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Project Grant Team
John S. Pazdar Patricia L. Hirschy Project Director Principal Investigator Capital Community College Asnuntuck Community College Hartford, Connecticut Enfield, Connecticut
This project was supported, in part, by the Peter A. Wursthorn National Science Foundation Principal Investigator Opinions expressed are those of the authors Capital Community College and not necessarily those of the Foundation Hartford, Connecticut
SPINOFFS
Spinoffs are relatively short learning modules inspired by the LTAs. They can be easily implemented to support student learning in courses ranging from prealgebra through calculus. The Spinoffs typically give students an opportunity to use mathematics in a real world context.
LTA - SPINOFF 15A The Capture-Recapture Method
LTA - SPINOFF 15B Florida Scrub-Jay Populations and Habitat
LTA - SPINOFF 15C Population Models with Recursive Equations
Brian Smith - AMATYC Writing Team Member McGill University, Montreal, Quebec, Canada
Mario Triola - AMATYC Writing Team Member Dutchess Community College, Poughkeepsie, New York
Janet Rebmann - NASA Scientist/Engineer Kennedy Space Center, Florida
**NASA - AMATYC - NSF
- 20**
SPINOFF 15A
The Capture-Recapture Method
The capture-recapture method is often used to determine the size of a population. This method involves capturing a sample of a species, marking each captured member, and then returning each marked member to its general population. Then a second sample is captured, and the percent of marked subjects provides an estimate of the percent of the entire population that is marked. We can use this percent to set up an equation and solve for the unknown population size.
For example, suppose 20 mice are captured in Sherman live traps, marked, and then set free. Assume that later, a sample of 10 mice is captured, and 5 of them have marks. This later sample suggests that 50% of the population of mice have been marked. Thus, we can write the equation, 0.5x = 20, where x represents the number of mice in the population. Solving this equation yields x = 40 as a reasonable estimate of the population size.
Due to changing coastal dunes and construction of homes and businesses, the Southeastern Beach Mouse (with a central/southern Florida habitat) has undergone a large reduction in population size and has been declared a threatened species. Consequently, there is an interest in monitoring the size of its population. This is an ideal application of the capture-recapture method.
Exercises
In the Treasure Shores Park region of Florida’s Indian River County, traps are set and 191 mice are captured and marked. Later, a second sample of 140 mice is captured and it is found that 88 of them have been marked. Estimate the population size.
In one tract of the Archie Carr region, 8 mice are captured and marked. Later, another 8 mice are captured and all of them are found to have been marked. Estimate the population size.
