Package Tree shape' of Elementary Latin - Exam 12 | LATIN 1, Exams of Latin language

Download Package Tree shape' of Elementary Latin - Exam 12 | LATIN 1 and more Exams Latin language in PDF only on Docsity! Package ‘apTreeshape’ April 17, 2009 Date 2009-03-13 Version 1.4-1 Title Analyses of Phylogenetic Treeshape Author Nicolas Bortolussi <nicolas.bortolussi@imag.fr>, Eric Durand <eric.durand@imag.fr>, Michael Blum <michael.blum@imag.fr>, Olivier Francois <olivier.francois@imag.fr> Maintainer Eric Durand <eric.durand@imag.fr> Depends R (>= 2.0.0) Suggests ape, quantreg, Bhat Description apTreeshape is mainly dedicated to simulation and analysis of phylogenetic tree topologies using statistical indices. It is a companion library of the ’ape’ package. It provides additional functions for reading, plotting, manipulating phylogenetic trees. It also offers convenient web-access to public databases, and enables testing null models of macroevolution using corrected test statistics. Trees of class “phylo” (from ’ape’ package) can be converted easily. License GPL (>= 2) Encoding latin1 Repository CRAN Date/Publication 2009-03-17 18:17:23 R topics documented: aldous.test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 all.equal.treeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 as.phylo.treeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 as.treeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 cladesize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 colless . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 cutreeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1 2 aldous.test dbtrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 hivtree.treeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 index.test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 likelihood.test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 maxlik.betasplit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 pandit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 plot.treeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 rtreeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 sackin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 shape.statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 shift.test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 smaller.clade.spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 spectrum.treeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 subtree.test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 summary.treeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 tipsubtree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 treebase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 treeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 universal.treeshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Index 38 aldous.test Visualizing balance via scatter diagrams Description A graphical test to decide if tree data fit the Yule or the PDA models. Usage aldous.test(tree, xmin=20, ...) Arguments tree An object of class "treeshape". xmin An object of class "numeric" that defines the range of the x-axis. The mini- mal parent clade size displayed in the graphical representation (default: xmin=20). ... further arguments to be passed to plot(). Details A binary tree contains a set of splits (m, i) = (size of parent clade, size of smaller daughter clade) which can be plotted as a scatter diagram. Aldous’ proposal for studying tree balance is that, given a large phylogenetic tree, one should estimate the median size of the smaller daughter clade as a as.phylo.treeshape 5 Examples ## Trees with permutations data(carnivora.treeshape) tree=carnivora.treeshape tree$merge[8,]=c(tree$merge[8,2],tree$merge[8,1]) all.equal(tree, carnivora.treeshape) ## Trees with different heights merge=matrix(NA, 3, 2) merge[,1]=c(-3,-1,2); merge[,2]=c(-4,-2,1);tree1=treeshape(merge) merge[,1]=c(-1,-3,1); merge[,2]=c(-2,-4,2);tree2=treeshape(merge) plot(tree1, tree2) all.equal(tree1, tree2) all.equal(tree1, tree2, height=TRUE) ## Trees with different names tree3=treeshape(tree1$merge, c("a", "b", "c", "d")) tree4=treeshape(tree1$merge, c("1", "2", "3", "4")) plot(tree3, tree4) all.equal(tree3, tree4) all.equal(tree3, tree4, names=TRUE) as.phylo.treeshape Conversion among tree objects Description as.phylo is a generic function - described in the APE package - which converts an object into a tree of class "phylo". This method is an adataption of this generic method to convert objects of class "treeshape" in objects of class "phylo". Usage ## S3 method for class 'treeshape': as.phylo(x, ...) Arguments x An object of class"treeshape". ... further arguments to be passed to or from other methods. Value An object of class "phylo". 