Compare two growth models
Exponential growth is a model for times when limits such as food, space, and disease have little effect. As the population gets larger, more individuals can reproduce, so the number added during each equal time interval grows. On a graph, this pattern forms a J-shaped curve.
Logistic growth adds environmental limits. Growth can be rapid while the population is small, then slow as competition, disease, predation, space, or other conditions limit further increase. The idealized curve approaches carrying capacity and has an S shape.
Treat carrying capacity as a model, not a permanent ceiling
Carrying capacity, often written K, is the population size a particular environment can support under its current conditions. When population size is far below K, resources may allow rapid growth. Near K, the model predicts slower net growth because fewer resources remain available per individual.
Real carrying capacity can change. A drought may reduce available water and food, while habitat restoration may increase usable space. A disease outbreak or storm can also push a population away from the smooth pattern predicted by a simple logistic model. Use the model to explain a pattern while naming the conditions it leaves out.
Remember these ideas
Key ideas
- Exponential growth produces a J-shaped model when limits have little effect.
- Logistic growth slows as a population approaches the environment’s carrying capacity.
- Carrying capacity depends on current resources and conditions, so it can change.
- Growth models simplify real populations and should be checked against evidence and context.
Make the reasoning visible
Explain a rabbit-population curve
- 1
A grassland starts with 20 rabbits and abundant food, water, shelter, and space. The population rises faster during each early interval, resembling exponential growth.
- 2
As the population becomes larger, rabbits use food and shelter more quickly. Competition increases, so births no longer exceed deaths by as much.
- 3
The curve bends and fluctuates around about 120 rabbits. In this simplified model, 120 is an estimate of carrying capacity under those conditions.
- 4
A long drought reduces plant growth and available water. Predict a lower carrying capacity rather than assuming 120 is a permanent maximum.
Try the next step
Read a changing growth pattern
A fish population rises from 40 to 170 in a protected pond, then stays between 160 and 185 for several years. After invasive plants reduce open water, it settles near 120. Explain both parts of the pattern using carrying capacity.
What additional evidence would help you decide whether habitat loss, disease, harvesting, or another factor caused the later decline?