Year 0Reserve -/haFished -/haCatch - kg/ha/yrreadyFPS 0

Drag to orbit, wheel or pinch to zoom. Orange buoys mark the reserve boundary (left of the line: closed to fishing). Each fish stands for several animals; the number of fish in a zone follows the modelled density times the zone area. Boats appear in proportion to fishing effort. Drifting dots are larvae crossing the boundary.

Reef Fish Stocks: Beverton-Holt Recruitment, Fishing Pressure and Marine Reserve Spillover

One reef, two zones: a no-take reserve and a fished area. Fish are born from a larval pool, settle on coral (Beverton-Holt), die naturally or are caught, and swim across the boundary. Find how much fishing the reef can bear and what a reserve changes.

Fishing and reserve

Fish biology and reef

Connectivity

Live readouts

Adult density through time (fish per hectare)

Steady-state yield against fishing mortality

Beverton-Holt recruitment curve

Experiment: does a reserve pay off?

Holds your current settings and sweeps the reserve fraction from 0 to 80 percent, running each to steady state. Total yield (kg/ha/yr of the whole reef) and total fish are listed together with the textbook prediction for the unconnected case.

Independent numerical checks

Controls

Fishing mortality F is the fraction of the fished stock caught per year (instantaneous rate). Poaching lets a share of that pressure leak into the reserve.
Coral cover scales how many young fish the reef can hold: a bleached reef settles fewer recruits (lower plateau of the recruitment curve).
Larval dispersal moves a share of the larvae to the other zone; adult spillover is the daily wandering of fish across the boundary.
The speed slider sets simulated years per real second; Pause freezes time; every slider can be changed while running.

The science

Recruitment. Larvae settle onto limited habitat, so the number of young fish saturates: R = A S / (1 + A S / R_max) (Beverton-Holt). S is the larval supply per hectare in adult-equivalents, A the number of recruits per adult per year when the habitat is empty (A = fecundity x early survival), and R_max = 60 h recruits per hectare per year, with h the coral cover. R_max and the average adult mass of 0.45 kg are illustrative values, not measurements of a real species.

Stock dynamics. dN/dt = R - (M + F) N for each zone, with natural mortality M and fishing mortality F. For a single isolated zone the steady state is N* = R_max (1/(M+F) - 1/A), positive only while M + F < A: past that the stock cannot replace itself and collapses. Catch is Y = w F N*.

Maximum sustainable yield. Setting dY/dF = 0 gives F_MSY = sqrt(M A) - M. The page compares it with the maximum found by scanning the numerical solution. Fishing harder than F_MSY lowers the long-term catch as well as the stock.

Two zones. Area fractions are p (reserve) and 1 - p. A fraction d of each zone's larvae drifts into the other zone's pool, and adults exchange at rate D across the boundary with flux J = D (N_r - N_f) 4 p (1 - p) fish per year (a diffusion-like spillover whose size is largest when the zones are equal). Fishing pressure in the reserve is F times the poaching share.

What it leaves out. No size or age structure (so no big old fecund females, a main real benefit of reserves), no habitat choice, no predators or prey, no catch rules, no randomness, no sex change, and a single combined species. Fish counts on screen are a symbolic sample of the modelled density. Real fishery assessments use stock-specific data; read the shapes of the curves rather than the numbers. Models built with Blender, scene by Three.js.