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name layout title date author sourceslug tags
phylogenetic-tree-balance
post
Exploring phylogenetic tree balance metrics
2012-10-10
Scott Chamberlain
_drafts/2012-10-10-phylogenetic-tree-balance.Rmd
R
phylogenetic
tree shape

I need to simulate balanced and unbalanced phylogenetic trees for some research I am doing. In order to do this, I do rejection sampling: simulate a tree -> measure tree shape -> reject if not balanced or unbalanced enough. But what is enough? We need to define some cutoff value to determine what will be our set of balanced and unbalanced trees.

A function to calculate shape metrics, and a custom theme for plottingn phylogenies.

{% highlight r linenos %} foo <- function(x, metric = "colless") { if (metric == "colless") { xx <- as.treeshape(x) # convert to apTreeshape format colless(xx, "yule") # calculate colless' metric } else if (metric == "gamma") { gammaStat(x) } else stop("metric should be one of colless or gamma") }

theme_myblank <- function() { stopifnot(require(ggplot2)) theme_blank <- ggplot2::theme_blank ggplot2::theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), plot.background = element_blank(), axis.title.x = element_text(colour = NA), axis.title.y = element_blank(), axis.text.x = element_blank(), axis.text.y = element_blank(), axis.line = element_blank(), axis.ticks = element_blank()) } {% endhighlight %}

Simulate some trees

{% highlight r linenos %} library(ape) library(phytools)

numtrees <- 1000 # lets simulate 1000 trees trees <- pbtree(n = 50, nsim = numtrees, ape = F) # simulate 500 pure-birth trees with 100 spp each, ape = F makes it run faster {% endhighlight %}

Calculate Colless' shape metric on each tree

{% highlight r linenos %} library(plyr) library(apTreeshape)

colless_df <- ldply(trees, foo, metric = "colless") # calculate metric for each tree head(colless_df) {% endhighlight %}

{% highlight text %} V1 1 -0.1761 2 0.2839 3 0.4639 4 0.9439 5 -0.6961 6 -0.1161 {% endhighlight %}

{% highlight r linenos %}

Calculate the percent of trees that will fall into the cutoff for balanced and unbalanced trees

col_percent_low <- round(length(colless_df[colless_df$V1 < -0.7, "V1"])/numtrees, 2) * 100 col_percent_high <- round(length(colless_df[colless_df$V1 > 0.7, "V1"])/numtrees, 2) * 100 {% endhighlight %}

Create a distribution of the metric values

{% highlight r linenos %} library(ggplot2)

a <- ggplot(colless_df, aes(V1)) + # plot histogram of distribution of values geom_histogram() + theme_bw(base_size=18) + scale_x_continuous(limits=c(-3,3), breaks=c(-3,-2,-1,0,1,2,3)) + geom_vline(xintercept = -0.7, colour="red", linetype = "longdash") + geom_vline(xintercept = 0.7, colour="red", linetype = "longdash") + ggtitle(paste0("Distribution of Colless' metric for 1000 trees, cutoffs at -0.7 and 0.7 results in\n ", col_percent_low, "% (", numtrees*(col_percent_low/100), ") 'balanced' trees (left) and ", col_percent_low, "% (", numtrees*(col_percent_low/100), ") 'unbalanced' trees (right)")) +
labs(x = "Colless' Metric Value", y = "Number of phylogenetic trees") + theme(plot.title = element_text(size = 16))

a {% endhighlight %}

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Create phylogenies representing balanced and unbalanced trees (using the custom theme)

{% highlight r linenos %} library(ggphylo)

b <- ggphylo(trees[which.min(colless_df$V1)], do.plot = F) + theme_myblank() c <- ggphylo(trees[which.max(colless_df$V1)], do.plot = F) + theme_myblank()

b {% endhighlight %}

center

Now, put it all together in one plot using some gridExtra magic.

{% highlight r linenos %} library(gridExtra)

grid.newpage() pushViewport(viewport(layout = grid.layout(1, 1))) vpa_ <- viewport(width = 1, height = 1, x = 0.5, y = 0.49) vpb_ <- viewport(width = 0.35, height = 0.35, x = 0.23, y = 0.7) vpc_ <- viewport(width = 0.35, height = 0.35, x = 0.82, y = 0.7) print(a, vp = vpa_) print(b, vp = vpb_) print(c, vp = vpc_) {% endhighlight %}

center

And the same for Gamma stat, which measures the distribution of nodes in time.

{% highlight r linenos %} gamma_df <- ldply(trees, foo, metric="gamma") # calculate metric for each tree gam_percent_low <- round(length(gamma_df[gamma_df$V1 < -1, "V1"])/numtrees, 2)100 gam_percent_high <- round(length(gamma_df[gamma_df$V1 > 1, "V1"])/numtrees, 2)100 a <- ggplot(gamma_df, aes(V1)) + # plot histogram of distribution of values geom_histogram() + theme_bw(base_size=18) + scale_x_continuous(breaks=c(-3,-2,-1,0,1,2,3)) + geom_vline(xintercept = -1, colour="red", linetype = "longdash") + geom_vline(xintercept = 1, colour="red", linetype = "longdash") + ggtitle(paste0("Distribution of Gamma metric for 1000 trees, cutoffs at -1 and 1 results in\n ", gam_percent_low, "% (", numtrees(gam_percent_low/100), ") trees with deeper nodes (left) and ", gam_percent_high, "% (", numtrees(gam_percent_high/100), ") trees with shallower nodes (right)")) +
labs(x = "Gamma Metric Value", y = "Number of phylogenetic trees") + theme(plot.title = element_text(size = 16)) b <- ggphylo(trees[which.min(gamma_df$V1)], do.plot=F) + theme_myblank() c <- ggphylo(trees[which.max(gamma_df$V1)], do.plot=F) + theme_myblank()

grid.newpage() pushViewport(viewport(layout = grid.layout(1,1))) vpa_ <- viewport(width = 1, height = 1, x = 0.5, y = 0.49) vpb_ <- viewport(width = 0.35, height = 0.35, x = 0.23, y = 0.7) vpc_ <- viewport(width = 0.35, height = 0.35, x = 0.82, y = 0.7) print(a, vp = vpa_) print(b, vp = vpb_) print(c, vp = vpc_) {% endhighlight %}

center


Get the .Rmd file used to create this post at my github account - or .md file.

Written in Markdown, with help from knitr.