14  Community similarity

Beta diversity quantifies the dissimilarity between communities (multiple samples), as opposed to alpha diversity, which focuses on variation within a community (one sample). In microbiome research, commonly used metrics of beta diversity include:

Notably, only some of these measures are actual distances, as this is a mathematical concept whose definition is not satisfied by certain ecological measures, such as the Bray-Curtis index. Therefore, the terms dissimilarity and beta diversity are preferred.

Method description Assay type Beta diversity metric
Quantitative profiling Absolute counts Bray-Curtis
Relative profiling Relative abundances Bray-Curtis
Aitchison distance Absolute counts Aitchison
Aitchison distance clr Euclidean
Robust Aitchison distance rclr Euclidean
Presence/Absence similarity Relative abundances Jaccard
Presence/Absence similarity Absolute counts Jaccard
Phylogenetic distance Rarefied counts Unifrac

In practice, beta diversity is usually represented as a dist object. Such an object is a triangular matrix where the distance between each pair of samples is encoded by a specific cell. This distance matrix can then undergo ordination, which is an important ecological tool to reduce the dimensionality of data for a more efficient analysis and visualization. Ordination techniques aim to capture as much essential information from the data as possible and turn it into a lower dimensional representation. Dimension reduction is bound to lose information but commonly used ordination techniques can preserve relevant information of sample similarities in an optimal way, which is defined in different ways by different methods.

Based on the type of algorithm, ordination methods in microbiome research can be generally divided in two categories:

The former includes Principal Coordinate Analysis (PCoA), Principal Component Analysis (PCA) and Uniform Manifold Approximation and Projection for Dimension Reduction (UMAP), whereas the latter is mainly represented by distance-based Redundancy Analysis (dbRDA). First, we will discuss unsupervised ordination methods and then proceed to supervised ones.

Let us now prepare some demonstration data for the practical examples.

# Load mia and import sample dataset
library(mia)
data("GlobalPatterns", package = "mia")
tse <- GlobalPatterns

# Beta diversity metrics like Bray-Curtis are often
# applied to relabundances
tse <- transformAssay(
    tse, assay.type = "counts", method = "relabundance")

# Other metrics like Aitchison to clr-transformed data
tse <- transformAssay(
    tse, assay.type = "relabundance", method = "clr", pseudocount = TRUE)

# Add group information Feces yes/no
tse$Group <- tse$SampleType == "Feces"

14.1 Divergence

Divergence measure refers to a difference in community composition between the given sample(s) and a reference sample. This can be evaluated with addDivergence(). Reference and algorithm for the calculation of divergence can be specified as reference and FUN, respectively.

tse <- addDivergence(
    tse,
    assay.type = "counts",
    reference = "median",
    FUN = getDissimilarity)

14.2 Unsupervised ordination

Unsupervised ordination methods analyze variation in the data without additional information on covariates or other supervision of the model. Among the different approaches, Multi-Dimensional Scaling (MDS) and non-metric MDS (NMDS) can be regarded as the standard. They are jointly referred to as PCoA. For this demonstration, we will analyse beta diversity in GlobalPatterns, and observe the variation between stool samples and those with a different origin.

14.2.1 Comparing communities by beta diversity analysis

A typical comparison of community compositions starts with a visual representation of the groups by a 2D ordination. Then we estimate relative abundances and MDS ordination based on Bray-Curtis index between the groups, and visualize the results.

In the following examples dissimilarity is calculated with the function supplied to the FUN argument. Several metrics of beta diversity are defined by the vegdist() function of the vegan package, which is often used in this context. However, such custom functions created by the user also work, as long as they return a dist object. In either case, this function is then applied to calculate reduced dimensions via an ordination method, the results of which can be stored in the reducedDim slot of the TreeSE. This entire process is contained by the runMDS() and runNMDS() functions.

# Load package to plot reducedDim
library(scater)

# Run PCoA on relabundance assay with Bray-Curtis distances
tse <- runMDS(
    tse,
    FUN = getDissimilarity,
    method = "bray",
    assay.type = "relabundance",
    name = "MDS_bray")

Sample dissimilarity can be visualized on a lower-dimensional display (typically 2D) using the plotReducedDim() function from the scater package. This also provides tools to incorporate additional information encoded by color, shape, size and other aesthetics. Can you find any difference between the groups?

