Systematics - BIO 615

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1 Outline 1. Optimality riteria: Parsimony continued 2. istance vs character methods 3. uilding a tree vs finding a tree - lustering vs Optimality criterion methods 4. Performance of istance and clustering methods erek S. Sikes University of laska Four steps - each should be explained in methods 1. haracter (data) selection (not too fast, not too slow) Why did you choose these data? 2. lignment of ata (hypotheses of primary homology) How did you align your data? Two problems to solve Parsimony 1. etermine optimality criterion score (tree length) for each tree (easy / fast) 3. nalysis selection (choose the best model / method(s)) - data exploration Why did you chose your analysis method? 4. onduct analysis 2. Search over all possible trees to find the tree(s) that is/are the best according to the optimality criterion (e.g. shortest; hard for more than 11 OTUs) Some relationships Trees rooted binary tree of n OTUs 2n-3 branches Thus, an unrooted tree with n OTUs has 2n-3 rooted versions. Parsimony Parsimony & ladistics - Strict cladists typically use only parsimony methods & justify this choice on philosophical grounds eg it provides the least falsified hypothesis - Parsimony has also been interpreted as a fast approximation to maximum likelihood avalli-sforza and dwards (1967:555), stated that parsimony s success is probably due to the closeness of the solution it gives to the projection of the maximum likelihood tree and parsimony certainly cannot be justified on the grounds that evolution proceeds according to some minimum principle. - Parsimony is often used in conjunction with other methods (by those who use statistical phylogenetic methods) 1

2 Parsimony Given a set of characters, such as aligned sequences, parsimony analysis works by determining the fit (number of steps) of each character on a given tree The sum over all characters is called Tree Length Most parsimonious trees (MPTs) have the minimum tree length needed to explain the observed distributions of all the characters Parsimony etermining tree length site 5! ! G!species1!!species2! G!species3!!species4 T! G!species5 G Sites 1-4 are constant Parsimony uninformative, site 6 is an autapomorphy = 1 change only, ignored by cladistic software, counted by PUP (variable but parsimony uninformative) t 100k trees/sec PUP would take over 2 billion years to evaluate all trees for 21 OTUs Number of OTUs , , ,027, ,459, ,729, ,749,310, ,234,143, ,905,853,580,625 Number of unrooted trees ,458,046,676, ,190,283,353,629, ,898,783,962,510, ,332,659,870,762,850, ,643,095,476,699,771, ,200,794,532,637,891,559,375 For n taxa # trees= (2n-5)! n-3 (n-3)! Tree searching If 11 or fewer OTUs can do an exhaustive search - this guarantees the shortest tree(s) will be found (an exact solution) - every possible tree for n taxa examined - slowest and most rigorous method - provides a frequency histogram of tree scores xhaustive Search Tree searching Step 1 Starting tree, any 3 taxa If OTUs can do a branch and bound search - this also guarantees the shortest tree(s) will be found but not all trees are examined (also an exact solution) dd fourth taxon () in each of three possible positions -> three trees Step 2a 2b 2c dd fifth taxon () in each of the five possible positions on each of the three trees - > 15 trees, and so on... - families of trees that cannot lead to shorter trees are discarded and not examined - save time - read text for details on method - faster than exhaustive search - no histogram of tree scores 2

3 Tree searching For more than 25 OTUs (most datasets) must use other methods, heuristic searching - approximate methods - do not guarantee the shortest tree will be found - fastest method (but less rigorous) - many issues to consider to employ best strategy for searching tree space - can get trapped in local optima while searching for global optima (shortest trees) (to be continued see lecture on large datasets) Tree searching heuristic searching - approximate methods 1. starting tree is obtained by some clustering method eg stepwise addition or neighbor-joining 2. This tree is then subjected to branch swapping (movement of branches to new places on tree) - each swap makes a new topology which is scored using the Optimality riterion - hope is to find a more optimal tree through extensive branch swapping ata types haracter data - OTU x character matrix! OTUs!!!characters!!!!! ! Species1!!TGTTG! Species2!!TGTTGT! Species3! Species4!!TGTG!!TGTGTGG! ata types istance data - OTU x OTU matrix! species1 0 species1 species2 species3 species4 species species species These are uncorrected distances - they can be corrected to improve chance of finding correct tree (see upcoming lecture on models of evolution) ata types istance methods vs haracter methods - epending on the data can prefer the same or different topologies - ven if the same topology is chosen, only character based methods allow an estimate of ancestral states (which characters are changing where on the tree) - Once characters have been converted to distances we lose this information - Important for understanding historical forms of molecules or adaptations! 3

