Sampling

The Petersen capture recapture method was used to estimate the number of black bears in Pennsylvania in 2018

A group of researchers took into account the number of bears that died between initial tagging and the recapture.

A bear is considered to have a current tag if it was tagged in the previous year. Taking into account the bears that died, the number of black bears with current tags available to be captured in 2018 was 690 During the year 2018, the number of black bears captured was 2017 of which 73 had a current tag.

(Source: www.pgc.pa.gov)

Calculate an estimate for the number of black bears in Pennsylvania in 2018

The researchers only considered a black bear to have a current tag during the second capture if it was tagged in the previous year.

Explain the effect on your estimate in part (a) if they did not do this and instead included all tags. You should give a reason for your answer.

The approach used by the researchers considered the issues around tag loss.

Give one other assumption of the Petersen capture recapture method that they should have considered in their research.

Researchers used the Petersen capture recapture method to estimate the number of humpback whales off the coasts of California, Oregon and Washington.

They used aerial photographs to identify the whales, recording the whales’ unique markings in the first sampling rather than tagging the whales.

In 1995 they recorded the markings of 331 individual whales. In 1996 they identified 264 individual whales of which 104 had been identified in the previous year. (Source: digitalcommons.unl.edu)

Calculate an estimate for the number of humpback whales off the coasts of California, Oregon and Washington in 1996

Discuss the validity and reliability of this estimate.

Paul uses the Petersen capture recapture method in order to find an estimate for the number of trout living in a lake.

To do this, Paul catches an initial sample of 50 trout from the lake and he tags each trout. He then releases the trout back into the lake.

For his second sample, Paul catches a sample of 80 trout from the lake. He finds that 16 of these trout have tags.

Explain what needs to be true about his two samples for them to be valid for the capture recapture method.

Using his results, Paul is able to work out an estimate for the number of trout living in the lake.

Find Paul’s estimate for the number of trout and discuss the validity and the reliability of his estimate.

David is writing a project about iguanas.

He finds data on the internet posted by a biologist investigating iguanas on the Galapagos Islands.

The biologist captured and tagged a sample of iguanas in La Loberia. The tagged iguanas were then released back from where they were captured.

After a few days the biologist captured at random a second sample of iguanas in La Loberia and recorded the number of tagged iguanas in this sample.

Here is the biologist’s data.

(Source: www.discoveringgalapagos.org.uk)

Work out an estimate of the total number of iguanas in La Loberia.

Discuss the reliability of using the biologist’s data to work out an estimate of the total number of iguanas in La Loberia.

It is suggested that some of the tags might have fallen off the iguanas between the two samples.

If this had happened, describe the effect it would have on the estimate worked out in part (a).

Tamiki wants to estimate the number of pigeons in a park.

He catches a sample of 48 pigeons in the park, tags each pigeon and then releases it.

A week later, Tamiki catches a sample of 20 pigeons in the park.

He uses the Petersen capture recapture formula to estimate that there are 240 pigeons in the park.

Work out how many of the 20 pigeons in Tamiki’s sample had tags.

Comment on the reliability of Tamiki’s estimate by considering the assumptions that he needed to make in order to use the Petersen capture recapture formula.

According to an internet site, an estimate of the number of reindeer in a region of Ontario is 5000

(Source: www.ontario.ca

Giovani wants to verify this estimate.

He goes to the region of Ontario, captures a sample of 250 reindeer, attaches a tag to each reindeer and then releases the 250 reindeer back into the same region of Ontario.

Three days later, Giovani returns to the same region of Ontario and catches a sample of 98 reindeer.

He finds that 5 of these reindeer are tagged.

Giovani concludes that this information can be used to verify the estimate of 5000

Discuss the appropriateness of Giovani’s method and of his conclusion.

As part of your discussion you should show your calculations and state any assumptions made.