During an ecological study of an agricultural fish pond in Ibadan, Oyo State, a student em… — JAMB UTME

During an ecological study of an agricultural fish pond in Ibadan, Oyo State, a student employed the mark-release-recapture technique to estimate the population size of tilapia (*Oreochromis niloticus*). In the initial sampling, $120$ fish were captured, marked with harmless plastic tags, and released back into the pond. Two days later, a second sample of $150$ fish was netted, out of which $30$ individuals were found to be marked. What is the estimated total population size of tilapia fish in the pond?

Answer: 600 fish

Answer

The estimated total population size of tilapia fish in the pond is 600.

The correct answer is derived using the Lincoln index formula for population estimation:

N = \frac{M \times C}{R}

, where

M = 120

(initial marked sample),

C = 150

(total second sample), and

R = 30

(recaptured marked sample). Substituting these values yields

N = \frac{120 \times 150}{30} = 600

fish.

Step-by-Step Solution

Identify the values for the Lincoln Index (Lincoln-Petersen estimator) parameters from the problem statement.

Number marked in first capture (

M

) =

120

, total caught in second capture (

C

) =

150

, recaptured marked individuals (

R

) =

30

The capture-recapture method relies on the proportion of marked individuals in the second sample being equal to the proportion of marked individuals in the total population.

Apply the Lincoln Index formula

N = \frac{M \times C}{R}

N = \frac{120 \times 150}{30}

Multiplying the initial sample size by the second sample size and dividing by the recaptured marked count yields the total estimated population.

Perform the division and multiplication to solve for

N

N = 600

Simplifying

\frac{150}{30} = 5

, then

120 \times 5 = 600

fish.

Key Concept

Lincoln Index (Mark-Release-Recapture Method)

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