Kelp Forest Simulator (2D)

Side view of one square metre of sea floor. Light fades with depth, kelp grows toward it, urchins graze it and otters eat the urchins.

Scenarios

Controls

Live readout

Light and depth

Irradiance as % of surface light. Solid: with the present kelp canopy; dashed: clear water without kelp.

Population through time

Kelp biomass (kg/m2) and urchins (ind/m2, divided by 4)

Phase plane: kelp against urchins

Green curve: kelp is steady for that urchin density. Violet curve: urchins are steady for that kelp biomass. The circle is where you are; where the curves cross the system rests.

Numerical checks

The science

Light

Beer-Lambert: I(z) = I0 exp(-Kd z), with Kd = Kw + Kt + kb B / H: clear water, turbidity, and kelp self-shading (column mean). Kelp at depth H grows only when the light reaching it, Ib = I0 exp(-Kd H), is above the compensation level Ic; the growth limit is Lg = (Ib - Ic) / (Ik + Ib - Ic).

Kelp, urchins, otters

dB/dt = r Lg B (1 - B/K) - a U B/(h + B) (logistic growth minus type-II grazing).
dU/dt = ru U (1 - U/Ku) B/(B + hu) - mu U - co O U/(s + U) + eps (urchins fed by kelp, background loss, otter predation, and larvae arriving from elsewhere). B kg/m2, U per m2, otters O per hectare, time in years. Integrated with 4th-order Runge-Kutta, step 0.02 yr.

What to look for

Because larvae keep arriving, an urchin barren is a second stable state. Remove the otters and the forest flips to barren; bring them back and the barren does not recover until otters pass a higher threshold than the one that lost the forest (hysteresis). Murky or deep water raises the light needed to keep the forest alive.

Honest simplifications

One well-mixed square metre with no waves, no seasons, no kelp age structure and fixed otter density. The parameters are plausible round numbers (kelp can add tens of centimetres per day, a sea otter eats a quarter of its weight daily) chosen to show the mechanism, not fitted to a particular coast. A small spore bank (0.01 kg/m2) lets kelp return once grazing stops.

Sprites rendered in Blender (urchin, otter, fish, rocks, sand). Kelp, water and graphs are drawn in Canvas.