Q.50

In a sampling expedition near a peninsula, 180 dolphins from a large population of

dolphins were captured and marked by tagging their dorsal fins. The tagged dolphins

were then allowed to join back into the population. In a subsequent expedition, 42

dolphins were photographed from same large population. Among these, 7 dolphins

contained the tags. Assuming that the population size remains the same and that tags were

not lost, the estimated population size of dolphins in the peninsula is _____________.

(answer in integer)

Estimating Dolphin Population Size: Mark-Recapture Method Explained

The mark-recapture method estimates wildlife populations like dolphins using tagged samples. In this case, 180 dolphins were marked, and later 42 were recaptured with 7 tagged, yielding an estimated population of 1080 dolphins.

Mark-Recapture Formula

Capture-recapture relies on the Lincoln-Petersen index: N = (M × C) / R, where M is marked individuals (180), C is second sample size (42), and R is recaptured marked ones (7).

Plugging in values: N = (180 × 42) / 7 = 7560 / 7 = 1080. This assumes random mixing, no tag loss, and stable population size.

Step-by-Step Calculation

• Mark 180 dolphins and release them.
• Recapture 42 dolphins, finding 7 marked.
• Proportion of marked in recapture (7/42) equals marked in population (180/N).
• Solve: N = (180 × 42) / 7 = 1080.

Round to nearest integer as specified: 1080.

Common Errors in Options

Since this fill-in-the-blank yields 1080 exactly, typical wrong answers arise from misapplying the formula:

Correct answer avoids these: 1080.

Assumptions and Limitations

Method assumes tags persist, no births/deaths alter size, and perfect mixing occurs. Violations like tag loss inflate estimates; small samples add variability.[web:5][web:7]

For dolphin studies near peninsulas, this non-invasive tagging via dorsal fins suits large populations.