Phylogenies Continuous Characters

Updates: changed chronogram(tr) to chronopl(tr, lambda=0), a close approximation of Sanderson's NPRS method for making a tree ultrametric.

Also minor fixes.

```
##############################################################
# =============================================
# Lab 4: Continuous characters using APE in R
# =============================================
# by Nick Matzke and Nat Hallinan (and whoever else adds to this PhyloWiki page)
# Copyright 2011-infinity
# matzkeATberkeley.edu
# February 2011
#
# Please link/cite if you use this, email me if you have
# thoughts/improvements/corrections.
#
# Much of the text of this lab was derived from Nat
# Hallinan's 2009 lab for IB200b on continuous characters
# in R.
#
##############################################################
#
# Free to use/redistribute under:
# Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0)
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the above license, linked here:
#
# http://creativecommons.org/licenses/by-nc-sa/3.0/
#
# Summary:
#
# You are free:
#
# * to Share -- to copy, distribute and transmit the work
# * to Remix -- to adapt the work
#
# Under the following conditions:
#
# * Attribution -- You must attribute the work in the manner
# specified by the author or licensor (but not in any way that
# suggests that they endorse you or your use of the work).
# * Noncommercial -- You may not use this work for commercial purposes.
#
# * Share Alike -- If you alter, transform, or build upon this work,
# you may distribute the resulting work only under the same or
# similar license to this one.
#
# http://creativecommons.org/licenses/by-nc-sa/3.0/
#
###################################################################
#
# Assignment for Tuesday, Feb. 8
#
# Do the three questions and PRINT OUT the answers.
#
# Purpose: Learn more about tree-plotting and ancestral character
# reconstruction
#
###################################################################
# Stuff that is handy at the beginning of a script
######################################################
# R, close all devices/windows/ quartz windows
graphics.off()
# Turn off all BS stringsAsFactors silliness
# R tends to read
options(stringsAsFactors = FALSE)
######################################################
# Working directories:
# One of the first things you want to do, usually, is
# decide on your working directory
# On my Mac, this is the directory
wd = "/Users/nick/Desktop/_ib200a/ib200b_sp2011/lab04"
# On a PC, you might have to specify paths like this:
#wd = "c:\\Users\\nick\\Desktop\\_ib200a\\ib200b_sp2011\\lab03"
#desc: set working directory
setwd(wd)
#desc: get working directory
getwd()
#desc: list the files in the directory
list.files()
# Sourcing scripts
# Local sourcing:
# source a script (windows machines require \\ instead of /)
# sourcedir = '/_njm/'
#source3 = '_genericR_v1.R'
#source(paste(sourcedir, source3, sep=""))
# You need the APE package to source genericR_v1.R scripts
# install.packages("ape")
library(ape)
# Remote sourcing:
source("http://ib.berkeley.edu/courses/ib200b/scripts/_genericR_v1.R")
source("http://ib.berkeley.edu/courses/ib200b/scripts/_R_tree_functions_v1.R")
############################################
# Introduction
############################################
#
# Today we're just going to do some basic analysis of
# continuous characters using R. Most of it should be based on
# things that we learned today in class. We'll start with reading
# Nexus files and manipulating trees in R and then move
# on to character reconstruction.
#
############################################
# Class phylo
############################################
#
# The first thing that we're going to do today is learn about
# the class phylo. This is the object type used by APE to
# store and manipulate trees. First let's simulate a small
# tree of 4 taxa:
# QUESTION 1: Look up the function rcoal. What does it do? Explain
# in your own words how this kind of simulator works. (You may have
# to google some key words from the help page.)
simulated_tree = rcoal(4)
# To see what class the object stored in "simulated_tree" is:
class(simulated_tree)
# To see some details of the tree type:
summary(simulated_tree)
# To see more details, use some of my functions
# (remember the last lab):
summ(simulated_tree)
prt(simulated_tree)
