Principal Coordinates Analysis (PCoA) is a robust multivariate technique that translates complex dissimilarity data into interpretable low-dimensional space. Widely applied in microbial ecology and multi-omics, PCoA accommodates both Euclidean and non-Euclidean distance metrics (e.g., Bray-Curtis, UniFrac) to reveal patterns in beta diversity. Unlike PCA, which focuses on variable-level variance, PCoA emphasizes sample-level dissimilarities. Each axis represents a quantifiable proportion of total variance, enhancing interpretability. Easily implemented in R using the vegan and ggplot2 packages, PCoA empowers researchers to visualize group separation, explore ecological gradients, and uncover hidden biological structures in high-dimensional datasets with scientific rigor and statistical clarity.
What Is PCoA Analysis?
PCoA also known as classical multidimensional scaling, is a sophisticated unsupervised statistical method designed to translate complex dissimilarity relationships between biological samples into an interpretable, low-dimensional coordinate space. It is particularly favored in microbial ecology, metabolomics, and environmental genomics for uncovering latent patterns in beta diversity-differences in biological composition between samples or environments.
At its core, PCoA transforms a distance matrix (e.g., Bray-Curtis, Jaccard, UniFrac) into a set of orthogonal axes that represent the greatest variation between samples based on dissimilarity. These axes-known as principal coordinates-enable intuitive visualization and quantitative comparison of samples, revealing clustering patterns, group separation, or gradients driven by biological, environmental, or experimental factors.
Differences from Other Clustering and Ordination Methods
Understanding where PCoA fits within the broader multivariate analysis framework is crucial for selecting the most appropriate method for a given dataset. PCoA distinguishes itself from other techniques by its ability to operate on both Euclidean and non-Euclidean distance matrices, making it particularly suited for ecological and microbiome data. In contrast to PCA, which directly analyzes raw numeric data using Euclidean distance and emphasizes variance among variables, PCoA focuses on inter-sample dissimilarities derived from a distance or dissimilarity matrix-revealing relationships among samples rather than variables. While PCA outputs principal components useful in interpreting feature-level variation (e.g., gene expression), PCoA yields principal coordinates that reflect sample-level structural differences.
Additionally, when compared to t-distributed Stochastic Neighbor Embedding (t-SNE), PCoA offers a more statistically grounded and reproducible framework. Unlike t-SNE, which is non-metric, non-deterministic, and optimized for local structure visualization, PCoA preserves global distances and provides interpretable axes with associated variance explained. In summary, PCoA strikes a balance between mathematical rigor and visual clarity, making it especially advantageous when the goal is to discern biologically meaningful sample relationships across complex distance measures.
The Advantages of PCoA Analysis
PCoA has gained widespread adoption in multi-omic and ecological applications due to its unique advantages:
1. Compatibility with Non-Euclidean Metrics
PCoA handles Bray-Curtis, Jaccard, UniFrac, and other specialized distances that better model ecological and compositional data structures. This is essential when raw abundance values are sparse, compositional, or phylogenetically structured.
2. Beta Diversity Visualization
PCoA excels in plotting sample-level diversity differences (beta diversity), making it a foundational tool for comparing biological communities across time, treatment, geography, or genotype.
3. Eigenvalue Transparency
Each PCoA axis is accompanied by an eigenvalue that quantifies the variance it explains. This adds robustness and interpretability-researchers can statistically evaluate how well the lower-dimensional projection captures the original data.
4. Seamless Integration with PERMANOVA and Ecological Models
PCoA is often a precursor to PERMANOVA (Permutational Multivariate ANOVA) or ANOSIM, enabling rigorous testing of group differences based on distance matrices.
5. Accessible Implementation in R and Python
PCoA is readily implementable via standard statistical software ecosystems. In R, it integrates with vegan, phyloseq, and ggplot2, facilitating both computation and high-end visualization.
How to Read a PCoA Plot
Interpreting a PCoA plot requires both statistical acumen and biological insight. Here are the key components:
1. Axes (PCoA1, PCoA2)
Each axis represents a principal coordinate capturing a percentage of total dissimilarity. The first two axes often explain the majority of variance, but deeper exploration may require additional dimensions.
2. Sample Points
Each point represents a sample. Proximity indicates similarity; distance indicates dissimilarity.
3. Confidence Ellipses
Often added via statistical overlays (e.g., stat_ellipse()), ellipses show the dispersion of sample groups. Overlap suggests similarity; separation suggests distinct communities.
4. Group Separation
Clear separation along any axis may indicate meaningful biological or experimental differentiation (e.g., treatment effects, geographic regions, or microbial shifts).
PCoA with weighted unifrac distances across the whole dataset.(Zhang, L., et.al, 2022)
How to Perform PCoA Analysis in R
So, how to perform PCoA analysis in the R language? Here, the editor brings you an example. We will start with vegan built-in dune data.
Step 1: Load Required Libraries
install.packages("vegan")
install.packages("ggplot2")
library(vegan) # For distance and ordination methods
library(ggplot2) # For plotting
library(ggforce) # For enhanced aesthetics
Step 2: Prepare Input Data
data(dune)
data(dune.env)
Step 3: Compute Dissimilarity Matrix
dist_mat <- vegdist(dune, method = "bray")
Step 4: Conduct PCoA
pcoa_result <- cmdscale(dist_mat, eig = TRUE, k = 2)
Step 5: Extract Coordinates and Variance Explained
points <- as.data.frame(pcoa_result$points)
colnames(points) <- c("PCoA1", "PCoA2")
points$Management <- dune.env$Management
variance <- round(100 * pcoa_result$eig / sum(pcoa_result$eig), 2)
Step 6: Visualize with ggplot2
ggplot(points, aes(x = PCoA1, y = PCoA2, color = Management)) +
geom_point(size = 3) +
stat_ellipse(level = 0.95, linetype = 2, alpha = 0.3) +
labs(
title = "PCoA Analysis (Bray-Curtis)",
x = paste0("PCoA1 (", variance[1], "%)"),
y = paste0("PCoA2 (", variance[2], "%)")
) +
theme_minimal()
The diamond dataset pie plot result.
Conclusion
PCoA analysis stands as a scientifically rigorous, visually intuitive, and methodologically flexible tool for reducing complexity in high-dimensional biological data. Its capacity to accommodate diverse distance metrics and provide meaningful, variance-informed visualization makes it indispensable in microbial ecology, environmental genomics, and systems biology. By incorporating PCoA into R-based analytical pipelines, organizations and researchers alike can unlock deeper insights into biodiversity patterns, ecological interactions, and the hidden structure of omics datasets.
For research teams aiming to derive actionable insights from compositional or dissimilarity-based data, PCoA offers a critical analytic advantage-transforming biological complexity into clarity.
Reference
- Zhang, L., Zhang, M., Huang, S. et al. A highly conserved core bacterial microbiota with nitrogen-fixation capacity inhabits the xylem sap in maize plants. Nat Commun 13, 3361 (2022). https://doi.org/10.1038/s41467-022-31113-w
