Chapter 43, Problem 1TY

A student decides to conduct a mark-recapture experiment to estimate the population size of $n_x{l}_x{m}_x{l}_x{m}_x$ mosquitofish, a species of freshwater fish, in a small pond near his home. In the first catch, he marked 45 individuals. Two weeks later, he captured 62 individuals, of which 8 were marked. What is the estimated size of the population based on these data?

1. 134
2. 349
3. 558
4. 1,016
5. 22,320

Questions 2–5 refer to the following table:

Age

0 100 35 1.00 0 0

1 65 ? 0.65 0 0

2 45 15 ? 3 1.35

330 20 0.301 ?

4 10 10 0.10 10.10

5 0 0 0.00 1 0.0

Summary Introduction

Introduction:

In biology, population size is the definite number of organisms in the population. The total population size is calculated by given formula:

$\frac{{\text{Number of individuals in 1}}^{\text{st}}\text{catch}}{\text{Total population size, N}}\text{=}\frac{{\text{Number of marked recaptures in 2}}^{\text{nd}}\text{ catch}}{{\text{Total number of 2}}^{\text{nd}}\text{ catch}}$

OR

$\text{Total population size, N=}\frac{{\text{Number of marked individuals in 1}}^{\text{st}}\text{catch}\times {\text{Total number of 2}}^{\text{nd}}\text{catch}}{{\text{Number of marked recaptures in 2}}^{\text{nd}}\text{catch}}$

Populations are made of all individuals belonging to the same species who live together at the same time.

The density of population is the count of organisms per geographic area or volume, per unit. For example, the number of organisms per square meter, per hectare or per square ilo

Answer to Problem 1TY

The correct answer is option (b) 349.

Explanation of Solution

Explanation/justification for the correct answer:

Option (b) 349.

If,

Marked mosquito fish in 1^st catch = 45 individuals

Recaptured mosquito fish in 2^nd catch = 62

Marked recaptured mosquito fish in 2^nd catch= 20, then according to the formula,

$\begin{array}{c}\text{Total}\text{population}\text{size, N=}\frac{\text{Number}\text{of}\text{marked}{\text{individuals in1}}^{\text{st}}\text{catch}\times {\text{Total number of 2}}^{\text{nd}}\text{catch}}{\text{Number}\text{of}\text{marked}{\text{recaptures in 2}}^{\text{nd}}\text{catch}}\\ =\frac{45\times 62}{8}\\ =\frac{2790}{8}\\ =348.75\\ \approx 349\end{array}$

From the equation, the estimate total population size of mosquito fish is $348.75\approx 349$

So, this is the correct option.

Explanation for incorrect answer:

Option (a) 134. As explained in option (b), the estimated size of a population is not matched to given data. So, this is an incorrect option.

Option (c) 558. As explained in option (b), the estimated size of a population is not matched to given data. So, this is an incorrect option.

Option (d) 1.016. As explained in option (b), the estimated size of a population is not matched to given data. So, this is an incorrect option.

Option (e) 22.320. As explained in option (b), the estimated size of a population is not matched to given data. So, this is an incorrect option.