# "summary" functions like the "plot" function in that
# it produces a different output depending on the
# information that is passed to it. In this case it
# provides you with some basic info about the tree.
# As you can see this is a tree with n=4 tips, and since
# it is fully bifurcating it has
#
# (n-1 = 3) internal nodes
#
# and
# (2n-2 = 6) branches.
#
# To see a slightly different summary, just type "simulated_tree"
# and hit Enter. To see what the tree actually looks like type:
tree = simulated_tree
plot(tree)
# R actually codes for phylogenies as a list with several
# elements. The elements can be referenced using the "$".
# Type:
tree$tip.label
# This will return a character vector of 4 elements showing the
# names of the taxa in the tree. The order of the taxa is important,
# as the order of a vector of character states will correspond to
# the order of taxa. To see the structure of the tree itself type:
tree$edge
# This is a matrix with 2 columns and 6 rows. Each number in
# the matrix represents a node. Numbers 1 to n are the tips
# with each number referring to the equivalent element of the
# $tip.label vector; the number n+1 (in this case 5) refers
# to the root node; and the numbers above that are the other
# internal nodes. Each row represents a branch of the tree
# stretching from the node in column 1 to the node in column
# 2. This matrix is set up such that the branches that make
# up any clade are all grouped next to each other. Take a
# minute to compare the $edge matrix to you plotted tree.
# Make sure that you can see how this matrix codes for this
# tree.
#
# Finally, the branch lengths are stored in $edge.length:
tree$edge.length
# As you can see this is a numerical vector with six elements
# each corresponding to the branch lengths of one of the
# branches. The branches are in the same order as the
# branches in the $edge matrix. Does that make sense for
# the branch lengths you see in your plot?
#
# Other elements of the class phylo inclue $root.edge which
# gives the branch length of the root, if there is one, and
# node.label, a vector of the node names.
############################################
# Uploading Trees into R
############################################
#
# Continuous Character Format
#
# Open the Anoles Continuous file in a text editor. I stole
# this file from the Mesquite examples and according to them
# it comes from "the work of Jonathan Losos and colleagues
# (Losos et al., Science, 1998 and Losos & de Queiroz, Biol.
# J. Linn. Soc., 1997) on Anolis lizards of the caribbean
# that looks at convergence in ecomorphs." This file will be
# pretty much the same as the previous Nexus files that you
# looked at with the exception of the first character block.
# (There are two other character blocks in this file.) First
# thing to note is that the Datatype is set to "Continuous".
# Also, when you look at the actual matrix, you will see that
# it is filled with numeric values separated by spaces rather
# than the normal format.
#
#
# Reading Trees into R
# Open R and load the ape package.
library(ape)
# (If you haven't already, you have to install APE. Either:
#
# 1. type install.packages("ape")
#
# ...or...
#
# 2. Packages -> Package Installer --> search for APE and install (with dependencies)
#
#
# This next step is only necessary right now to fix a bug. It is
# not a problem in older versions of ape nor should it be a problem
# in the future. You should check for new versions of all your
# packages regularly; just go to Packages>Update packages. For
# now we need to open the read.nexus.R file and run it.
fn = "anoles_continuous.nex"
Anole.tree = read.nexus(fn)
###########################################
# Plotting Trees in R
###########################################
#
# Basic Tree Plotting
#
# OK, can you visualize the tree by reading the
# tip.label matrix? Don't worry; you don't have to.
# Type:
plot(Anole.tree)
# Isn't the plot function cool? You can make different shaped
# trees too. Try:
plot(Anole.tree,type="f")
# and
plot(Anole.tree,type="r")
# You can also make the tree face in different directions:
plot(Anole.tree,direction="d")
