Sustainable Harvest: Conservation Population Simulator

Population Controls

Growth rate r 0.35

Carrying capacity K 240

Annual harvest H 0

Sim speed 1.0×

Live Readout

GROWING

Population N

120

Years elapsed

0.0

Max Sustainable Yield (rK/4)

21.0 / yr

How it works

The population follows the logistic growth model with constant harvesting — the standard first model taught for renewable-resource conservation (fisheries, forestry, wildlife quotas):

dN/dt = r·N·(1 − N/K) − H

N = population size
r = intrinsic growth rate
K = carrying capacity of the habitat
H = individuals removed per year

Growth is fastest at N = K/2 and slows to zero as N approaches K (limited food, space, competition). Harvesting removes a fixed number every year regardless of population size. This creates two possible equilibria (dN/dt = 0), a stable one and an unstable one — solve the quadratic to find them:

N_eq = K/2 · (1 ± √(1 − 4H/(rK)))

The largest harvest rate for which a stable positive equilibrium still exists is the Maximum Sustainable Yield, reached exactly at N = K/2:

H_MSY = r·K / 4

H below H_MSY — population settles at a stable equilibrium; the habitat turns green and the herd holds steady forever.
H above H_MSY — no equilibrium exists; losses always exceed growth and the population declines to extinction no matter how large it starts.
"Set H = MSY" pins the harvest at the theoretical maximum sustainable rate for the current r and K, so you can watch the population balance right at the edge of collapse.

This is the exact model behind real fishing-quota and hunting-license science — a quota set even slightly above MSY looks fine for years before a sudden population crash.

Habitat capacity K

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