Duckweed Fertilizer Trial: Confounded by the Windowsill
A high school research class tests whether a liquid fertilizer increases duckweed growth. Students set up 12 identical 250-mL cups, each with 200 mL of pond water and 10 duckweed fronds. Six randomly chosen cups receive 0.5 mL of fertilizer; the other six receive 0.5 mL of distilled water. All cups begin on a bench beside a south-facing window, but the bench is full, so the students move the six water-only cups to a shelf 3 m away in the same room. After 14 days the fertilizer cups average 47 fronds (range 31-62) and the water-only cups average 29 fronds (range 25-34). The students report that the fertilizer increased growth by 60% and recommend it to the school greenhouse.
1. Identify the single most serious threat to the students' conclusion, explain how it could have produced the observed pattern, and evaluate the reported 60% figure.
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Threat: a perfectly confounded environmental variable.
- Treatment (fertilizer vs. water) and position (window bench vs. distant shelf) were changed together. No cup received fertilizer on the shelf, and no cup received water at the window.
- Light is the dominant limiting factor for duckweed growth in indoor cultures. Moving cups 3 m from a south window can cut irradiance by more than half, and it also changes temperature and day-to-day fluctuation.
- Because the two variables never vary independently, the 18-frond difference can be attributed entirely to light. The design cannot separate the two causes, no matter how large the difference is.
The 60% figure is over-interpreted.
- 47/29 = 1.62, so "60% increase" is just the ratio of two final standing counts. Final frond counts confound growth rate with starting size and with the duration of exponential growth.
- A mean ratio with no measure of spread (standard error, confidence interval) and no time series does not establish a rate difference.
- Averages hide the fertilizer group's wide range (31-62), which itself suggests uncontrolled variation within that group.
2. Describe the minimum redesign that would permit a causal claim, and explain what the true unit of replication is in this experiment.
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Redesign: randomize position, not just treatment.
- Keep all 12 cups in one physical region, e.g., a single rack, and randomly assign cup positions. Alternatively, use a randomized complete block design: divide the rack into 6 blocks of two positions, and place one fertilizer cup and one water cup at random within each block. Rotate positions periodically to average out gradients.
- Hold light, temperature, and water volume constant and record them; measure fronds non-destructively at day 0, 3, 7, 10, and 14 so growth rate (not just final count) can be compared; count blind to treatment.
- Add a vehicle control if the fertilizer is dissolved in anything besides water.
Unit of replication.
- The experimental unit is the cup, not the frond. Ten fronds in one cup share the same water, nutrients, and light; they are subsamples, not independent replicates.
- The sample size is therefore n = 6 per treatment, not n = 60. Statistics must be computed on cup means, and frond-to-frond variation within a cup cannot be used to inflate the degrees of freedom (pseudoreplication).
3. In the corrected experiment the fertilizer cups still grow faster, but their water turns visibly green and pH rises to 8.6 versus 7.4 in the controls. What alternative explanation must now be ruled out, and what experiment would separate it from a direct fertilizer effect on duckweed?
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Alternative explanation: the effect is indirect, mediated by algae.
- The fertilizer adds nitrogen and phosphorus, which algae use. Green water means algal biomass increased. Algal photosynthesis consumes CO2 and can push pH to 8.6; decay of dead algae releases bacterial CO2 and recycled nutrients.
- Duckweed could benefit indirectly (recycled nutrients from decomposition) or be harmed (shading, competition for carbon). Either way, the treatment is no longer "fertilizer acting on duckweed" but "fertilizer acting on the whole community."
Experiments that separate the pathways
- Replace the fertilizer with a defined inorganic nutrient solution (known N and P concentrations) added to cultures kept algae-free (filtered water, sealed or darkened below the surface, or antibiotic-treated). If duckweed still responds, the nutrient effect is direct.
- Add an algae-only treatment (fertilizer, no duckweed) to measure algal response and pH change independently.
- Measure dissolved N and P over time in both treatments, plus light reaching the fronds, so the mechanism can be traced.
- If shading is suspected, run a fertilizer treatment with a mesh that excludes algae but not light.
The claim to defend is not just "fertilizer correlates with growth" but "which component of the fertilizer, acting through which pathway, changes duckweed growth."