# Create ggplot object
p <- plotReducedDim(tse, "MDS_bray", colour_by = "Group")

# Calculate explained variance
e <- attr(reducedDim(tse, "MDS_bray"), "eig")
rel_eig <- e / sum(e[e > 0])

# Add explained variance for each axis
p <- p + labs(
    x = paste("PCoA 1 (", round(100 * rel_eig[[1]], 1), "%", ")", sep = ""),
    y = paste("PCoA 2 (", round(100 * rel_eig[[2]], 1), "%", ")", sep = "")
    )

p

MDS plot based on the Bray-Curtis distances on the GlobalPattern dataset.

A few combinations of beta diversity metrics and assay types are typically used. For instance, Bray-Curtis dissimilarity and Euclidean distance are often applied to the relative abundance and the clr assays, respectively. Besides beta diversity metric and assay type, the PCoA algorithm is also a variable that should be considered. Below, we show how the choice of these three factors can affect the resulting lower-dimensional data.

# Run NMDS on relabundance assay with Bray-Curtis distances
tse <- runNMDS(
    tse,
    FUN = getDissimilarity,
    method = "bray",
    assay.type = "relabundance",
    name = "NMDS_bray")

# Run MDS on clr assay with Aitchison distances
tse <- runMDS(
    tse,
    FUN = getDissimilarity,
    method = "euclidean",
    assay.type = "clr",
    name = "MDS_aitchison")

# Run NMDS on clr assay with Euclidean distances
tse <- runNMDS(
    tse,
    FUN = getDissimilarity,
    method = "euclidean",
    assay.type = "clr",
    name = "NMDS_aitchison")

Multiple ordination plots are combined into a multi-panel plot with the patchwork package, so that different methods can be compared to find similarities between them or select the most suitable one to visualize beta diversity in the light of the research question.

# Load package for multi-panel plotting
library(patchwork)

# Generate plots for all 4 reducedDims
plots <- lapply(
    c("MDS_bray", "MDS_aitchison", "NMDS_bray", "NMDS_aitchison"),
    plotReducedDim,
    object = tse,
    colour_by = "Group")

# Generate multi-panel plot
wrap_plots(plots) +
    plot_layout(guides = "collect")

Comparison of MDS and NMDS plots based on the Bray-Curtis or Aitchison distances on the GlobalPattern dataset.

The Unifrac method is a special case, as it requires data on the relationship of features in the form of a phylo tree. getDissimilarity() performs the calculation to return a dist object, which can again be used within runMDS().

tse <- runMDS(
    tse,
    FUN = getDissimilarity,
    method = "unifrac",
    name = "unifrac",
    tree = rowTree(tse),
    ntop = nrow(tse),
    assay.type = "counts")

plotReducedDim(tse, "unifrac", colour_by = "Group")

Unifrac distances scaled by MDS of the GlobalPattern dataset.

14.2.2 Rarefaction to mitigate impacts of uneven sequencing effort

The sequencing depth of a sample refers to the number of metagenomic reads obtained from the sequencing process. A variation in sequencing depth across the samples of a study may impact the calculation of alpha and beta diversity metrics (Patrick D. Schloss 2023). It is common to find significant variation in sequencing depth between samples. For instance, the samples of the TreeSummarizedExperiment dataset GlobalPatterns show up to a 40-fold difference in the number of metagenomic reads.

# Calculate the list of sequencing depths across samples
sequencing_depths <- colSums(assay(tse))
# Calculate variation between highest and lowest sequencing depth
depth_variation <- max(sequencing_depths)/min(sequencing_depths)
depth_variation
##  [1] 40.16

To address uneven sequencing effort, rarefaction aims to normalize metagenomic reads counts using subsampling. First, the user chooses the rarefaction depth and a number of iterations N. All the samples with metagenomic reads count below the rarefaction depth are removed and metagenomic reads are randomly drawn from the samples left to get subsamples fitting the rarefaction depth. Then a beta diversity metric is calculated from those subsamples and the process is iterated N times. Finally, beta diversity is estimated with the mean of all beta diversity values calculated on subsampled data.

There has been a long-lasting controversy surrounding the use of rarefaction in microbial ecology. The main concern is that rarefaction would omit data (McMurdie and Holmes 2014) (Patrick D. Schloss 2024). However, if the subsampling process is repeated a sufficient number of times, and if the rarefaction depth is set to the lowest metagenomic reads count found across all samples, no data will be omitted. Moreover, Patrick Schloss has demonstrated that rarefaction is “the only method that could control for variation in uneven sequencing effort when measuring commonly used alpha and beta diversity metrics” (Patrick D. Schloss 2023).

