Estimating population size — Grade 12 Life Sciences

Why ecologists sample

A population is a group of individuals of the same species living in the same area at the same time. Counting every individual (a census) is usually impossible, so ecologists count a sample and use it to estimate the whole population.

A sample must be random (to avoid bias) and large enough (to be representative). Repeating the sampling and averaging improves reliability.

Quadrats and transects

A quadrat is a square frame of known area placed at random. It suits plants and slow-moving animals.

📖 Population from quadrats

population ≈ (mean number per quadrat ÷ area of one quadrat) × total area

✏️ Worked example

1Ten 1 m² quadrats contain 4, 6, 3, 5, 2, 7, 4, 5, 6, 8 daisies: total 50, mean 5 per m².

2The field is 400 m², so population ≈ 5 × 400 = 2 000 daisies.

A transect is a line along which samples are taken at regular intervals. It shows how a population changes along a gradient, for example from a river bank to dry ground.

Capture–mark–recapture

For mobile animals, ecologists capture a sample, mark the animals harmlessly, release them, and later capture a second sample.

📖 Lincoln–Petersen index

N ≈ (M × C) ÷ R

M = number marked in the first sample; C = total caught in the second sample; R = number of marked animals recaptured.

✏️ Worked example

160 tortoises are marked and released. Two weeks later, 50 are caught, of which 12 are marked.

2N ≈ 60 × 50 ÷ 12 = 250 tortoises.

Assumptions: marked animals mix randomly with the population; marks are not lost and do not affect survival or behaviour; there are no births, deaths, immigration or emigration between samples; every animal has an equal chance of being caught.

Judging accuracy

Problem	Effect on estimate
Marked animals are easier to recapture (trap-happy)	R too large → N underestimated
Marked animals avoid traps (trap-shy) or marks wear off	R too small → N overestimated
Births or immigration between samples	More unmarked animals → N overestimated for the original population
Small sample sizes	Large random error; estimate unreliable

Counting large animals such as lions

Large carnivores live at low density and are hard to see, so several methods are used and compared:

Camera traps — individuals are identified from whisker-spot patterns or scars; the photographs act as “marks” in a capture–recapture model.
Call-up surveys — recorded sounds of prey draw lions to a point where they are counted; the result depends on how many lions respond.
Spoor (track) counts — tracks counted along roads are converted to density using a calibration; accuracy depends on soil type and the skill of the tracker.
Aerial counts — suit large herbivores on open plains; poor for animals in dense bush.

Essay tip: when evaluating whether a method gives an accurate estimate, discuss its assumptions, sources of bias, sample size, repetition, and whether results from different methods agree.

Answer in your exercise book, then open each memo to mark your work.

Question 1 · (4 marks)

Eight 0,5 m² quadrats contained 3, 5, 4, 6, 2, 4, 5 and 3 plants of a species. The field is 600 m². Estimate the population. Show working.

Show memo

Total = 32 ✓; mean = 32 ÷ 8 = 4 plants per quadrat ✓.
Density = 4 ÷ 0,5 = 8 plants per m² ✓.
Population ≈ 8 × 600 = 4 800 plants ✓.

Question 2 · (3 marks)

Ecologists mark 80 fish in a dam. Later they catch 75 fish, of which 15 are marked. Estimate the fish population.

Show memo

N = (M × C) ÷ R ✓ = (80 × 75) ÷ 15 ✓ = 400 fish ✓.

Question 3 · (4 marks)

State TWO assumptions of the capture–mark–recapture method and, for each, explain how breaking it would affect the estimate.

Show memo

Any TWO (2 marks each, assumption ✓ + effect ✓):
• Marks are not lost — if marks wear off, R is too small and N is overestimated.
• Marked animals mix randomly — if they stay together near the release point, R may be too large and N underestimated.
• No births, deaths or migration — new unmarked animals make N an overestimate.
• Marking does not affect survival or behaviour — if marked animals are caught more easily, N is underestimated.

Question 4 · (6 marks)

A reserve estimates its lion population using camera traps and a call-up survey. The camera traps give 48 lions; the call-up survey gives 31. Discuss which estimate is likely to be more accurate and why the results differ.

Show memo

Camera traps are likely more accurate ✓: individuals are identified from natural markings, so animals are not double-counted ✓, and the method works day and night over a long period ✓.
Call-up surveys depend on how many lions hear and respond ✓; shy lions or lions far away do not come, so the count is too low ✓.
Using more than one method and repeating surveys improves confidence in the estimate ✓.