Alpha diversity

Measures diversity within a single sample
Two key aspects:
- Richness: how many taxa are present
- Evenness: how evenly distributed the taxa are

Richness

\[ S = \text{Number of observed taxa} \]

Counts unique species/ASVs/OTUs in a sample

Simpson’s evenness

\[ E_{\mathrm{Simpson}} = \frac{1}{S \sum_{i=1}^{S} p_i^2} \]

where:

\(p_i\) = relative abundance of taxon \(i\)
\(S\) = number of taxa
Bounded between 0 (low evenness) and 1 (perfectly even)

Shannon diversity

\[ H' = - \sum_{i=1}^{S} p_i \log(p_i) \]

where:

\(p_i\) = relative abundance of taxon \(i\)
\(S\) = total number of taxa
Combines richness and evenness in one metric

Recommendation

Guidelines for alpha diversity: Cassol, Ibañez, and Bustamante (2025)

Richness: The number of observed unique features
Dominance: Berger-Parker
Information: Shannon
Phylogenetics: Faith

Demonstration

library(mia)
tse <- addAlpha(tse)

library(mia)
tse <- addAlpha(tse)

library(miaViz)
plotBoxplot(tse, col.var = "faith_diversity", x = "patient_status") +
    labs(x = "Diagnosis", y = "Faith's diversity")

Exercises

From OMA online book, Chapter 14: Alpha diversity

1.2, 1.3, 1.4, 1.9, 1.10

References

Cassol, Ignacio, Mauro Ibañez, and Juan Pablo Bustamante. 2025. “Key Features and Guidelines for the Application of Microbial Alpha Diversity Metrics.” Scientific Reports 15 (1). https://doi.org/10.1038/s41598-024-77864-y.