A virtual community of S species shares N individuals. The evenness slider sets a
geometric decay rate r applied to species ranked by abundance: at 100% evenness every species
gets an equal share (rank-abundance curve is flat); at 0% one species dominates almost the whole
population and the curve is steep. Both diversity indices are recomputed every frame directly from
the resulting proportions pi — nothing here is decorative.
rᵢ = rmin + (evenness/100)·(1−rmin) weight of rank i: wᵢ = rᵢ^(i−1)
pᵢ = wᵢ / Σwⱼ (relative abundance of species i)
Shannon: H' = −Σ pᵢ·ln(pᵢ) Simpson: D = 1 − Σ pᵢ²
Pielou evenness: J' = H' / ln(S) Effective species (Hill number): e^H'
- Species richness (S) — how many distinct species are present; raises the ceiling H'max = ln(S) even before evenness changes anything.
- Evenness — how equally individuals are spread across species; the strongest driver of H' at fixed richness.
- Total population (N) — how many individuals are drawn and rendered; changes the sample but not the proportions pᵢ.
- Randomize abundances — draws a fresh random rank-abundance curve at the current richness.
Real-world relevance: two habitats can have the same species richness yet very different H' —
a reef with one species crowding out the rest reads as far less diverse than one where abundance
is spread evenly, even though both host the same number of species.