The adonisplus package provides some utilities for permutational
multivariate analysis of variance, also known as adonis or PERMANOVA.
You can install the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("PennChopMicrobiomeProgram/adonisplus")library(tidyverse)To show an example, we’ll use a built-in data set from the FARMM study by Tanes et al. Participants consumed one of three diets for the duration of the study: omnivore, vegan, or exclusive enteral nutrition (EEN). On days 5-8, participants were given a combination of three antibiotics to clear out bacteria in the gut. Additionally, participants underwent a gut purge on day 8. The fecal microbiome and metabolome were sampled throughout the study. Here, we will work with the microbiome data, which was generated by shotgun metagenomic sequencing.
Our data objects are a data frame of sample info, farmm_samples, and a
matrix of Bray-Curtis distances between samples, farmm_bc. The
Bray-Curtis distances are derived from differences in the abundance of
the taxa that comprise the fecal microbiome. We have one distance for
each pair of samples. Let’s look at the data frame of samples.
farmm_samples## # A tibble: 414 × 11
## sample_id subject_id study_day diet antibiotics height weight age
## <chr> <dbl> <int> <fct> <fct> <dbl> <dbl> <dbl>
## 1 farmm.9005.00 9005 0 Omnivore pre 180 70 24
## 2 farmm.9005.02 9005 2 Omnivore pre 180 70 24
## 3 farmm.9005.03 9005 3 Omnivore pre 180 70 24
## 4 farmm.9005.04 9005 4 Omnivore pre 180 70 24
## 5 farmm.9005.06 9005 6 Omnivore current 180 70 24
## 6 farmm.9005.07 9005 7 Omnivore current 180 70 24
## 7 farmm.9005.08 9005 8 Omnivore current 180 70 24
## 8 farmm.9005.09 9005 9 Omnivore post 180 70 24
## 9 farmm.9005.10 9005 10 Omnivore post 180 70 24
## 10 farmm.9005.11 9005 11 Omnivore post 180 70 24
## # ℹ 404 more rows
## # ℹ 3 more variables: bacterial_16S_copies <dbl>, num_reads <dbl>,
## # host_frac <dbl>
The first column, sample_id provides a unique ID for each sample,
which is also used to label the samples in the distance matrix.
Before we get into any complicated stuff, let’s run a simple example
without any repeated measurements. Let’s ask if the diet groups were
different, using the last time point obtained for each participant.
We’ll make a new data frame, farmm_final, containing just the samples
we need.
farmm_final <- farmm_samples %>%
group_by(subject_id) %>%
filter(study_day == max(study_day)) %>%
ungroup()First, we’ll run a principal coordinates analysis (PCoA) of the final
time point using pcoaplus(). To use this function, we pipe in the data
frame of samples as the first argument. The second argument is the
distance matrix, farmm_bc. We need a third argument to specify which
column of the data frame matches the IDs in the distance matrix. The
functions in this package will automatically re-arrange the distance
matrix to match the data frame, so you can use the same distance matrix
over and over as you filter and re-arrange the samples. Here, we specify
this column as sample_id.
