An ichthyologist tags 200 fish in a lake and later captures a sample of 150 fish, 15 of which are tagged. Using the capture-recapture method, estimate the total fish population. If the estimate has a 5% margin of error, what is the maximum possible population?

Sun, 03 May 2026 15:43:52 +0000

**Why Tracking Fish Populations Matters—And How Scientists Do It**
In a time when data-driven decisions shape conservation, a quiet yet compelling method helps scientists understand aquatic ecosystems. One technique, used by ichthyologists, leans on simple math to estimate fish populations without disturbing natural habitats. The process begins when a researcher tags an initial batch of fish—often 200—across a lake or river. Days or weeks later, fish are recaptured, and researchers count how many are tagged. From this simple sample, a statistical approach uncovers broader truths about species abundance. Among the key questions driving this work is: What’s the total fish population? When tracking 150 fish later yields 15 tagged in the sample, a precise calculation follows—one that reveals not just numbers, but the health of an ecosystem. This method is gaining traction nationwide, fueled by growing interest in biodiversity monitoring and sustainable resource management. The reliability and simplicity of capture-recapture makes it a go-to for conservationists, researchers, and policymakers alike. When applied, the formula provides a strong estimate; when paired with a margin of error, it offers transparency about data confidence—skills increasingly valued in public science education. **The Capture-Recapture Equation: How It Estimates Populations**
The core idea is straightforward: if 200 fish are tagged and later, in a sample of 150 fish, 15 are tagged, the proportion of tagged individuals in the sample helps infer the total lake population. Using the basic capture-recapture formula, total population estimates emerge from cross-multiplying these counts. Let *N* represent the total population. The formula is:
Estimated *N* = (Number tagged × Total sample size) / Number tagged in sample
Plugging in the numbers:
*N* = (200 × 150) / 15 = 30,000 / 15 = 2,000 fish. This baseline estimate reflects population size under ideal, unbiased sampling.