JC · Biology Round 1/6 Score 0

Population Curve

Model population growth and manage sustainable fish stocks.

Population modelling

Assumption: a closed population with constant rates.

Population over time

Logistic Exponential Observations or quota

Growth and harvest

Both plots update when parameters change.

Adjust the controls, then press Check.

The biology

Exponential growth: N = N₀e^(rt). Logistic growth: dN/dt = rN(1 − N/K). The logistic increase is fastest at N = K/2. The doubling time for exponential growth at positive r is ln(2)/r. Under a constant annual fishing quota h, the theoretical maximum sustainable yield is rK/4. A quota above the maximum causes collapse in this simple model, and harvesting exactly at the maximum has no safety margin.