261:
92:'s size where it is impractical to count every individual. A portion of the population is captured, marked, and released. Later, another portion will be 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 assumes, rightly or wrongly, that the probability of capture is the same for all individuals. Other names for this method, or closely related methods, include
249:
25:
160:
234:
219:
335:) 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". In other words, the two visits to the study area are close enough in time so that no individuals die, are born, or move into or out of the study area 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.
1769:
2265:
196:
of individuals. Some individuals in this second sample will have been marked during the initial visit and are now known as recaptures. Other organisms 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
200:
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. Regardless of the total number of visits, the researcher simply records the date of each capture of each individual.
2946:
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
308:
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
175:
visits a study area and uses traps to capture a group of individuals alive. 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
1805:
is the frequency of time that the problem (e.g., an animal disease) occurs in the high-risk versus the low-risk sector. 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
1407:
2209:
The literature on the analysis of capture-recapture studies has blossomed since the early 1990s. There are very elaborate statistical models available for the analysis of these experiments. A simple model which easily accommodates the three source, or the three visit study, is to fit a
1913:
where the first term refers to the probability of detection (capture probability) in a high risk zone, and the latter term refers to the probability of detection in a low risk zone. Importantly, the formula can be re-written as a linear equation in terms of
1147:
399:
It is assumed 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).
2218:. These include "Spatially Explicit Capture-Recapture (secr)", "Loglinear Models for Capture-Recapture Experiments (Rcapture)", and "Mark-Recapture Distance Sampling (mrds)". Such models can also be fit with specialized programs such as
2027:
897:
1232:
2138:
650:
1908:
1714:
761:
2233:(used in open populations and for multiple census estimates) and Schnabel estimators (an expansion to the Lincoln–Petersen method for closed populations). These are described in detail by Sutherland.
1508:
925:+1) will be the estimate. The above form is more convenient for mathematical purposes."(see footnote, page 144). Chapman also found the estimator could have considerable negative bias for small
1584:
506:
562:
389:
204:
When capturing and marking organisms, ecologists need to consider the welfare of the organisms. If the chosen identifier harms the organism, then its behavior might become irregular.
2956:
Besbeas, P; Freeman, S. N.; Morgan, B. J. T.; Catchpole, E. A. (2002). "Integrating mark-recapture-recovery and census data to estimate animal abundance and demographic parameters".
2180:
991:
1458:
977:
1460:
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.
1218:
1184:
2937:
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
1740:
1610:
1801:
is defined as the fraction of a finite resource devoted to detecting the animal or person of interest from a high risk sector of an animal or human population, and
457:
429:
2230:
1924:
777:
459:). 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.
1818:). It was posited that only 5 out of 100 of the travelers could be detected, and 10 out of 100 were from the high risk area. Then the capture probability
2219:
1790:
The capture probability refers to the probability of a detecting an individual animal or person of interest, and has been used in both ecology and
1402:{\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)}}}}.}
660:
The
Lincoln–Petersen estimator is asymptotically unbiased as sample size approaches infinity, but is biased at small sample sizes. An alternative
2245:
models and other types of data. The integrated approach is more computationally demanding, but extracts more information from the data improving
905:
Surprisingly, Chapman's estimate was one conjecture from a range of possible estimators: "In practice, the whole number immediately less than (
2066:
581:
3038:
Phillips, C. A.; M. J. Dreslik; J. R. Johnson; J. E. Petzing (2001). "Application of population estimation to pond breeding salamanders".
902:
Note that the answer provided by this equation must be truncated not rounded. Thus, the
Chapman method estimates 28 turtles in the lake.
3284:
Schofield, J. R. (2007). "Beyond Defect
Removal: Latent Defect Estimation With Capture-Recapture Method", Crosstalk, August 2007; 27–29.
2572:
Sadinle, Mauricio (2009-10-01). "Transformed Logit
Confidence Intervals for Small Populations in Single Capture–Recapture Estimation".
2832:
3334:
2223:
3163:; Tsay, P. K.; Lin, S. H.; Shau, W. Y.; Chao, D. Y. (2001). "The applications of capture-recapture models to epidemiological data".
2387:; Tsay, P. K.; Lin, S. H.; Shau, W. Y.; Chao, D. Y. (2001). "The applications of capture-recapture models to epidemiological data".
1828:
1616:
674:
3236:
Evans, M.A.; Bonett, D.G.; McDonald, L. (1994). "A General Theory for
Analyzing Capture-recapture Data in Closed Populations".
