k z Mark and recapture is a method commonly used in ecology to estimate an animal population's size where it is impractical to count every individual. Surprisingly, Chapman's estimate was one conjecture from a range of possible estimators: "In practice, the whole number immediately less than (K+1)(n+1)/(k+1) or even Kn/(k+1) will be the estimate. The correlation between the parameter N̂ and its associated variance is shown to be significant for all the estimators. This page was last edited on 1 October 2020, at 23:22. confidence interval for the population size N can be obtained as: K The Lincoln–Petersen method[7] (also known as the Petersen–Lincoln index[5] or Lincoln index) can be used to estimate population size if only two visits are made to the study area. [18] Such models can also be fit with specialized programs such as MARK[19] or M-SURGE. 1 + If the chosen identifier harms the organism, then its behavior might become irregular. Another major application for these methods is in epidemiology,[3] where they are used to estimate the completeness of ascertainment of disease registers. − 100 {\displaystyle 1-\alpha /2} [1] A portion of the population is captured, marked, and released. − option. Oecologia [1] A portion of the population is captured, marked, and released. % α = 0.5 AK-SG-01-02, University of Alaska Fairbanks, pp. Original Papers Schofield, J. R. (2007). Importantly, the formula can be re-written as a linear equation in terms of f: Because this is a linear function, it follows that for certain versions of q for which the slope of this line (the first term multiplied by f) is positive, all of the detection resource should be devoted to the high-risk population (f should be set to 1 to maximize the capture probability), whereas for other value of q, for which the slope of the line is negative, all of the detection should be devoted to the low-risk population (f should be set to 0. Given those conditions, estimated population size is: It is assumed[8] that all individuals have the same probability of being captured in the second sample, regardless of whether they were previously captured in the first sample (with only two samples, this assumption cannot be tested directly). This example is (n, K, k) = (10, 15, 5). Other names for this method, or closely related methods, include capture-recapture, capture-mark-recapture, mark-recapture, sight-resight, mark-release-recapture, multiple systems estimation, band recovery, the Petersen method,[2] and the Lincoln method. + Categories: / 1 3,000 new books annually, covering a wide range of subjects including biomedicine and the life sciences, clinical medicine, 0.5 0.5 When capturing and marking organisms, ecologists need to consider the welfare of the organisms. 1 N Plant-animal interactions {\displaystyle n/N} ( ( These are described in detail by Sutherland. level even for small populations and extreme capture probabilities (near to 0 or 1), in which cases other confidence intervals fail to achieve the nominal coverage levels.[10]. ). / / % A biologist wants to estimate the size of a population of turtles in a lake. ) 0.5 / These unmarked animals are usually given a tag or band during the second visit and then are released. illegal drug addicts, people infected with HIV, etc.). ) ) We can solve the above equation for the values of q for which the slope will be positive to determine the values for which f should be set to 1 to maximize the capture probability: This is an example of linear optimization. Community ecology ± "[9](see footnote, page 144). The integrated approach is more computationally demanding, but extracts more information from the data improving parameter and uncertainty estimates. Oecologia publishes innovative ecological research of general interest to a broad international audience. Methods + Springer is one of the leading international scientific publishing companies, publishing over 1,200 journals and more than These include "Spatially Explicit Capture-Recapture (secr)",[16] "Loglinear Models for Capture-Recapture Experiments (Rcapture)",[17] and "Mark-Recapture Distance Sampling (mrds)". 0.5 k {\displaystyle k/K} ⁡ Special Topics n [13] For example, an application of the model in the 1920s was to detect typhoid carriers in London, who were either arriving from zones with high rates of tuberculosis (probability q that a passenger with the disease came from such an area, where q>0.5), or low rates (probability 1-q). Johannes Petersen to estimate plaice, Pleuronectes platessa, populations. Since the number of marked individuals within the second sample should be proportional to the number of marked individuals in the whole population, an estimate of the total population size can be obtained by dividing the number of marked individuals by the proportion of marked individuals in the second sample. 1 {\displaystyle {\hat {\sigma }}_{0.5}={\sqrt {{\frac {1}{k+0.5}}+{\frac {1}{K-k+0.5}}+{\frac {1}{n-k+0.5}}+{\frac {k+0.5}{(n-k+0.5)(K-k+0.5)}}}}} N=n*K/k. ( n 0.5 k Manuscript Types: (2001) Integrated Tagging and Catch-at-Age Analysis (ITCAAN). Smith, and D. Witherell, Alaska Sea Grant College Program Report No. There are very elaborate statistical models available for the analysis of these experiments. The above form is more convenient for mathematical purposes. + {\displaystyle 100(1-\alpha )\%} {\displaystyle 100(1-\alpha )\%} exp + K Kruse, N. Bez, A. Booth, M.W. + − Concepts, Reviews, and Syntheses Physiological ecology The Lincoln–Petersen estimator is asymptotically unbiased as sample size approaches infinity, but is biased at small sample sizes. A derivation is found here: Talk:Mark and recapture#Statistical treatment. / ) should equal the proportion of the total population that is marked ( − α Lipcius, D. Pelletier, C. Roy, S.J. Thus, the Chapman method estimates 28 turtles in the lake.

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