McMurdie, Paul J, and Susan Holmes. 2014. “Waste Not, Want Not: Why Rarefying Microbiome Data Is Inadmissible.” PLoS Computational Biology 10 (4): e1003531.
Schloss, Patrick D. 2024. “Waste Not, Want Not: Revisiting the Analysis That Called into Question the Practice of Rarefaction.” mSphere 9 (1): e00355–23. https://doi.org/10.1128/msphere.00355-23.
Schloss, Patrick D. 2023. “Rarefaction Is Currently the Best Approach to Control for Uneven Sequencing Effort in Amplicon Sequence Analyses.” bioRxiv, 2023–06. https://doi.org/10.1101/2023.06.23.546313.

Before applying rarefaction, selecting the most variable features can help minimize variation caused by random subsampling. These features have the highest read counts, while rare features tend to increase sampling variation. This approach facilitates comparison of results between non-rarefied and rarefied distance calculations later on.

# Let us see what happens when we operate with ntop highest variance features
ntop <- 5

# Calculate the standard deviations for each row
row_sds <- rowSds(assay(tse, "counts"))

# Get the indices of the top 5 rows with the highest standard deviations
top_indices <- order(row_sds, decreasing = TRUE)[1:ntop]

# Subset the tse object based on the top indices
tse_sub <- tse[top_indices, ]

Let us first convert the count assay to centered log ratio (clr) assay and calculate MDS with Aitchison distance without rarefaction:

# Centered log-ratio transformation to properly apply Aitchison distance

tse_sub <- transformAssay(
  tse_sub,
  assay.type = "counts",
  method = "clr",
  pseudocount = 1
  )

# Run MDS on clr assay with Aitchison distance
tse_sub <- runMDS(
  tse_sub,
  FUN = getDissimilarity,
  method = "euclidean",
  assay.type = "clr",
  name = "MDS_aitchison"
  )

Then let’s do the same with rarefaction:

# Define custom transformation function..
clr <- function (x) {
  vegan::decostand(x, method="clr", pseudocount=1)
}

# Run transformation after rarefactions before calculating the beta diversity..
tse_sub <- runMDS(tse_sub,
  assay.type = "counts",
  ntop = nrow(tse_sub),
  FUN = getDissimilarity,
  method = "euclidean",
  niter = 10, # Number of iterations
  sample = min(colSums(assay(tse_sub, "counts"))), # Rarefaction depth
  transf = clr, # Applied transformation
  replace = TRUE,
  name = "MDS_aitchison_rarefied"
  )

# Generate plots for non-rarefied and rarefied Bray-Curtis distances scaled by
# MDS
plots <- lapply(
  c("MDS_aitchison", "MDS_aitchison_rarefied"),
  plotReducedDim,
  object = tse_sub)

# Generate multi-panel plot
wrap_plots(plots) +
  plot_layout(guides = "collect")

ntop is a runMDS() option. Here it is set to total number of features in GlobalPatterns dataset so that they are not filtered. If ntop was not set to the total number of features, only the ntop features with highest variance would be used for dimensionality reduction and the other features would be filtered.

When rarefaction is not done, the getDissimilarity() utilizes vegan::vegdist() function while in rafection vegan::avgdist() is applied. The argument sample is set to the smallest metagenomic reads count across all samples. This ensures that no sample will be removed during the rarefaction process.

The argument niter is by default set to 100 but 10 iterations is often sufficient for beta diversity calculations.

To use transformations after the rarefaction of the samples and before the beta diversity calculation, we can use the argument transf.

We can also plot the correlation between principal coordinates PCx and PCy for both the rarefied and non-rarefied distance calculations:

library(ggpubr)

p <- lapply(1:2, function(i){
  # Principal axes are sign invariant;
  # align the signs; if the correlation is negative then swap the other axis
  original <- reducedDim(tse_sub, "MDS_aitchison")[, i]
  rarefied <- reducedDim(tse_sub, "MDS_aitchison_rarefied")[, i]

  temp  <- ggplot(data = data.frame(original, rarefied), aes(x = original, y = rarefied)) +
    geom_point() + geom_smooth(method = "lm") +
    stat_cor(method = "pearson") +
    labs(title = paste0("Principal coordinate ", i))
  return(temp)
})
wrap_plots(p)

The mia package’s addAlpha() and getDissimilarity() functions support rarefaction in alpha and beta diversity calculations. Additionally, the rarefyAssay() function allows random subsampling of a given assay within a TreeSummarizedExperiment dataset.

