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Biology 11–12 · Year 11

Duckweed population growth: frond counts against the exponential and logistic models

Module 4: Ecosystem Dynamics (Population Dynamics)

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The idea

A population with space and nutrients doubles at a fixed interval; as the surface fills, growth slows toward a carrying capacity.

What you need

  • Lemna minor (common duckweed) from an aquarium supplier or a clean pond, 20 fronds per container
  • Clear containers with 500 mL of low-nutrient medium (the SAPS note recommends water in which one wheat grain has been boiled, made up to a litre, pH 6 to 8)
  • A windowsill or lamp giving steady light; thermometer; tally counter; camera for daily photographs
  • For a further run: a second series with double the medium concentration, and a third with a small surface area (a narrow jar)

How to do it

  1. Place 20 healthy fronds on the medium in each of three containers and record the temperature.
  2. Count fronds every day for 14 to 21 days at the same time, counting a bud as a frond once it is clearly separate; photograph each container.
  3. Calculate the growth rate r = ln(N_t / N_0) / t over the early days and the doubling time ln 2 / r.
  4. Plot frond number against day on ordinary and logarithmic axes; note where the log plot stops being straight.
  5. Fit the logistic model by choosing a carrying capacity that matches the levelling-off, and compare containers of different surface area.
  6. Relate the levelling-off to competition for surface and light.

What you should see

At about 22 degrees Celsius Lemna minor doubles about every three days (the SAPS figure), so 20 fronds become about 80 in six days and about 320 in twelve if space does not limit, while a narrow jar levels off well below that. With r = 0.231 per day (from a three-day doubling), N0 = 20 and a carrying capacity of 500, the logistic model gives 200 fronds at day 12 against 320 for unlimited growth (computed). The learner knows it worked when the early log plot is straight with a slope near 0.23 per day and the later points bend below it.

What changes

What you change
surface area or nutrient concentration
What you measure
frond number over time; growth rate r and carrying capacity K
What you keep the same
  • temperature
  • light
  • starting fronds
  • counting rule
  • medium volume

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

  • Populations grow by a fixed number each day; unrestricted growth adds a fixed fraction, so the count doubles at intervals.
  • Carrying capacity is a wall the population hits; growth slows gradually as resources per individual fall.
  • The growth rate r changes as the population grows in the logistic model; r is constant and the realised growth falls as N approaches K.

Safety card

Low riskLearners carry it out

Hazards

  • Pond water microorganisms if fronds are collected from the wild

Controls

  • Wash hands after handling; use supplier stock where possible

Note

No hazardous chemicals; RiskAssess (https://www.riskassess.com.au/). Do not release duckweed into waterways.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

  • Biology Stage 6 Syllabus (2017), current: Year 11 taught to the end of 2026 and Year 12 to Term 3 2027BIO11-11BIO11/12-2BIO11/12-3BIO11/12-5
  • Biology 11–12 Syllabus (2025), Year 11 focus area Evolution and ecosystems; new syllabus not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027BI-11-03
  • Biology 11–12 Syllabus (2025), Year 11 Working scientifically; new syllabus not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027BI-11WS-02BI-11WS-03BI-11WS-05
  • Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

  1. www.nsw.gov.au/education-and-training/nesa/curriculum/science/biology-stage-6-2017
  2. www.nsw.gov.au/sites/default/files/noindex/2025-03/biology-stage-6-syllabus-2017.docx
  3. curriculum.nsw.edu.au/learning-areas/science/biology-11-12-2025/outcomes
  4. curriculum.nsw.edu.au/learning-areas/science/biology-11-12-2025/content/year-11/fad715a0de
  5. www.saps.org.uk/teaching-resources/resources/744/using-duckweed-in-the-lab
  6. openstax.org/books/biology-2e/pages/45-3-environmental-limits-to-population-growth
  7. mathworld.wolfram.com/LogisticEquation.html

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