4 Optimality riteria vs clustering methods Methods of Phylogenetic Inference - more fundamental split is not between methods that use distance data vs character data - ut between methods that use optimality criteria vs those that do not (sometimes called algorithmic methods, or clustering methods) - lustering methods are fast because they build only one tree ( one-tree methods ) - ut, often a dataset will be explained equally well by multiple, sometimes thousands of trees uilding a tree vs Finding a tree uilding or onstructing a tree vs Finding a tree - ach tree is a hypothesis of relationships - For n OTUs we know how many alternative hypotheses there are before we do any analysis - The question to be answered: Is the signal in your data strong enough to weed through these hypotheses? - ie an your data reject all but one (or a few) of these hypotheses? uilding a tree vs Finding a tree - Methods that build a tree do not use optimality criteria - They do not test hypotheses, they do not evaluate the alternative hypotheses for n taxa - Instead, they create a single tree from the data, they build (create, construct) a tree - Since hypotheses are not tested I contend these trees are not scientific, they are good places to start a search for optimal trees, or a means to explore the data - (ut will find the true tree if the distance matrix is an exact reflection of the true tree) uilding a tree vs Finding a tree omparison: lustering method 1. uild a tree (eg with NJ) 2. Stop Optimality riteria (eg parsimony) 1. uild a tree (eg with NJ) 2. Score tree with criterion 3. Try to improve tree with branch swapping 4. Goto step 1 until +/- all trees are scored 5. Stop when search is done lustering Methods - UPGM UPGM (Unweighted Pair-Group Method using rithmetic averages) for ultrametric data - Sokal & Michener phenetics / phenograms - assumes / requires equal rates of evolution on all branches - false for most real data - descendents are equidistant from ancestor onstraints: e1 = e2 e4 = e1 + e3 e5 + e4 = e9 + e8 + e6 etc. H I J F G e1 e2 e6 e7 e3 e4 e8 e5 e9 SOLUT TIM or IVRGN 4

5 lustering Methods - UPGM UPGM Very sensitive to unequal rates among lineages Real data rarely are ultrametric Should no longer be used True tree Neighbor-Joining (NJ) - Saitou & Nei (1987) - unjustifiably popular method but better than UPGM - clustering method to deal with non-ultrametric data - no assumption of clock-like evolution - approximation of the Minimum volution tree (thus not phenetic ) - for many datasets, however, NJ fails to produce the M tree - it gets close but better trees often exist - eg 27,000 equal or better trees than the NJ tree published by Hedges et al (1992) - Swofford et al thus, hard to justify an NJ tree as a reasonable estimate of phylogeny (Swofford & Sullivan, text) Neighbor-Joining (NJ) Farris et al. (1996) ladistics 12: Farris et al. (1996) ladistics 12: NJ obscures ambiguities in the data - sensitive to the input order of the OTUs - epending on the sorting of the OTUs different trees might result - This problem was addressed by jumbling the input order for building multiple NJ trees - Typically people do NJ-bootstrapping which reduces but does not eliminate the problem of ignoring ambiguities in the data No means to decide which is better - (no optimality criterion) Two NJ trees built from same dataset with differently sorted OTUs Your text - istance methods (Yves Van de Peer) - Repeatedly mentions that optimality criteria methods suffer the drawback that all tree topologies have to be investigated - lustering methods, in contrast, produce only one tree (- I consider this a huge weakness) - This is like saying: the advantage of NJ is that it ignores alternative equally good or possibly better estimates of phylogeny - Similar to the pheneticists goal to produce a stable tree that was not necessarily a phylogeny NJ often considered inferior but is preferred by those who consider a quickly produced tree more important than accuracy or honest presentation of the signal in their data If a more rigorous method, an optimality criterion method, finds the same tree as NJ Publish the more rigorously obtained tree! (the NJ tree in this case tells us nothing extra - and publishing only the NJ tree tells readers that not much effort or care was put into the analysis) 5

