B45: Investigating Populations
Sampling techniques and estimating population size
Key Definitions
Quadrat: A square frame (usually 0.5 m × 0.5 m or 1 m × 1 m) placed on the ground to define a sample area. Organisms within the quadrat are counted or their percentage cover is estimated.
Transect: A line (rope or tape measure) placed across a habitat along which samples are taken at regular intervals. Used for systematic sampling to study how the distribution of organisms changes across an environmental gradient.
Capture-mark-recapture: A method for estimating the population size of mobile animals. Organisms are captured, marked, released, then recaptured. The proportion of marked organisms in the second catch is used to estimate total population.
Random sampling: Selecting sample locations using a random method (e.g. random number coordinates) to avoid bias and ensure every part of the area has an equal chance of being sampled.
Systematic sampling: Taking samples at regular intervals along a line or grid. Used to study patterns of change across an environmental gradient (e.g. from a field edge into a wood).
Quadrats and Random Sampling
Quadrats are used to estimate the population of slow-moving or sessile (non-moving) organisms such as plants, limpets and barnacles.
How to Use Quadrats for Random Sampling
- Lay out two tape measures at right angles along two edges of the study area to create a grid
- Use a random number generator (or random number table) to generate pairs of coordinates
- Place the quadrat at each coordinate pair
- Count the number of organisms of the target species in each quadrat (or estimate percentage cover for plants that are hard to count individually)
- Repeat for a large number of quadrats (at least 10) to get reliable data
- Calculate the mean number per quadrat
- Estimate the total population using the formula below
Estimated total population = Mean number per quadrat × (Total area of habitat ÷ Area of one quadrat)
Worked Example 1: Estimating Daisy Population
A student uses a 1 m × 1 m quadrat to estimate the population of daisies in a field measuring 50 m × 80 m. They place 10 quadrats randomly and count the following numbers of daisies: 5, 3, 7, 4, 6, 2, 5, 8, 4, 6.
Step 1: Calculate the mean number per quadrat:
Mean = (5 + 3 + 7 + 4 + 6 + 2 + 5 + 8 + 4 + 6) ÷ 10 = 50 ÷ 10 = 5.0 daisies per m²
Step 2: Calculate the total area of the habitat:
Total area = 50 × 80 = 4,000 m²
Step 3: Estimate the total population:
Total population = 5.0 × 4,000 = 20,000 daisies
Worked Example 2: Using a 0.5 m × 0.5 m Quadrat
A biologist uses a 0.5 m × 0.5 m quadrat to estimate buttercup numbers in a meadow of 10,000 m². In 20 randomly placed quadrats, the total count is 60 buttercups.
Step 1: Calculate the mean per quadrat:
Mean = 60 ÷ 20 = 3.0 buttercups per quadrat
Step 2: Calculate the area of one quadrat:
Area of quadrat = 0.5 × 0.5 = 0.25 m²
Step 3: Calculate the mean per m²:
Mean per m² = 3.0 ÷ 0.25 = 12.0 buttercups per m²
Step 4: Estimate the total population:
Total population = 12.0 × 10,000 = 120,000 buttercups
Transects and Systematic Sampling
Transects are used to study how the distribution of organisms changes across a habitat, for example from a shaded woodland edge into an open field.
How to Use a Belt Transect
- Lay a tape measure (the transect line) from one point to another across the habitat (e.g. from a hedge into a field)
- Place quadrats at regular intervals along the line (e.g. every 2 m or every 5 m)
- Record the species present and their abundance (count or percentage cover) in each quadrat
- Plot the results as a kite diagram or line graph to show how distribution changes with distance
Random vs Systematic Sampling: Use random sampling (quadrats at random coordinates) when you want an unbiased estimate of the total population in a uniform habitat. Use systematic sampling (transects at regular intervals) when you want to study how species distribution changes across an environmental gradient, such as from a pond edge into dry ground or from light to shade.
Example 3: Transect from a Shaded Woodland into Open Grassland
A student lays a 30 m transect line from deep inside a wood into an open field. A 1 m × 1 m quadrat is placed every 5 m and the percentage cover of grass is recorded:
| Distance from wood (m) | 0 | 5 | 10 | 15 | 20 | 25 | 30 |
|---|---|---|---|---|---|---|---|
| Grass cover (%) | 5 | 12 | 30 | 55 | 75 | 85 | 90 |
The results show that grass cover increases with distance from the woodland. This is because light intensity increases away from the tree canopy, allowing grass (which needs full sunlight for photosynthesis) to outcompete shade-tolerant woodland plants.
