A single ancestral lineage (root, centre) undergoes a stochastic
birth-death branching process — the same model biologists use to
describe adaptive radiation, from the Cambrian explosion to
Darwin's finches. Each living tip can speciate (branch into
a new lineage occupying an aquatic, terrestrial or aerial niche)
or go extinct, each generation, with independent
probability.
dN/dt = (λ − μ)·N (N = living species, λ = speciation rate, μ = extinction rate)
H = −Σ p_i·ln(p_i) (Shannon diversity across the 3 niches, p_i = share in niche i)
- Evolution speed — how fast simulated time (millions of years) advances.
- Speciation rate λ — per-generation chance a living species splits into two, radiating outward into a new adaptive zone.
- Extinction pressure μ — per-generation chance a living species is lost (habitat loss, competition, climate).
- Mass extinction — instantly removes most living species at once, mirroring events like the End-Permian or K–Pg extinction, then lets the survivors radiate again.
When λ > μ the tree keeps branching outward and diversity climbs;
when μ > λ the population shrinks toward a bottleneck — exactly the
dynamic behind real-world conservation concerns about habitat loss
and over-exploitation tipping a lineage's balance negative.