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Chapter 14: Problem 63

One implicit assumption when using the capture-recapture method to estimate the size of a population is that when individuals are tagged in the capture stage, these individuals are not affected in any harmful way by the tags. Sometimes, though, tagged individuals become affected, with the tags often making them more likely prey to predators (imagine, for example, tagging fish with bright yellow tags that make them stand out or tagging a bird on a wing in such a way that it affects its ability to fly). If that were the case, would the capture-recapture method be likely to underestimate or overestimate the size of the population? Explain your answer.

Short Answer

Expert verified
The capture-recapture method would likely overestimate the size of the population, as the loss of tagged individuals due to increased predation would lead to an influx in the perceived overall size of the population.

Step by step solution

01

Understand the Capture-Recapture Method

In the capture-recapture method, a number of individuals are captured, tagged, and then released back into the population. After a certain period, a second sample is captured. The proportion of tagged individuals in the second sample is used to estimate the total population size.
02

Consider the Effect of Tags making individuals more likely prey

In the given situation, the tags make the tagged individuals more likely to be prey. This means that between the initial capture and the recapture, a larger than proportional amount of tagged individuals would be preyed upon and hence would not be present in the recapture.
03

Analyze the Effect on the Population Estimate

Since the second sample would likely contain fewer tagged individuals due to the increased predation, the method would think that the initial tagging represented a smaller proportion of the total population than it did. As such, the total population would be overestimated.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Population Estimation
The capture-recapture method is essential for estimating population sizes, especially when it isn't feasible to count every individual. Here鈥檚 how it works:
  • First, you capture a sample of the population and tag each individual before releasing them back into the wild.
  • After allowing some time for those individuals to mix back into the population, you capture a second sample.
The key here is to check what fraction of this second sample consists of tagged individuals from the first capture. With this fraction, you can estimate the total population size. This method assumes that the population size does not change significantly between the two captures due to births, deaths, immigration, or emigration. It also assumes that tagged individuals have the same chance of being caught as untagged ones in the second sample, which is crucial to making the estimation accurate.
Tagging Impact
Tagging individuals in a population is a critical step in the capture-recapture method, but it comes with certain impacts. This process involves placing a mark or tag that is unique to each individual in the initial capture. While necessary for the method to work, tagging can have unforeseen effects. These tags should ideally be:
  • Non-invasive and should not hinder the individual鈥檚 natural behavior.
  • Invisible to predators to prevent making tagged individuals easier prey.
Harmful or visible tags can skew the results of your population estimation. For instance, if tagged animals become more visible or hampered by the tags, they could be caught by predators more frequently than their untagged counterparts. This could lead to a lower number of tagged individuals in the second capture, subsequently leading to an overestimation of the total population size.
Predation and Measurement Bias
Measurement bias in the capture-recapture method can arise from factors like predation. When tagged individuals are more visible to predators, they are likely to be consumed at a higher rate. Here's how that affects your estimate:
  • The proportion of tagged individuals in the second sample decreases.
  • This decrease suggests, incorrectly, that the tagged group was a smaller segment of the total population.
  • As a result, the estimation formula produces a larger estimated population size than actually exists.
This bias highlights the importance of considering all possible effects of tagging when using the capture-recapture method. By understanding these impacts, you can better account for them and achieve a more accurate population estimation.

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Most popular questions from this chapter

Refer to the following story: The manufacturer of a new vitamin (vitamin \(X\) ) decides to sponsor a study to determine the vitamin's effectiveness in curing the common cold. Five hundred college students having a cold were recruited from colleges in the San Diego area and were paid to participate as subjects in this study. The subjects were each given two tablets of vitamin \(X\) a day. Based on information provided by the subjects themselves, 457 of the 500 subjects were cured of their colds within 3 days. (The average number of days a cold lasts is 4.87 days.) As a result of this study, the manufacturer launched an advertising campaign based on the claim that "vitamin \(X\) is more than \(90 \%\) effective in curing the common cold." List four different problems with the study that indicate poor design.

Imagine you have a very large coin jar full of nickels, dimes, and quarters. You would like to know how much money you have in the jar, but you don't want to go through the trouble of counting all the coins. You decide to estimate how many nickels, dimes, and quarters are in the jar using the capture- recapture method. After shaking the jar well, you draw a first sample of 150 coins and get 36 quarters, 45 nickels, and 69 dimes. Using a permanent ink marker you tag each of the 150 coins with a black dot and put the coins back in the jar, shake the jar really well to let the tagged coins mix well with the rest, and draw a second sample of 100 coins. The second sample has 28 quarters, 29 nickels, and 43 dimes. Of these, 4 quarters, 5 nickels, and 8 dimes have black dots. Estimate how much money is in the jar. (Hint: You will need a separate calculation for estimating the quarters, nickels, and dimes in the jar.)

Refer to a study on the effectiveness of an HPV (human papilloma virus) vaccine conducted between October 1998 and November \(1999 .\) HPV is the most common sexually transmitted infection-more than 20 million Americans are infected with HPV-but most HPV infections are benign, and in most cases infected individuals are not even aware they are infected. (On the other hand, some HPV infections can lead to cervical cancer in women.) The researchers recruited 2392 women from 16 different centers across the United States to participate in the study through advertisements on college campuses and in the surrounding communities. To be eligible to participate in the study, the subjects had to meet the following criteria: (1) be a female between 16 and 23 years of age, (2) not be pregnant, (3) have no prior abnormal Pap smears, and (4) report to have had sexual relations with no more than five men. At each center, half of the participants were randomly selected to receive the HPV vaccine, and the other half received a placebo injection. After 17.4 months, the incidence of HPV infection was 3.8 per 100 woman-years at risk in the placebo group and 0 per 100 woman-years at risk in the vaccine group. In addition, all nine cases of HPV-related cervical precancerous growths occurred among the placebo recipients. (a) Describe the sample for the study. (b) Was the sample chosen using random sampling? Explain.

Starting in \(2004,\) a study to determine the number of lake sturgeon on Rainy River and Lake of the Woods on the United States-Canada border was conducted by the Canadian Ministry of Natural 91影视, the Minnesota Department of Natural 91影视, and the Rainy River First Nations. Using the capture- recapture method, the size of the population of lake sturgeon on Rainy River and Lake of the Woods was estimated at \(N=160,286\). In the capture phase of the study, 1700 lake sturgeon were caught, tagged, and released. Of these tagged sturgeon, seven were recaptured during the recapture phase of the study. Based on these figures, estimate the number of sturgeon caught in the recapture phase of the study. [Source: Dan Gauthier, "Lake of the Woods Sturgeon Population Recovering," Daily Miner and News (Kenora, Ont.), June \(11,2005,\) p. 31.]

To estimate the population in a rookery, 4965 fur seal pups were captured and tagged in early August. In late August, 900 fur seal pups were captured. Of these, 218 had been tagged. Based on these figures, estimate the population of fur seal pups in the rookery. [Source: Chapman and Johnson, "Estimation of Fur Seal Pup Populations by Randomized Sampling," Transactions of the American Fisheries Society, 97 (July 1968), 264-270.
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