6 as.treeshape Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr〉> Olivier Francois <〈olivier.francois@imag.fr〉> See Also as.phylo as.treeshape Examples data(primates) plot(primates) library(ape) primates.phylo=as.phylo(primates) plot(primates.phylo) as.treeshape Conversion among tree objects Description as.treeshape is a generic function which converts an tree object into an object of class "treeshape". There is currently a single method for this generic function. Usage ## S3 method for class 'phylo': as.treeshape(x, model, p, ...) Arguments x An object to be converted into another class. Currently, it must be an object of class "phylo". model The model to use when the tree to convert is not binary. If NULL (default), the tree is not converted. One of "biased", "pda", "aldous" or "yule" character string. p The parameter for the model "biased". ... Further arguments to be passed to or from other methods. cladesize 7 Details as.treeshape can convert trees that are not binary. When trying to convert a tree with poly- tomies, this function may either reject the tree (if model=NULL) or simulate the tree. The polytomy is replaced by a randomized subtree with n tips where n is the size of the polytomy. The subtree is simulated using the PDA, Yule, Aldous or biased model. Value An object of class "treeshape" or an object of classes "treeshape" and "randomized.treeshape" if the original tree was not binary. Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr〉> Olivier Francois <〈olivier.francois@imag.fr〉> See Also as.phylo.treeshape dbtrees for examples about polytomy resolutions. Examples library(ape) data(bird.orders) ## Data set from APE plot(bird.orders) ## "treeshape" conversion tree=as.treeshape(bird.orders) plot(tree) summary(tree) cladesize Compute the number of children of a randomly chosen node Description cladesize takes a random internal node in a tree, and computes its number of descendants (clade size). Usage cladesize(tree) 10 cutreeshape References Mooers, A. O. and Heard, S. B. (1997) Inferring Evolutionnary Process from Phylogenetic Tree Shape. The Quarterly Review of Biology, 72, 31 – 54. Blum, M., Francois, O. and Janson, S. The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance; manuscript available from http://www-timc.imag.fr/Olivier.Francois/bfj.pdf. Flajolet, P. and Louchard, O. (2001) Analytic Variations on the Airy Distribution. Algorithmica, 31, 361 – 377. See Also sackin Examples ## Colless' index for a randomly generated PDA tree (unnormalized value) tpda<-rtreeshape(1,tip.number=70,model="pda") colless(tpda[[1]],norm="pda") ## Histogram of Colless' indices for randomly generated Yule trees main="Colless' indices for randomly generated Yule trees" xlab="Colless' indices" hist(sapply(rtreeshape(300,tip.number=50,model="yule"),FUN=colless,norm="yule"), freq=FALSE,main=main,xlab=xlab) ## Change the number of tips hist(sapply(rtreeshape(300,tip.number=100,model="yule"),FUN=colless,norm="yule"), freq=FALSE,main=main,xlab=xlab) cutreeshape Cut objects of class "treeshape" Description Prunes or cuts an object of class "treeshape" from a specificed internal node, either by spec- ifying a top or bottom direction. This function returns either the top part or the bottom part of a tree. Usage cutreeshape(tree, node, type) cutreeshape 11 Arguments tree An object of class "treeshape". node An integer representing the node at which the tree will be pruned or cut. node should be in the range 1, . . . , treesize− 1. type A character string equals to either "top" or "bottom". Details If the type argument is "top", the tree is pruned from node. The resulting tips correspond to the ancestral branches present at the same height as the given node. New tip labels are assigned to the tips. If the type specified is "bottom", the subtree under node is returned. The tips are not renamed (they keep their former names) and the specified node is the root of the new tree. Value An object of class "treeshape" Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr〉> Olivier François <〈olivier.francois@imag.fr〉> See Also tipsubtree Examples ## Data set provided with the library. Type help(cytochromc) for more infos. data(carnivora.treeshape) data(hivtree.treeshape) ## Examples of "bottom" cutting: bottom.tree=cutreeshape(carnivora.treeshape, 3, "bottom") plot(carnivora.treeshape, bottom.tree) bottom.tree=cutreeshape(carnivora.treeshape, 8, "bottom") plot(carnivora.treeshape, bottom.tree) ## Examples of "top" pruning: top.tree=cutreeshape(hivtree.treeshape, 158, "top") plot(hivtree.treeshape, top.tree) 12 dbtrees dbtrees Download trees from