248:
189:
Sufficient time should be allowed to pass for the marked individuals to redistribute themselves among the unmarked population.
1474:
3060:
2368:
3009:
Maunder, M. N. (2004). "Population viability analysis, based on combining integrated, Bayesian, and hierarchical analyses".
260:
2615:
Drenner, Ray (1978). "Capture probability: the role of zooplankter escape in the selective feeding of planktivorous fish".
2858:
3002:
Arkiv för
Zoologi (Zoology Files), Kungliga Svenska Vetenskapsakademien (The Royal Swedish Academy of Sciences) Serie 2
2241:
Modelling mark-recapture data is trending towards a more integrative approach, which combines mark-recapture data with
1746:
135:, where they are used to estimate the completeness of ascertainment of disease registers. Typical applications include
3329:
3207:
Bonett, D.G.; Woodward, J.A.; Bentler, P.M. (1986). "A Linear Model for
Estimating the Size of a Closed Population".
3150:
3079:
2922:
2681:
2534:
2504:
68:
46:
2642:
MacKenzie, Darryl (2002). "How should detection probability be incorporated into estimates of relative abundance?".
1519:
575:
In the example (n, K, k) = (10, 15, 5) the
Lincoln–Petersen method estimates that there are 30 turtles in the lake.
468:
39:
2389:
3090:
2048:, for which the slope of the line is negative, all of the detection should be devoted to the low-risk population (
201:
The "capture histories" generated are analyzed mathematically to estimate population size, survival, or movement.
3324:
517:
344:
147:
elderly living in the community), or with particular conditions (e.g. illegal drug addicts, people infected with
2655:
1422:
It has been shown that this confidence interval has actual coverage probabilities that are close to the nominal
3314:
2878:
1142:{\displaystyle K+n-k-0.5+{\frac {(K-k+0.5)(n-k+0.5)}{(k+0.5)}}\exp(\pm z_{\alpha /2}{\hat {\sigma }}_{0.5}),}
164:
218:
3277:
Petersen, C. G. J. (1896). "The Yearly Immigration of Young Plaice Into the Limfjord From the German Sea",
2149:
3339:
2319:
1425:
944:
933:(page 146), but was unconcerned because the estimated standard deviations were large for these cases.
2194:
3091:"Use of Integrated Modeling to Enhance Estimates of Population Dynamics Obtained from Limited Data"
2299:
33:
2559:
Some properties of the hypergeometric distribution with applications to zoological sample censuses
233:
1189:
309:
they are recaptured animals. This example is (n, K, k) = (10, 15, 5). The problem is to estimate
2214:
model. Sophisticated mark-recapture models can be fit with several packages for the Open Source
2215:
1154:
403:
This implies that, in the second sample, the proportion of marked individuals that are caught (
177:
50:
2796:
3319:
2294:
1779:
182:
140:
2040:) is positive, all of the detection resource should be devoted to the high-risk population (
1719:
1589:
3105:
3018:
2836:
2289:
2022:{\displaystyle P=\left({\frac {5}{10}}q-{\frac {5}{90}}(1-q)\right)f+{\frac {5}{90}}(1-q).}
1783:
3265:
Lincoln, F. C. (1930). "Calculating Waterfowl Abundance on the Basis of Banding Returns".
2996:(1961). "Mortality rate calculations on ringed birds with special reference to the Dunlin
2818:
2774:
892:{\displaystyle {\hat {N}}_{C}={\frac {(n+1)(K+1)}{k+1}}-1={\frac {11\times 16}{6}}-1=28.3}
8:
2278:
2242:
2186:
1224:
979:
661:
434:
406:
193:
3109:
3022:
3253:
3220:
3188:
3129:
2981:
2895:
2715:
2698:
2597:
2481:
2458:
2433:
2414:
2211:
3224:
3180:
3146:
3121:
3117:
3075:
3056:
2973:
2969:
2955:
2918:
2752:
2720:
2677:
2601:
2589:
2530:
2500:
2463:
2406:
2364:
2198:
3133:
2993:
2985:
2817:
Laake, Jeff; Borchers, David; Thomas, Len; Miller, David; Bishop, Jon (2015-08-17).
2044:
should be set to 1 to maximize the capture probability), whereas for other value of
3245:
3216:
3172:
3113:
3026:
2965:
2887:
2710:
2651:
2624:
2581:
2453:
2445:
2398:
1774:
2434:"Estimating the Number of People Who Inject Drugs in A Rural County in Appalachia"
159:
139:
the number of people needing particular services (e.g. services for children with
3192:
2876:
Schnabel, Z. E. (1938). "The Estimation of the Total Fish Population of a Lake".
