Hasegawa test (MP & ML) Parsimony analysis of the most recent data favoured H2 However, analyses constrained by H1 produced trees that required only 3 extra steps (<1% tree length) 4. Shimodaira-Hasegawa test (ML only) The Templeton test was used to evaluate these trees and showed that the slightly longer H1 tree found in the constrained analyses was not significantly worse than the unconstrained H2 tree The morphological data do not allow choice between H1 and 5. Bayesian Posterior Probabilities (BI only) H2 Kishino-Hasegawa test Kishino-Hasegawa test Sites favouring tree A! Sites favouring tree B! • Uses differences in the support provided by individual sites If the difference between trees for two trees to determine if the overall differences between ! (tree lengths or likelihoods) is the trees are significantly greater than expected from ! attributable to sampling error, then random sampling error Expected characters will randomly support Mean 0! tree A or B and the total difference Distribution of Step/Likelihood differences at each will be close to zero • A parametric test - depends on assumptions: site! The observed difference is – that the characters are independent Under the null hypothesis the significantly greater than zero if it – and identically distributed (the same assumptions underlying the mean of the differences in is greater than 1.95 standard statistical interpretation of bootstrapping) parsimony steps or likelihoods for deviations each site is expected to be zero, This allows us to reject the null and the distribution normal hypothesis and declare the sub- • It can be used with parsimony and maximum likelihood - optimal tree significantly worse implemented in PHYLIP and PAUP* From observed differences we than the optimal tree (p < 0.05) calculate a standard deviation 2 Systematics - Bio 615 Kishino-Hasegawa test - an example Kishino-Hasegawa test - an example Ochromonas! Ciliate SSUrDNA Maximum likelihood tree Ciliate SSUrDNA data Symbiodinium! Ochromonas 99-100 Symbiodinium Most parsimonious tree Prorocentrum! 95-100 Parsimony analysis yields a 11! Prorocentrum Sarcocystis! very similar tree Theileria! Parsimonious character 7! Sarcocystis Plagiopyla n! 81-86 Theileria - in particular, parsimonious optimization of the 3! 100 Plagiopyla n Plagiopyla f! 100 33! character optimization Trimyema c! Plagiopyla f presence and absence of 48! 100 Trimyema s! 15-0 Trimyema c indicates four separate origins hydrogenosomes suggests 27! Trimyema s Cyclidium p! 3! 69-99 of hydrogenosomes within Cyclidium g! 11-0 100 Glaucoma four separate origins of 6! Colpodinium ciliates Cyclidium l! 3! 75! Glaucoma! hydrogenosomes within 35-17 Tetrahymena Colpodinium! Paramecium the ciliates 3! 7! Cyclidium p Tetrahymena! 41-30 12! Paramecium! 78-99 Cyclidium g 3! 89-91 Cyclidium l Discophrya! 100-99 Trithigmostoma! 46-26 Discophryal Opisthonecta! 23! Trithigmostoma Colpoda! 3! Opisthonecta 18-0 100-98 Dasytrichia! Questions 50-53 Dasytrichia Entodinium! 1! 67-99 17! Entodinium 3! Spathidium Spathidium! - how reliable is this result? 100 3! Loxophylum! 53-45 56! Homalozoon - in particular how well Loxophylum Decay indices and BS for parsimony Homalozoon! 69-78 5! 100 42 Metopus c! 4! Metopus c and distance analyses indicate relative supported is the idea of 3! Metopus p Metopus p! 45-72 83-82 Stylonychia! multiple origins? Stylonychia support for clades Onychodromous! Onychodromous 100 27! Oxytrichia Oxytrichia! - how many origins can we 96-100 Differences between the ML, MP and Loxodes! Colpoda 10! 100 Loxodes Tracheloraphis! confidently infer? distance trees generally reflect the less Spirostomum! 100 63! Tracheloraphis 100 Spirostomum well supported relationships Gruberia! 26! Blepharisma! anaerobic ciliates with hydrogenosomes 18! Gruberia 80-50 Blepharisma 3! Kishino-Hasegawa test - an example Kishino-Hasegawa test - an example Parsimony analyses with Ochromonas! Ochromonas! Symbiodinium! Symbiodinium! topological constraints - to Prorocentrum! Prorocentrum! Test summary and results - origins of ciliate hydrogenosomes Sarcocystis! Sarcocystis! Theileria! Theileria! find the shortest trees that Plagiopyla n! Plagiopyla n! Plagiopyla f! Plagiopyla f! forced hydrogenosomal Constrained analyses used to find Trimyema c! Trimyema c! N!o.!! C!on!s!t!ra!!i!n!t!! Ex!t!ra!!! D!iff!!e!r!e!n!c!e!! Trimyema s! Trimyema s! ciliate lineages together and S!ig!!n!if!i!c!!a!n!tl!y!! most parsimonious trees with less Cyclidium p! Cyclidium p! O!rig!!i!n!s!! tre!!e!! St!e!p!s!! an!d!!SD!! Cyclidium g! Metopus c! w!o!rs!!e!?! than four separate origins of Cyclidium l! Metopus p! thereby reduced the number Dasytrichia! Dasytrichia! 4! M!L! +1!0!! -! -! hydrogenosomes Entodinium! Entodinium! of separate origins of 4 M P - -13± 18 N!o! Loxophylum! Cyclidium g! Homalozoon! Cyclidium l! Hydrogenosomes. 3 (cp,p!t)! +13 -21± 22 N!o! Tested against ML tree Spathidium! Loxophylum! Metopus c! Spathidium! 3 (cp,r!c) +113 -337± 40 Y!e!s! Metopus p! Homalozoon! 3 (cp,m!) +47 -147± 36 Y!e!s! Trees with 2 or 1 origin are all Loxodes! Loxodes! Each of the constrained Tracheloraphis! Tracheloraphis! 3 (pt,r!!c) +96 -279± 38 Y!e!s! significantly worse than the ML tree Spirostomum! Spirostomum! Gruberia! Gruberia! parsimony trees were 3 (pt,m!!) +22 -68± 29 Y!e!s! Blepharisma! Blepharisma! Discophrya! Discophrya! compared to the ML tree 3 (rc,m!) +63 -190± 34 Y!e!s! We can confidently conclude that Trithigmostoma! Trithigmostoma! 2 (pt,c!!p,r!c) +123 -432 40 Stylonychia! Stylonychia! with the KH test to ± Y!e!s! there have been at least three Onychodromous!