# and
# plot(Anole.tree,direction="u")
# You can manipulate many other visual factors of the tree,
# including the position size and font of the text. Type
# help("plot.phylo") for more info. In the next two sections
# we will explore how to modify specific branches of the tree.
#
# Identifying Branches
# You can now use this plotted tree to identify the number
# of a given node. To do this we will use the "identify" function.
# identify is another function that gives a different result
# for different arguments. It is an interactive function,
# which means that its output depends on where you click on a
# plot. When fed an object of class phylo, identify will return
# the number corresponding to a node that you click on. Type:
identify(Anole.tree)
# ...and click on a node in the tree.
# The number it returns is the number of that node. You can
# find which branch ends with this node by using the which
# function, which returns the index of a vector for which a
# given statement is true. Type:
which(Anole.tree$edge[,2]==node number)
# or just:
which(Anole.tree$edge[,2]==identify(Anole.tree))
# ...and then click a node
#
# Modifying Branch Color
#
# You can use that information to change the color of the
# branch you've identified. To do this we have to create a
# vector of numbers that correspond to a color for each branch
# of the tree. Since we want most of tree to stay black, we will
# first create a vector of length 58 full of 1s:
br.col = rep(1,58)
# Then we will change the number corresponding to the branch we
# want to a 2 for red (or maybe give another number a try):
# picking an arbitrary branch number to color
branch_number_to_color = 31
# 4 for blue
br.col[branch_number_to_color] = 4
# Now we'll draw the tree again but add information about the
# colors of the branches. Type:
plot(Anole.tree,edge.color=br.col)
# Identifying Nodes
#
# You may also want to identify an entire clade. This is a
# little trickier; it relies on the assumption that the branches
# that make up a clade are all next to each other in our $edge
# matrix. The first thing that we will do is identify a bunch
# of info about a node:
clade.info = identify(Anole.tree,tips=TRUE)
# and click on the root node of a clade
#
# clade.info is now a list with two elements: node which is the
# node for the root of the tree, and tips which is a vector of
# the tip numbers.
# Print "clade.info" to screen:
(clade.info)
# So the first branch of our clade will be
# the one that ends at the node we picked:
start = which(Anole.tree$edge[,2] == clade.info$node)
# We will find the last listed branch in our clade by taking
# advantage of the fact that it has to end in one of the taxa
# from our clade; so we need to find out which branches end
# in each of the tips that are in this clade:
tip.branches = match(clade.info$tips,Anole.tree$edge[,2])
# "match" returns a vector of the order that the elements of
# its first argument are found in its second argument. So
# that data.order is a vector ordered in the same way as
# the taxa in the $tips vector, but with the numbers
# representing the index of the branches that those
# taxa appear in the $edge matrix. Therefore the
# last branch in our clade is:
end = max(tip.branches)
# Now start is the first branch or our node and end is the last.
#
#
#
# Modifying Branch Widths for a Node
#
# We can now use this info to make those branches four
# times as wide as the others. Once again we need to
# create a vector of numbers corresponding to the branches.
br.wid = rep(1,58)
br.wid[start:end] = 4
plot(Anole.tree, edge.color=br.col, edge.width=br.wid)
# Well, I don't know about for your plot, but mine did
# not work perfectly. It made the correct branches big, but
# it did not get the correct cross branches. Hopefully they
# correct that soon. Keep checking for updates.
# (Note added in 2011: this seems to work fine now.)
#
# Incidentally,
# although the edge.width does not get the correct cross branches,
# edge.color will. Let's make those branches blue, instead of
# thick (4=blue).
#
plot(Anole.tree, edge.color=br.wid, edge.width=4)
