Hubbell's Unified Neutral Theory of Biodiversity (2001) makes a radical simplifying assumption: within a trophically similar guild, all individuals — regardless of species — have identical per-capita birth, death and dispersal probabilities. Diversity patterns are not explained by niche differences but by pure demographic stochasticity ("ecological drift") acting on a fixed-size, zero-sum community. This page runs the model on a 2D lattice (the classic spatially-explicit formulation used in Chave & Leigh's neutral-theory papers) rather than a 3D block — the birth-death-speciation mechanics below are identical either way; only the neighbor topology used for local dispersal changes shape.
Each simulation step is a birth–death event on a torus lattice of J individuals:
1. pick a random individual to die
2. with probability ν: it is replaced by a brand-new species
(point-mutation speciation)
3. otherwise: it is replaced by a copy of a random
neighbor (local dispersal, 4-connected wraparound grid)
or of any community member (global / well-mixed)
Because the community size J never changes, every birth is exactly balanced by a death — the defining "zero-sum" dynamic. Repeating this many times produces ecological drift: species wander in abundance by chance alone, most drift to extinction, and the ones replacing them arise from speciation. At dynamic equilibrium between speciation and drift-extinction, richness and the shape of the abundance distribution are governed by the fundamental biodiversity number θ ≈ 2Jν (exact in the well-mixed/global limit), producing Fisher's classic hollow-curve log-series distribution — a few common species and many rare ones, exactly like real forest and reef surveys. The θ readout on the left updates live with the speciation slider so you can watch the predicted equilibrium richness move before the lattice catches up to it.
- Speciation rate ν — how often a death is replaced by an entirely new species instead of a copy of an existing neighbor. Higher ν → higher equilibrium richness and a flatter (less hollow) rank-abundance curve.
- Local vs. global dispersal — local replacement copies only a lattice neighbor, so identical species clump into visible spatial patches (real dispersal limitation); global replacement samples the whole community, erasing spatial structure and converging fastest onto the θ prediction.
- Mass disturbance — instantly kills 30% of the community at random, mimicking a disturbance event, then lets drift and speciation rebuild diversity from the survivors.
- Shannon diversity H′ = −Σ pᵢ ln(pᵢ) over the current species proportions pᵢ; higher H′ means more even, more diverse.
Drag the lattice to pan and scroll/pinch to zoom into individual patches; the rank-abundance panel below plots every species' abundance on log-log axes, the standard way ecologists visualize Fisher's hollow curve.
This is a real, still-debated model in community ecology — it competes with niche-based theories (competitive exclusion, resource partitioning) as an explanation for why tropical forests and coral reefs sustain so many co-existing, ecologically similar species.