B. Diversity of Living Things · Diversity of Living ThingsSampling a Local Ecosystem: Methods, Ethics and the Simpson's Index
B2.3 A1.2 A1.4 A1.5 A1.6 A1.13About 75 minutes
Learning goals- I can choose an appropriate sampling technique for a pond, marsh, field or forest floor and explain why.
- I can estimate population density and population size from quadrat and mark-recapture data.
- I can calculate and interpret Simpson's diversity index.
- I can plan fieldwork that is safe and ethical, and classify the organisms I collect using taxonomic principles.
Words to know
sample
A small part of a population or community that is studied in order to draw conclusions about the whole.
random sampling
Choosing sample locations by chance (e.g. random numbers) so that every spot has an equal chance of being picked, avoiding bias.
quadrat
A square frame of known area used to count organisms or estimate percent cover.
transect
A line across a habitat along which samples are taken at regular intervals, to show how a community changes across an environmental gradient.
pitfall trap
A container sunk into the ground so that walking invertebrates fall in and can be counted and released.
mark-recapture
A method for estimating population size: capture and mark some animals, release them, then recapture a second sample and count how many are marked.
population density
The number of individuals per unit area (or volume), e.g. 16 plants per m².
Simpson's diversity index (D)
A number from 0 to 1 that combines richness and evenness: the probability that two individuals picked at random belong to different species.
You can't count everything
How many beetles live in a hectare of Ontario meadow? How many crayfish in a pond? Counting every one is impossible, so ecologists sample: they study small, carefully chosen parts and use them to estimate the whole. The curriculum expects you to use proper sampling techniques in a marsh, pond, field or other ecosystem, and to classify what you find.
In Grade 9 you used a quadrat to compare richness and evenness. Now you will choose among several methods, collect data that are fair, calculate estimates, and use a diversity index.
Choosing a method
- Quadrats for plants and slow or non-moving organisms (wildflowers, mosses, barnacles). Count individuals, or estimate percent cover. Typical sizes: 0.25 m² (50 cm × 50 cm) for small plants, larger for shrubs.
- Transects to see change across a gradient, such as forest → meadow → pond, or a lakeshore into deep water. A line transect records what touches the line at regular intervals; a belt transect places quadrats along the line.
- Pitfall traps for ground-walking invertebrates (beetles, spiders).
- Sweep nets swung through tall grass for insects and spiders.
- Dip nets and kick nets in ponds and streams for aquatic invertebrates. Mayfly, stonefly and caddisfly larvae are sensitive to pollution, so finding them suggests good water quality.
- Berlese funnel to extract tiny soil animals: a lamp gently warms and dries the soil from above, and the animals move down into a collecting jar.
- Mark-recapture for mobile animals (fish, crayfish, small mammals, butterflies).
Fair sampling: choose spots randomly (e.g. with random numbers on a grid) or systematically (every 5 m along a transect). Choosing "interesting-looking" spots introduces bias. Take several samples, since one sample can be unusual.
Worked exampleLet's estimate density and population size from quadrats
A student places five 0.25 m² quadrats randomly in a 400 m² lawn and counts dandelions: 3, 5, 2, 4, 6. Estimate the density per m² and the total number in the lawn.
- Mean per quadrat: (3 + 5 + 2 + 4 + 6) ÷ 5 = 20 ÷ 5 = 4 dandelions per 0.25 m².
- Density: 4 ÷ 0.25 m² = 16 dandelions/m².
- Population estimate: 16 /m² × 400 m² = 6400 dandelions.
- Precision: the counts vary from 2 to 6 per quadrat, so report "about 6000" or "6.4 × 10³" rather than implying an exact count. More quadrats would make the estimate more reliable.
About 16 dandelions per m², or roughly 6400 (about 6000) in the whole lawn.
Mark-recapture
To estimate the size of a mobile population:
- Capture a sample, mark each animal harmlessly (a dab of non-toxic paint on a crayfish shell, a tiny fin clip), count them (M), and release them.
- Wait for them to mix back into the population.
- Capture a second sample (C) and count how many are already marked (R).
If the marked animals are now evenly mixed, the fraction marked in the second sample equals the fraction marked in the whole population: R ÷ C = M ÷ N, so
N = (M × C) ÷ R (the Lincoln-Petersen estimate)
Assumptions: marks don't fall off or harm the animals; marked animals mix randomly; no animals are born, die, arrive or leave between samples.
Worked exampleLet's estimate a fish population by mark-recapture
Biologists catch and fin-clip 40 pumpkinseed sunfish in a small pond, then release them. A week later they catch 50 sunfish, of which 8 have clipped fins. Estimate the population.
- M = 40 (marked first), C = 50 (second catch), R = 8 (recaptured marked).
- N = (M × C) ÷ R = (40 × 50) ÷ 8 = 2000 ÷ 8 = 250.
- Check the logic: 8 of 50 = 16% of the second catch were marked, so the 40 marked fish should be about 16% of the population: 40 ÷ 0.16 = 250 ✓.
About 250 pumpkinseed sunfish.
