English

Biodiversity Index

High schoolBiologyExact community diversity metrics and seeded uniform sampling without replacement

Edit species abundance, draw a real seeded sample and compare observed richness with the rarefaction expectation. Click individuals to remove them from the community.

A 40B 25C 20D 10E 5

The full community is shown. Outlined individuals are the last uniform sample without replacement. Click an individual to remove it, or use the species controls.

Measurement notebook

Change the setup, test a prediction and save the result. Up to 12 snapshots are kept.

About this experiment

Edit a five-species community, inspect every individual and take a reproducible finite sample. Compare richness, evenness, Shannon diversity and Gini-Simpson diversity with the expected richness of different sample sizes.

Learning goals

  • Distinguish richness from abundance-weighted diversity.
  • Calculate Shannon and Gini-Simpson indices from species counts.
  • Compare an observed sample with its exact rarefaction expectation.

How to use it

  1. 1Draw a community sample and inspect which individuals were actually selected.
  2. 2Change the planned sample size and confirm the old sample remains frozen.
  3. 3Compare an even community with a dominant-species community.
  4. 4Remove a species, then empty the community and inspect which metrics become undefined.

The model

Shannon diversity weights richness and relative abundance.
Gini-Simpson is the chance that two independent community draws differ in species.
Rarefaction predicts sample richness without replacement.

Assumptions

  • All individuals of a species are equivalent. Samples are uniform without replacement from the complete edited community.
  • Shannon uses natural logarithms. Gini-Simpson here means 1 minus the sum of squared community proportions, not its finite-sample unbiased correction.
  • Rarefaction computes the exact expected number of represented species using absence probabilities for sampling without replacement.
  • An empty community has zero richness and undefined abundance-weighted diversity. Zero-count species contribute zero to Shannon diversity.
  • Changing community counts clears its previous sample. Changing the planned sample size does not redraw it. Each species count is limited to 100; the dominant preset caps its total at 125 to keep an 80 percent dominant species editable.

Try this in class

  1. Q1Can two communities have equal richness but different Shannon diversity?
  2. Q2Why can a sample miss a species that exists in the full community?

Frequently asked questions

Why does the sample richness differ from the curve?

The curve is an expectation over possible random samples. The outlined individuals show one actual seeded sample.

Is an empty community assigned zero Shannon diversity?

No. Its species proportions are undefined, so the interface labels that diversity index undefined.