farmm_final %>%
pcoaplus(distmat = farmm_bc, sample_id_var = sample_id)## # A tibble: 30 × 13
## sample_id Axis.1 Axis.2 subject_id study_day diet antibiotics height weight
## <chr> <dbl> <dbl> <dbl> <int> <fct> <fct> <dbl> <dbl>
## 1 farmm.90… -0.251 -0.271 9005 15 Omni… post 180 70
## 2 farmm.90… 0.0656 0.203 9006 15 Omni… post 176 87.3
## 3 farmm.90… -0.255 -0.146 9010 15 Omni… post 171. 63.4
## 4 farmm.90… -0.167 -0.218 9015 15 Omni… post 173 61.3
## 5 farmm.90… -0.309 -0.209 9019 15 Omni… post 174. 66.3
## 6 farmm.90… -0.0329 0.349 9030 15 Omni… post 180. 90
## 7 farmm.90… -0.0226 0.115 9033 15 Omni… post 170. 78.6
## 8 farmm.90… 0.0233 0.439 9036 15 Omni… post 178 75.8
## 9 farmm.90… -0.131 0.186 9037 15 Omni… post 176 71.3
## 10 farmm.90… -0.147 0.180 9040 15 Omni… post 173 71
## # ℹ 20 more rows
## # ℹ 4 more variables: age <dbl>, bacterial_16S_copies <dbl>, num_reads <dbl>,
## # host_frac <dbl>
We see that pcoaplus() has returned a new data frame, with two new
columns, Axis.1 and Axis.2. We could use this to go straight into
ggplot(), but our data frame has a custom plot method that adds in
some nice details, like the percent variation for each axis. When
calling plot(), we override the default mapping to color the samples
by diet. We also add a few elements to the ggplot object, to set the
color scale and change the theme.
farmm_final %>%
pcoaplus(distmat = farmm_bc, sample_id_var = sample_id) %>%
plot(color = diet) +
scale_color_brewer(palette = "Set1") +
theme_bw()
It looks like the microbiome of the EEN diet group is different from
that in the omnivore and vegan groups. Let’s test for differences
between the diet groups using adonisplus(). As with pcoaplus(), we
pipe in the data frame of study info as the first argument, then provide
the distance matrix as the second argument. Our third argument is a
formula to specify the statistical model. The formula must have
distmat on the left-hand side, which allows us to re-use the same
formula with different distance matrices. As before, we add an
additional argument to let the function know which column of the data
frame corresponds to the IDs in the distance matrix.
farmm_final %>%
adonisplus(
distmat = farmm_bc, formula = distmat ~ diet,
sample_id_var = sample_id)## # A tibble: 3 × 6
## term df sumsq r.squared statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 diet 2 1.84 0.168 2.73 0.001
## 2 Residual 27 9.07 0.832 NA NA
## 3 Total 29 10.9 1 NA NA
Our result looks like the output of adonis() from the vegan package,
but it’s been tidied up into a data frame. If you have your own results
from adonis(), you can tidy them up yourself using the tidy.adonis()
function from this package.
It looks like the diet groups are different, but we don’t know which
pairs are different. My guess would be that EEN is different than
omnivores and vegans, and that omnivores aand vegans are not different
from each other. To run the pairwise comparisons, we’ll use
adonispost(). The arguments to this function are the same as
adonisplus(), but we add an additional argument, which, to specify
the variable on which we want to carry out pairwise comparisons.
farmm_final %>%
adonispost(
distmat = farmm_bc, formula = distmat ~ diet,
sample_id_var = sample_id, which = diet)## # A tibble: 4 × 7
## comparison term df sumsq r.squared statistic p.value
## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 All diet diet 2 1.84 0.168 2.73 0.001
## 2 Omnivore - Vegan diet 1 0.445 0.0671 1.30 0.159
## 3 Omnivore - EEN diet 1 1.15 0.159 3.39 0.001
## 4 Vegan - EEN diet 1 1.16 0.165 3.56 0.001
The results are as expected. So, far we could have done all of this work
using the functions in vegan and ape, without much difficulty.
However, the adonisplus package really shines when we have
experimental designs with repeated measures.
Let’s move beyond a single time point, to see how the microbiome changes over time for each diet. To get an overview, we’ll re-generate Figure 2A from the paper.
farmm_samples %>%
pcoaplus(distmat = farmm_bc, sample_id_var = "sample_id") %>%
plot(color = study_day) +
facet_grid(~ diet) +
scale_color_viridis_c(direction = -1) +
theme_bw()
The paper reports that “EEN led to a significant change in the microbiota composition within 3 days of the dietary phase relative to the vegan and omnivore group.” The next sentence says, “The vegan and omnivore groups were not significantly different from each other until day 7, which marks the introduction of PEG.” Let’s check that out for ourselves.
