What is Carrying Capacity?
Carrying capacity (K) is the maximum population size an environment can sustain given its food, water, space and other resources. It's a central concept in population ecology that explains why populations don't grow forever.
Carrying capacity is the maximum stable population size a habitat can support long-term; as a population nears K, growth slows due to limited resources, following the logistic growth model dN/dt = rN(1−N/K).
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Step-by-step worked examples
A population of 500 deer has r=0.3 and K=1000. Find the current growth rate.
dN/dt = rN(1−N/K) = 0.3×500×(1−500/1000) = 150×0.5 = 75 deer/year
A bacterial colony has N=900, K=1000, r=0.5. How fast is it growing?
dN/dt = 0.5×900×(1−900/1000) = 450×0.1 = 45 cells/hour
If N=K exactly, what is dN/dt?
dN/dt = rN(1−N/N) = rN×0 = 0 Growth stops — the population is at equilibrium
Flashcards
Quick quiz
Q1.In dN/dt = rN(1−N/K), what does K represent?
Q2.What happens to growth rate as N approaches K?
Q3.A population with N=1000, K=1000 has dN/dt =?
Q4.Which is NOT a factor limiting carrying capacity?
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Common mistakes
Carrying capacity is a fixed number forever. — Correct: K can change if resources, climate or habitat change.
Populations always stay at exactly K. — Correct: Populations often oscillate above and below K.
Higher r always means higher K. — Correct: r (growth rate) and K (capacity) are independent parameters.
Exceeding K has no consequences. — Correct: Overshooting K usually causes a population crash from resource depletion.
FAQ
What is carrying capacity in biology?
It's the maximum population size (K) an environment can sustain indefinitely given available resources.
What is the carrying capacity formula?
dN/dt = rN(1−N/K), the logistic growth equation, where growth slows as N approaches K.
What are examples of carrying capacity?
A pond supporting 200 fish, or an island supporting 50 deer before resources run out.
How do you calculate carrying capacity effects on growth?
Plug N, K and r into dN/dt = rN(1−N/K) to find the current population growth rate.