Capture-Mark-Recapture Method
For mobile animals (e.g. woodlice, snails, beetles), quadrats cannot be used because the animals move. Instead, the capture-mark-recapture method estimates population size:
- Capture a sample of the animals and count them (1st catch = n₁)
- Mark each animal in a harmless way (e.g. small dot of non-toxic paint) and release them
- Wait sufficient time for the marked animals to mix back into the population
- Capture a second sample (2nd catch = n₂) and count how many are already marked (m₂)
- Use the formula to estimate total population
Estimated population size = (n₁ × n₂) ÷ m₂
Where: n₁ = number caught in 1st sample, n₂ = number caught in 2nd sample, m₂ = number of marked organisms recaptured in 2nd sample
Assumptions of capture-mark-recapture: (1) Marked animals mix fully back into the population; (2) The marking does not affect survival (e.g. does not make animals more visible to predators); (3) The marking does not rub off; (4) The population is closed – no animals die, are born, immigrate or emigrate between the two sampling events; (5) Each animal has an equal chance of being captured in both samples.
Worked Example 4: Estimating Woodlouse Population
A student captures 40 woodlice in a first sample, marks each with a small dot of non-toxic paint, and releases them. The next day, they capture 50 woodlice in a second sample. Of these, 10 are already marked.
Solution:
n₁ = 40, n₂ = 50, m₂ = 10
Population = (40 × 50) ÷ 10 = 2,000 ÷ 10 = 200 woodlice
Worked Example 5: Estimating Snail Population
In a garden, 25 snails are captured, marked and released. Two days later, 30 snails are captured, of which 6 are marked.
Solution:
n₁ = 25, n₂ = 30, m₂ = 6
Population = (25 × 30) ÷ 6 = 750 ÷ 6 = 125 snails
Required Practical: Using Quadrats and Transects
This is a required practical for GCSE Biology. You need to be able to:
- Use a quadrat to sample the distribution of organisms in a habitat
- Use random sampling to estimate population size
- Use a transect to investigate how distribution changes across an environmental gradient
- Calculate mean, median, mode and range from your data
- Consider sources of error and how to improve reliability
Improving Reliability and Validity
- Larger sample size – more quadrats gives a more representative mean and reduces the effect of anomalies
- Random placement – avoids bias (e.g. placing quadrats only where you can see the target organism)
- Repeat the investigation – doing it multiple times and calculating a mean of means improves reliability
- Standardised method – same person counting, same quadrat size, same time of day
Statistical Analysis: Mean, Median, Mode and Range
When analysing quadrat data, you need to calculate:
| Measure | Definition | How to Calculate | Example Data: 3, 5, 5, 7, 12, 4, 6 |
|---|---|---|---|
| Mean | The average – sum of values divided by number of values | Add all values, divide by count | (3+5+5+7+12+4+6) ÷ 7 = 42 ÷ 7 = 6.0 |
| Median | The middle value when data is ordered | Order values, find the middle one | Ordered: 3, 4, 5, 5, 6, 7, 12 → middle = 5 |
| Mode | The most common value | Find the value that appears most often | 5 (appears twice) |
| Range | The spread of data | Largest value minus smallest value | 12 − 3 = 9 |
Worked Example 6: Statistical Analysis of Quadrat Data
A student counts dandelions in eight 1 m² quadrats: 4, 8, 6, 3, 7, 5, 9, 2.
Mean = (4 + 8 + 6 + 3 + 7 + 5 + 9 + 2) ÷ 8 = 44 ÷ 8 = 5.5
Median – ordered data: 2, 3, 4, 5, 6, 7, 8, 9 → two middle values are 5 and 6, so median = (5 + 6) ÷ 2 = 5.5
Mode – all values appear once, so there is no mode
Range = 9 − 2 = 7
Comparison: Quadrats vs Transects vs Capture-Mark-Recapture
| Feature | Quadrats (Random) | Transects (Systematic) | Capture-Mark-Recapture |
|---|---|---|---|
| Used for | Plants and slow-moving organisms | Studying distribution changes across gradients | Mobile animals |
| Sampling type | Random | Systematic (regular intervals) | Capture-based |
| What it measures | Population density or percentage cover | Distribution along a gradient | Total population size |
| Key calculation | Mean × (total area ÷ quadrat area) | Graph distribution against distance | (n₁ × n₂) ÷ m₂ |
| Advantages | Simple, quick, unbiased if random | Shows patterns of change | Works for moving animals |
| Limitations | Only works for stationary or slow organisms | Does not estimate total population | Assumes closed population, marks must not affect survival |
Practice Questions
Q1: Foundation A student uses a 1 m × 1 m quadrat to estimate the population of clover plants in a field measuring 100 m × 60 m. They count clover in 10 randomly placed quadrats and record: 12, 8, 15, 10, 7, 14, 9, 11, 13, 6. Calculate the mean number per quadrat and estimate the total population of clover in the field.