# That worked. Maybe if you want to light up a whole clade,
# you should stick with colors. Thickness can be saved for
# the whole tree or individual branches.
#######################################################
# Likelihood Calculations, and Branch Lengths
#######################################################
#
# Graffen Branch Lengths
#
# To make any type of likelihood calculation we need branch lengths, but this
# tree does not have any. We've talked some in class, and we will talk more
# later about where your branch lengths should come from. However, sometimes
# you can not find branch lengths. In that case there are several ways of
# generating branch lengths. In practice, if you have to use branch lengths
# that are not justified, you should generate many different sets of such
# branch lengths in order to make sure that your conclusions are robust to
# your assumptions. However, in this case it doesn't really matter, so
# we'll just generate some and use them.
#
# The ape function compute.brlen has one internal method for assigning
# branch lengths; that method is based on
# Graffen, Phil. Trans. R. Soc. B (1989) 326, 119-157.
# I will not discuss the details because I do not understand them.
#
# To add Graffen branch lengths to our tree type:
#
Anole.Graf = compute.brlen(Anole.tree)
#
# Plotting Branch Lengths
#
# Now let's plot that tree with the branch lengths listed:
plot(Anole.Graf)
# That shows the branch lengths graphically, to add actual numbers
# to the plot we will use the edgelabels function, which adds text
# to the branches. The nodelabels and tiplabels functions do the
# same thing for other parts of the plot. Type:
edgelabels(Anole.Graf$edge.length)
# OK, that's just ugly. Try this instead:
plot(Anole.Graf)
edgelabels(round(Anole.Graf$edge.length, digits=3), frame="n", adj=c(0.5,-0.1), cex=0.6)
# That should look better. If the numbers are still too cramped,
# try just blowing up the graphics window. So what did all those
# commands do? $edge.length is a vector of the branch lengths
# for the tree; the round(vector,digits=3) return a vector with
# all the values in that vector rounded to 3 decimal places;
# frame="n" removed that ugly green box; adj determines the
# position of the text with the first number being the horizontal
# position and the second the vertical; and cex=0.6 shrunk the
# text to 60% of normal.
#
# Alternatively you could add an axis to the plot that
# corresponds to the branchlengths.
#
axisPhylo()
# That's nice, and that is usually the way branch lengths are
# indicated anyways.
#
# Random Branch Lengths
#
# Graffen branch lengths are cool, and have at least some biological
# justification, but they will always give you the same results. It
# would be nice to generate random branch lengths, so that we can
# look at multiple sets of branch lengths for comparisons. Any function
# that returns a numeric value can be used to generate branch lengths
# with compute.brlen. To generate a random set of branch lengths type:
Anole.rand = compute.brlen(Anole.tree, runif, min=0, max=10)
# runif is a function that generates draws from a uniform random
# distributions. min and max are arguments passed to the runif
# function setting the minimum and maximum value of that
# distribution. So that for every branch this command will
# run the function runif(min=0,max=10) to generate a branch
# length.
#
# Let's see what this tree looks like:
plot(Anole.rand)
axisPhylo()
# That's cool. The only real problem that I see, is that this tree
# is not ultrametric. To make it ultrametric let's use the
# chronogram (now chronopl function:
# NOTE: chronogram doesn't work with newer versions of R, replace with
# chronopl with lambda=0
# Anole.ultra = chronogram(Anole.rand,scale=100)
Anole.ultra = chronopl(Anole.rand, lambda=0)
# scale sets the depth of the root for this tree. Why don't you
# plot it with an axis to see what it looks like. This function uses
# the NPRS(non-parametric rate smoothing) algorithm from
# Sanderson, Mol. Biol. and Evo. (1997) 14, 1218-1231.
###################################################
# Continuous Characters
###################################################
#
#
# Reading a Data Matrix
#
# The first step is to get our data out of the nexus file.
# read.nexus only reads the tree. Unfortunately R does not
# have a function for reading continuous data directly from
# a nexus file. Instead we will have to use the regular
# old read.table function.
#
# Before we do that we need to create a vector of character
# names so that we can keep track of what the different
# characters are. First open the anole_continuous.nex file in
# a text editor and scroll down to the data matrix with the
# continuous characters. Under CHARSTATELABELS you will
# find the names of all the character states. We want to
# create a vector starting with taxon followed by all the
# state names in that same order, e.g. in R, type:
#
data.names = c("taxon", "snout-vent length", "mass","foreleg", "hindleg", "tail", "lamellae")