2524:
2418:
2284:
144:
3030:
3037:
2270:
2585:
3308:
2862:
2593:
2449:
332:
322:
3294:
3184:
3125:
2977:
2724:
2467:
2410:
2032:
Because this is a linear function, it follows that for certain versions of
1797:
The capture probability is often defined as a two-variable model, in which
1791:
132:
3228:
2250:
1768:
2133:{\displaystyle \left({\frac {5}{10}}q-{\frac {5}{90}}(1-q)\right)>0,}
3257:
2899:
2056:
for which the slope will be positive to determine the values for which
225:
172:
136:
89:
3088:
2052:
should be set to 0. We can solve the above equation for the values of
645:{\displaystyle {\hat {N}}={\frac {nK}{k}}={\frac {10\times 15}{5}}=30}
431:) should equal the proportion of the total population that is marked (
3160:
2384:
2246:
3299:
3249:
3176:
3159:
2891:
2739:
2628:
2402:
2281:, for estimation of population size when the elements are numbered.
1220:
3140:
240:
85:
2561:. UC Publications in Statistics. University of California Press.
1810:
that a passenger with the disease came from such an area, where
2797:"Loglinear Models for Capture-Recapture Experiments (Rcapture)"
2036:
for which the slope of this line (the first term multiplied by
1903:{\displaystyle P={\frac {5}{10}}fq+{\frac {5}{90}}(1-f)(1-q),}
1709:{\displaystyle \epsilon ={\frac {(n-k+1)(K-k+1)}{(k-2)(k-3)}}}
2947:
No. AK-SG-01-02, University of Alaska Fairbanks, pp. 123–146.
2656:
10.1890/0012-9658(2002)083[2387:hsdpbi]2.0.co;2
3209:
British Journal of Mathematical and Statistical Psychology
756:{\displaystyle {\hat {N}}_{C}={\frac {(n+1)(K+1)}{k+1}}-1}
3072:
The Estimation of Animal Abundance and Related Parameters
2816:
2574:
Communications in Statistics - Simulation and Computation
2497:
The Estimation of Animal Abundance and Related Parameters
1778:, in a capture-release small mammal population study for
148:
3089:
Schaub, M; Gimenez, O.; Sierro, A.; Arlettaz, R (2007).
2363:(6th ed.). Pearson Benjamin Cummings. p. 119.
2060:
should be set to 1 to maximize the capture probability:
1503:{\displaystyle N\approx \mu \pm {\sqrt {\mu \epsilon }}}
2229:
Other related methods which are often used include the
197:
or band during the second visit and then are released.
154:
3295:
A historical introduction to capture-recapture methods
2795:
Rivest, Louis-Paul; Baillargeon, Sophie (2014-09-01).
2482:"Recapture Definition & Meaning - Merriam-Webster"
2189:. In more complex cases, where more than one resource
1794:
for detecting animal or human diseases, respectively.
1157:
338:
Given those conditions, estimated population size is:
3206:
3141:
Williams, B. K.; J. D. Nichols; M. J. Conroy (2002).
2912:
2152:
2069:
1927:
1831:
1722:
1619:
1592:
1522:
1477:
1428:
1235:
1192:
994:
947:
780:
677:
584:
520:
471:
437:
409:
347:
2260:
3235:
3050:
2343:
2174:
2132:
2021:
1902:
1734:
1708:
1604:
1578:
1502:
1452:
1401:
1212:
1178:
1141:
971:
891:
755:
644:
567:the formula used for the Lincoln–Petersen method.
556:
500:
451:
423:
383:
192:Next, the researcher returns and captures another
131:Another major application for these methods is in
2794:
1419:≈ 30 with a 95% confidence interval of 22 to 65.
3306:
3267:United States Department of Agriculture Circular
2522:
2193:is devoted to more than two areas, multivariate
298:= Number of animals captured on the second visit
3040:Transactions of the Illinois Academy of Science
2383:
304:= Number of recaptured animals that were marked
3279:Report of the Danish Biological Station (1895)
3053:Hierarchical Modeling and Inference in Ecology
1579:{\displaystyle \mu ={\frac {(n-1)(K-1)}{k-2}}}
501:{\displaystyle {\frac {k}{K}}={\frac {n}{N}}.}
3143:Analysis and Management of Animal Populations
2775:"Spatially Explicit Capture-Recapture (secr)"
2556:
2552:
2550:
2548:
2546:
1747:Talk:Mark and recapture#Statistical treatment
331:(also known as the Petersen–Lincoln index or
316:
292:= Number of animals marked on the first visit
2518:
2516:
2344:Southwood, T. R. E.; Henderson, P. (2000).