6 lustering Methods dvocates argue that we can do NJ ootstrapping - method to assess the strength of the signal in the data - to assess the precision of the estimate - consider a bogus clustering method that builds a tree by alphabetically ordering the OTUs according to their names & ignores the data - bootstrapping this method would produce scores of 100% for every branch - obviously meaningless lustering Methods NJ is the primary method of the N arcoding protocol: HRT, P..N., PNTON,.H., URNS, J.M., JNZN,.H. & HLLWHS, W Ten species in one: N barcoding reveals cryptic species in the neotropical skipper butterfly straptes fulgerator. Proceedings of the National cademy of Sciences of the US 101, rower,.v.z Problems with N barcodes for species delimitation: ten species of straptes fulgerator reassessed (Lepidoptera: Hesperiidae). Systematics and iodiversity rower bootstrapped their NJ tree - found support for at least 3 but not more than 7 clades that may correspond to cryptic species - Not 10! Suspected cryptic species - adults look identical Optimality riterion for istances Minimum volution (M) - Uses distance data (preferably corrected data) - Optimality criterion (searches tree space, much more rigorous & time consuming than NJ) - Tree that minimizes the sum of the lengths of the branches is the best estimate of phylogeny - Parsimony using distance data - etter than NJ but still weaker than character methods Minimum volution xample Philips, M. J., F. elsuc,. Penny Genome-scale phylogeny and the detection of systematic biases. M 21(7): Reevaluated Rokas et al s (2003) dataset of 8 yeast genomes (106 nuclear genes, 127, 026 nucleotides) - ompared the two types of statistical error: Stochastic (random) error - deviation between estimate and true value due to sampling, by definition will vanish with infinite data - assessed using branch support measures Systematic error - deviation between estimate and true value due to violated assumptions in the estimation method - will not vanish with infinite data - branch support tells us nothing 6

7 Minimum volution xample - Random error +/- gone with huge dataset of 124,026 characters - Systematic error evident in M analysis (tree on right) (even with corrected distance data!) (& loss of data) - 100% branch support values indicate no random error Minimum volution xample Zwickl,. J. &. M. Hillis Increased taxon sampling greatly reduces phylogenetic error. Sys. iol. 51(4): investigated impact of taxon sampling on accuracy of estimates of phylogenies - all optimality criteria saw a reduction in error with increased taxon sampling - however, Minimum volution saw the smallest benefit and had overall the highest error rates - another source of phylogenetic error - use of a method that has a higher failure rate than other methods Summary 1. Two data types: istance & haracter 2. Two ways to get a tree : lustering methods & Optimality riteria methods (building vs searching) 3. ll clustering methods are distance based - ut not all distance methods are clustering methods (Minimum volution) Tree Method Optimality lustering riterion algorithm istances UPGM NJ Minimum evolution ata type haracters Parsimony, Maximum Likelihood Summary istance methods Should only be used with corrected data (see lecture on models of evolution) Phylogenetic error can result from use of distances that don t reflect true distances ssessment of strength of signal is critical to modern phylogenetics but seemingly the opposite goal of clustering (one-tree) methods haracter evolution / ancestral state data are lost ranch lengths sometimes estimated as less than minimum possible (observed = minimum) Less capable with difficult dataset (eg Rokas et al) than character methods (eg Parsimony) Summary 6. If dataset is clean, strong historical signal, low rate heterogeneity, distance methods typically do fine 7. If a comparison is made with more powerful, non-distance methods, as it should be, why bother using distance methods at all? 8. Only justification I can think of, which is weak, is that distance methods are very efficient [ = fast] (and if you are lucky, they will choose the same tree as the more powerful methods) 9. ue to their speed these methods are ideal for data exploration prior to final analyses 10. lustering methods (eg NJ) do not try to find globally optimal trees Terms - from lecture & readings 2n-3" tree length" MPT (most parsimonious tree(s))" exhaustive (exact) search" branch & bound search" heuristic search" tree space" tree islands" branch swapping" ancestral states" optimality criteria" clustering method" distance data" character (discrete) data" UPGM" ultrametric data" Neighbor-joining" minimum evolution" stochastic (random) error" systematic error" 7

8 Study questions What does ʻtree lengthʼ mean for a Parsimony analysis?" What are the differences between the 3 different means of searching for optimal trees? When would you use each? Pros & cons?" What are tree islands & why are they important? How does NJ deal with tree islands?" ompare & contrast optimality criteria methods with clustering methods. Is the requirement that tree space be extensively searched a drawback or advantage of optimality criterion methods?" What are the requirements of the data for an ultrametric method? re these requirements typically met by real data?" Why is it hard to justify a NJ tree as a reasonable estimate of phylogeny?" ompare & contrast stochastic error with systematic error." ll clustering methods use (distance? or character?) data. " ll distance methods are clustering methods (True or False)?" 8