# Now, I've editted the nexus file to remove everything except the
# data matrix itself. That means just leave the taxon names,
# the numbers and the spaces around them. This was saved as
# anoles_continuous_data_table.txt. Open it in a text editor
# and look at it also.
#
# Now we can read the data:
#
fn2 = "anoles_continuous_data_table.txt"
(Anole.data = read.table(fn2, row.names=1, col.names=data.names))
# row.names=1 made the first column be the names of the rows.
# col.names set the column names as the the elements of our vector.
#
# We had to start our vector with a "taxon", because the first column
# of our input file was the taxon names, and the actual data did not
# start until the second column. Since the first column has no name,
# it does not matter what the first element of the vector is. You
# could have set up this table in any program; the advantage of
# using Mesquite is that you know the taxon names for the data
# will exactly match the taxon names for the tree.
#
# The problem now is that the order of the taxa differs between our
# tree and our data matrix, and we need to fix that. The first step
# is to identify the order that the names in the tree appear in
# the data matrix. To do this we will use the match function:
data.order = match(Anole.ultra$tip.label, rownames(Anole.data))
# rownames returns a vector containing the names of the rows, so
# that data.order is a vector ordered in the same way as the taxa
# in the tree, but with the numbers representing the order that
# those taxa appear in the data matrix.
#
# Now we can easily use that vector to rearrange our data matrix
# to match the tree:
Anole.ordered = Anole.data[data.order, ]
# Do you see why that worked? If not, you should review the sections
# on indexing from the previous lab.
#
# Plotting data on the Tree
# So now let's just look at the data on our tree, to see how it is
# distributed. First plot the tree again, but this time without
# names:
plot(Anole.ultra, show.tip.label=FALSE, x.lim=c(0,110))
# show.tip.label=FALSE removes the tip labels, and x.lim=c(0,110)
# sets the x-axis with a little extra space on the right side beyond
# the 100 units of tree depth. Now add the data to the tips:
tiplabels(Anole.ordered[,1], frame="n", adj=c(0,0.5), cex=0.8)
# Just for looking that's OK, but it really doesn't tell you anything.
# You can repeat those two commands to look at the distribution of the
# other characters. Maybe it would look better if we did it with
# colors (see the last section for how to do this).
#
# Ancestral State Reconstruction
#
# Let's do an actual analysis with the data. Let's reconstruct the
# ancestral states of these data. To do this we will use the ace
# function. We probably want to do these analyses on the logs of
# our data not the actual data values four a couple of reasons:
# these values run from zero to infinity and can not be negative
# as their logs can; and it is probably more reasonable to assume
# that multiplying a measurement by a given factor will be
# evolutionarily equivalent, not adding a given amount. For example
# it makes sense that going from 2 inches to 3 inches is equivalent
# to going from 2 feet to 3 feet not from 2 feet to 2 feet and 1 inch.
#
# To log transform our data:
Anole.log = log(Anole.ordered)
# If you run ace without any additional commands, it will do a Maximum
# Likelihood analysis using Brownian motion.
Anole.ASR = ace(Anole.log[,1],Anole.ultra)
# You may get some "warnings".
#
# This will produce a list with several elements. To see them all
# type "Anole.ASR". $loglik is the natural log of the maximum
# likelihood; $ace contains the reconstructions at the nodes;
# $sigma2 shows the value of the parameters for the Brownian motion model;
# and $CI95 shows the 95% confidence intervals for those reconstructions.
#
# You can also use ace to reconstruct the ancestral nodes using other methods.
# To reconstruct the nodes using independent contrasts:
ace(Anole.log[,1], Anole.ultra, method="pic")
# For independent contrasts not scaled by branch lengths:
ace(Anole.log[,1],Anole.ultra,method="pic",scaled=FALSE)
# For generalized least squares you first have to define a correlation
# structure. There are several different functions to do this, we will
# use the simplest:
Anole.cor = corBrownian(1, Anole.ultra)
# You can find other correlation structures in the ape manual.
# They all start with "cor". Now we will use that to reconstruct the
# ancestral nodes by Generalized Least Squares:
ace(Anole.log[,1],Anole.ultra,method="GLS",corStruct=Anole.cor)
