Comparison of organisms: Does phenotypic similarity match phylogenetic

similarity?

Assume you have run Phenotype Microarray experiments for several organisms, e.g. bacterial strains. Assume further that you have numerous metadata for these strains, for example their genetic similarity and their geographical and ecological origins.

The data set wittmann_et_al contains bacterial strains from different phylogenetic clusters (see the respective publication). For each of the strains the geographic and ecological origin is known.

In this example we compare phenotypic to phylogenetic similarity using

* graphical approaches such as heat maps

* bootstrapping to assess significance of phenotypic clusters

* multiple comparison of overall AUC values across phylogenetic clades

Author: Johannes Sikorski

Load R packages and data

library(opm)
library(opmdata)
library(pvclust)
data(wittmann_et_al)

For demonstration purposes, some plates are removed from the data set

wittmann_small <- subset(wittmann_et_al,
  query = list(MLSTcluster = c("Ax1", "Ax2", "Ax4", "Ax6")))

Check the dimensions of the data set:

dim(wittmann_small)

## [1]  33 382  96

Display phenotypic similarity of strains using a heat map approach

• The row dendrogram will be coloured by the metadata information on phylogenetic clusters Ax1, Ax2, Ax4 and Ax6
• The curve parameter “Area under the Curve” (AUC) will be used

heat_map(wittmann_small,
  as.labels = list("strain", "replicate", "MLSTcluster"),
  as.groups = "MLSTcluster",
  cexRow = 1.5,
  use.fun = "gplots",
  main = "Heatmap on AUC data",
  subset = "AUC",
  xlab = "Well substrates on Generation-III Biolog plate",
  ylab = "strains, replicates, and their MLST cluster affiliation")

Result

• Obviously the four phylogenetic clades Ax1, Ax2, Ax4 and Ax6, indicated by the four different colours on the row dendrogram, fit to the phenotypic similarity clustering
• Only one strain from clade Ax2 (strain CCUG 47074, second replicate) falls into the phenotypic similarity cluster of clade Ax4
• Similarly, a clade Ax4 strain clusters with Ax2 strains with respect to the phenotype

Are these phenotypic similarity clusters statistically robust?

• We use the R package pvclust to test this (run demo("cluster-with-pvalues") for details).

x <- t(extract(wittmann_small, list("strain", "replicate", "MLSTcluster")))
x.pvc <- pvclust(x, method.dist = "euclidean", method.hclust = "ward",
  nboot = 100)

## The "ward" method has been renamed to "ward.D"; note new "ward.D2"

## Bootstrap (r = 0.5)... Done.
## Bootstrap (r = 0.59)... Done.
## Bootstrap (r = 0.7)... Done.
## Bootstrap (r = 0.79)... Done.
## Bootstrap (r = 0.9)... Done.
## Bootstrap (r = 1.0)... Done.
## Bootstrap (r = 1.09)... Done.
## Bootstrap (r = 1.2)... Done.
## Bootstrap (r = 1.29)... Done.
## Bootstrap (r = 1.4)... Done.

plot(x.pvc, hang = -1)
pvrect(x.pvc, max.only = FALSE)

Result

According to the AU p-values there is significant support for some of the observed phenotypic similarity clusters (highlighted with rectangles).

Is there any significant difference in overall AUC values across

strains of the phylogenetic clades?

• we apply the multcomp algorithm for multiple comparisons of groups using a Tukey-type contrast matrix
• we compare AUC values across the phylogenetic clades which are identified by the metadata entry MLSTcluster

test <- opm_mcp(wittmann_small, model = ~ MLSTcluster, m.type = "aov",
  linfct = c(Tukey = 1))

old.mar <- par(mar = c(3, 15, 3, 2)) # adapt margins in the plot
plot(test)

par(old.mar) # reset to default plotting settings

The numerical output of the statistical test is called as follows:

mcp.summary <- summary(test)
mcp.summary$model$call <- NULL # avoid some unnecessary output
mcp.summary

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Multiple Comparisons of Means: Tukey Contrasts
## 
## 
## Linear Hypotheses:
##                Estimate Std. Error t value Pr(>|t|)
## Ax2 - Ax1 == 0   7.6426     6.7838   1.127    0.669
## Ax4 - Ax1 == 0   9.4230     6.7838   1.389    0.501
## Ax6 - Ax1 == 0   6.8870     7.2823   0.946    0.777
## Ax4 - Ax2 == 0   1.7803     4.9542   0.359    0.984
## Ax6 - Ax2 == 0  -0.7557     5.6175  -0.135    0.999
## Ax6 - Ax4 == 0  -2.5360     5.6175  -0.451    0.969
## (Adjusted p values reported -- single-step method)

Result

• There is no statistically significant difference across all AUC values between the strains of the different phylogenetic clades Ax1, Ax2, Ax4 and Ax6.
• Though there is no statistical support, the graphical analysis using the heat map approach suggest a correlation between phylogenetic similarity and phenotypic similarity.

Synopsis

• A graphical approach such as a heat map can be used to test for differences between a certain phenotypic similarity and s similarity regarding any other set of traits, as long as these are coded in the metadata.
• The statistical robustness can be tested using two different bootstrap procedures.
• The overall difference between multiple groups (as coded in the metadata) can be tested statistically.