internet databases. Description dbtrees connects to the internet phylogenetic tree database TreeBASE or Pandit, downloads trees with specified ID numbers, and converts them into either the "treeshape" or the "phylo" format. Can solve polytomies. Usage dbtrees(db, tree, class="phylo", type="s", quiet=FALSE, model=NULL, p=0.3) Arguments db A character string equals to the name of the database to connect: "pandit" or "treebase". tree A vector or list of ID corresponding to the trees to be downloaded. class The class of the downloaded objects: must be one of "phylo" (default) or "treebase". type The type of the tree: an object of class "character" equals to either "s" (default) or "f" (seed or full). This option is only used for the Pandit database. quiet A logical value. If TRUE, nothing will be printed on screen. If FALSE (default), informations about the status of the download are displayed. model Argument to be passed to as.treshape.phylo. One of NULL (default), "pda", "biased", "aldous" or "yule" p Argument to be passed to as.treshape.phylo (only for the biased specia- tion model). Details The aim of this function is to provide a simple method to retrieve trees and to put them into the "treeshape" or "phylo" format, in order to be able to apply the methods of ape or apTreeshape. This function connects to internet database and download trees using their internal reference num- ber. There is currently no option to retrieve trees from names. See references for more details about the Pandit and TreeBASE databases and the description of their data. This function can solve trees with polytomies using simulation methods (see as.treeshape for more details about the polytomy resolution). Value An object of class "treeshape" or class "phylo" if only one tree is requested, a list of trees otherwise. index.test 15 Arguments tree An object of class "treeshape". model The null hypothesis of the test. One of "yule" (default) or "pda". alternative A character string specifying the alternative hypothesis of the test. One of "less" (default) or "greater". n.mc An integer representing the number of random trees to be generated and required to compute a p-value from a Monte Carlo method. Details A test on tree data that either rejects the Yule or the PDA models. This test is based on a Monte Carlo estimate of the p-value. Replicates are generated under the Yule or PDA models, and their Colless’ (Sackin’s) indices are computed. The empirical distribution function of these statistics is then computed thanks to the "ecdf" R function. The p-value is then deduced from its quantiles. The less balanced the tree is and the larger its Colless’s (Sackin’s) index. The alternative "less" should be used to test whether the tree is more balanced (less unbalanced) than predicted by the null model. The alternative "greater" should be used to test whether the tree is more unbalanced than predicted by the null model. The computation of p-values may take some time depending on the number of replicates |n.mc| and the size of the simulated tree. Value model the null model. statistic the test statistic. p.value the p-value of the test. alternative the alternative hypothesis of the test. Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr 〉> Olivier Francois <〈olivier.francois@imag.fr〉> References Mooers, A. O., Heard, S. B. (Mar., 1997) Inferring Evolutionnary Process from Phylogenetic Tree Shape. The Quarterly Review of Biology, 72, 31 – 54. Blum, M., Francois, O. and Janson, S. The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance; manuscript available from http://www-timc.imag. fr/Olivier.Francois/bfj.pdf. See Also subtree.test colless sackin 16 likelihood.test Examples ## Test on a randomly generated Yule tree with 30 tips a<-rtreeshape(1,30,model="yule") a<-a[[1]] ## Is it more balanced than a Yule tree ? colless.test(a,alternative="less",model="yule") ## Is it less balanced than a PDA tree ? colless.test(a,model="pda",alternative="greater") ## Test on the phylogenetic tree hiv.treeshape: is it more balanced than ## predicted by the Yule model? data(hivtree.treeshape) ## The tree looks compatible with the null hypothesis colless.test(hivtree.treeshape, alternative="greater", model="yule") ## What happen when we look at the top the tree? colless.test(cutreeshape(hivtree.treeshape, 160, "top"), alternative="greater", model="yule") colless.test(cutreeshape(hivtree.treeshape, 160, "top"), alternative="greater", model="pda") ## Test with the Sackin's index: is the HIV tree less balanced than ## predicted by the PDA model? sackin.test(hivtree.treeshape,alternative="greater",model="pda") ## The p.value equals to 1... likelihood.test Test the Yule