Read the passage carefully. Then study the vocabulary cards — click one at a time (8-second peek) — and finish with the matching practice.
Imagine you're standing at the edge of a small pond, and your job is to figure out how many largemouth bass live in it. You can't drain the pond. You can't see through the water. And you definitely can't count every fish one by one. So what do you do? You use a clever sampling method called mark-recapture, first refined by Frederick C. Lincoln in 1930 to count waterfowl, and independently developed by C.G.J. Petersen for fish populations.
The idea is elegant: catch a sample of organisms, give each one a harmless mark (a tag, a dot of paint, a clipped scale), return them, and let them mix back into the population. After enough time for the marked animals to redistribute, you go back and catch a second sample. Some of the animals you catch will already carry your mark — these are your recaptures. The proportion of marked individuals in the second sample mirrors the proportion of marked individuals in the entire population. From that ratio, you can estimate N, the total population size.
Where M is the number marked and released in the first capture, C is the total number caught in the second capture, and R is the number of recaptured (already-marked) individuals in that second capture. This is the Lincoln–Peterson Index.
The method only works if a handful of assumptions hold true. The population must be closed — no significant births, deaths, immigration, or emigration between captures. Marks must not fall off or kill the animal. Marked individuals must mix randomly back into the population. And every animal — marked or not — must have an equal chance of being captured. Violate any of these and your estimate drifts away from reality. That's why field biologists report estimates with confidence intervals: the math is exact, but biology is messy. A percent error calculation against a known true count lets us measure how messy.
Today you'll work with a "pond" of dried beans. You don't have to wade through cattails, but you do have to do the math — and then think hard about which assumptions a real pond would shatter.
Click any card to reveal the definition for 8 seconds. You can re-open cards as many times as you want — only one card at a time, though.
Click a word on the left, then click its matching definition on the right. 1 point each.
Fill in each blank with the correct vocabulary term from the word bank. Correct answers will highlight green. 1 point each.
Answer in complete sentences using vocabulary from Part 1. 1 point each (self-graded against the rubric on the results page).
Run the simulation three times. Record your numbers and calculate. Percent error = |Estimate − True| ÷ True × 100.
| Trial | M | C | R | N estimate | True N | % Error |
|---|---|---|---|---|---|---|
| 1 | ||||||
| 2 | ||||||
| 3 | ||||||
| AVG | Average % Error → | |||||
Dr. Ana Vélez has studied red-backed salamanders along a forested stream in Vermont for fifteen years. In June 2023, she captured 120 salamanders, marked each with a non-toxic visible implant elastomer (VIE) tag, and returned them to the cover boards where she found them. Two weeks later, she returned and captured 96 salamanders. Of those, 24 were recaptures — they still carried her VIE tags.
When she ran the same study the following June (2024), she marked 120 salamanders again. This time, two weeks later, she captured 96 salamanders and found only 8 recaptures. The forest had not been disturbed. A small culvert had been installed upstream during the previous fall, however, allowing salamanders to disperse into a connected wetland for the first time.
Dr. Vélez's preliminary report concluded that the salamander population had "more than tripled" between the two years. Her advisor flagged the report and asked her to reconsider.
A neighboring class ran 10 mark-recapture trials on a tub with a known true population of 200. Their estimates are shown below.
Answer each part fully. AP-style rubrics reward specific use of vocabulary, justification with data, and explicit links between cause and effect. 4 points (self-graded against rubric on results page).
Mark-Recapture Jeopardy — Five categories. Higher value = harder question. Each correct answer adds bonus points to your final grade.
Self-graded sections (How/Why, FRQ) use the rubrics below. Be honest — your future self will thank you.
| Section | Points | Max |
|---|
Rubric: Give yourself 1 point if your answer uses correct vocabulary, addresses both what and why/how, and is at least one complete sentence.
Rubric: 1 point per FRQ part that (a) directly answers what was asked, (b) uses lab data or specific examples to justify, and (c) names at least one Lincoln-Peterson assumption or term.