# Evaluating phylogenetic hypotheses

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1 Evaluating phylogenetic hypotheses Methods for evaluating topologies Topological comparisons: e.g., parametric bootstrapping, constrained searches Methods for evaluating nodes Resampling techniques: bootstrapping, jackknifing, symmetric resampling Character-based methods: Bremer support (or decay index), Relative Bremer support, etc. Model dependence (stability analysis) Bayesian phylogenetics

2 Nodal support Resampling techniques A resampling technique operates by calculating a tree from each of the several pseudoreplicate matrices, each of which is obtained by randomly selecting characters (sites) from the original matrix. This procedure is repeated a number of times (i.e. 1,000). A resampling frequency is then calculated for each group, this being the fraction of pseudoreplicate trees on which the group occurs Bootstrapping (Felsenstein, 1985): Characters are resampled with replacement Jackknifing (Farris et al. 1996; Farris 1997): Characters are resampled by independent removal (with probability of e -1 ) Symmetric resampling (Goloboff et al., 2003) Resampling techniques as optimality criteria Search strategies for resampling

3 Bootstrapping

4 Jackknifing It simplifies the relationship between frequency and support. For data with no missing entries, the expected jackknife frequency of a group G set off by k uncontradicted characters is just 1-e -k. Bootstrapping has the same expectation, but only when the total number n of characters in the matrix is very large. Otherwise, the expected frequency depends on both k and n. Then the bootstrap frequency of G would change with seemingly irrelevant factors, such as the number of autapomorphies or the number of characters supporting groups entirely separate from G. Outgroup TaxonA TaxonB TaxonC e -k Bootstrap proportion = 96.3% for (A, B) Jackknife proportion = 86.7% for (A, B)

5 Nodal support Character-based techniques Bremer support (branch support; decay index) (Bremer 1988): The number of extra steps required before a clade is lost from the strict consensus tree of near-minimum-length cladograms. This can be calculated by the step (fit) difference between two trees. Given two trees, when character I fits the most parsimonious tree better, the fit difference for that character in the two trees is favorable to the most parsimonious tree (f i ). When character I fits the least parsimonious tree better, the fit difference is contradictory (c i ). Define F = f i, and C = c i. The Bremer support measures support of groups using simply the difference F C. Partitioned Bremer support (Baker & DeSalle 1997): describes the relative support of a given partition over a tree generated under multiple partitions. Relative Fit Difference (RFD) or Relative Bremer support (Goloboff & Farris 2001): takes into account evidence in favor and against a given node

6 Model dependence (Sensitivity analysis sensu Wheeler 1995) Sensitivity analysis (SA) is the study of how the variation in the output of a model (numerical or otherwise) can be apportioned, qualitatively or quantitatively, to different sources of variation, and how that given model depends upon the information fed into it. Andrea Saltelli, 2000

7 Alignments are parameter-dependent (Fitch & Smith 1983; Waterman et al. 1992) Different parameters Different alignments (or homologies) Different phylogenetic hypotheses How can we make use of such variation in our phylogenetic analyses?

8 Sensitivity Analysis in systematics Data exploration Evaluate sensitivity of hypotheses to parameter variation Evaluate stability of nodes to parameter variation Criteria for choosing optimal analytical parameters Character-based congruence methods Topological-based congruence methods Wheeler, W. C Sequence alignment, parameter sensitivity, and the phylogenetic analysis of molecular data. Syst. Biol. 44: Wheeler, W. C Measuring topological congruence by extending character techniques. Cladistics 15:

9 16S 18S 28S COI H3 MOR MOL TOT ILD

10 What is sensitivity analysis? The same raw data are explored under different analytical conditions Molecular data: Parsimony: effect of indels, nucleotide transformations, etc. Maximum Likelihood: effect of models and model corrections Morphological data: Effect of implied weighting on cladogram topology (Prendini, 2003)

11 How can we represent results from a sensitivity analysis? Present all trees obtained under the different conditions examined Strict consensus of all trees obtained under the different conditions Navajo rugs (or sensitivity plots) Frequency that a given node is obtained under the different analytical conditions This does not require choosing a hypothesis

12 Strict consensus of all trees under one parameter set Strict consensus of all trees under all parameter sets

13 GAP: CHANGE RATIO TRANSVERSION:TRANSITION RATIO Mytiloidea Arcoidea Limopsoidea Pteroidea Pinnoidea Ostreoidea Anomioidea Limoidea Pectinoidea node 1: Pteriomorphia node 2 node 3 node 4 node 5 node 6 node 7 node 8 Anomioidea + Pectinoidea Anomioidea + Limoidea Anomioidea + node 5 inf inf inf inf

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