Mark-Recapture Population Estimation

Overview

How do you count animals you can't see all at once? That's one of the most basic problems in ecology, and the mark-recapture method is one of the field's most fundamental solutions. The logic is disarmingly simple: capture a sample of animals, mark them so you can identify them later, release them back into the population, wait for them to mix in, then capture again. The proportion of marked individuals in your second sample tells you something about the total population size.

If you marked 20 turtles and your second catch of 30 includes 6 marked ones, then roughly 20% of the population is marked, which means the total is around 100. That's the Lincoln-Petersen estimator in a nutshell. The real skill lies in understanding when the assumptions hold and what happens when they don't.

What You'll Do

Run multiple capture sessions in a simulated field environment. In the first session, capture animals and apply marks—paint marks on turtle shells, wing tags on butterflies, ear clips on mice, or fin clips on sculpins. Release them and let the population mix. In subsequent sessions, capture again and record how many individuals are marked versus unmarked.

Calculate population estimates using the Lincoln-Petersen method and Chapman's bias-corrected modification. Compute confidence intervals. Then critically evaluate whether the key assumptions are met: Are all individuals equally likely to be caught? Are marks being retained? Is the population closed (no births, deaths, immigration, or emigration between sessions)? Each animal system violates these assumptions in different ways, which is half the point.

Learning Objectives

1. Apply the Lincoln-Petersen method and Chapman's correction to estimate population size from capture data
2. Evaluate whether mark-recapture assumptions are met (equal catchability, no mark loss, population closure) and identify likely violations
3. Calculate confidence intervals for population estimates and understand what drives estimate precision
4. Compare estimates across multiple sampling sessions and assess consistency

Animal Systems

• Painted Turtles — In a pond; turtles are long-lived and site-faithful, making them good candidates for closed-population methods
• Monarch Butterflies — At a migration waystation; high turnover means the closed-population assumption is shaky, which makes the exercise more interesting
• Deer Mice — In a meadow with Sherman live-traps; trap-happiness and trap-shyness create classic capture heterogeneity problems
• Tide Pool Sculpins — In rocky intertidal pools; small isolated pools approximate closed populations, but fish can move between pools at high tide

Background

The basic mark-recapture idea dates back to at least the early 1900s, when C.G.J. Petersen used it to estimate fish populations in Danish waters. Lincoln independently applied the same logic to waterfowl banding data. The method has since been extended in dozens of directions—Jolly-Seber models handle open populations, Pollock's robust design combines open and closed models, and modern spatial capture-recapture methods estimate both abundance and density.

But the core logic hasn't changed. You're using the ratio of marked to unmarked animals in a resample to infer population size. The method works because that ratio, in expectation, equals the ratio of your original marked sample to the total population. When the assumptions are met, it's remarkably powerful. When they're not, your estimates can be badly biased—and learning to diagnose those biases is one of the most important skills in wildlife ecology.