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8.4 Effect of Density on Populations

Syllabus
2025
Topic
8.4
Level
—

Learning objectives

8.4A—Explain how the density of a population affects and is determined by resource availability in the environmentExplain how the density of a population affects and is determined by resource availability in the environment.• Carrying capacity is the sustainable abundance of a species that can be supported by the ecosystem’s total• As limits to growth attributable to density-dependent and density-independent factors are imposed, a logistic growth model typically ensues. Relevant equation: Logistical Growth— dN dt rN KN K max= − where dt = change in time N = population size dN = change in population size rmax = maximum per capita growth rate of population K = carrying capacity

Density, Resources, and Logistic Growth

Carrying capacity (KK) is the sustainable abundance of a species that an ecosystem's total available resources can support. If resources become more or less available, the carrying capacity can change.

Limiting factor Relationship to density Population effect
Density-dependent Its effect becomes stronger as density rises, such as competition as resources are depleted Birth rate may fall or death rate may rise as NN approaches KK
Density-independent Its effect is not caused by how crowded the population is Can reduce population size at low or high density

\frac{dN}{dt}=r_{\max}N\left(\frac{K-N}{K}\right)

NN = population size; dN/dtdN/dt = change in population size per unit time; rmax⁡r_{\max} = maximum per-capita growth rate; KK = carrying capacity. The fraction (K−N)/K(K-N)/K is the resource-limitation term: it becomes smaller as NN approaches KK.

Illustrative calculation: with N=200N=200 individuals, K=500K=500 individuals, and rmax⁡=0.10 year−1r_{\max}=0.10\,\text{year}^{-1}, dN/dt=(0.10)(200)[(500−200)/500]=12dN/dt=(0.10)(200)[(500-200)/500]=12 individuals per year. Growth is positive but below the unconstrained rate of 20 individuals per year because resources limit it.

When NN is much smaller than KK, the limiting fraction is near 1 and growth resembles exponential growth. As NN approaches KK, the fraction approaches 0, so net growth slows and the population tends to stabilize.

Carrying capacity is not a permanent maximum fixed for all time. It represents sustainable abundance under current resource conditions, and density-independent events can move a population away from that level.