model vs PDA (uniform) model. Description likelihood.test uses the function shape.statistic to test the Yule model against the PDA model. The test is based on a Gaussian approximation for the log-ratio of likelihoods. Usage likelihood.test(tree, model = "yule", alternative="two.sided") Arguments tree An object of class "treeshape" on which the test is performed. model The null hypothesis of the test. It must be equal to one of the two character strings "yule" or "pda". alternative A character string specifying the alternative hypothesis of the test. Must be one of "two.sided" (default), "less" or "greater". likelihood.test 17 Details A test on tree data that either rejects the Yule of the PDA model. The test is based on the ratio of the likelihood of the PDA model to the likelihood of the Yule model (shape.statistic). The less balanced the tree is the larger its shape statistic is. The alternative "less" should be used to test whether the tree is less unbalanced than predicted by the null model. The alternative "greater" should be used to test whether the tree is more unbalanced than predicted by the null model. Under the Yule model, the test statistic has approximate Gaussian distribution of mean = 1.204 ∗ n − log n− 1 − 2 and variance = 0.168 ∗ n − 0.710, where n is the number of tips of the tree. The Gaussian approximation is accurate for n greater than 20. Under the PDA model, the test statistic has approximate Gaussian distribution of mean ∼ 2.03 ∗ n−3.545∗ √ n− 1 and variance ∼ 2.45∗ (n−1)∗ log n− 1, where n is the number of tips of the tree. The Gaussian approximation is however accurate for very large n (n greater than 10000(?)). The values of the means and variances have been obtained from an analogy with binary search tree models in computer science. The function includes corrections for small sizes under the PDA model, and uses empirical values of variances estimated throught Monte Carlo replicates as follows variance ∼ 1.570 ∗ n ∗ log n− 5.674 ∗ n+ 3.602 ∗ √ n+ 14.915 Value likelihood.test returns a list which includes: model the null model used by the test statistic the test statistic p.value the p.value of the test alternative the alternative hypothesis of the test Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr〉> Olivier François <〈olivier.francois@imag.fr〉> References Fill, J. A. (1996), On the Distribution of Binary Search Trees under the Random Permutation Model. Random Structures and Algorithms, 8, 1 – 25. 20 pandit pandit Phylogenetic trees from the Pandit database Description This set contains two trees extracted from the Pandit Database,cytochromc and rhodopsin. Usage data(cytochromc) data(rhodopsin) Format These data are stored as objects of class "treeshape". Details Cytochromes c (cytC) can be defined as electron-transfer proteins.This data set describes the phy- logenetic relationships of cytC of mitochondria and bacteria. G-protein-coupled receptors, GPCRs, constitute a vast protein family that encompasses a wide range of functions (including various autocrine, paracrine and endocrine processes). The rhodopsin- like GPCRs themselves represent a widespread protein family that includes hormone, neurotrans- mitter and light receptors. Source Ambler, R. P. (May, 1991) Sequence variability in bacterial cytochromes c. Biochimica et Biophys- ica Acta, 1058, 42-7, for more details about bacterial cytochromes c. Attwood T. K. and Findlay J. B. (Feb., 1993) Design of a discriminating fingerprint for G-protein- coupled receptors. Protein Engineering, 6, 176-67, for more details about G-protein-coupled recep- tors. Examples ## Example tree in Treeshape format data(cytochromc) plot(cytochromc) summary(cytochromc) data(rhodopsin) plot(rhodopsin) plot.treeshape 21 plot.treeshape Plot phylogenetic treeshapes. Description Plot method for objects of class "treeshape". Usage ## S3 method for class 'treeshape': plot(x, y, ...) Arguments x An object of class "treeshape". y An object of class "treeshape". ... Further arguments to be passed to plot(). Details If two trees are specified, they are plotted on the same window. This option is provided is order to facilitate the comparison between two trees. Value A null value is returned. Results are displayed on graphical window. Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr〉> Olivier Francois <〈olivier.francois@imag.fr〉> See Also plot for the basic plotting function in R Examples ## Visual representation of the universal tree of life provided in data data(universal.treeshape) plot(universal.treeshape) ## Visual representation of two trees at the same time data(carnivora.treeshape) plot(carnivora.treeshape, cutreeshape(carnivora.treeshape, 8, "bottom")) 22 rtreeshape rtreeshape Generate a list of random binary trees according to a given model Description This function generates a tree or a list of trees of class "treeshape" according to the Yule, PDA, Biased models. Speciation-specified models are also allowed. Usage rtreeshape(n, tip.number, p = 0.3, model="", FUN="") Arguments n The number of trees to generate. tip.number The number of tips of the trees to generate. Can be a vector. p Only used when model="biased". It represents the bias factor of the tree to generate. model A character string equals to "yule", "pda", "aldous" or "biased". FUN A two variables (n and i) function. Details The "FUN" and "model" arguments cannot be specified at the same time. An error will be re- turned if both arguments are specified. If tip.number is a vector, n trees will be generated for each size contained by tip.number Q enables you to build trees of class "treeshape" according to the Markov branching model described by D. Aldous. Qn(i) is the probability that the left daughter clade of an internal node with n descendents contains i tips. The Qn(i) need not sum to one. Still, be carefull when you specify this distribution: computational errors may occur for complicated distributions and/or large trees. The Yule model, also known as Markov model, can be described as follows. At any time, all the extant branches have the same probability to split into two subspecies. The PDA model (Proportional to Distinguishable Arrangements) is not a model of growing tree. Instead, each tree with n tips has the same probability to be generated under this model. There is (2n− 3)!! possible trees with n tips. The Biased model is a model of growing tree. When a species with speciation rate r splits, one of its descendent species is given the rate pr and the other is given the speciation rate 1 − pr where p is a probability parameter. The Biased model was introduced by Kirkpatrick and Slatkin (1993). The Aldous’ Branching (AB) model is defined by the following symmetric split distribution q(n, i) = n/(2 ∗ h(n − 1)) ∗ (1/(i(n − i))), where h(n) is the nth harmonic number. The AB model is hardly motivated by biological considerations. shape.statistic 25 References Mooers, A. O., Heard, S. B. (Mar., 1997) Inferring Evolutionnary Process from Phylogenetic Tree Shape. The Quarterly Review of Biology, 72, 31 – 54, for more details about the Sackin’index and its signification about the balance of phylogenetic trees. Blum, M., Francois, O. and Janson, S. The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance; manuscript available from http://www-timc.imag.fr/Olivier.Francois/bfj.pdf. See Also colless sackin.test Examples ## Index of Sackin of a PDA tree : tpda<-rtreeshape(1,tip.number=70,model="pda") tpda<-tpda[[1]] sackin(tpda,norm="pda") ## Histogram of the Sackin's indices for randomly generated Yule trees, ## with no normalization main="Histogram of Sackin's indices for randomly generated Yule trees" xlab="Sackin's index" hist(sapply(rtreeshape(300,tip.number=50,model="yule"),FUN=sackin,norm="yule"), freq=FALSE, main=main, xlab=xlab) ## Change the size of the trees: hist(sapply(rtreeshape(300,tip.number=100,model="yule"),FUN=sackin,norm="yule"), freq=FALSE, main=main, xlab=xlab) shape.statistic Computes the log of the likelihood ratio (yule/pda) Description shape.statistic computes the logarithm of the ratio of the likelihoods under the Yule model and the PDA model of the given tree. Usage shape.statistic(tree, norm=NULL) Arguments tree An object of class "treeshape". norm A character string equals to NULL for no normalization, "yule" for the Yule model normalization or "pda" for the pda normalization. 26 shape.statistic Details The log of the likelihood ratio is proportional to∑ (logN(v)− 1), for all internal node v (where N(v) is the number of internal nodes descending from the node v ). The ratio of the likelihoods enables to build the most powerful test of the Yule model against the PDA one. (Neyman-Pearson lemma). Under the PDA model, the log ratio has approximate Gaussian distribution of mean ∼ 2.03 ∗ n− 3.545 ∗ √ n− 1 and variance ∼ 2.45 ∗ (n − 1) ∗ log n− 1, where n is the number of tips of the tree. The Gaussian approximation is accurate for very large n (n greater than 10000(?)). The normalization of the ratio uses tabulated empirical values of variances estimated from Monte Carlo simulations. The normalization uses the formula: variance ∼ 1.570 ∗ n ∗ log n− 5.674 ∗ n+ 3.602 ∗ √ n+ 14.915 Under the Yule model, the log ratio has approximate Gaussian distribution of mean = 1.204 ∗ n− log n− 1 − 2 and variance = 0.168 ∗ n − 0.710, where n is the number of tips of the tree. The Gaussian approximation is accurate for n greater than 20. Value An object of class numeric containing the shape statistic of the tree. Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr〉> Olivier François <〈olivier.francois@imag.fr〉> References Fill, J. A. (1996), On the Distribution of Binary Search Trees under the Random Permutation Model. Random Structures and Algorithms, 8, 1 – 25, for more details about the normalization and proofs. Examples data(universal.treeshape) tree <- universal.treeshape plot(tree) summary(tree) likelihood.test(tree, model = "yule", alternative = "two.sided") likelihood.test(tree, model = "pda", alternative = "two.sided") ## Histogram of shape statistics for a list of Yule trees ## (may take some time to compute) main="Histogram of shape statistics"; xlab="shape statistic" hist(sapply(rtreeshape(1000,tip.number=100,model="yule"),FUN=shape.statistic, shift.test 27 norm="yule"), freq=FALSE, main=main, xlab=xlab) ## Does it fit the Gaussian distribution with mean=0 and sd=1 ? x<-seq(-3,3,by=0.001) lines(x,dnorm(x)) shift.test Testing diversification rate variation in phylogenetic trees Description A statistical test of diversification rate shift within an evolutionary process. Usage shift.test(tree, node, lambda1, lambda2, nrep, silent) Arguments tree An object of class treeshape. node An integer value that represents the internal node at which the test is done. It ranges from 1 to the number of tips minus 2. lambda1 A positive numerical value (object of class numeric) that represents an ances- tral diversification rate in the lineage ending at node. lambda2 A positive numerical value (object of class numeric) that represents the shifted diversification rate after the speciation event at node. nrep Number of Monte-carlo replicates in the computation of the P-value. silent A boolean indicating whether the test is silent or verbose. Details This function implements a test of diversification rate shift based on the Delta1 statistic (Moore et al. 2004). We introduced some simplifications of the test statistic using basic results in branching process. Value The function provides textual results and a P-value for the null hypothesis of no diversification rate shift against a (lambda2/lambda1)-fold shift at the node under consideration. Author(s) Eric Durand 〈eric.durand@imag.fr〉 Olivier Francois 〈olivier.francois@imag.fr〉 30 subtree.test Value A sequence of size n-1 (where n is the number of tips of the tree) containing the number of subtrees of each size. spectrum.treeshape(tree)[1] is the number of subtrees with n tips (equal to 1). spectrum.treeshape(tree)[n-1] is the number of cherries of the tree (subtrees with 2 tips). Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr〉> Olivier Francois <〈olivier.francois@imag.fr〉> See Also smaller.clade.spectrum Examples ## A random Yule tree with 30 tips tr<-rtreeshape(n=1,tip.number=30,model="yule") tr<-tr[[1]] spectre=spectrum.treeshape(tr) spectre ## Number of cherries of the tree : nrow(tr$merge)==29 spectre[29] subtree.test Test the Yule or PDA hypothesis Description subtree.test tests the likelihood of the Yule or the PDA hypothesis and computes the p-value of the test. The test is based on the number of subtrees of a given size in the tree. Usage subtree.test(tree, size , alternative = "two.sided") Arguments tree An object of class "treeshape". size The size of the subtrees to test for. alternative The alternative hypothesis of the test. It can be "two.sided" (default), "less" or "greater". subtree.test 31 Details See references for the mathematical details of the test. It uses a Gaussian approximation to compute the p-value. Value A list containing the following arguments : statistic the value of the statistic used in the test p.value the p-value of the test alternative the alternative hypothesis used for the test Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr〉> Olivier Francois <〈olivier.francois@imag.fr〉> References Blum, M. and François, O. (2005) Minimal clade size and external branch length under the neutral coalescent Advances in Applied Probability (2005), 37.3. See Also sackin.test colless.test Examples ## Generate a random pda tree with 50 tips tr<-rtreeshape(n=1,tip.number=50,model="pda") tr<-tr[[1]] ## Test the yule hypothesis, using subtrees of size 2 (Cherries), ## with the alternative hypothesis "less" subtree.test(tr,size=2,alternative="less") 32 summary.treeshape summary.treeshape Print a summary of an object of class "treeshape" Description This function prints a compact summary of a phylogenetic tree of class "treeshape") Usage ## S3 method for class 'treeshape': summary(object, ...) Arguments object an object of class "treeshape". ... further arguments passed to or from other methods. Details summary.treeshape prints the following information: the number of tips of the tree, its Col- less’ index, and the expected values and standard deviations of the Colless’ index under the PDA and Yule models.The expected value of the Colless’ index under the Yule model is given according to the formula: n ∗ log n + n ∗ (γ − 1 − log 2) where n is the number of tips of the tree and γ the Euler’s constant. The standard deviation under the Yule model is given by: √ (3− π26 − log 2) ∗ n. The expected value of the Colless’ index under the PDA model is given according to the formula: √ π ∗ n3/2. The standard deviation under the PDA model is given by: √ 10 3 − π ∗ n 3/2. Value A NULL value is returned, the results are simply printed. Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr〉> Olivier François <〈olivier.francois@imag.fr〉> See Also summary colless for more informations about the expected values under the Yule and PDA models. treeshape 35 Source Bininda-Emonds, O. R., Gittleman, J. L. and Purvis, A. (1999) Building large trees by combining phylogenetic information: a complete phylogeny of the extant Carnivora (Mammalia). Biological Reviews, 74, 143 – 175. for more details about "carnivora.treeshape". Hayasaka, K., Gojobori, T. and Horai, S. (1988) Molecular phylogeny and evolution of primate mi- tochondrial DNA. Molecular Biology and Evolution, 5, 626 – 644, for more details about "primates". Examples # Example tree in Treeshape format data(carnivora.treeshape) plot(carnivora.treeshape) data(primates) plot(primates) treeshape Builds an object of class treeshape Description treeshape builds a tree of class "treeshape" from a n*2 matrix, where n is the number of internal nodes of the tree. There are no informations about the heights of the branches in an object of class "treeshape". Formally, a "tree shape" is a phylogenetic tree where the label of the tips are ignored. Here, the label of the tips can be kept or ignored. If a names vector is provided, then the names of species are attached to the tips of the tree. Otherwise, tips are simply labeled with their numbers in the tree. Trees of class "treeshape" are always binary. Usage treeshape(nodes, names) Arguments nodes nodes is a n*2 matrix containing the node structure of the tree. names names is a vector which contains the names of the tips. Details A tree of class "treeshape" is a fully dichotomous binary tree. The purpose of the class "treeshape" is to study the topology of phylogenetic trees. The heights of branches are not provided for a tree of that class because we mainly focus on the balance aspect of the trees. The ’i’th row of the nodes matrix represents the children of the node number i in the tree (nodes[i,1] being the left child, and nodes[i,2] being the right child). A positive value represents an in- ternal node, while a negative one stands for a tip of the tree. The last row always represents the children of the root of the tree. 36 universal.treeshape Value An object of class "treeshape" Author(s) Michael Blum <〈michael.blum@imag.fr〉> Nicolas Bortolussi <〈nicolas.bortolussi@imag.fr〉> Eric Durand <〈eric.durand@imag.fr〉> Olivier François <〈olivier.francois@imag.fr〉> References Semple, C. and Steel, M. (2003) Phylogenetics. Oxford Lecture Series In Mathematics and its Ap- plications, 24, for the mathematical definitions and tools for phylogenetic trees. See Also rtreeshape Examples ## Nodes will define the nodes of a five tips tree nodes<-matrix(nrow=4,ncol=2) nodes[1,]<-c(-5,-4) nodes[2,]<-c(1,-1) nodes[3,]<-c(-3,2) nodes[4,]<-c(-2,3) ## Now we can build the tree and plot it. tree1<-treeshape(nodes) plot(tree1) ## Computation of the sackin index for the tree : sackin(tree1) ## Label will define the names of the tips label=c("a", "b", "c", "d", "e") tree2<-treeshape(nodes, label) plot(tree1, tree2) universal.treeshape Universal phylogenetic tree of life universal.treeshape 37 Description This data set describes the Universal Tree of Life described by CR Woese, in the treeshape class. "The universal phylogenetic tree not only spans all extant life, but its root and earliest branchings represent stages in the evolutionary process before modern cell types had come into being." Usage data(universal.treeshape) Format universal.treeshape is an object of class "treeshape". References Woese, C. R. (July, 2000) Interpreting the universal phylogenetic tree, 97, 392 – 8396 (Proc. Natl. Acad. Sci. USA). Examples ## Example tree in "treeshape" format data("universal.treeshape") ## Summary of the tree summary(universal.treeshape) ## Visual representation of the tree plot(universal.treeshape)