Estimate abundance with sampling assumptions and uncertainty

Mechanism before a label

Population size counts individuals within a defined boundary; density divides abundance by area or volume. A census attempts complete coverage, while sampling estimates a total from a subset. Spatially clumped populations can make a few convenient samples misleading.

For a simple mark-recapture model, the marked fraction of a later sample approximates the marked fraction of the population: R/C≈M/N, giving N≈MC/R. This assumes closure, retained recognizable marks, mixing and sufficiently comparable capture probabilities.

Marking must not change survival or detection, and R=0 makes this simple ratio undefined rather than an infinite verified population. These lessons use fictional records only. Actual organism capture requires permissions, humane methods and qualified supervision; it is not assigned here.

Predict, compare and calculate

The following record is an original synthetic teaching dataset. Its assigned conditions are not a claim that an actual organism was measured. Write your prediction before revealing the changed condition.

Virtual capture record	Value (individuals)
Initially marked M	40
Second sample C	50
Marked recaptures R	10

Independent fictitious samples from an idealized closed population.

Your prediction before comparison

This scratch prediction is not saved automatically. Copy it to the lesson notebook to retain it.

Evidence conditionReference comparisonChanged condition / follow-up

Estimate abundance with sampling assumptions and uncertainty

Supplied synthetic evidence: Independent fictitious samples from an idealized closed population.

Virtual capture record: reference condition

Quantity	Value	Unit
Initially marked M	40	individuals
Second sample C	50	individuals
Marked recaptures R	10	individuals

Task: If marked individuals avoid recapture, which direction of bias would you expect from MC/R, holding other counts fixed?

Small-sample bias and uncertainty are not represented by this point estimate.

Compare with the conditional interpretation

Estimated N=40×50/10=200.

The sample marked fraction is10/50=0.2. If that represents the population fraction40/N, N≈200. Over a10-hectare boundary, estimated density would be20 individuals per hectare.

Case index for this investigation

0. Distinguish directional responses, activity and fitness
1. Track energy flow and distinguish production from standing biomass
2. Estimate abundance with sampling assumptions and uncertainty
3. Compare exponential and density-limited growth models
4. Use per-capita evidence to identify density dependence
5. Infer direct and indirect interactions from controlled contrasts
6. Separate richness, evenness and sampling completeness
7. Connect disturbance, nutrient cycles and evidence-based intervention

No numerical confidence, laboratory credit or independent mastery is inferred from opening a supplied case. Save your first prediction and comparison in the notebook.

Reset this unsaved comparison

Change one ecological assumption at a time

Bounded synthetic arithmetic practice, not a fitted ecosystem model or physical investigation. Scratch controls are not saved or graded. Record your first prediction and selected outputs in the lesson notebook.

Marked MSecond sample CRecaptured R

R/C=0.2000. N≈M×C/R=200.00 individuals. This is a point estimate, not an exact count or confidence interval.

Halve R and explain the sensitivity. Closure, mixing, retained marks and comparable capture probability are assumptions; real capture is not assigned.

Reset practice

Worked reasoning

The sample marked fraction is10/50=0.2. If that represents the population fraction40/N, N≈200. Over a10-hectare boundary, estimated density would be20 individuals per hectare.

Estimated N=40×50/10=200.

Apply to a new case

If marked individuals avoid recapture, which direction of bias would you expect from MC/R, holding other counts fixed?

Compare your reasoning with the worked response

Recapture R is reduced, so the simple estimate rises and can overestimate abundance. State why equal detectability is doubtful rather than reporting the point estimate as an exact census.

This public response supplies feedback, not a score for independent reasoning. Record which part of your prediction changed and why.

Evidence and investigation boundary

Small-sample bias and uncertainty are not represented by this point estimate. Low recapture counts make the estimate unstable and demand appropriate interval methods.

For a supervised investigation, predeclare the question, biological unit of replication, treatment/comparison assignment, quantities and units, exclusion rules, graph and uncertainty method. Keep the raw records and the first prediction separate from later revisions. A simulated case does not supply laboratory hours or establish AP authorization. No physical manipulation is required by this lesson.

Source and continuation

Framework topics: 8.3. Current AP Biology framework; supporting scientific reference. Sources checked 30 October 2026; all teaching wording, questions and numbers here are original. Return to AP Biology to compare this mechanism with another scale of organization.