12 Community Diversity
Community diversity is a central concept in microbiome research. Several diversity indices are available in the ecological literature.
The main categories of diversity indices include species richness, evenness, and diversity: each of these emphasizes different aspects of the community heterogeneity (Whittaker 1960), (Willis 2019). The Hill coefficient combines many standard indices into a single equation that provides observed richness, inverse Simpson, Shannon diversity, and generalized diversity as special cases, with varying levels of emphasis on species abundance values. Thus, the term alpha diversity is often used to collectively refer to all these variants.
Diversity summarizes the distribution of species abundances in a given sample into a single number that depends on both species richness and evenness (see below). Diversity indices measure the overall community heterogeneity that considers both of these aspects simultaneously. A number of ecological diversity measures are available. In general, diversity increases together with increasing richness and evenness. Phylogenetic diversity (PD), (Faith 1992), is a variant that incorporates information from phylogenetic relationships between species, unlike most other commonly used diversity indices. The addAlpha() function uses a faster reimplementation of the widely used function in picante W et al. (2010). The method uses the default rowTree from the TreeSummarizedExperiment object (tse).
Richness refers to the total number of species in a community (sample). The simplest richness index is the number of species observed in a sample (observed richness). Assuming limited sampling from the community, however, this may underestimate the true species richness. Several estimators have been developed to address this, including for instance ACE (A and SM 1992) and Chao1 (A 1984) indices. Richness estimates do not aim to characterize variations in species abundances.
Nonparametric richness estimators such as Chao1 and ACE, however, must not be used with amplicon sequence variant (ASV) data. Algorithms that generate ASVs, like DADA2 and Deblur, typically remove singletons, which are essential for these richness calculations. This removal leads to meaningless results. Although ASVs offer higher resolution than operational taxonomic units (OTUs) and are increasingly used, the removal of singletons invalidates the application of Chao1 and ACE. Therefore, alternative alpha diversity metrics that do not depend on singletons or doubletons should be considered, or OTUs could be used specifically for alpha diversity analysis to retain low-abundance taxa. Additionally, the inability of denoising algorithms to distinguish true singleton sequences from artifacts further complicates the issue, making traditional richness estimators unsuitable for ASV datasets, which are often standardized for sequencing depth.(Deng, Umbach, and Neufeld 2024)
Evenness focuses on the distribution of species abundances, and it can thus complement the number of species. Pielou’s evenness is a commonly used index, obtained by normalizing Shannon diversity by (the natural logarithm of) observed richness.
These main classes of alpha diversity are sometimes complemented with indices of dominance or rarity:
Dominance indices are in general negatively correlated with alpha diversity. A high dominance is obtained when one or a few species have a high share of the total species abundance in the community. Note that dominance indices are generally inversely correlated with other alpha diversity indices.
Rarity indices characterize the concentration of species at low abundance. Prevalence and detection thresholds determine rare species whose total concentration will determine the value of a rarity index.
12.1 Alpha diversity estimation in practice
12.1.1 Calculate diversity measures
Alpha diversity can be estimated with addAlpha() wrapper function that interact with other packages implementing the calculation, such as vegan (Oksanen et al. 2020).
These functions calculate the given indices, and add them to the colData slot of the SummarizedExperiment object with the given name.
The estimated values can then be retrieved and analyzed directly from the colData, for example, by plotting them using plotColData() from the scater package (McCarthy et al. 2020). Here, we use the observed species as a measure of richness.
Certain indices have additional options, here observed has detection parameter that control the detection threshold. Species over this threshold is considered as detected. See full list of options from from help(addAlpha).
# First, let's load some example data.
library(mia)
data("GlobalPatterns", package="mia")
tse <- GlobalPatterns
# Estimate (observed) richness
tse <- addAlpha(
tse, assay.type = "counts", index = "observed", name = "observed",
detection = 10)
# Check some of the first values in colData
head(tse$observed)
## [1] 3144 3791 2319 761 671 1004You can calculate multiple indices simultaneously by specifying multiple indices in the index parameter.
