Logistic growth — Science definition

Defined in 2 courses:

Growth that starts fast but slows and levels off as a population nears the limits of its environment, producing an S-shaped curve. (Life Science: Biology)
Growth that slows as a population nears the limits of its environment, producing an S-shaped curve that levels off at carrying capacity. (Physics & Environmental Science)

Where it is taught

Populations & Communities — Ecosystems & Conservation Decisions, Life Science: Biology, Grade 10
Population Ecology — Ecology, Populations & Biodiversity, Physics & Environmental Science, Grade 12

In use

A useful idealized model predicts an S-shaped pattern called logistic growth.
Populations & Communities

Questions using logistic growth

Problem 1

Distinguish exponential from logistic growth and state which is sustainable in a closed environment.

Answer and explanation

Exponential growth means the population increases by a constant proportion each interval, so numbers rise ever more steeply with no limit. Logistic growth begins in the same way but slows as the population approaches carrying capacity, levelling off when resource limits take effect. Only logistic growth is sustainable in a closed environment, because exponential growth necessarily exceeds any finite resource supply and ends in a crash.

Response criteria

State a biologically accurate conclusion.
Show the data, mechanism, or calculation that supports it.
Include units, conditions, or limits where relevant.

Problem 2

In logistic growth, why does growth slow as N approaches K?

Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

The model's factor 1−N/K reduces per-capita growth; real mechanisms and K can change with conditions.

Problem 3

For continuous logistic growth with r=0.5 yr⁻¹,K=800 and N=200, find dN/dt. Compare with N=400.

Answer and explanation

At200:0.5×200×0.75=75 individuals/year. At400:0.5×400×0.5=100/year. Total growth rises even while per-capita growth falls.

At200:0.5×200×0.75=75 individuals/year.

At400:0.5×400×0.5=100/year.

Total growth rises even while per-capita growth falls.

Response criteria

Use the stated measurements or conditions, with correct units.
Connect the result to the physical or environmental mechanism or evidence relationship.
Identify the assumption, model limit or further evidence requested.

Problem 4

Independent chapter check: For continuous logistic growth with r=0.5 yr⁻¹,K=800 and N=200, find dN/dt. Compare with N=400.

Answer and explanation

At200:0.5×200×0.75=75 individuals/year. At400:0.5×400×0.5=100/year. Total growth rises even while per-capita growth falls.

At200:0.5×200×0.75=75 individuals/year.

At400:0.5×400×0.5=100/year.

Total growth rises even while per-capita growth falls.

Response criteria

Use the stated measurements or conditions, with correct units.
Connect the result to the physical or environmental mechanism or evidence relationship.
Identify the assumption, model limit or further evidence requested.

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