14.2.3 Other ordination methods

Other dimension reduction methods, such as PCA and UMAP, are inherited from the scater package.

tse <- runPCA(
    tse,
    name = "PCA",
    assay.type = "counts",
    ncomponents = 10)

plotReducedDim(tse, "PCA", colour_by = "Group")

PCA plot on the GlobalPatterns data set containing sample from different sources.

As mentioned before, applicability of the different methods depends on your sample set and research question.

tse <- runUMAP(
    tse,
    name = "UMAP",
    assay.type = "counts",
    ncomponents = 3)

plotReducedDim(tse, "UMAP", colour_by = "Group", ncomponents = c(1:3))

UMAP plot on the GlobalPatterns data set containing sample from different sources.

14.2.4 Explained variance

The percentage of explained variance is typically shown in PCA ordination plots. This quantifies the proportion of overall variance in the data that is captured by the PCA axes, or how well the ordination axes reflect the original distances.

Sometimes a similar measure is shown for MDS/PCoA. The interpretation is generally different, however, and hence we do not recommend using it. PCA is a special case of PCoA with Euclidean distances. With non-Euclidean dissimilarities PCoA uses a trick where the pointwise dissimilarities are first cast into similarities in a Euclidean space (with some information loss i.e. stress) and then projected to the maximal variance axes. In this case, the maximal variance axes do not directly reflect the correspondence of the projected distances and original distances, as they do for PCA.

In typical use cases, we would like to know how well the ordination reflects the original similarity structures; then the quantity of interest is the so-called “stress” function, which measures the difference in pairwise similarities between the data points in the original (high-dimensional) vs. projected (low-dimensional) space.

Hence, we propose that for PCoA and other ordination methods, users would report relative stress, which varies within the unit interval and is better if smaller. This can be calculated as shown below.

# Quantify dissimilarities in the original feature space
d0 <- as.matrix(getDissimilarity(t(assay(tse, "relabundance")), "bray"))

# PCoA Ordination
tse <- runMDS(
  tse,
  FUN = getDissimilarity,
  name = "PCoA",
  method = "bray",
  assay.type = "relabundance")

# Quantify dissimilarities in the ordination space
dp <- as.matrix(dist(reducedDim(tse, "PCoA")))

# Calculate stress i.e. relative difference 
# in the original and projected dissimilarities
stress <- sum((dp - d0)^2) / sum(d0^2)

A Shepard plot visualizes the original versus the ordinated dissimilarity between the observations.

ord <- order(as.vector(d0))
df <- data.frame(d0 = as.vector(d0)[ord],
                 dmds = as.vector(dp)[ord])

ggplot(df, aes(x = d0, y = dmds)) +
  geom_smooth() +
  geom_point() +
  labs(title = "Shepard plot",
       x = "Original distance",
       y = "MDS distance",
       subtitle = paste("Stress:", round(stress, 2))) +
  theme_bw()

14.3 Supervised / constrained ordination

dbRDA is a supervised counterpart of PCoA. It maximize the variance with respect to the covariates provided by the user. This can be used to quantify associations between each covariate and community composition (beta diversity). The table below summarizes the relations between the supervised and unsupervised ordination methods.

supervised ordination unsupervised ordination
Euclidean distance RDA PCA
non-Euclidean distance dbRDA PCoA/MDS, NMDS, UMAP

In summary, the “dbRDA” is the more general method that allows a wider variety dissimilarity, or beta diversity, indices. This method is available via mia::getRDA(), which calls vegan::dbrda(). By default, this uses Euclidean distances, which is equivalent to the ordinary RDA. However, the dbRDA method (mia::getRDA()) allows the use of other dissimilarity indices as well.

Let us next demonstrate dbRDA with the enterotype dataset. Here samples correspond to patients. The colData lists the clinical status of each patient and a few covariates such as gender and age.

# Load data
data("enterotype", package = "mia")
tse2 <- enterotype

# Apply relative transform
tse2 <- transformAssay(tse2, method = "relabundance")

14.3.1 Redundancy analysis

dbRDA can be perfomed with the addRDA() function. In addition to the arguments previously defined for unsupervised ordination, this function takes a formula to control for variables and an action to treat missing values. Along with clinical status, which is the main outcome, we control for gender and age, and exclude observations where one of these variables is missing.

