Problem 7 - Biology: The Dynamic Science

Question

One day you caught and marked 90 butterflies in a population. A week later, you returned to the population and caught 80 butterflies, including 16 that had been marked previously. What is the size of the butterfly population? a. 170 b. 450 c. 154 d. 186 e. 106

Step-by-Step Solution

Answer

The size of the butterfly population is predicted to be around 450. So, the correct answer is (b) 450.

Step 1: Identify the given values

Given that 90 butterflies were caught and marked the first time. Then on the second visit, 80 butterflies were caught including 16 that had previously been marked.

Step 2: Formula

The formula for the mark and recapture method is: \( Size \, of \, the \, population = \frac{M \cdot C}{R} \), where M indicates the number of organisms marked on the first visit, C is the total number caught on the second sampling and R is the number of marked organisms recaptured during the second sampling.

Step 3: Substitution and calculation

Substitute the given values into the formula: \( Size \, of \, the \, population = \frac{90 \cdot 80}{16} \). Calculate this and the estimated population size is approximately 450.

Key Concepts

Population Estimation

Population estimation is a vital method in ecology to determine the number of individuals in a group, usually without counting each one individually. An effective technique for this is the Mark and Recapture Method. This method is especially useful for studying wildlife populations. It involves capturing a number of individuals from a population, marking them non-harmfully, and releasing them back into their environment.

Later, a second sample of the population is captured, some of which will be the marked individuals. By using a simple formula: \( \, N = \frac{M \cdot C}{R} \, \), ecologists can estimate the total population size \( N \). Here, \( M \) is the number of marked individuals in the first capture, \( C \) is the total number of individuals captured in the second instance, and \( R \) is the number of marked individuals recaptured. This method assumes the marked individuals have thoroughly mixed back into the population and that it remains constant between sampling rounds.

• Allows estimation without counting every single individual.
• Useful for mobile or elusive species.
• Relies on specific assumptions about population dynamics and mixing.

Ecological Sampling

Ecological sampling methods like mark and recapture help to study and manage wildlife by providing data on population and behavioral dynamics. These approaches are often used to survey populations without causing harm to the organisms involved.

There are a few key steps in ecological sampling using the mark and recapture method:

• Choose a representative sample area.
• Ensure that marking is non-invasive and does not affect the organisms' survival.
• Allow sufficient time for marked individuals to blend back into the population.
• Use statistical methods to analyze data for accuracy.

This method is crucial for making informed decisions about conservation efforts and understanding species interactions within ecosystems. However, it is important to consider limitations such as changes in population due to births, deaths, or migrations between the two samplings. Biological statisticians often address these factors to refine population estimates.

Butterfly Population Dynamics

Understanding butterfly population dynamics is essential for conserving these beautiful and ecologically significant insects. Butterflies serve as important pollinators and indicators of environmental health. The mark and recapture method provides valuable insights into their population size and movement patterns.

For butterflies, the method requires careful consideration. These factors include life stage, seasonality, and habitat preferences. For example, recapture rates might differ due to breeding seasons or migration patterns. During ecological studies, butterflies are typically captured using nets, gently marked on their wings with a small dot, and released.

Monitoring their dynamics enables ecologists to understand:

• The impact of climate change and habitat loss on populations.
• Interactions with other species within the ecosystem.
• Effectiveness of conservation measures.

Through consistent mark and recapture studies, scientists can develop strategies to protect butterfly habitats and ensure their survival for future generations.