|
|
| Line 1: |
Line 1: |
| {{merge from|Tag and release|discuss=Talk:Mark and recapture#Merge discussion| date=May 2013}}
| |
| {{More footnotes|date=March 2008}}
| |
| [[File:Collar tagged Rock Hyrax.JPG|thumb|Collar tagged Rock Hyrax]]
| |
| [[File:Jackdaw with a ring.JPG|thumb|Jackdaw with a numbered aluminum ring on its left tarsus]]
| |
| [[File:Novisuccinea chittenangoensis 5.png|thumb|Biologist is marking a [[Chittenango ovate amber snail]] to monitor the population.]]
| |
| [[File:Novisuccinea chittenangoensis 4.png|thumb|alt=right side view of a snail with a number 87 on its shell|Marked Chittenango ovate amber snail.]]
| |
| '''Mark and recapture''' is a method commonly used in [[ecology]] to estimate an animal [[population]]'s size. A portion of the population is captured, marked, and released. Later, another portion is captured and the number of marked individuals within the sample is counted. 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. The method is most useful when it is not practical to count all the individuals in the population. 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'''<ref name="krebs119">,{{Cite book|
| |
| title=Ecology|
| |
| last1=Krebs|
| |
| first1=Charles J.|
| |
| edition=6th|
| |
| isbn=978-0-321-50743-3|
| |
| page=119|
| |
| year=2009}}</ref> and '''the Lincoln method'''.
| |
|
| |
|
| Another major application for these methods is in [[epidemiology]]{{Citation needed|date=February 2012}}, where they are used to estimate the completeness of ascertainment of disease registers. Typical applications include [[estimating]] the number of people needing particular services (i.e. services for children with [[learning disabilities]], services for [[medically frail]] elderly living in the community), or with particular conditions(i.e. illegal drug addicts, people infected with [[HIV]], etc.).{{Citation needed|date=February 2012}}
| |
|
| |
|
| ==Field work related to mark-recapture==
| | [http://Suwonyouth.org/?document_srl=265218 suwonyouth.org]Probably one of the best of the arguably beige dryer and washing machine sets could be the Whirlpool - Duet 4. Should you need a banner that could stay strong in winds, then the 9 [http://kakaotv.net/?document_srl=1348981 ounce mesh] vinyl ought to indicate ([http://www.stereomood.com/users/washerijay/dashboard stereomood.com]) be what you choose. Whirlpool cabrio washer error codes ul For many householders, deck cleaning might be more stressful before they even [http://hub.mili.csom.umn.edu/member_profile/cabrioaeast whirlpool cabrio washer manual top load] can begin to get that pressure washer than through the deed itself.<br><br>When you've got a drying drum that is this size it is possible to easily fit countless items or extremely large items, such as comforters, with ease. A wise purchase always starts with all the exact knowledge of what one whirlpool cabrio dryer pf code [https://theartscentregc.zendesk.com/entries/53520154-How-You-Can-Obtain-Cuisinart-Multiclad-Pro-Completed-Appropriately whirlpool duet washer owners manual] wants.<br><br>On the opposite hand, a dedicated article marketing service puts its entire team's focus into writing and editing superior articles to your site. Of course books of short stories are simply in all [http://Pictures.yt/social/groups/four-tips-to-reinvent-your-menards-jobs-and-win/ book stores]. Home depot coupons [https://support.audiogeneral.com/entries/86948666-Ten-Steps-To-Produce-New-Habits article] As in letter writing, notes cause impressions to become formed about one. [http://cabrioohope.svbtle.com/ whirlpool duet reviews consumer reports] An online writer must keep to the number 1 rule for those [http://foodandme.in/members/zugghomesley/activity/263217/ writers]. |
| Typically a [[researcher]] visits a study area and uses traps to capture a group of individuals alive{{Citation needed|date=May 2013}}. Each of these individuals is marked with a unique identifier (e.g., a numbered tag or band), and then is released unharmed back into the environment. A mark recapture method was first used for ecological study in 1896 by [[C.G. Johannes Petersen]] to estimate plaice, ''[[Pleuronectes platessa]]'', populations.<ref name="Southwood">Southwood, T.R.E. & Henderson, P. (2000) ''Ecological Methods'', 3rd edn. Blackwell Science, Oxford.</ref>
| |
| | |
| Sufficient time is allowed to pass for the marked individuals to redistribute themselves among the unmarked population{{Citation needed|date=May 2013}}.
