Phylogenies for Comparative MethodsWhat is a phylogeny?How do we estimate a phylogeny?Continuous-time Markov ChainsMarkov ModelsMarkov models on a treeMCMCExampleWe did read a paper, right?QuestionsPhylogeniesBret LargetDepartments of Botany and of StatisticsUniversity of Wisconsin—MadisonFebruary 8, 20111 / 39What is a Phylogeny?Part of a statistical model for comparative studies that explainscovariance among measurements of traits due to commonancestry.Tony IvesA connected, acyclic edge-weighted, semi-labeled graph wheretip nodes are labeled to represent taxa and edge weights usuallyrepresent the expected number of nucleotide substitutions persite.C´ecile An´eTruth.Ken SytsmaPhylogenies for Comparative Methods What is a phylogeny? 2 / 39How do we estimate a phylogeny?There are a multitude of methods to estimate phylogenies fromvarious sorts of data.Presently, the most common approaches use multiple alignments ofDNA sequence data, but this is not always the case (especially whensome taxa are represented by fossils).There are methods for trait data, amino acid sequences, AFLPmarkers, restriction sites, and others.When selecting a method to construct a phylogeny, it is important tounderstand the underlying assumptions.Phylogenies for Comparative Methods How do we estimate a phylogeny? 3 / 39Methods of Phylogenetic ReconstructionPrimary methods of phylogenetic reconstruction include these:ParsimonyUPGMANeighbor joining (and variants)Maximum likelihoodBayesian approachesHere are important considerations for each with regard to finding a tree fora comparative analysis.Phylogenies for Comparative Methods How do we estimate a phylogeny? 4 / 39ParsimonyParsimony seeks the tree topology that requires the fewest totalchanges on each edge of the tree.Parsimony does not directly estimate edge lengths.For a given site, there can be multiple equally parsimonious ways tomap the minimum number of changes onto a tree.If a tree topology is selected by parsimony, additional methods areneeded to find branch lengths.There are conditions (especially long branch attraction) where theparsimony method is likely to select the incorrect tree topology.Evaluation of the parsimony score on a single tree is computationallyfast, but searching for the single most parsimonious tree when thereare many taxa requires heuristic methods that may not find the trueoptimal tree.Phylogenies for Comparative Methods How do we estimate a phylogeny? 5 / 39UPGMAUPGMA acts directly on a pairwise distance matrices among taxa; itis an algorithm for producing a tree from such a distance matrix, nota model.UPGMA produces rooted ultrametric trees (trees where all tips areequidistant from the root).Such trees are consistent with a molecular clock hypothesis in whichthe expected rate of nucleotide substitution is constant across alllineages.To use UPGMA, one needs to specify how distances between taxa arecalculated; a common choice is the maximum likelihood distancebetween the sequences, but this also requires a selection of amaximum likelihood model.UPGMA and other distance methods are often used when data otherthan DNA sequences are used.Phylogenies for Comparative Methods How do we estimate a phylogeny? 6 / 39UPGMA (cont.)When the true underlying rates of nucleotide substitution are notequal, UPGMA can be biased against finding the correct treetopology.In formal likelihood-based tests, it is exceedingly rare with realsequence data to find examples where the molecular clock hypothesisis not strongly rejected.Phylogenies for Comparative Methods How do we estimate a phylogeny? 7 / 39Neighbor-joiningEquivalently to UPGMA, neighbor-joining is an algorithm forproducing trees directly from pairwise distances.Unlike UPGMA, neighbor-joining produces an unrooted tree topologywith branch lengths.For comparative methods purposes, a root needs to be selected (oftenby using outgroups), but the resulting tree will not be ultrametric.Just as with UPGMA, neighbor-joining is an algorithm that makestrees rapidly from even large pairwise distance matrices, but to be acomplete method requires a specification of how the distances arecalculated.Both UPGMA and neighbor-joining lose information when reducingaligned DNA sequences to distances, and in many settings are lessaccurate in reconstructing the phylogeny than methods that workwith sequence data directly.Phylogenies for Comparative Methods How do we estimate a phylogeny? 8 / 39Maximum LikelihoodMaximum likelihood depends on an explicit continuous-time Markovchain model for how DNA sequence (or other data) changes along atree.There are many variants among likelihood models that make fewer orgreater restrictions among parameters.Similar to parsimony, maximum likelihood requires a heuristic searchacross tree space.Calculating the likelihood score for a given tree with branch lengths isabout as computationally difficult as finding a parsimony score, butthe need to optimize all parameter values in addition to branchlengths makes maximum likelihood more computationally intensive,especially for larger trees and large data sets.The resulting tree has branch lengths.The search for the best tree can be restricted to ultrametric trees.Variations include ultrametric trees with rates that can change alongthe tree (often in a penalized way).Phylogenies for Comparative Methods How do we estimate a phylogeny? 9 / 39Bayesian MethodsThe Bayesian paradigm differs from the other methods in that the endresult is a probability distribution on tree space, not a single best tree.This distribution is typically represented by a large random (but notindependent) sample of trees selected by Markov chain Monte Carlo.It is common for people to compute a consensus tree from theBayesian sample as a single representative of the distribution.Bayesian methods can use the same likelihood models as used inmaximum likelihood, and actually often use models richer inparameters than is feasible with maximum likelihood (for example, bypartitioning data into parts, each with separate sets of parameters).Bayesian methods are computationally intensive for large data setsand trees; they are computationally favorable to maximum likelihoodplus bootstrapping, but not for finding a single maximum likelihoodtree.Bayesian methods can be restricted to ultrametric trees or not.Phylogenies for Comparative Methods How do we estimate a phylogeny? 10 / 39Bayesian Methods (cont.)To account for phylogenetic uncertainty in a comparative analysis,one
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