MY SIMULATOR

Island Ecosystem Lab

Burn it, flood it, invade it — then watch it recover.

INTERACTIVE 3D

Ecosystem year 0.0Native 0%Invader 0%FPS 0

Island Ecosystem Disturbance Lab: Fire, Flood, Invaders & Recovery

A disturbance is a sudden event that removes biomass. Strike the island with fire, a river flood or an invasive plant, then watch how fast the native forest regrows, which species wins the empty ground, and how herbivores and predators follow. Pick a tool, click the island (or the map), and read the numbers.

Scenario

Ecosystem time warp

Live state intact

Vegetation through time (mean over land)

Herbivores and predators

Why: a fire or flood removes forage, herbivores starve, predators follow a few years later; the Lotka-Volterra loop then oscillates back.

1 · Fire

Fire spreads cell to cell with a probability set by fuel, dryness, wind and uphill slope. Dry fuel above a critical level makes the whole island burn (percolation).

2 · Flood

Water rises over 2 days, holds 1 day, falls over 4 days. Only land low above the river (HAND) is inundated; silt leaves a nutrient pulse, but long immersion kills trees.

3 · Regrowth

Logistic regrowth: a burnt patch needs about ln(9(1-N0)/N0)/r years to reach 90 %.

4 · Invasive species

Two species compete for the same ground. If both competition coefficients exceed 1 the winner is whoever gets there first — a burn clears the board.

5 · Animals

Experiments (measured vs predicted)

Run an experiment. They run on a copy of the island and do not disturb the live one.

Independent numerical checks

Also run outside the browser: node src/check.js (logistic regrowth and t90 closed forms, Fisher-KPP lattice front speed, fire = flood-fill cluster, percolation threshold, predator-prey Jacobian, bounds).

Educational model. Biomass is a dimensionless fraction of local carrying capacity; fauna are dimensionless densities; fire/flood losses of animals and the nutrient pulses are [assumptions]. Dispersal is in cells²/year (one cell = 5 m). Trees are drawn larger than life so single cells read from orbit. No real island or forecast is represented.

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Hero, Map, Ground buttons (keys H, T, G).
Click or tap the island (or the small map) with the selected tool: Ignite starts a fire; Seed invader plants the alien species. Lightning ignites a random fuelled cell. River flood sends a flood wave of the chosen crest down the valley.
While a fire or flood is happening the clock shows event time (hours or days) and the ecology is paused; afterwards it runs in years at the chosen time warp.
Sliders change the model live. Reset island rebuilds the pre-disturbance forest (60-year spin-up).

The science

Disturbance and resilience. A disturbance removes biomass quickly. Engineering resilience (Holling) is the speed of return, about 1/(return time); ecological resilience is how big a shock the system absorbs before it settles into a different stable state. The panel reports the measured time to regain 90 % of the pre-disturbance native biomass and compares it with the well-mixed logistic prediction.

Regrowth. Each land cell: dN/dt = r (1 + 0.8 n) N (1 - N - a_NI I) + D_N ∇²N + s (1 - N - I) - g H N/(N + 0.15), with n a decaying nutrient pulse after fire or flood (n falls by 1/e in 3 years, [assumption]), seed rain s, and Holling type II grazing. Isolated, this is logistic growth N(t) = K/(1 + ((K-N₀)/N₀)e^-rt); the time to 90 % is t₉₀ = (1/r) ln(9(K-N₀)/N₀).

Competition and the invader. dI/dt = r_I I (1 - I - a_IN N) + D_I ∇²I. With a_IN > 1 an invader cannot start inside intact forest (N = 1 gives negative growth). With a_IN, a_NI > 1 the Lotka-Volterra competition system is bistable: the faster species that occupies the cleared ground first wins (priority effect). That is why disturbance opens the door to invasion. The spread of an invasion into empty ground is a Fisher-KPP front with speed 2√(r D); on a lattice the speed is the minimum over λ of [r + D(2coshλ - 2)]/λ, which the check reproduces.

Fire. Stochastic spread on the 8-neighbour lattice: each burning cell ignites each unburnt neighbour with probability p = 0.35 · dryness · fuel · e^{0.07 w cosθ} · e^{1.2 tanφ} / d per 15-minute step, for 2 + 4 · fuel steps (w wind speed in m/s, θ angle between wind and spread direction, φ slope, d = 1 or √2). Fuel = native + 1.6 × invader biomass, so grassy invaders make fires more likely (the grass-fire cycle). Fire is a percolation process: with certain spread (p = 1) the burnt set is exactly the connected fuel cluster, and spanning fires appear only above a fuel density of about 0.407 for this lattice (typical literature value; checked here). Burnt cells keep 3 % of their biomass, gain an ash/nutrient pulse and leave a snag.

Flood. Height Above Nearest Drainage (HAND) is the height of a cell above the nearest river cell, found by breadth-first search. A cell is inundated to depth max(0, crest(t) - HAND). Native biomass decays as exp(-k · days · min(1, depth/1.5)); the invader tolerates inundation twice as well [assumption]. A 1-D bucket hydrograph replaces real hydraulics: no momentum, no sediment transport.

Animals. Herbivores H and predators P: dH/dt = H(e G - m H) - a H P, dP/dt = P(b a H - d) with forage G = native + 0.25 invader biomass. Near the coexistence point the eigenvalues of the Jacobian give a period 2π/Im λ and a damping rate -Re λ (checked against the simulation). Fire and flood kill a share of animals proportional to the area hit [assumption]. Animal icons are samples of the densities.

Not modelled: fire spotting, crown vs surface fire, weather change during a fire, seed banks, tree age classes, species-specific traits, real hydrodynamics, evolution. Constants marked [assumption] are illustrative; the qualitative behaviour (percolation, priority effects, delayed predator response) is what the model is for.