To investigate both claims, we’ll limit the data set to the
pre-antibiotics period, and call it farmm_preabx.
farmm_preabx <- farmm_samples %>%
filter(antibiotics %in% "pre")Now, we’ll run adonisplus() on a sample set with repeated measures. We
need to provide two additional arguments. First, we give the variable
within which the measures are repeated, subject_id in our case.
Secondly, we need to tell adonisplus() how to randomly re-assign each
variable in the formula. Here, we tell it to randomly re-assign diet
between subjects, and randomly shuffle the study days within each
subject.
farmm_preabx %>%
adonisplus(
distmat = farmm_bc, formula = distmat ~ diet * study_day,
sample_id_var = sample_id, rep_meas_var = subject_id,
shuffle = c(diet = "between", study_day = "within"))## # A tibble: 5 × 6
## term df sumsq r.squared statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 diet 2 4.34 0.104 8.62 0.001
## 2 study_day 1 0.504 0.0121 2.00 0.001
## 3 diet:study_day 2 0.663 0.0159 1.32 0.001
## 4 Residual 144 36.2 0.868 NA NA
## 5 Total 149 41.7 1 NA NA
If you run this function yourself, you’ll notice that it takes a lot
longer than it takes to run adonis(). As we randomly re-assign diets
and time points, we re-run the adonis() function once for each
re-assignment or permutation.1 The functions used by adonisplus()
to carry out the restricted permutations are named
shuffle_within_groups() and shuffle_between_groups(), if you want to
use them elsewhere.
Having found a difference between the diets overall, we wish to know
which diet pairs are different. As before, we use adonispost() and
tell it to run pairwise comparisons of diet by setting which = diet.
farmm_preabx %>%
adonispost(
distmat = farmm_bc, formula = distmat ~ diet * study_day,
sample_id_var = sample_id, rep_meas_var = subject_id,
shuffle = c(diet = "between", study_day = "within"),
which = diet)## # A tibble: 12 × 7
## comparison term df sumsq r.squared statistic p.value
## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 All diet diet 2 4.34 0.104 8.62 0.001
## 2 All diet study_day 1 0.504 0.0121 2.00 0.001
## 3 All diet diet:study_day 2 0.663 0.0159 1.32 0.001
## 4 Omnivore - Vegan diet 1 1.68 0.0635 6.61 0.119
## 5 Omnivore - Vegan study_day 1 0.0804 0.00305 0.317 0.726
## 6 Omnivore - Vegan diet:study_day 1 0.0358 0.00136 0.141 0.988
## 7 Omnivore - EEN diet 1 1.89 0.0683 7.59 0.025
## 8 Omnivore - EEN study_day 1 0.628 0.0227 2.53 0.001
## 9 Omnivore - EEN diet:study_day 1 0.523 0.0189 2.10 0.001
## 10 Vegan - EEN diet 1 2.99 0.109 11.8 0.001
## 11 Vegan - EEN study_day 1 0.668 0.0245 2.64 0.001
## 12 Vegan - EEN diet:study_day 1 0.399 0.0146 1.58 0.001
In the pairwise comparisons, we find that the microbiome of the omnivore and vegan groups was not different during the pre-antibiotics period, based on Bray-Curtis distance. Conversely, the microbiome of the EEN group was different from both the omnivores and vegans.
Notice that, for all the comparisons above, we’ve been able to use the
same distance matrix, farmm_bc. Each time we called a function using
the distances, the distance matrix was automatically filtered and
re-arranged to match the samples in our data frame. How convenient!
Footnotes
-
In fact, the
adonis()function has some built-in capability to carry out restricted permutations, but because the built-in methods permute the samples and not the study groups, the between-subject permutations don’t work if you don’t have exactly the same number of samples per subject. Consequently, our data set would not work with the built-in permutation methods inadonis(). ↩