# Perform RDA
tse2 <- addRDA(
    tse2,
    assay.type = "relabundance",
    formula = assay ~ ClinicalStatus + Gender + Age,
    distance = "bray",
    na.action = na.exclude)

# Store results of PERMANOVA test
rda_info <- attr(reducedDim(tse2, "RDA"), "significance")

The importance of each variable on the similarity between samples (i.e. loadings) can be assessed from the results of PERMANOVA, automatically provided by the addRDA() function. It performs first dbRDA and then applies permutational test to its results.

Permutational Analysis of Variance (PERMANOVA; (2001)) is a widely used non-parametric multivariate method that aims to estimate the actual statistical significance of differences in the observed community composition between two groups of samples.

Anderson, Marti J. 2001. “A New Method for Non-Parametric Multivariate Analysis of Variance.” Austral Ecology 26 (1): 32–46. https://doi.org/10.1111/j.1442-9993.2001.01070.pp.x.

PERMANOVA tests the hypothesis that the centroids and dispersion of the community are equivalent between the compared groups. A p-value smaller than the significance threshold indicates that the groups have a different community composition. This method is implemented with the adonis2 function from the vegan package. You can find more on PERMANOVA from here.

We see that both clinical status and age explain more than 10% of the variance, but only age has statistical significance.

rda_info$permanova |>
   knitr::kable()
Df SumOfSqs F Pr(>F) Total variance Explained variance
Model 6 1.1157 1.940 0.035 3.991 0.2795
ClinicalStatus 4 0.5837 1.522 0.134 3.991 0.1463
Gender 1 0.1679 1.751 0.128 3.991 0.0421
Age 1 0.5245 5.471 0.001 3.991 0.1314
Residual 30 2.8757 NA NA 3.991 0.7205

Next, we proceed to visualize the weight and significance of each variable on the similarity between samples with an RDA plot, which can be generated with the plotRDA() function from the miaViz package.

# Load packages for plotting function
library(miaViz)

# Generate RDA plot coloured by clinical status
plotRDA(tse2, "RDA", colour.by = "ClinicalStatus")

From above, we can see that only age significantly describes differences between the microbial profiles of different samples. Such visual approach complements the previous results obtained with PERMANOVA.

14.3.2 Visualize dbRDA loadings

Let us visualize the model coefficients or loadings for species that exhibit the largest differences between the groups. This gives some insights into how the groups tend to differ from each other in terms of community composition.

plotLoadings(tse2, "RDA", ncomponents = 2, n = 20)

In the example above, the largest differences between the two groups can be attributed to Bifidobacterium and -1.

14.3.3 Checking the homogeneity condition

It is important to note that the application of PERMANOVA assumes homogeneous group dispersions (variances). This can be tested with the PERMDISP2 method (Anderson 2006) by using the same assay and distance method than in PERMANOVA.

———. 2006. “Distance-Based Tests for Homogeneity of Multivariate Dispersions.” Biometrics 62: 245–53. https://doi.org/10.1111/j.1541-0420.2005.00440.x.

To ensure that the homogeneity assumption holds, we retrieve the corresponding information from the results of RDA. None of the p-values is lower than the significance threshold, and thus homogeneity is observed.

Note

PERMANOVA assumes that the group dispersion is homogeneous. Homogeneous dispersion means that the variation within groups is smaller than the variation between groups, making the groups distinct. If this assumption is not met, the results can be misleading.

addRDA() performs homogeneity test automatically.

rda_info$homogeneity |>
    knitr::kable()
Df Sum Sq Mean Sq F N.Perm Pr(>F) Total variance Explained variance
ClinicalStatus 4 0.2511 0.0628 2.7440 999 0.118 1.0288 0.2440
Gender 1 0.0103 0.0103 0.4158 999 0.527 0.9283 0.0111
Age 29 0.3272 0.0113 17.0255 999 0.400 0.3319 0.9860

As the group dispersion is homogenic, PERMANOVA can be seen as an appropriate choice for comparing community compositions.

14.4 Case studies

14.4.0.1 Visualizing the most dominant genus on PCoA

In this section, we visualize the most dominant genus on PCoA. A similar visualization was proposed by (2021). First, let us agglomerate the data at the Genus level and identify the dominant taxa for each sample.