2339:
2337:
2335:
2333:
2331:
2329:
557:{\displaystyle {\hat {N}}={\frac {nK}{k}},}
384:{\displaystyle {\hat {N}}={\frac {nK}{k}},}
2992:
2906:
2543:
2348:(3rd ed.). Oxford: Blackwell Science.
771:The example (n, K, k) = (10, 15, 5) gives
3145:. San Diego, California: Academic Press.
2851:
2821:. Comprehensive R Archive Network (CRAN).
2819:"Mark-Recapture Distance Sampling (mrds)"
2714:
2641:
2457:
209:Different methods of "mark and recapture"
69:Learn how and when to remove this message
3074:. Caldwel, New Jersey: Blackburn Press.
2940:
2931:
2915:Ecological Census Techniques: A Handbook
2875:
2799:. Comprehensive R Archive Network (CRAN)
2777:. Comprehensive R Archive Network (CRAN)
2617:Journal of the Fisheries Board of Canada
2513:
2499:. Caldwel, New Jersey: Blackburn Press.
2352:
2326:
2236:
1767:
158:
32:This article includes a list of general
3264:
3008:
2737:McCrea, R.S. and Morgan, B.J.T. (2014)
2696:
2614:
2571:
2204:
1468:The mean value ± standard deviation is
766:
3307:
2772:
2731:
2671:
1814:>0.5), or low rates (probability 1−
1763:
936:
3069:
2667:
2665:
2494:
2431:
2358:
2175:{\displaystyle q>{\frac {1}{10}}.}
570:
286:= Number of animals in the population
3051:Royle, J. A.; R. M. Dorazio (2008).
2825:
2740:"Analysis of capture-recapture data"
2488:
2425:
1756:) = (10, 15, 5) gives the estimate
1463:
1415:) = (10, 15, 5) gives the estimate
655:
254:Marked Chittenango ovate amber snail
155:Field work related to mark-recapture
18:
2913:William J. Sutherland, ed. (1996).
2529:(2nd ed.). Benjamin/Cummings.
2377:
664:of population size is given by the
16:Animal population estimation method
13:
3300:Analysis of capture-recapture data
3221:10.1111/j.2044-8317.1986.tb00843.x
3200:
2662:
1447:
966:
38:it lacks sufficient corresponding
14:
3351:
3288:
2438:American Journal of Public Health
3335:Environmental Sampling Equipment
3118:10.1111/j.1523-1739.2007.00743.x
2970:10.1111/j.0006-341X.2002.00540.x
2263:
1453:{\displaystyle 100(1-\alpha )\%}
972:{\displaystyle 100(1-\alpha )\%}
259:
247:
232:
217:
23:
2869:
2810:
2788:
2766:
2690:
2674:Ecological Models and Data in R
2635:
2608:
2565:
2917:. Cambridge University Press.
2676:. Princeton University Press.
2474:
2312:
2113:
2101:
2013:
2001:
1977:
1965:
1894:
1882:
1879:
1867:
1700:
1688:
1685:
1673:
1668:
1650:
1647:
1629:
1559:
1547:
1544:
1532:
1444:
1432:
1388:
1370:
1367:
1349:
1243:
1133:
1121:
1090:
1078:
1066:
1061:
1043:
1040:
1022:
963:
951:
833:
821:
818:
806:
788:
730:
718:
715:
703:
685:
591:
527:
511:A rearrangement of this gives
354:
1:
2879:American Mathematical Monthly
2773:Efford, Murray (2016-09-02).
2305:
394:
165:Chittenango ovate amber snail
84:is a method commonly used in
2753:"Chapman and Hall/CRC Press"
1745:A derivation is found here:
7:
3031:10.1016/j.actao.2003.11.008
2432:Allen; et al. (2019).
2256:
2197:is often used, through the
1213:{\displaystyle 1-\alpha /2}
274:
114:multiple systems estimation
10:
3356:
2359:Krebs, Charles J. (2009).
1179:{\textstyle z_{\alpha /2}}
320:
317:Lincoln–Petersen estimator
167:to monitor the population.
