Question

Describe how a researcher would determine the size of a penguin population in Antarctica using the mark and release method.

Short answer

Use the mark and release method: mark a sample, release, recapture a new sample, count marked, and apply the formula \( N = \frac{M \times C}{R} \) to estimate the population size.

Step-by-step solution

Capture and Mark

First, the researcher captures a sample of penguins from the population. These captured penguins are then marked with a temporary, harmless marker that allows them to be easily identified if recaptured. It is crucial to ensure that the marking does not affect their survival or behavior.

Release the Penguins

After marking, the researcher releases the penguins back into their natural habitat. The penguins are given enough time to mix back into the larger population, ensuring they have an equivalent chance of being recaptured as any unmarked penguin in the population.

Recapture a Second Sample

The researcher captures another sample of penguins after a suitable period. This second sample should also be random and large enough to provide statistically reliable data.

Count Marked Penguins in the Second Sample

In the second sample of penguins, the researcher counts how many of them are marked. This count is crucial for estimating the total population using the ratio of marked to unmarked penguins in this sample.

Calculate Population Size

Use the formula \[ N = \frac{M imes C}{R} \] where \( N \) is the estimated population size, \( M \) is the number of marked penguins in the first sample, \( C \) is the total number of penguins caught in the second sample, and \( R \) is the number of marked penguins recaptured in the second sample. Substitute the values to estimate the total penguin population.

Key concepts

Penguin Population Estimation

Estimating the population of penguins in the vast expanses of Antarctica presents a unique set of challenges. Unlike closed environments, these areas are open and dynamic, making a direct count impractical. Here, scientists adopt the **Mark and Release Method**, a clever approach designed to infer population sizes without the need to observe or disturb every individual.
The primary objective is to provide an estimate that is as accurate as possible using indirect yet precise techniques. Researchers aim to minimize disturbances to the penguins while gathering reliable data. The method is grounded in statistical reasoning, applying mathematical models to biological data.
Such estimations are fundamental for conservation efforts and understanding ecological impacts. Having a grasp on population size allows researchers to assess the health of a species, track environmental changes, and even address concerns regarding human activities.

Capture and Mark Technique

The essence of the Capture and Mark Technique is in capturing a manageable number of penguins from the larger population. This task requires ethical considerations, ensuring the penguins' well-being throughout the process.

• **Capture Phase:** Penguins are caught using nets or similar methods, ensuring minimal stress or harm. The capture locations are chosen to be representative of the overall habitat to get a fair sample.
• **Marking Phase:** Upon capture, each penguin is marked with a temporary, non-toxic tag. This mark is typically visible – a harmless dye is often used. The mark must not alter the penguins’ behavior or make them more noticeable to predators.
• **Release Phase:** After marking, penguins are promptly released back into their environment. They need time to reintegrate into their colony, which allows the marked penguins to randomly mix with the unmarked population.

Careful execution of these steps ensures the collected data is representative of the entire population, a crucial part of the estimation process.

Population Size Calculation

Calculating the total penguin population involves a blend of observation and mathematics. Once the second sample is collected, with some marked penguins among them, researchers can estimate the total population using a specialized formula.
The formula employed is \[N = \frac{M \times C}{R}\]where:

• \(N\) = Estimated total population size
• \(M\) = Number of marked penguins in the first sample
• \(C\) = Total number of penguins recaptured in the second sample
• \(R\) = Number of marked penguins found in the second sample

This ratio-based formula hinges on the likelihood that the proportion of marked penguins in the second sample mirrors the proportion in the entire population.
By substituting the values collected from the field into this formula, researchers derive the estimated number of penguins, thus providing valuable insights into population dynamics.