Q2: Higher A biologist uses a 0.5 m × 0.5 m quadrat to estimate the population of sea anemones on a rocky shore of area 500 m². In 15 quadrats, a total of 45 anemones are counted. Calculate the estimated total population.
Q3: Foundation Describe how to use random sampling with quadrats to estimate the population of a plant species in a meadow. Explain why random placement is important.
Q4: Higher In a capture-mark-recapture study of beetles, 60 beetles are captured and marked on day 1. On day 2, 80 beetles are captured, of which 16 are marked. Calculate the estimated population. State two assumptions of this method and explain how each could affect the result if it were not true.
Q5: Foundation A student records the number of daisies per quadrat along a transect from a shaded area under a tree to an open sunny field. The results are: 2, 3, 5, 8, 14, 20, 25. Calculate the mean, median, mode and range of this data.
Q6: Higher Explain the difference between random and systematic sampling. Give an example of when each method would be the most appropriate choice.
Answers
- Mean = (12 + 8 + 15 + 10 + 7 + 14 + 9 + 11 + 13 + 6) ÷ 10 = 105 ÷ 10 = 10.5 clover plants per m²
Total area of field = 100 × 60 = 6,000 m²
Area of one quadrat = 1 × 1 = 1 m²
Estimated total population = 10.5 × (6,000 ÷ 1) = 63,000 clover plants - Mean per quadrat = 45 ÷ 15 = 3.0 anemones per quadrat
Area of one quadrat = 0.5 × 0.5 = 0.25 m²
Mean per m² = 3.0 ÷ 0.25 = 12.0 anemones per m²
Estimated total population = 12.0 × 500 = 6,000 anemones - Method: (1) Lay two tape measures at right angles along the edges of the meadow to create a coordinate grid. (2) Use a random number generator to produce pairs of coordinates. (3) Place a quadrat at each random coordinate. (4) Count the number of the target plant species in each quadrat. (5) Repeat for at least 10 quadrats. (6) Calculate the mean number per quadrat. (7) Multiply the mean by the total number of quadrats that would fit in the meadow (total area ÷ quadrat area). Random placement is important because it avoids bias – if the sampler chose where to place quadrats, they might consciously or unconsciously place them where the plant is common (or avoid difficult areas), giving an unrepresentative result. Random sampling ensures every part of the meadow has an equal chance of being selected, so the estimate is more reliable and valid.
- Estimated population = (n₁ × n₂) ÷ m₂ = (60 × 80) ÷ 16 = 4,800 ÷ 16 = 300 beetles. Two assumptions: (1) The population is closed – no beetles enter or leave, are born or die between the two sampling events. If new beetles immigrated, the population would be larger than estimated because the proportion of marked beetles in the second sample would be lower (fewer recaptures relative to the total). (2) The marking does not affect survival – if the paint made marked beetles more visible to predators, fewer marked beetles would survive to the second sample. This would reduce m₂, making the estimated population appear larger than it actually is.
- Data: 2, 3, 5, 8, 14, 20, 25 (already in order)
Mean = (2 + 3 + 5 + 8 + 14 + 20 + 25) ÷ 7 = 77 ÷ 7 = 11.0
Median = the 4th value (middle of 7) = 8
Mode = no value repeats, so no mode
Range = 25 − 2 = 23
The increasing numbers along the transect suggest daisy abundance increases from shade to sun, as daisies need light for photosynthesis. - Random sampling uses chance (e.g. random number coordinates) to select sample locations, ensuring every part of the area has an equal probability of being sampled. It is most appropriate when you want to estimate the total population of a species across a relatively uniform habitat. For example, estimating the number of dandelions across a school field using randomly placed quadrats. Systematic sampling takes samples at regular intervals along a line or grid, following a defined path (transect). It is most appropriate when you want to study how species distribution changes across an environmental gradient. For example, placing quadrats every 2 m along a transect from a pond edge into dry ground to investigate how plant species change with distance from water. Random sampling gives an unbiased population estimate; systematic sampling reveals patterns of distribution that random sampling might miss.