| |
| | |
| Next, the researcher returns and captures another [[Sample (statistics)|sample]] of individuals{{Citation needed|date=May 2013}}. Some of the individuals in this second sample will have been marked during the initial visit and are now known as recaptures. Other animals captured during the second visit will not have been captured during the first visit to the study area. These unmarked animals are usually given a tag or band during the second visit and then are released{{Citation needed|date=May 2013}}.
| |
| | |
| Population size can be estimated from as few as two visits to the study area. Commonly, more than two visits are made, particularly if estimates of survival or movement are desired{{Citation needed|date=May 2013}}. Regardless of the total number of visits, the researcher simply records the date of each capture of each individual. The "capture histories" generated are analyzed mathematically to estimate population size, survival, or movement{{Citation needed|date=May 2013}}.
| |
| | |
| In the epidemiological setting, different sources of patients take the place of the repeated field visits in [[ecology]]. To take a concrete example, establishing a register of children with [[Type 1 diabetes]] children were identified from hospital admission records, from general practitioners (family doctors), and from the records of the local Diabetes Association{{Citation needed|date=May 2013}}. None of these sources had a complete list, but by putting them together it was possible to do two things, first to see how many children were identified in total, and secondly to estimate how many more children with [[Type 1 diabetes]] were living in the vital community.{{Citation needed|date=April 2013}}
| |
| | |
| ==Lincoln-Petersen method of analysis==
| |
| {{main|Lincoln index}}
| |
| The '''Lincoln-Petersen method'''<ref name="seber">Seber, G.A.F.. The Estimation of Animal Abundance and Related Parameters. Caldwel,New Jersey: Blackburn Press. ISBN 1-930665-55-5</ref> (also known as the Petersen-Lincoln index<ref name="Southwood"/> or [[Lincoln index]]) can be used to estimate population size if only two visits are made to the study area. This method assumes that the study population is "closed"{{Citation needed|date=May 2013}}. In other words, the two visits to the study area are close enough in time so that no individuals die, are born, move into the study area ([[immigrate]]) or move out of the study area ([[emigrate]]) between visits. The model also assumes that no marks fall off animals between visits to the field site by the researcher, and that the researcher correctly records all marks.
| |
| | |
| Given those conditions, estimated population size is:
| |
| | |
| :<math>N = \frac{MC}{R},</math>
| |
| | |
| where
| |
| | |
| : ''N'' = Estimate of total population size
| |
| : ''M'' = Total number of animals captured and marked on the first visit
| |
| : ''C'' = Total number of animals captured on the second visit
| |
| : ''R'' = Number of animals captured on the first visit that were then recaptured on the second visit
| |
| | |
| ===Adaptation of the Lincoln-Petersen method===
| |
| It is assumed (Krebs, 1998) 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 implies that, in the second sample, the proportion of marked individuals that are caught (<math>R/M</math>) should equal the proportion of the total population that is caught (<math>C/N</math>). For example, if half of the marked individuals were recaptured, it would be assumed that half of the total population was included in the second sample.
| |
| | |
| In symbols,
| |
| :<math>\frac{R}{M} = \frac{C}{N}.</math> | |
| | |
| A rearrangement of this gives
| |
| :<math>N=\frac{MC}{R}, </math>
| |
| the formula used for the Lincoln–Petersen method (Krebs, 1998).
| |
| | |
| ===Sample calculation===
| |
| A biologist wants to estimate the size of a population of turtles in a lake. She captures 10 turtles on her first visit to the lake, and marks their backs with paint. A week later she returns to the lake and captures 15 turtles. Five of these 15 turtles have paint on their backs, indicating that they are recaptured animals.
| |
| | |
| : <math>N = \frac{MC}{R} = \frac{10\times 15}{5} = 30</math>
| |
| | |
| In this example, the Lincoln–Petersen method estimates that there are 30 turtles in the lake.