2672:Bolker, Benjamin (2008).
2586:10.1080/03610910903168595
2523:Charles J. Krebs (1999).
3330:Environmental statistics
2495:Seber, G. A. F. (1982).
2450:10.2105/AJPH.2018.304873
2300:Shadow Effect (Genetics)
982:for the population size
329:Lincoln–Petersen method
163:Biologist is marking a
53:more precise citations.
3325:Statistical data types
3165:Statistics in Medicine
3070:Seber, G.A.F. (2002).
2699:"The Health of London"
2557:Chapman, D.G. (1951).
2526:Ecological Methodology
2390:Statistics in Medicine
2216:R programming language
2185:This is an example of
2176:
2134:
2023:
1904:
1787:
1736:
1735:{\displaystyle k>3}
1710:
1606:
1605:{\displaystyle k>2}
1580:
1504:
1454:
1403:
1214:
1180:
1143:
973:
893:
757:
646:
558:
502:
453:
425:
385:
178:C.G. Johannes Petersen
168:
110:mark-release-recapture
98:capture-mark-recapture
88:to estimate an animal
3315:Ecological techniques
2295:GPS wildlife tracking
2237:Integrated approaches
2177:
2143:which simplifies to:
2135:
2024:
1905:
1780:London Wildlife Trust
1771:
1737:
1711:
1607:
1581:
1505:
1455:
1404:
1227:random variable, and
1215:
1181:
1144:
974:
894:
758:
662:less biased estimator
647:
559:
503:
454:
426:
386:
266:Tagged Common Ringlet
183:Pleuronectes platessa
162:
141:learning disabilities
3098:Conservation Biology
2290:Abundance estimation
2205:More than two visits
2201:or its derivatives.
2150:
2067:
1925:
1829:
1786:local nature reserve
1784:Gunnersbury Triangle
1720:
1617:
1590:
1520:
1475:
1426:
1233:
1190:
1155:
992:
986:can be obtained as:
945:
778:
675:
582:
518:
469:
435:
407:
345:
180:to estimate plaice,
3110:2007ConBi..21..945S
3023:2004AcO....26...85M
2839:on 21 February 2006
2279:German tank problem
2243:population dynamics
2187:linear optimization
1764:Capture probability
1186:corresponds to the
980:confidence interval
937:Confidence interval
452:{\displaystyle n/N}
424:{\displaystyle k/K}
122:the Petersen method
3340:Population ecology
2346:Ecological Methods
2212:Poisson regression
2172:
2130:
2019:
1900:
1788:
1732:
1706:
1602:
1576:
1500:
1450:
1399:
1210:
1176:
1139:
969:
889:
767:Sample calculation
753:
642:
571:Sample calculation
554:
498:
449:
421:
381:
169:
126:the Lincoln method
82:Mark and recapture
3171:(20): 3123–3157.
3062:978-1-930665-55-2
2623:(10): 1370–1373.
2484:. 21 August 2023.
2397:(20): 3123–3157.
2370:978-0-321-50743-3
2231:Jolly–Seber model
2199:simplex algorithm
2167:
2099:
2083:
1999:
1963:
1947:
1865:
1846:
1704:
1574:
1498:
1464:Bayesian estimate
1394:
1392:
1330:
1303:
1276:
1246:
1124:
1082:
875:
848:
791:
745:
688:
666:Chapman estimator
656:Chapman estimator
634:
613:
594:
549:
530:
493:
480:
376:
357:
94:capture-recapture
79:
78:
71:
3347:
3274:
3261:
3232:
3196:
3156:
3137:
3095:
3085:
3066:
3047:
3034:
3005:
2989:
2948:
2944:
2938:
2935:
2929:
2928:
2910:
2904:
2903:
2873:
2867:
2866:
2861:. Archived from
2855:
2849:
2848:
2846:
2844:
2835:. Archived from
2829:
2823:
2822:
2814:
2808:
2807:
2805:
2804:
2792:
2786:
2785:
2783:
2782:
2770:
2764:
2763:
2761:
2759:
2750:
2748:
2746:
2735:
2729:
2728:
2718:
2697:Unknown (1921).
2694:
2688:
2687:
2669:
2660:
2659:
2650:(9): 2387–2393.
2639:
2633:
2632:
2612:
2606:
2605:
2580:(9): 1909–1924.