# How do the results of these different methods differ? What about
# the confidence intervals?
#
# ace can also be used to reconstruct ancestral states for discrete
# characters, and is in many ways more flexible than Mesquite. See
# the ape manual for instructions.
#
# Plotting data with error bars
#
# So, we have all these reconstructions with errors, but often it is difficult
# to visualize what they mean from numbers alone. First let's transform our
# results back to a non-log scale:
Anole.ace = exp(Anole.ASR$ace)
Anole.CI95 = exp(Anole.ASR$CI95)
# Then, let's do a simple plot of are data against our nodes:
plot(31:59,Anole.ace, ylim=c(min(Anole.CI95), max(Anole.CI95)))
# This plots the reconstructions against the node numbers. We reset
# the range of the y axis to provide enough space for us to add
# the error bars.
#
# Now to add the error bars:
segments(31:59, Anole.CI95[,1], 31:59, Anole.CI95[,2])
# This function will draw a series of lines between the first
# set of coordinates and the second. To figure out which nodes
# these results correspond to, you can plot the tree and add
# the node labels:
Anole.ultra$node.label = 31:59
plot(Anole.ultra, edge.width=5, show.node.label=TRUE)
# Or you could plot the tree and use identify to click on the nodes.
#
# QUESTION 2. What is the ancestral state for the most recent common
# ancestor of angusticeps and strahmi? 95% CI?
#
# Plotting Reconstructions on the tree as colors
#
# There is not a straight forward way to do this. The problem is that the
# basic colors don't tell us that much. Instead let's create a new set
# of colors over a more easy to interpret range and assign them values.
# Then assign those colors to our branches based on their values.
#
# The first step is to organize our data in the same order as the branches:
data.branches = rep(0,58)
data.branches[match(1:30, Anole.ultra$edge[,2])] = Anole.ordered[,1]
data.branches[match(32:59, Anole.ultra$edge[,2])] = Anole.ace[2:29]
# Now we create a vector of 100 new colors that range from red as the
# lowest color through white as the highest:
color.range = heat.colors(100)
# heat.colors is one particular set of colors to see others go to
# help("heat.colors"). To see what the colors we just made look like:
plot(1:100,cex=1.5,col=color.range)
# Then we need to assign every value from our data as an integer between
# 0 and 100 that is proportional to the data for that branch. First let's
# find the range of our data in order to decide what colors should be
# assigned to what numbers:
min(data.branches)
max(data.branches)
# I got 35.3 and 183, so let's run our colors from 30 to 200.
data.rounded = data.branches-30
data.rounded = round(data.rounded*99/170)+1
# We will use this to create a new vector of colors, where the order of
# the colors corresponds to the order of the branches, and the colors
# correspond to the value of our data on that branch:
color.data = color.range[data.rounded]
# Now we just use that to plot our results:
plot(Anole.ultra,edge.width=5,edge.color=color.data)
# OK, so the problem with that is almost all the data is in the
# bottom of the range, so you don't see most of the differences.
# We can fix that by taking the log of the data:
data.rounded = log(data.branches - 30)
data.rounded = round(data.rounded*99 / log(170)) + 1
color.data = color.range[data.rounded]
plot(Anole.ultra, edge.width=5, edge.color=color.data)
# You may want to add a scale bar to this plot:
value.range = rep(NA,11)
value.range[ 1: (6*2-1) ] = round(exp((c( 5:1*20, 1)-1) * log(170)/99) + 30, digits=1)
# Next, type:
legend(locator(), legend=value.range, fill=color.range[c(10:1*10, 1)], y.intersp=0.5, cex=0.8)
# Then left click on the figure where you want the legend to go,
# right click and select stop. (Ummm, on a Mac sometimes you
# can't right click: Try <ctrl> click, or <enter>, your guess is
# probably better than mine.)
#
# I'll leave it up to you to figure out what all those commands mean.
# QUESTION 3. Print out this picture for me.
# Save Your Work
#
# We're going to use this same data set next time: File>Save workspace..
```

page revision: 2, last edited: 11 Feb 2011 20:41