Population Sampling

Essential Question

How can scientists estimate a population without counting every organism?

How many oak trees are in a forest, or how many turtles live in a pond? Counting every one is almost never possible. In this lesson, you’ll learn how scientists use samples to estimate population size, and how to tell a good sampling plan from a poor one. By the end, you should be able to use quadrat counts and mark-recapture data to estimate how many individuals live in an area.

Why Scientists Sample

• Population size: the number of individuals of a species in an area
• A census counts every individual
• A sample counts only a small part
• Scientists use a sample to estimate the whole population

The population size is the number of individuals of one species living in an area. A census counts every individual, but that is rarely possible for a large area or for animals that hide and move. Instead, scientists take a sample, which means they count a small part of the area or a small number of individuals, and then use the sample to estimate the whole population. A good estimate is not exactly right, but it is close enough to show whether a population is large or small, and whether it is changing over time.

Quadrat Sampling

• A quadrat is a square frame of known area
• Count the organisms inside each quadrat
• Population density: individuals per unit of area
• Estimate = mean density × total area

Quadrat sampling works well for plants and for animals that move slowly or not at all, such as barnacles. A quadrat is a square frame with a known area, often 1 m × 1 m. Place several quadrats, count the organisms inside each one, and find the mean count. The mean count divided by the area of one quadrat is the population density, the number of individuals per unit of area, such as plants per m². Multiply the density by the area of the whole habitat to estimate the total population. The figure shows the steps with made-up numbers.

Mark and Recapture

• Used for animals that move around
• Capture some animals, mark them, and release them
• Later, capture a second sample
• The share of marked animals estimates the share of the population you marked

Animals that move around, such as turtles, fish, and beetles, are hard to count in a quadrat. In mark-recapture, scientists capture a number of animals (M), mark them in a way that does not harm them, and release them. After the marked animals have mixed back into the population, they capture a second sample (C) and count how many of them are marked (R). If R out of C animals in the second sample are marked, then the marked animals make up about the same share of the whole population. That gives the estimate N ≈ (M × C) ÷ R. The method assumes that marked animals mix evenly, that none are lost or added between samples, and that marks do not fall off or change an animal’s chance of being caught.

Sampling Well

• Place quadrats at random, not where organisms are easy to find
• A larger sample gives a more reliable estimate
• Repeat the same method to track change over time
• An estimate is not exact, so report it as an estimate

A sample is only useful if it represents the whole population. If quadrats are placed only where organisms are easy to find, such as beside a stream, the sample is biased and the estimate will be too high. Scientists reduce bias by choosing quadrat locations at random, for example with random numbers. A larger sample also helps, because a few unusual quadrats matter less when there are many. Using the same method each time lets scientists compare estimates from different years and tell whether a population is growing, shrinking, or staying about the same.

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Worked Examples

Try each problem on your own first, then open the solution to check your work.

Example 1: Dandelions in a Lawn

A student places ten 1 m² quadrats at random in a 2,500 m² lawn and counts the dandelions in each. The graph shows the counts (sample data). Find the mean number of dandelions per quadrat, the population density, and an estimate of the number of dandelions in the whole lawn.

Show the solution

1. Add the counts: 3 + 5 + 2 + 4 + 6 + 3 + 4 + 5 + 2 + 6 = 40 dandelions
2. Mean per quadrat: 40 dandelions ÷ 10 quadrats = 4.0 dandelions per quadrat
3. Density: 4.0 dandelions ÷ 1 m² = 4.0 dandelions per m²
4. Scale up: 4.0 dandelions/m² × 2,500 m² = 10,000 dandelions
5. Reasoning: this is an estimate, because only 10 m² of the 2,500 m² were counted. Random placement helps keep it from being biased.
6. Answer: 4.0 dandelions per quadrat and per m²; about 10,000 dandelions in the lawn.

Example 2: Turtles in a Pond

Researchers capture 60 turtles in a pond, mark each one, and release them. A week later they capture 45 turtles, and 9 of them are marked. Estimate the number of turtles in the pond. Then name one assumption your estimate depends on.

Show the solution

1. Identify the values: M = 60 marked, C = 45 caught the second time, R = 9 marked in the second sample
2. Share marked in the second sample: 9 ÷ 45 = 0.20, which is 20%
3. Use the share: the 60 marked turtles are about 20% of the population, so N ≈ 60 ÷ 0.20 = 300. This is the same as (60 × 45) ÷ 9 = 300.
4. Assumption: the marked turtles mixed evenly with the others, and no turtles were born, died, or left the pond between the two samples.
5. Answer: About 300 turtles.

Example 3: Does Sample Size Matter?

Students estimated the density of a plant on a lawn using different numbers of random quadrats. The graph shows their estimates (sample data). The estimate from 40 quadrats was 4.0 plants per m². Describe the pattern. By what percent was the 2-quadrat estimate higher than the 40-quadrat estimate? What does this show about sample size? Use data as evidence.

Show the solution

1. Pattern: as the number of quadrats increases from 2 to 40, the estimate falls from 7.0 to 4.0 plants per m², and the changes get smaller.
2. Calculate: (7.0 − 4.0) plants/m² ÷ 4.0 plants/m² × 100 = 75% higher
3. Claim: larger samples give more reliable estimates.
4. Evidence: the 2-quadrat estimate (7.0 plants/m²) was 75% higher than the 40-quadrat estimate (4.0 plants/m²). The 20-quadrat estimate (4.1) was within 0.1 of it.
5. Reasoning: with only a few quadrats, one unusually crowded or empty quadrat can change the mean a lot. With more quadrats, unusual ones are averaged out.
6. Answer: The 2-quadrat estimate was 75% higher. Larger samples give more reliable estimates.

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Practice

Tell a census from a sample, use quadrat counts and mark-recapture data to estimate population size, and judge whether a sampling plan is a good one. Try it on your own first, then check your work with the answer key.

• Population Sampling Practice Worksheet (PDF)
• Population Sampling Practice Answer Key (PDF)

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Lesson Slides

• 2.2 Population Sampling Slides (PDF)

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Big Ideas

• A census counts every individual; a sample counts a part
• Quadrat estimate: mean density × total area
• Mark-recapture estimate: N ≈ (M × C) ÷ R
• Random placement reduces bias
• Larger samples give more reliable estimates

Back to the essential question: scientists estimate a population by counting a sample and scaling it up to the whole area. For plants and slow-moving animals, they use quadrats and multiply the mean density by the area. For animals that move, they use mark-recapture and the share of marked animals in a second sample. Random placement and a large enough sample make the estimate more reliable. Next, you’ll use population sizes to see how populations grow over time.

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