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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 since the tags can make individuals more prone to predation, reducing the proportion of tagged individuals available for recapture.

Step by step solution

01

- Understanding Capture-Recapture

The capture-recapture method is a technique for estimating the size of a wildlife population. First, a sample of the population is captured, marked or tagged, and released. Later, another sample is captured and the number of marked individuals in this second sample is counted. The proportion of marked individuals in the second sample is assumed to be the same as the proportion of marked to unmarked individuals in the whole population.
02

- Assessing the Impact of Tagging

Implicit in the method is the assumption that the tagging does not affect the survival or behavior of the tagged animals. If this assumption is violated because the tags make individuals more detectable or vulnerable to predation, it's likely that a higher proportion of the tagged individuals will be removed from the population relative to the untagged ones. This means that the second sample may have fewer tagged individuals than expected if the tagging were neutral.
03

- Estimation Bias Due to Tagging Effect

Given that the tagged individuals are more likely to be predated upon, they will be disproportionately lost from the population, leading to a lower number of recaptured tagged individuals during the second sampling phase. This leads to an underestimate of the proportion of tagged individuals in the population, and thus, the overall population size is overestimated.

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Key Concepts

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

Wildlife Population Estimation
Estimating wildlife populations is critical for conservation efforts, environmental management, and understanding the dynamics of ecosystems. One of the most practical methods for estimating the size of a wildlife population is the capture-recapture method. This method involves capturing a number of individuals from the population, tagging them in a harmless manner, and releasing them back into the environment. After some time, a second capture is done, and scientists note how many of the recaptured animals are tagged.

The key to successful wildlife population estimation using this method is the ratio of tagged to untagged individuals in the second capture. Assuming that the tagged animals mix evenly with the rest of the population and that their tagging does not influence their survival or visibility, the ratio can be used to estimate the total population size. Mistakes in this estimation process can have significant repercussions for wildlife management and conservation strategies. Therefore, ensuring the accuracy of the tagging and recapture process is essential to obtain reliable data.

Improving Accuracy in Population Estimates

To improve the accuracy of population estimates, it's important to repeat the capture-recapture process multiple times, use non-intrusive tagging methods, and account for possible factors that could alter animal behavior or survival rates due to tagging.
Biological Sampling Techniques
Biological sampling techniques like capture-recapture are crucial in gathering data about living organisms without disturbing their natural habitats significantly. This particular technique is not limited to estimating animal populations, but can also be adapted for plants and microorganisms in various environmental contexts.

Sampling involves careful planning to ensure that the data collected is representative of the population as a whole. This includes selecting the right size and location of the sample area, the timing of the captures, and the methods used for tagging. In addition to capture-recapture, other techniques such as quadrat sampling, transect sampling, and mark and recapture are used to study population density, distribution, and diversity.

Considerations for Ethical Sampling

Ethical considerations play a vital role in biological sampling. Researchers must ensure minimal impact on individuals' lives and the environment. Minimizing stress during capture, using safe and quick tagging methods, and ensuring that the marked individuals can continue their normal activities are all practices that align with ethical sampling.
Environmental Statistics
Environmental statistics is a field of study that applies statistical methods to environmental science. It's used to understand and make decisions about the natural world, from wildlife population management to pollution monitoring. When applying statistical methods such as the capture-recapture technique, it's crucial to consider all variables that may affect the outcome, including natural and human-made factors.

In the context of the capture-recapture method, various assumptions are made, such as equal probability of capture for all individuals, no effect of tagging on individual's survival or behavior, and that the populations are 'closed' during the study period, with no migration, births, or deaths. Violating these assumptions can lead to biased estimates, leading to poor decision-making in environmental management.

Addressing Statistical Challenges in Capture-Recapture

To tackle the statistical challenges in capture-recapture studies, biostatisticians use innovative models to estimate population size while accounting for potential biases. This includes modifying the basic capture-recapture model to accommodate various survival rates, different probabilities of capture, and the effects of tagging on individual animals. These refined models contribute to more accurate environmental statistics, leading to better conservation and management practices.

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Most popular questions from this chapter

Refer to a clinical trial named APPROVe designed to determine whether Vioxx, a medication used for ar. thritis and acute pain, was effective in preventing the recurrence of colorectal polyps in patients with a history of colorectal adenomas. APPROVe was conducted between 2002 and 2003 and involved 2586 participants, all of whom had a history of colorectal adenomas. The participants were randomly divided into two groups: 1287 were given 25 milligrams of Vioxx daily for the duration of the clinical trial (originally intended to last three years), and \(1299 \mathrm{pa}\) tients were given a placebo. Neither the participants nor the doctors involved in the clinical trial knew who was in which group. During the trial, 72 of the participants had cardiovascular events (mostly heart attacks or strokes). Later it was found that 46 of these people were from the group taking the Vioxx and only 26 were from the group taking the placebo. Based on these results, the clinical trial was stopped in 2003 and Vioxx was taken off the market in \(2004 .\) (a) Describe the control and treatment groups in APPROVe.

Leading-question bias. The way the questions in many surveys are phrased can itself be a source of bias. When a question is worded in such a way as to predispose the respondent to provide a particular response, the results of the survey are tainted by a special type of bias called leading-question bias. The following is an extreme hypothetical situation intended to drive the point home. In an effort to find out how the American taxpayer feels about a tax increase, the Institute for Tax Reform conducts a "scientific" one-question poll. Are you in favor of paving higher taxes to bail the federal government out of its disastrous economic policies and its mismanagement of the federal budget? Yes. No Ninety-five percent of the respondents answered no. (a) Explain why the results of this survey might be invalid. (b) Rephrase the question in a neutral way. Pay particular attention to highly charged words. (c) Make up your own (more subtle) example of leadingquestion bias. Analyze the critical words that are the cause of bias.

The critically endangered Maui's dolphin is currently restricted to a relatively small stretch of coastline along the west coast of New Zealand's North Island. The dolphins are "captured" by just collecting samples of DNA and "tagged" by identifying their DNA fingerprint. A 2010 2011 capture- recapture study "captured" and "tagged" 26 Maui's dolphins in \(2010 .\) In 2011,27 Maui's dolphins were "recaptured" and through their DNA, 12 were identified as having been "tagged" in 2010. Based on these figures, estimate the population of Maui's dolphins in 2011. [Source: Oremus, \(\mathbf{M}_{\cdot,}\) et al, "Distribution, group characteristics and movements of the critically endangered Maui's Dolphin (Cephalorhynchus hectori maui)." Endangered Species Research, preprint.]

(a) For the capture-recapture method to give a reasonable estimate of \(N\), what assumptions about the two samples must be true? (b) Give reasons why the assumptions in (a) may not hold true in many situations.

Refer to the following story: The dean of students at Tasmania State University wants to determine how many undergraduates at TSU are familiar with a new financial aid program offered by the university. There are 15,000 undergraduates at TSU, so it is too expensive to conduct a census. The following sampling method is used to choose a representative sample of undergraduates to poll. Start with the registrar's alphabetical listing containing the names of all undergraduates. Randomly pick a number between \(l\) and \(100,\) and count that far down the list. Take that name and every I00th name after it. For example, if the random number chosen is \(73,\) then pick the \(73 \mathrm{rd}, 173 \mathrm{rd}, 273 \mathrm{rd}\) and so forth, names on the list. (The sampling method illustrated in this survey is known as systematic sampling.) (a) Explain why the method used for choosing the sample is not simple random sampling. (b) If \(100 \%\) of those responding claimed that they were not familiar with the new financial aid program offered by the university, is this result more likely due to sampling variability or to sample bias? Explain.

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