For example: index = c("observed", "shannon")
Let’s visualize the results against selected colData variables (sample type and final barcode).
library(scater)
plotColData(
tse,
"observed",
"SampleType",
colour_by = "Final_Barcode") +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
labs(expression(Richness[Observed]))
We can then analyze the statistical significance. We use the non-parametric Wilcoxon or Mann-Whitney test, as it is more flexible than the commonly used Student’s t-Test, since it does not assume normality.
pairwise.wilcox.test(
tse[["observed"]], tse[["SampleType"]], p.adjust.method = "fdr")
##
## Pairwise comparisons using Wilcoxon rank sum exact test
##
## data: tse[["observed"]] and tse[["SampleType"]]
##
## Feces Freshwater Freshwater (creek) Mock Ocean
## Freshwater 0.4 - - - -
## Freshwater (creek) 0.3 0.3 - - -
## Mock 0.3 0.3 0.3 - -
## Ocean 0.8 1.0 0.3 0.3 -
## Sediment (estuary) 0.3 0.8 0.3 0.3 0.8
## Skin 0.3 0.8 0.3 0.3 0.8
## Soil 0.3 0.3 0.5 0.3 0.3
## Tongue 0.3 0.5 0.3 0.8 0.5
## Sediment (estuary) Skin Soil
## Freshwater - - -
## Freshwater (creek) - - -
## Mock - - -
## Ocean - - -
## Sediment (estuary) - - -
## Skin 1.0 - -
## Soil 0.3 0.3 -
## Tongue 0.3 0.3 0.3
##
## P value adjustment method: fdr12.1.2 Faith phylogenetic diversity
The Faith index is returned by the function addAlpha(). It utilizes the widely used function in picante W et al. (2010).
Because tse is a TreeSummarizedExperiment object, its phylogenetic tree is used by default. However, the optional argument tree must be provided if tse does not contain one.
12.2 Alpha diversity measure comparisons
We can compare alpha diversities for example by calculating correlation between them. Below, a visual comparison between shannon and faith indices is shown with a scatter plot.
tse <- addAlpha(tse, assay.type = "counts", index = "shannon")
plotColData(tse, x = "shannon", y = "faith") +
labs(x="Shannon index", y="Faith (phylogenetic) index") +
geom_smooth(method = "lm")
cor.test(tse[["shannon"]], tse[["faith"]])
##
## Pearson's product-moment correlation
##
## data: tse[["shannon"]] and tse[["faith"]]
## t = 2.2, df = 24, p-value = 0.04
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.02719 0.68822
## sample estimates:
## cor
## 0.4102Let us visualize results from multiple alpha diversity measures against a given sample grouping available in colData (here, sample type). These have been readily stored in the colData slot, and they are thus directly available for plotting.
library(patchwork)
# Create the plots
plots <- lapply(
c("observed", "shannon", "faith"),
plotColData,
object = tse,
x = "SampleType",
colour_by = "SampleType")
# Fine-tune visual appearance
plots <- lapply(
plots, "+",
theme(axis.text.x = element_blank(),
axis.title.x = element_blank(),
axis.ticks.x = element_blank()))
# Plot the figures
wrap_plots(plots, ncol = 1) +
plot_layout(guides = "collect")
12.3 Visualizing significance in group-wise comparisons
Next, let’s compare the Shannon index between sample groups and visualize the statistical significance. Using the stat_compare_means function from the ggpubr package, we can add visually appealing p-values to our plots.
To add adjusted p-values, we have to first calculate them.
library(ggpubr)
library(tidyverse)
index <- "shannon"
group_var <- "SampleType"
# Subsets the data. Takes only those samples that are from feces, skin, or
# tongue.
tse_sub <- tse[ , tse[[group_var]] %in% c("Feces", "Skin", "Tongue") ]
# Changes old levels with new levels
tse_sub$SampleType <- factor(tse_sub$SampleType)
# Calculate p values
pvals <- pairwise.wilcox.test(
tse_sub[[index]], tse_sub[[group_var]], p.adjust.method = "fdr")
# Put them to data.frame format
pvals <- pvals[["p.value"]] |>
as.data.frame()
varname <- "group1"
pvals[[varname]] <- rownames(pvals)
# To long format
pvals <- reshape(
pvals,
direction = "long",
varying = colnames(pvals)[ !colnames(pvals) %in% varname ],
times = colnames(pvals)[ !colnames(pvals) %in% varname ],
v.names = "p",
timevar = "group2",
idvar = "group1"
) |>
na.omit()
# Add y-axis position
pvals[["y.position"]] <- apply(pvals, 1, function(x){
temp1 <- tse[[index]][ tse[[group_var]] == x[["group1"]] ]
temp2 <- tse[[index]][ tse[[group_var]] == x[["group2"]] ]
temp <- max( c(temp1, temp2) )
return(temp)
})
pvals[["y.position"]] <- max(pvals[["y.position"]]) +
order(pvals[["y.position"]]) * 0.2
# Round values
pvals[["p"]] <- round(pvals[["p"]], 3)
# Create a boxplot
p <- plotColData(
tse_sub, x = group_var, y = index,
show_boxplot = TRUE, show_violin = FALSE) +
theme(text = element_text(size = 10)) +
stat_pvalue_manual(pvals)
p
Article on ggpubr package provides further examples for estimating and highlighting significances.