The logistic model of population growth produces a sigmoid (S-shaped) curve.
Logistic Growth model
Number of generations
Population size (N)
K = 1,500
1,500 – N
The growth of laboratory populations of paramecia fits an S-shaped curve.
These organisms are grown in a constant environment lacking predators and competitors.
Some populations overshoot K before settling down to a relatively stable density.
The growth of laboratory populations fits an S-shaped curve which hovers around the Carrying Capacity of the area.
Number of Paramecium/mL
Number of Daphnia/50 mL
(b) A Daphnia population in the lab
(a) A Paramecium population in the lab
Life history traits favored by natural selection may vary with population density and environmental conditions.
K-selection = density-dependent selection, selects for life history traits that are sensitive to population density.
r-selection = or density-independent selection, selects for life history traits that maximize reproduction.
There are two general questions about regulation of population growth:
What environmental factors stop a population from growing indefinitely?
Why do some populations show radical fluctuations in size over time, while others remain stable?
In density-independent populations, birth rate and death rate do not change with population density.
In density-dependent populations, birth rates fall and death rates rise with population density.
Density-dependent birth and death rates are an example of negative feedback that regulates population growth.