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The science
Neutral community model
All individuals are ecologically equivalent. On an 80 x 80 torus (J = 6400 plants, each cell is about 5 cm here) one generation is J death-and-birth events: a random cell dies and is replaced either by a brand-new species (probability ν, speciation or immigration) or by the offspring of a plant within the dispersal window, a square of half-width r cells. This is the Hubbell-style zero-sum drift model, identical to the 2D page.
Diversity measures
Richness S; Shannon H = -Σ pi ln pi (maximum ln S when all abundances are equal); Simpson 1 - D with D = Σ pi2; Pielou evenness J' = H / ln S; dominant share max pi.
Ecological drift
Without speciation and with global dispersal the expected Simpson diversity decays as E[1-Dt] = (1-D0)(1 - 2/J2)t per birth-death event (t counts events). Local dispersal makes patches of the same species, slowing mixing and changing the rank-abundance curve. Speciation at rate ν balances drift and gives a steady state with a fundamental biodiversity number θ = 2Jν in the large-community theory.
What you see
Each plant is placed on its cell; flower form depends on the species number mod 3, hue is the species id, and height is a fixed random trait per species. The towers in front are the 20 most abundant species (height = abundance / the largest abundance). The anemometer and drifting seeds speed up with the dispersal radius, sparks mark new species, and a disturbance clears a disc and lets neighbours recolonise it (as in the 2D page, instantly), shown by an expanding ring.
Independent checks
(1) Shannon index of a synthetic perfectly even 25-species grid equals ln 25. (2) 400 independent replicate Moran runs (J = 100, 500 events) are compared with the closed-form decay above. (3) Live conservation law: abundances always sum to J; the mean dispersal distance of the kernel computed by exact enumeration is compared with a Monte Carlo estimate.
Honest simplifications
Neutral theory assumes no niches, no competition differences, no environmental variation and a flat 2D torus; real meadows have all of these. A 5 cm cell and the three flower shapes are purely visual, and the number 80 x 80 is far smaller than a real meadow. Speciation here is a stand-in for immigration from a regional pool. Educational model, not a conservation tool.