By the end of this lesson
- Use random quadrat sampling to estimate population size.
- Compare populations in two areas with a fair method.
- Evaluate sample size, bias and the limitations of the estimate.
BIG QUESTION
How can you count a population that is far too large to count?
Random sampling of a small, known area allows a defensible estimate for the whole area, with stated uncertainty.
Plan a fair comparison
The independent variableThe variable that is deliberately changed in an investigation. is the area sampled, for example a mown lawn compared with an unmown field edge. The dependent variableThe variable that is measured in an investigation to see how it is affected by the independent variable. is the number of the chosen species per quadrat, such as daisy plants.
Control the quadrat size, the number of quadrats in each area, the counting rule, the time of year and the person or criteria used to identify the species.
Method: place quadrats at random
Lay two long tapes at right angles to form axes along two edges of each area. Use a random number generator to choose coordinates, and place the corner of a quadratA square frame of known area, placed on the ground to sample the organisms in an area. (for example 0.5 m × 0.5 m) at each coordinate.
random samplingPlacing quadrats at random positions, such as coordinates from a random number generator, to avoid bias. avoids choosing places that “look typical” or are easiest to reach, which would introduce bias. Take at least 10 quadrats per area, more if counts vary widely.
Count consistently
Decide in advance how to count individuals that overlap the quadrat edge, for example count those touching the top and left sides but not the bottom and right.
If individuals cannot be separated, such as grasses, record percentage coverThe percentage of the area of a quadrat that is covered by a particular species. instead of number and state that the measure changed.
Data handling and interpretation
Calculate the mean number per quadrat, divide by the quadrat area to get population densityThe number of individuals of a species per unit area, such as per m²., then multiply by the total area: estimated population = mean per quadrat × (total area ÷ quadrat area).
Illustrative example: a mean of 6.4 daisies per 0.25 m² quadrat in a 400 m² lawn gives 6.4 × (400 ÷ 0.25) = 10 240, an estimate of roughly 10 000 daisies. The range of counts shows how much confidence to place in the difference between two areas.
Safety and limitations
Check the site for hazards, such as water, steep ground, stinging plants, animal waste and traffic. Wear suitable clothing, wash hands after fieldwork and do not damage organisms or habitats.
Limitations include small sample size, clumped distributions, misidentification, trampling and the snapshot nature of one visit. The estimate is an estimate, not an exact count.
Planning the quadrat investigation
Name each variable explicitly.
| Variable type | In this investigation | Why it matters |
|---|---|---|
| Independent | Area sampled (for example lawn or field edge). | This is the factor being compared. |
| Dependent | Number of the chosen species per quadrat. | Used to calculate density and population size. |
| Control variables | Quadrat size, number of quadrats, counting rule, date. | Differences can then be attributed to the area. |
| Sampling method | Random coordinates from a number generator. | Removes selection bias. |
| Reliability check | Repeat quadrats and look at the range. | Shows variation between samples. |
Language that earns precision
- quadrat
- A square frame of known area used to sample organisms.
- random sampling
- Choosing sample positions so every position has an equal chance of being chosen.
- population density
- The number of individuals per unit area.
- percentage cover
- The proportion of a quadrat’s area covered by a species, used when individuals cannot be counted.
Common misconceptions
Claim: Throwing a quadrat over your shoulder is random.
Correction: Throwing is haphazard and can be biased or unsafe. Use coordinates from random numbers.
Claim: The estimate gives the exact population size.
Correction: It is an estimate from a sample; more quadrats generally give a more representative mean.
Claim: You only need one quadrat if it looks typical.
Correction: Choosing a “typical” spot is biased, and one sample shows nothing about variation.
Match the answer to the command word
Include random placement, quadrat size, number of quadrats, the counting rule and how the estimate is calculated.
Show mean per quadrat, then scale up by total area ÷ quadrat area. Keep units consistent.
Recall, apply, then justify
Describe how a student could use quadrats to compare the number of daisy plants on a mown lawn and an unmown field.
Hint
Random placement, same quadrat, repeats, counting, calculation.
Suggested marking points
- Use the same size quadrat in both areas.
- Place quadrats randomly, for example using random coordinates on tape-measure axes.
- Use the same number of quadrats (for example at least 10) in each area.
- Count the daisy plants in each quadrat using the same rule for plants on the edge.
- Calculate the mean per quadrat (or density) for each area and compare.
A field has an area of 2000 m². A student’s 1 m² quadrats contained a mean of 3.5 buttercups (illustrative data). Calculate the estimated buttercup population.
Hint
How many 1 m² quadrats would fit in the field?
Suggested marking points
- 2000 ÷ 1 = 2000 quadrat areas (or 3.5 × 2000 shown).
- 7000 buttercups.
Evaluate whether a student who used five quadrats in each area can conclude that the lawn has a larger daisy population than the field.
Planning hint
Sample size, range, overlap and bias.
What a strong design includes
- Five quadrats is a small sample, so the means may not represent each area.
- If the ranges of counts overlap widely, the difference may be due to chance.
- Daisies may be clumped, increasing variation between quadrats.
- Non-random placement would bias the result.
- More quadrats would give a more reliable mean.
- A statistical test could assess whether the difference is significant.
- The conclusion applies only to that date and those areas.