| |
| | |
| ===A refined form, the Chapman Estimator===
| |
| The Lincoln-Peterson estimator is asymptotically unbiased as sample size approaches infinity, but is biased at small sample sizes.<ref name="Chapman1951">{{cite journal|author=Chapman, D.G.|title=Some properties of the hypergeometric distribution with applications to zoological sample censuses|year=1951}}</ref> An alternative [[shrinkage estimator|less biased estimator]] of population size is given by the Chapman Estimator:<ref name="Chapman1951"/>
| |
| | |
| :<math>N = \frac{(M+1)(C+1)}{R+1} - 1,</math>
| |
| | |
| where, as before,
| |
| | |
| : ''N'' = Estimate of total population size
| |
| : ''M'' = Total number of animals captured and marked on the first visit
| |
| : ''C'' = Total number of animals captured on the second visit
| |
| : ''R'' = Number of animals captured on the first visit that were then recaptured on the second visit
| |
| | |
| An approximately unbiased [[variance]] of ''N'', or var(''N''), can be estimated as:
| |
| | |
| : <math> \operatorname{var}(N) = \frac{(M+1)(C+1)(M-R)(C-R)}{(R+1)(R+1)(R+2)}.</math>
| |
| | |
| ==More than two visits==
| |
| The literature on the analysis of capture-recapture studies has blossomed since the early 1990s{{Citation needed|date=May 2013}}. There are very elaborate statistical models available for the analysis of these experiments{{Citation needed|date=May 2013}}. A simple model which easily accommodates the three source, or the three visit study, is to fit a [[Poisson regression]] model. Sophisticated mark-recapture models can be fit using Rcapture,<ref name=CRAN>{{cite web|title=CRAN - Package Rcapture|url=http://cran.r-project.org/web/packages/Rcapture/index.html|accessdate=29 May 2013}}</ref> a package of the Open Source [[R programming language]], or specialized programs such as [[MARK (Software)|MARK]] <ref name=MARK>{{cite web|title=Program MARK|url=http://www.warnercnr.colostate.edu/~gwhite/mark/mark.htm|accessdate=29 May 2013}}</ref> or [[M-SURGE]].<ref name=Logiciels>{{cite web|title=Logiciels|url=http://www.cefe.cnrs.fr/biom/Logiciels.htm}}</ref> Other related methods which are often used include the [[Jolly-Seber model]] (used in open populations and for multiple census estimates) and Schnabel estimators (described above as an expansion to the Lincoln-Peterson method for closed populations). These are described in detail by Sutherland.<ref name="sutherland">{{cite book|title=Ecological Census Techniques: A Handbook|editor=William J. Sutherland|year=1996|publisher=Cambridge University Press|isbn=0521478154}}</ref>
| |
| | |
| ==Integrated approaches==
| |
| Modelling mark-recapture data is trending towards a more integrative approach,<ref name="maunder1">Maunder M.N. (2003) Paradigm shifts in fisheries stock assessment: from integrated analysis to Bayesian analysis and back again. Natural Resource Modeling 16:465-475</ref> which combines mark-recapture data with [[population dynamics]] models and other types of data. The integrated approach is more computationally demanding, but extracts more information from the data improving [[parameter]] and [[uncertainty]] estimates.<ref name="maunder2">Maunder, M.N. (2001) Integrated Tagging and Catch-at-Age Analysis (ITCAAN). In Spatial Processes and Management of Fish Populations, edited by G.H. Kruse,N. Bez, A. Booth, M.W. Dorn, S. Hills, R.N. Lipcius, D. Pelletier, C. Roy, S.J. Smith, and D. Witherell, Alaska Sea Grant College Program Report No. AK-SG-01-02, University of Alaska Fairbanks, pp. 123-146.</ref>
| |
| | |
| ==See also==
| |
| {{portal|Ecology}}
| |
| * [[German tank problem]], for estimation of population size when the elements are numbered.