🐠🐠🐠🐠🐠🐠🐠🐠🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟
The second catch: 50 sunfish, of which 8 (🐠) carry a fin clip and 42 (🐟) do not. Because 8 out of 50 are marked, the 40 marked fish make up about 8/50 of the whole pond's population.Measuring diversity: Simpson's diversity index
Richness and evenness can be combined into one number. Simpson's diversity index is
D = 1 − Σ n(n − 1) ÷ [N(N − 1)]
where n is the number of individuals of each species and N is the total number of individuals. (Σ means "add up for every species.")
- D ranges from 0 (only one species: no diversity) toward 1 (many species, evenly spread).
- D is the probability that two individuals picked at random are different species.
Worked exampleLet's calculate Simpson's index for two sites
Two quadrats each contain 20 plants of 4 species.
- Site A: 10, 6, 3, 1
- Site B: 17, 1, 1, 1
Calculate D for each and compare.
- N = 20 at both sites, so N(N − 1) = 20 × 19 = 380.
- Site A: n(n − 1) for each species: 10 × 9 = 90; 6 × 5 = 30; 3 × 2 = 6; 1 × 0 = 0. Sum = 126. D = 1 − 126 ÷ 380 = 1 − 0.332 = 0.67.
- Site B: 17 × 16 = 272; the three single plants give 0 each. Sum = 272. D = 1 − 272 ÷ 380 = 1 − 0.716 = 0.28.
- Both sites have the same richness (4), but Site A is much more even, so its D is higher.
- Report D to two decimal places; more digits would claim more precision than one quadrat supports.
Site A: D = 0.67 (two random plants are different species 67% of the time). Site B: D = 0.28. Site A is more diverse.
Classifying what you collect
Once organisms are collected, sort them using taxonomic principles: look for the diagnostic features from this unit (legs, body regions, shells, segments, leaf arrangement, spores) and use a dichotomous key or field guide to reach the lowest rank you can confidently identify. It is fine to stop at phylum, class or order ("beetle larva, order Coleoptera") rather than guess a species. Record uncertain identifications honestly.
Ethics and safety in the field (A1.4):
- Get permission for private land; follow park rules (collecting is often not allowed).
- Minimize harm: handle animals gently, keep them cool and wet, and return them where they were found; replace logs and stones.
- Never collect species at risk.
- Near water: never work alone, stay out of deep or fast water, and wear a life jacket where needed.
- Wear long pants and closed shoes, plus a hat and sunscreen on sunny days; check for ticks; avoid poison ivy, and never touch wild parsnip or giant hogweed, whose sap can cause severe burns on skin exposed to sunlight.
- Wash your hands after fieldwork.
Just for funWhy did the ecologist bring a hula hoop to the meadow?
She needed a quadrat, and circles work too. (It's true: ecologists sometimes use circular sample plots. A hoop with a 56 cm radius covers about 1 m².)
Hands-on activityMark-recapture simulation with dried beans
You need: a large bowl, at least 2 cups of dry white beans (or macaroni), a permanent marker (or about 40 dark beans to swap in), a measuring cup, a notebook and a calculator.
The beans in the bowl are a population of "fish" in a lake whose size you don't know.
- Scoop out a sample of about 40 beans. Count them exactly (M). Mark each one with the marker (or replace each with a dark bean). Return them to the bowl.
- Mix thoroughly, which models the fish swimming around.
- Without looking, scoop a second sample (C). Count the total and the number marked (R).
- Estimate N = (M × C) ÷ R. Return the beans and mix.
- Repeat steps 3 and 4 four more times. Record all trials in a table and calculate the mean estimate.
- Finally, count every bean (the "true" population). Calculate the percent error of your mean: |estimate − actual| ÷ actual × 100%.
- Repeat one trial without mixing in step 2. What happens?
What to look for: individual trials vary, but the mean of five trials is usually within about 10 to 20% of the true count. Without mixing, the marked beans stay together on top, so R is too high or too low and the estimate is badly off, showing why the "random mixing" assumption matters. Keep beans away from small children.
Your turn
1Which sampling method would you use for (a) wildflowers in a meadow, (b) beetles on a forest floor, (c) crayfish in a stream, (d) plant changes from a beach into a dune?
(a) quadrats; (b) pitfall traps; (c) mark-recapture (or kick nets for presence); (d) a transect (line or belt).
2Why should quadrat locations be chosen randomly?
To avoid bias: people tend to pick spots that look interesting, which would over- or under-estimate populations.
3Six 1 m² quadrats contain 2, 0, 3, 1, 2, 4 trilliums. Estimate the density.
Mean = (2 + 0 + 3 + 1 + 2 + 4) ÷ 6 = 12 ÷ 6 = 2 trilliums/m².
4In a mark-recapture study, 30 painted turtles are marked. Later, 24 are caught and 6 are marked. Estimate the population.
N = (30 × 24) ÷ 6 = 720 ÷ 6 = 120 turtles.
5A sample has 5 individuals of one species only. What is Simpson's D?
