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Biology · Grades 9–12

Population change and carrying capacity

Use births, deaths and movement as separate terms.

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Balance

Population change = births + immigration − deaths − emigration over the stated interval.

Limits

Resources and interactions can constrain growth; growth is not indefinitely exponential in a finite environment.

Carrying capacity

Carrying capacity is a model-dependent environmental support level, not an eternally fixed number.

Data

A change in count can reflect detection differences as well as real demographic change.

Worked examples

A model starts with 100 organisms, has 20 births, 5 immigrants, 10 deaths and 3 emigrants. Find the final population.

100 + 20 + 5 − 10 − 3 = 112.

112

What does emigration mean?

Emigration is outward movement.

Leaving the population area.

Check your understanding

  1. Why is unlimited exponential growth unrealistic in a finite habitat?

    1. Organisms contain no matter.
    2. Mathematics never models biology.
    3. Resources and other constraints become important.

  2. A population changes from 80 to 100. Find its percentage increase.

  3. Why can carrying capacity change over time?

Answers and marking notes

Answers and marking notes
  1. Resources and other constraints become important.

    Finite resources and interactions limit growth.

  2. 25 %

    (100 − 80)/80 × 100 = 25%.

  3. Environmental conditions, resources and interactions can change.

    It is not a universal permanent constant for a species.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.