Estimate the population size of a bird species if in 100 sightings along a migration path, 25 were ringed, and it is known that 500 of the birds had been ringed before the sightings?

To estimate the population size of a bird species based on the given information, we can use a capture-recapture method called the Lincoln-Petersen Index. This method assumes that the proportion of marked birds in the second sample is representative of the overall population.

The Lincoln-Petersen Index formula is as follows:

Population Size (N) = (Total Number of Individuals in First Sample * Total Number of Individuals in Second Sample) / Number of Recaptured Individuals

Let's break down the given information to calculate the estimated population size:

1. Total Number of Individuals in First Sample:
The first sample consists of 100 sightings along the migration path. Therefore, the total number of individuals in the first sample is 100.

2. Total Number of Individuals in Second Sample:
Out of the 100 sightings, 25 were ringed birds. Since the proportion of marked birds in the second sample represents the overall population, we can use the following proportion:

(Number of Marked Birds in Second Sample) / (Total Number of Individuals in Second Sample) = (Number of Marked Birds in Population) / (Total Population)

Using this proportion, we can solve for the total number of individuals in the second sample:

(25) / (Total Number of Individuals in Second Sample) = (500) / (Total Population)

Cross-multiplying the ratio:
25 * (Total Population) = 500 * (Total Number of Individuals in Second Sample)

Now, let's plug the given values into the formula:

25 * (Total Population) = 500 * 100

Simplifying the equation:
25 * (Total Population) = 50,000

Dividing both sides by 25:
Total Population = 2,000

Therefore, the estimated population size of the bird species is 2,000. Please note that this is an estimate based on the assumptions of the Lincoln-Petersen Index.