Σ n(n − 1) = 5 × 4 = 20; N(N − 1) = 20; D = 1 − 20/20 = 0 (no diversity).
6Give two ways to make fieldwork more ethical.
Any two: return organisms where found; handle gently and keep them moist and cool; replace logs and stones; get permission; never collect species at risk; take only what you need.
7State one assumption of mark-recapture.
Any one: marks don't harm animals or fall off; marked animals mix randomly; no births, deaths, immigration or emigration between samples; marked animals are as likely to be caught as unmarked ones.
More practice: warm-up
A square frame of known area used for sampling.
2What does a transect show?
How a community changes along a gradient (a line across a habitat).
3What range of values can Simpson's D take?
From 0 (one species) up toward 1 (high diversity).
4What is a pitfall trap used for?
Catching ground-walking invertebrates to count and release.
5Name one invasive Ontario plant whose sap can burn your skin in sunlight.
Wild parsnip or giant hogweed.
More practice: on your own
1Calculate D for a quadrat with 4 species: 5, 5, 5, 5 individuals.
N = 20; N(N − 1) = 380. Σ n(n − 1) = 4 × (5 × 4) = 80. D = 1 − 80/380 = 1 − 0.211 = 0.79.
2Compare your answer above with Site A (D = 0.67) and Site B (D = 0.28). What does this show about evenness?
All have 4 species and 20 plants, but the perfectly even quadrat has the highest D (0.79), Site A next and the dominated Site B the lowest: greater evenness gives a higher D when richness is equal.
3A student marks 25 butterflies with a dot of paint on their wings, but the paint makes them easier for birds to see. How will this affect the population estimate?
Marked butterflies are eaten more, so fewer marked ones are recaptured (R too small). Since N = MC/R, a smaller R makes the estimate too high.
4Why is it better to identify an unknown larva to order (e.g. caddisfly, Trichoptera) than to guess its species?
An identification at a higher rank that is certain is more useful and honest than a species guess that may be wrong, which would make the data unreliable.
5A lawn study uses only one quadrat, placed where the student saw many dandelions. Name two problems and suggest fixes.
Bias (non-random placement) and too small a sample (one quadrat). Fix: place several quadrats using random coordinates and average the counts.
Challenge
1A pond survey with a dip net finds: mayfly larvae 12, caddisfly larvae 8, midge larvae 20. Calculate Simpson's D and comment on water quality.
N = 40; N(N − 1) = 1560. Σ n(n − 1) = 132 + 56 + 380 = 568. D = 1 − 568/1560 = 1 − 0.364 = 0.64. Mayflies and caddisflies are pollution-sensitive, and they make up half the sample, which suggests fairly good water quality.
2In a mark-recapture study of crayfish, M = 60, C = 45, R = 9. A week later, a second study gives M = 60, C = 40, R = 12. Calculate both estimates and suggest two reasons they differ.
Study 1: 60 × 45 ÷ 9 = 300. Study 2: 60 × 40 ÷ 12 = 200. Reasons: random sampling variation; crayfish dying, hatching or moving between studies; marks lost; marked crayfish behaving differently (e.g. trap-shy or trap-happy).
3Design a sampling plan to compare invertebrate diversity in a mowed park lawn and an unmowed meadow. Include the method, how sites are chosen, the data recorded, the calculation, and two safety or ethics points.
Sample plan: pitfall traps (5 in each habitat), placed at random grid coordinates at least 5 m apart, open for 24 h with covers; record each animal identified to order with a key; release all. Calculate Simpson's D and richness for each habitat; compare means. Safety/ethics: get permission from the city; check traps daily and release animals; check for ticks, avoid poison ivy and wild parsnip; fill in holes afterwards.
Quiz
1. Which method is best for studying how plant communities change from a forest into a marsh?
2. Four 0.25 m² quadrats contain 3, 1, 2, 2 plants. The density is:
3. In mark-recapture, M = 50, C = 40, R = 10. N is about:
4. A sample has species counts 2 and 2. What is Simpson's D?
5. Why are sample sites chosen randomly?
6. Which is an ethical field practice?
Big idea (B2.3): students learn to choose and use proper sampling methods (quadrats, transects, pitfall traps, nets, mark-recapture), estimate density and population size, calculate Simpson's diversity index, and work safely and ethically outdoors (A1.2, A1.4, A1.5, A1.6, A1.13).
How to help: The bean simulation needs only a kitchen bowl. If you can, do a real quadrat or pitfall survey together in a backyard or park (with permission); a pitfall trap can be a yogurt cup sunk in the soil overnight with a cover.
Common difficulties:
- Forgetting to convert quadrat area (count per 0.25 m² is not per m²).
- Simpson's index arithmetic: use n(n − 1), not n², and remember 1 × 0 = 0.
- Mixing up M, C and R in mark-recapture.
Safety: never sample near deep or fast water without an adult; check for ticks; learn to recognize poison ivy, wild parsnip and giant hogweed.
Sources: sampling methods and the Lincoln-Petersen estimate from standard ecology texts; Simpson (1949); wild parsnip and giant hogweed warnings from the Ontario Invasive Plant Council.