An ecological survey was conducted in the Borgu sector of Kainji Lake National Park to est… — JAMB UTME

An ecological survey was conducted in the Borgu sector of Kainji Lake National Park to estimate the population size of grasscutters (*Thryonomys swinderianus*). In the initial phase, $80$ grasscutters were captured, marked with ear tags, and released back into the habitat. One week later, a second sample of $100$ grasscutters was captured, out of which $20$ individuals retained their mark. If post-marking field monitoring established that $10\%$ of all originally marked animals lost their tags during the interval, what is the estimated total population size of grasscutters in the study area?

Answer: 360 grasscutters

Answer

The estimated total population size of grasscutters in the study area is 360.

Accounting for a 10% tag loss reduces the active marked population from 80 to 72 individuals. Applying the Lincoln-Petersen index formula (

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

) with

M = 72

C = 100

, and

R = 20

gives an estimated total population size of 360 grasscutters.

Step-by-Step Solution

Calculate the effective number of marked individuals (

M_{eff}

) in the population considering the 10% tag loss.

M_{eff} = 80 \times (1 - 0.10) = 72

marked individuals.

Animals that lost their tags no longer register as marked upon recapture, effectively reducing the active marked proportion in the population.

Substitute

M_{eff} = 72

, total recaptured

C = 100

, and marked recaptured

R = 20

into the Lincoln-Petersen index formula

N = \frac{M_{eff} \times C}{R}

N = \frac{72 \times 100}{20} = 360

The proportion of marked individuals in the recaptured sample equals the proportion of effective marked individuals in the total population.

Key Concept

Lincoln-Petersen Mark-Recapture Index with Sampling Bias Adjustment

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