Chapter 53, Problem 1IQ

In a mark-recapture study, an ecologist traps, marks, and releases 25 voles in a small wooded area. A week later she traps 30 voles, 10 of which are marked. What is her estimate of the vole population in that area?

Summary Introduction

To determine: The approximate population of vole in the given area by the mark-recapture method.

Introduction: An ecologist traps, marks, and releases 25 voles in a small wooded area. The ecologist again traps 30 voles after a gap of one week and observes that 10 of them have the mark.

Explanation of Solution

The vole population can be calculated by the formula given below:

Estimated population size (N) =$\frac{\text{sn}}{\text{x}}$        (I)

Here, N is the estimated size of the population, s is the number of animals initially marked and released, n is the number in second sampling, and x is the recaptured marked animals.

Substituting the values of s=25, n=30, and x=10 in equation (I) to find the estimated population size of voles.

$\begin{array}{l}\text{N=}\frac{\text{25×30}}{\text{10}}\\ \text{N=75}\text{voles}\end{array}$

The estimated population size (N) of voles is 75 voles.

Conclusion

Thus, the estimated size of the vole population in the given area is 75 voles.