| |
| * [[Tag and release]]
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| * {{Cite journal|last=Besbeas|first=P|coauthors=Freeman, S. N., Morgan, B. J. T., Catchpole, E. A.|title=Integrating mark-recapture-recovery and census data to estimate animal abundance and demographi parameters.|journal=Biometrics|volume=58|pages=540–547|doi=10.1111/j.0006-341X.2002.00540.x|pmid=12229988|year=2002|issue=3}}
| |
| * {{Cite journal
| |
| |last=Martin-Löf |first=P.|authorlink=Per Martin-Löf
| |
| |title=Mortality rate calculations on [[bird ringing|ringed birds]] with special reference to the [[Dunlin]] ''Calidris alpina''
| |
| |journal=Arkiv för Zoologi (Zoology files), Kungliga Svenska Vetenskapsakademien (The Royal Swedish Academy of Sciences) Serie 2
| |
| |volume=Band 13
| |
| |issue=21
| |
| |year=1961
| |
| }}
| |
| * {{Cite journal|last=Maunder|first=M. N.|title=Population viability analysis, based on combining integrated, Bayesian, and hierarchical analyses|journal=Acta Oecologica|volume=26|pages=85–94|doi=10.1016/j.actao.2003.11.008|year=2004|issue=2}}
| |
| * {{Cite journal|last=Phillips|first=C. A.|coauthors=M. J. Dreslik, J. R. Johnson, and J. E. Petzing|year=2001|title=Application of population estimation to pond breeding salamanders|journal=Transactions of the Illinois Academy of Science|volume=94|issue=2|pages=111–118}}
| |
| * {{Cite book|last=Royle|first=J. A.|coauthors=R. M. Dorazio|title=Hierarchical Modeling and Inference in Ecology|publisher=Elsevier|year=2008|isbn=1-930665-55-5}}
| |
| * {{Cite book|last=Seber|first=G.A.F.|title=The Estimation of Animal Abundance and Related Parameters|publisher=Blackburn Press|location=Caldwel,New Jersey|isbn=1-930665-55-5}}
| |
| * {{Cite journal|last=Schaub|first=M|coauthors=Gimenez, O., Sierro, A., and Arlettaz, R|year=2007|title=Use of Integrated Modeling to Enhance Estimates of Population Dynamics Obtained from Limited Data|journal=Conservation Biology|volume=21|issue=4|pages=945–955|doi= 10.1111/j.1523-1739.2007.00743.x|pmid=17650245}}
| |
| * {{Cite book|last=Williams|first=B. K.|coauthors=J. D. Nichols, and M. J. Conroy|title=Analysis and Management of Animal Populations|publisher=Academic Press|location=San Diego, California|year=2002|isbn=0-12-754406-2}}
| |
| | |
| ==Further reading==
| |
| * Bonett, D.G., Woodward, J.A., & Bentler, P.M. (1986). "A Linear Model for Estimating the Size of a Closed Population", ''British Journal of Mathematical and Statistical Psychology, 39,'' 28-40.
| |
| * Evans, M.A., Bonett, D.G., & McDonald, L. (1994). "A General Theory for Analyzing Capture-recapture Data in Closed Populations." ''Biometrics, 50,'' 396-405.
| |
| * Lincoln, F. C. (1930). "Calculating Waterfowl Abundance on the Basis of Banding Returns". ''United States Department of Agriculture Circular'', 118, 1–4.
| |
| * Petersen, C. G. J. (1896). "The Yearly Immigration of Young Plaice Into the Limfjord From the German Sea", ''Report of the Danish Biological Station (1895)'', 6, 5–84.
| |
| * Schofield, J. R. (2007). "Beyond Defect Removal: Latent Defect Estimation With Capture-Recapture Method", Crosstalk, August, 2007; 27-29.
| |
| | |
| ==External links==
| |
| * [http://www.pitt.edu/~yuc2/cr/history.htm A historical introduction to capture-recapture methods]
| |
| | |
| {{DEFAULTSORT:Mark And Recapture}}
| |
| [[Category:Ecological techniques]]
| |
| [[Category:Epidemiology]]
| |
| [[Category:Statistical data types]]
| |
| [[Category:Environmental statistics]]
| |