Exam Tips
- In population estimation calculations, always show your working – marks are awarded for correct method even if arithmetic is wrong
- When a quadrat is not 1 m × 1 m, you must calculate its area first and convert to per m² before multiplying by total habitat area
- For capture-mark-recapture, remember the formula: (n₁ × n₂) ÷ m₂ – the second number in the numerator is the total of the second catch, not just the unmarked ones
- When asked to describe a method, always mention random placement (for quadrats) and repeating (for reliability)
- Know the assumptions of capture-mark-recapture: closed population, marking doesn't affect survival, marks don't rub off, complete mixing. Examiners often ask how violating an assumption would affect the result
- When calculating median with an even number of data points, remember to find the mean of the two middle values
- This is a required practical – make sure you can describe the full method including equipment, variables to control and how to make results reliable
🔬 Required Practical
Field Investigations Using Quadrats and Transects
Investigate the distribution of a plant species using quadrats and transects.
Method (random sampling): 1) Lay two tape measures at right angles to create a coordinate grid. 2) Use random numbers to generate coordinates. 3) Place a quadrat at each coordinate. 4) Count the target species or estimate percentage cover. 5) Repeat for at least 10 quadrats. 6) Calculate the mean per quadrat and estimate total population.
Method (transect): 1) Lay a tape measure across the habitat (e.g. from shade into light). 2) Place quadrats at regular intervals along the line. 3) Record species abundance in each quadrat. 4) Plot distribution against distance to identify patterns.
Variables: Independent = distance along transect (systematic) or sampling location (random); Dependent = number or percentage cover of species; Control = quadrat size, time of day, counting method.
Improving reliability: Use more quadrats, repeat the investigation, use random coordinates to avoid bias, standardise the counting method.
🔢 Maths Skills
Mathematical Skills
Estimating population size: mean per quadrat × (total area ÷ quadrat area). For a 1m² quadrat with mean of 5 daisies in a 4,000m² field: 5 × 4,000 = 20,000 daisies.
Capture-mark-recapture: population = (n&sub1; × n&sub2;) ÷ m&sub2;. For example, 40 captured and marked, then 50 recaptured with 10 marked: (40 × 50) ÷ 10 = 200.
Statistical measures: mean = sum ÷ count; median = middle value; mode = most common; range = highest − lowest.
⚠️ Common Misconceptions
Watch Out!
Students often think one quadrat is enough for a reliable estimate. Wrong: One quadrat gives a reliable result Correct: Multiple quadrats (at least 10) are needed for a reliable mean — one sample may be in an unusually rich or poor area
Students often think random sampling means just picking spots yourself. Wrong: Random sampling means picking wherever you want Correct: True random sampling uses a random number generator for coordinates — picking spots yourself introduces bias (e.g. choosing areas where you can see the plant)
✍️ 6-Mark Question
Extended Answer
6 marks: Describe how to investigate the distribution of a plant species using quadrats and transects.
To investigate distribution using random sampling with quadrats: lay two tape measures at right angles along the edges of the study area; use a random number generator to produce pairs of coordinates; place a 1m² quadrat at each coordinate; count the number of the target species (or estimate percentage cover); repeat for at least 10 quadrats; calculate the mean per quadrat. For a transect investigation: lay a tape measure across the habitat from one environment to another (e.g. from shade into open ground); place quadrats at regular intervals (e.g. every 2m) along the transect line; record the abundance of the target species in each quadrat; plot the results as a graph of abundance against distance. The transect method shows how distribution changes across an environmental gradient, while random sampling gives an unbiased estimate of the total population. Using both methods together gives a more complete picture.
Mark scheme: Up to 3 marks for describing quadrat method with key details, up to 3 marks for describing transect method with key details
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
A student uses ten 0.5m × 0.5m quadrats in a 2,000m² field and counts buttercups: 3, 7, 2, 5, 4, 8, 1, 6, 3, 5. Calculate the mean, median, mode and range. Estimate the total population. Evaluate the reliability of this estimate — what could the student do to improve it? If the student had placed quadrats only near the edge of the field, how would this affect the result?
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