Salosensaari, Aaro, Ville Laitinen, Aki Havulinna, Guillaume Méric, Susan Cheng, Markus Perola, Liisa Valsta, et al. 2021. “Taxonomic Signatures of Cause-Specific Mortality Risk in Human Gut Microbiome.” Nature Communications 12: 1–8. https://www.nature.com/articles/s41467-021-22962-y. 
# Agglomerate to genus level
tse_genus <- agglomerateByRank(tse, rank = "Genus")

# Convert to relative abundances
tse_genus <- transformAssay(
    tse, method = "relabundance", assay.type = "counts")

# Add info on dominant genus per sample
tse_genus <- addDominant(
    tse_genus, assay.type = "relabundance", name = "dominant_taxa")
# Overview
summarizeDominance(
    tse_genus, rank = "Genus", digits = 3, name = "dominant_taxa")
##  # A tibble: 17 × 3
##    dominant_taxa                n rel_freq
##    <chr>                    <int>    <dbl>
##  1 Bacteroides                  5    0.192
##  2 Crenothrix                   3    0.115
##  3 Faecalibacterium             2    0.077
##  4 Prochlorococcus              2    0.077
##  5 Streptococcus                2    0.077
##  6 CandidatusNitrososphaera     1    0.038
##  # ℹ 11 more rows

Next, we perform PCoA with Bray-Curtis dissimilarity.

tse_genus <- runMDS(
    tse_genus,
    FUN = getDissimilarity,
    name = "PCoA_BC",
    method = "bray",
    assay.type = "relabundance")

Finally, we get the top taxa and and visualize their abundances on PCoA. Note that a 3D interactive version of the plot below can be found in Appendix C.

# Getting the top taxa
top_taxa <- getTop(tse_genus, top = 6, assay.type = "relabundance")

# Naming all the rest of non top-taxa as "Other"
most_abundant <- lapply(
    colData(tse_genus)$dominant_taxa, function(x){
        if (x %in% top_taxa) {x} else {"Other"}
    })

# Storing the previous results as a new column within colData
colData(tse_genus)$most_abundant <- as.character(most_abundant)

# Calculating percentage of the most abundant
most_abundant_freq <- table(as.character(most_abundant))
most_abundant_percent <- round(
    most_abundant_freq / sum(most_abundant_freq) * 100,
    1)

# Retrieving the explained variance
e <- attr(reducedDim(tse_genus, "PCoA_BC"), "eig")
var_explained <- e / sum(e[e > 0]) * 100

# Define colors for visualization
my_colors <- c(
    "black", "blue", "lightblue", "darkgray", "magenta", "darkgreen", "red")

# Visualization
p <- plotReducedDim(tse_genus, "PCoA_BC", colour_by = "most_abundant") +
    scale_colour_manual(
        values = my_colors,
        labels = paste0(
            names(most_abundant_percent), "(", most_abundant_percent, "%)")) +
    labs(
        x = paste("PC 1 (", round(var_explained[1], 1), "%)"),
        y = paste("PC 2 (", round(var_explained[2], 1), "%)"),
        color = "")

p

Similarly, we visualize and compare the sub-population.

# Calculating the frequencies and percentages for both categories
freq_TRUE  <- table(as.character(most_abundant[tse_genus$Group]))
freq_FALSE <- table(as.character(most_abundant[!tse_genus$Group]))
percent_TRUE  <- round(freq_TRUE  / sum(freq_TRUE)  * 100, 1)
percent_FALSE <- round(freq_FALSE / sum(freq_FALSE) * 100, 1)

# Visualization
plotReducedDim(
    tse_genus[ , colData(tse_genus)$Group == TRUE], "PCoA_BC",
    colour_by = "most_abundant") +

    scale_colour_manual(
        values = my_colors,
        labels = paste0(names(percent_TRUE), "(", percent_TRUE, "%)")) +

  labs(
      x = paste("PC 1 (", round(var_explained[1], 1), "%)"),
      y = paste("PC 2 (", round(var_explained[2], 1), "%)"),
      title = "Group = TRUE", color = "")


plotReducedDim(
    tse_genus[ , colData(tse_genus)$Group == FALSE], "PCoA_BC",
    colour_by = "most_abundant") +

    scale_colour_manual(
        values = my_colors,
        labels = paste0(names(percent_FALSE), "(", percent_FALSE, "%)")) +

    labs(
        x = paste("PC 1 (", round(var_explained[1], 1), "%)"),
        y = paste("PC 2 (", round(var_explained[2], 1), "%)"),
        title = "Group = FALSE", color = "")

Summary

As a final note, we provide a comprehensive list of functions for the evaluation of dissimilarity indices available in the mia and scater packages. The calculate methods return a reducedDim object as an output, whereas the run methods store the reducedDim object into the specified TreeSE.

For more information on sample clustering, you can refer to:

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