EXAMPLE 3.30

Estimate the number of least flycatchers. You are interested in the number of least flycatchers migrating along a major route in the north-central United States. You set up “mist nets” that capture the birds but do not harm them. The birds caught in the net are fitted with a small aluminum leg band and released. Last year, you banded and released 200 least flycatchers. This year, you repeat the process. Your net catches 120 least flycatchers, 12 of which have tags from last year’s catch.

The proportion of your second sample that have bands should estimate the proportion in the entire population that are banded. So if N is the unknown number of least flycatchers, we should have approximately

Solve for N to estimate that the total number of flycatchers migrating while your net was up this year is approximately