Population Growth Curves and Carrying Capacity
In a logistic growth model, population growth slows as resources become limited. Carrying capacity is estimated from a sustained population level. Density-dependent and density-independent effects are distinguished by how their effect per individual changes with crowding.
What a learner can do afterwards
- Labels the phases of a growth curve and explains what limits each one.
- Distinguishes a density-dependent factor from a density-independent one with an example of each.
- Estimates carrying capacity from a plotted curve.
1 · Read
Carrying capacity K is the largest population a habitat's resources support over time. Closed cultures may decline after nutrients run out. Without migration, stable numbers mean births roughly equal deaths.
In a separate stable woodland, annual rabbit counts settle at 498, 502, 500 and 501, suggesting K near 500. Use the sustained level, not the start or fastest rise. The culture's brief plateau alone cannot establish K.
Density is individuals per area or volume. Density-dependent effects change with density, measured per individual or fraction affected. Crowding can intensify competition for food, space or nitrates, disease, predation and waste, reducing survival or reproduction.
Density-independent effects do not change with density when measured per individual. This covers survival and reproduction. Unchanged death risk from a flood is one example. Compare equal-sized areas at different densities; total deaths alone cannot classify effects. Weather and crowding can interact.
Exponential models are J-shaped without resource limits. Hourly bacterial doubling in rich broth lasts only while nutrients remain. Logistic growth from well below K slows toward K in an S-shape. Yeast can show this pattern temporarily; real populations may differ.
A deer herd can stop growing in grass-covered fields. Grass cover does not establish suitable food. Food quality, disease or predators may limit growth; counts cannot identify causes. Seasons, habitat damage and competitors can change K.
Logistic growth slows toward carrying capacity K. Classify limiting effects by how they change with density. Real populations can grow, level off or decline.
Original lesson, questions, worked solutions and flashcards written for this dataset.
The rewritten readings were written for this dataset. The other reading adapts Khan Academy's article on exponential and logistic growth. The population-regulation video is linked from Khan Academy. Publisher license terms for the Khan Academy material have not been verified.
2 · Watch
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