How to Calculate Carrying Capacity
What is Carrying Capacity?
Carrying capacity (K) is the maximum population size an environment can sustainably support. Logistic growth produces an S-shaped sigmoid curve: dP/dt = rP(1 − P/K).
Step-by-Step Guide
- 1P(t) = K / (1 + ((K−P₀)/P₀) × e^(−rt))
- 2Growth is maximum at P = K/2
- 3As P → K, growth slows to zero
Worked Examples
Input
P₀=100 · r=0.3 · K=1000 · t=10
Result
P(10) ≈ 958
Approaches K asymptotically
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