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Unit 3 · Topic 3.4

3.4 Carrying Capacity

Carrying capacity is the largest population an environment can support over the long run. When a population overshoots it, resources are used faster than they're replaced, and the population often suffers a sharp dieback.

Key terms

  • carrying capacity (K)
  • overshoot
  • dieback
  • limiting resource

What carrying capacity means

Carrying capacity (K) is the maximum number of individuals of a species that an environment can support indefinitely. It's set by limiting resources like food, water, nesting sites, space and sunlight. If a resource runs short, birth rates fall and death rates rise until the population roughly matches what the environment can sustain.

Carrying capacity isn't fixed. A wet year with lots of plant growth can raise K for herbivores; a drought or habitat destruction can lower it. Human activities often lower K for wildlife by removing habitat.

Overshoot and dieback

Populations don't always stop neatly at K. If a population grows quickly and there's a delay before resource shortages take effect, it can overshoot, meaning it rises above K. While it's above K, it uses resources faster than they can be replaced, damaging its own food supply. Then comes dieback (also called a crash): a sharp drop in numbers from starvation, disease or failed reproduction.

Because the overshoot may have damaged the environment, K can be lower after the crash than it was before. The population may then settle at a lower level or keep oscillating around K.

A real example

In 1944, the U.S. Coast Guard released 29 reindeer on St. Matthew Island in the Bering Sea. The island had plenty of lichen to eat and no wolves or other predators. The herd grew to about 6,000 by 1963, far more than the island could feed. The reindeer ate the slow-growing lichen faster than it could regrow. After a harsh winter, the population crashed to just 42 animals by 1966.

This case shows overshoot, resource depletion and dieback very clearly. It also shows why predators and harsh conditions often help keep populations near K.

Reading the graph

On a graph of population size over time, carrying capacity is usually drawn as a horizontal dashed line. A population following logistic growth rises in an S-shape and levels off at that line. An overshoot shows the curve rising above the line, followed by a steep drop.

If a graph shows a population oscillating up and down around a level, estimate K as the average level the population fluctuates around.

Carrying capacity and people

Scientists debate Earth's carrying capacity for humans. Technology, like fertilizers, irrigation and trade, has raised the number of people Earth can feed. But using up groundwater, eroding soil and changing the climate could lower it. Because humans use very different amounts of resources, estimates depend heavily on how people live.

Worked examples

Try each one yourself first, then open the solution.

  1. Example 1Calculator allowed

    Calculating a crash

    The St. Matthew Island reindeer herd went from about 6,000 animals in 1963 to 42 in 1966. Calculate the percent decrease.

    Show the solution
    1. Step 1: Percent change = (new − old) ÷ old × 100.
    2. Step 2: (42 − 6,000) ÷ 6,000 = −5,958 ÷ 6,000 = −0.993.
    3. Step 3: −0.993 × 100 = −99.3%.

    Answer: About a 99.3% decrease.

  2. Example 2

    Explaining overshoot

    A deer population on an island with no predators grows past the island's carrying capacity. Describe what happens to the plants and the deer over the next several years, and explain why the carrying capacity may end up lower than before.

    Show the solution
    1. Step 1: Above K, the deer eat plants faster than they regrow, so plant cover and food supply decline.
    2. Step 2: As food runs short, deer starve or become weak and diseased, and fewer fawns survive. The population suffers a sharp dieback.
    3. Step 3: Overgrazing damaged the plants and possibly the soil, so the island can't produce as much food as before.
    4. Step 4: With less food available, the carrying capacity is lower than it was originally.

    Answer: Deer overgraze, food declines and the population crashes; because the habitat was damaged, the new carrying capacity is lower.

Common mistakes

  • Thinking carrying capacity never changes. It shifts with resources, weather and habitat damage.
  • Using ‘dieback’ for any decline. Dieback is a sharp drop after overshooting carrying capacity.
  • Forgetting the time lag. Overshoot happens because a population keeps growing before resource shortages catch up.

On the exam

  • Expect to identify K on a described graph and explain overshoot and dieback using resource depletion.
  • Percent change calculations are common. Show the setup and keep the negative sign or say ‘decrease’.

Connected topics

Videos

  • APES Video Notes 3.4 - Carrying Capacity

    Jordan Dischinger-SmedesWatch on YouTube (opens in a new tab)

  • 3.3 Carrying Capacity

    Mrs. Campbell's APESWatch on YouTube (opens in a new tab)

  • Ecological Carrying Capacity-Biology

    MooMooMath and ScienceWatch on YouTube (opens in a new tab)

  • Exponential and logistic growth in populations | High school biology | Khan Academy

    Khan AcademyWatch on YouTube (opens in a new tab)

  • APES Topic 3.4, Carrying Capacity

    Tony VillarrealWatch on YouTube (opens in a new tab)

Check yourself

5 questions on 3.4 Carrying Capacity. Pick an answer to see if you got it, and why.

Question 1 of 5

Pronghorn on a dry rangeland have plenty of grass, but in summer they must travel long distances to the few water holes, and many young die. A rancher installs several water tanks across the range. What is the most likely effect on the pronghorn's carrying capacity?

Question 2 of 5

Why do many animal populations overshoot their carrying capacity instead of leveling off smoothly?

In 1944, 29 reindeer were released on St. Matthew Island, a remote island in the Bering Sea with thick mats of lichen, the reindeer's main winter food, and no wolves or other large predators.

Surveys counted about 1,350 reindeer in 1957 and about 6,000 in 1963. By then, the lichen had been heavily grazed. After a very harsh winter in 1963–64, only 42 reindeer were found in 1966.

Based on D. R. Klein, "The Introduction, Increase, and Crash of Reindeer on St. Matthew Island," Journal of Wildlife Management 32, no. 2 (1968)

Question 3 of 5

Which statement best describes what happened to the reindeer population between 1963 and 1966?

Question 4 of 5Calculator allowed

By about what percent did the reindeer population decrease from 1963 to 1966?

Question 5 of 5

Which factor best explains the rapid growth of the population between 1944 and 1963?

0 of 5 answered