Question

In a mark–recapture study to estimate the size of a rodent population, researchers catch and mark 30 individuals. Two days later, they again capture a number of rodents and find that 20% of the individuals are marked. Assuming no births, deaths, or migrations, what is the estimated size of the population?

Answer 1

The estimated size of the rodent population based on the mark–recapture study, assuming a 20% recapture rate of marked individuals, is 150 individuals.

Step-by-step explanation:

In a mark–recapture study to estimate the size of a rodent population, researchers catch and mark 30 individuals. Two days later, they again capture a number of rodents and find that 20% of the individuals are marked. Assuming no births, deaths, or migrations, the estimated size of the population can be found using the Lincoln-Petersen estimator:

M/N = m/n

Where M is the total number of individuals marked in the first catch (30), N is the total population size (unknown), m is the number of marked individuals recaptured (20% of second catch), and n is the number of individuals in the second catch (the total number caught).

Since 20% of the second catch are marked individuals, we take 20% of n to find m:

m = 0.20 * n

Now, we rearrange the Lincoln-Petersen formula to solve for N:

N = (M * n) / m

Because m = 0.20 * n, when we substitute, we get:

N = (30 * n) / (0.20 * n)

Notice that 'n' cancels out, and we are left with:

N = 30 / 0.20

N = 150

Therefore, the estimated size of the rodent population is 150 individuals.

Answer 2

Answer: The estimated size of the population is 150

Explanation: For the Mark-Recapture method, there is a formula that can be used:

N = (M × C)/R

where :

N = estimated number of individuals in the population

M = number of individuals captured and arked

C = total number captured the second time (with and without a mark)

R= number of individuals ecaptured (those with a mark)

So with this formula we can calculate an estimation of the population of rodents. Because there is no number of rodents captured the second time given, we will assume 30 was caught again, making the 20% found marked being 6. We calculate it as:

N = (M × C)/R

:N = ( 30 × 30)/ 6

:N = 900/6

:N = 150 estimated rodents in the population