2569:
2563:
2562:
2554:
2541:
2540:
2520:
2511:
2510:
2492:
2486:
2485:
2478:
2472:
2471:
2461:
2429:
2423:
2422:
2381:
2375:
2374:
2356:
2350:
2349:
2341:
2324:
2323:
2320:"Mark-Recapture"
2316:
2273:
2268:
2267:
2266:
2181:
2179:
2178:
2173:
2168:
2160:
2139:
2137:
2136:
2131:
2120:
2116:
2100:
2092:
2084:
2076:
2028:
2026:
2025:
2020:
2000:
1992:
1984:
1980:
1964:
1956:
1948:
1940:
1909:
1907:
1906:
1901:
1866:
1858:
1847:
1839:
1822:was defined as:
1775:Myodes glareolus
1741:
1739:
1738:
1733:
1715:
1713:
1712:
1707:
1705:
1703:
1671:
1627:
1611:
1609:
1608:
1603:
1585:
1583:
1582:
1577:
1575:
1573:
1562:
1530:
1509:
1507:
1506:
1501:
1499:
1491:
1459:
1457:
1456:
1451:
1408:
1406:
1405:
1400:
1395:
1393:
1391:
1347:
1336:
1331:
1329:
1309:
1304:
1302:
1282:
1277:
1275:
1261:
1259:
1254:
1253:
1248:
1247:
1239:
1219:
1217:
1216:
1211:
1206:
1185:
1183:
1182:
1177:
1175:
1174:
1170:
1148:
1146:
1145:
1140:
1132:
1131:
1126:
1125:
1117:
1113:
1112:
1108:
1083:
1081:
1064:
1020:
978:
976:
975:
970:
898:
896:
895:
890:
876:
871:
860:
849:
847:
836:
804:
799:
798:
793:
792:
784:
762:
760:
759:
754:
746:
744:
733:
701:
696:
695:
690:
689:
681:
651:
649:
648:
643:
635:
630:
619:
614:
609:
601:
596:
595:
587:
563:
561:
560:
555:
550:
545:
537:
532:
531:
523:
507:
505:
504:
499:
494:
486:
481:
473:
458:
456:
455:
450:
445:
430:
428:
427:
422:
417:
390:
388:
387:
382:
377:
372:
364:
359:
358:
350:
263:
251:
236:
221:
74:
67:
63:
60:
54:
49:this article by
40:inline citations
27:
26:
19:
3355:
3354:
3350:
3349:
3348:
3346:
3345:
3344:
3305:
3304:
3291:
3250:10.2307/2533383
3203:
3201:Further reading
3177:10.1002/sim.996
3153:
3093:
3082:
3063:
3011:Acta Oecologica
3004:. Band 13 (21).
2998:Calidris alpina
2952:
2951:
2945:
2941:
2936:
2932:
2925:
2911:
2907:
2892:10.2307/2304025
2874:
2870:
2857:
2856:
2852:
2842:
2840:
2831:
2830:
2826:
2815:
2811:
2802:
2800:
2793:
2789:
2780:
2778:
2771:
2767:
2757:
2755:
2751:
2744:
2742:
2738:
2736:
2732:
2703:Hosp Health Rev
2695:
2691:
2684:
2670:
2663:
2640:
2636:
2629:10.1139/f78-215
2613:
2609:
2570:
2566:
2555:
2544:
2537:
2521:
2514:
2507:
2493:
2489:
2480:
2479:
2475:
2430:
2426:
2403:10.1002/sim.996
2382:
2378:
2371:
2357:
2353:
2342:
2327:
2318:
2317:
2313:
2308:
2285:Tag and release
2269:
2264:
2262:
2259:
2239:
2207:
2159:
2151:
2148:
2147:
2091:
2075:
2074:
2070:
2068:
2065:
2064:
1991:
1955:
1939:
1938:
1934:
1926:
1923:
1922:
1857:
1838:
1830:
1827:
1826:
1766:
1721:
1718:
1717:
1672:
1628:
1626:
1618:
1615:
1614:
1591:
1588:
1587:
1563:
1531:
1529:
1521:
1518:
1517:
1490:
1476:
1473:
1472:
1466:
1427:
1424:
1423:
1348:
1337:
1335:
1313:
1308:
1286:
1281:
1265:
1260:
1258:
1249:
1238:
1237:
1236:
1234:
1231:
1230:
1202:
1191:
1188:
1187:
1166:
1162:
1158:
1156:
1153:
1152:
1127:
1116:
1115:
1114:
1104:
1100:
1096:
1065:
1021:
1019:
993:
990:
989:
946:
943:
942:
941:An approximate
939:
861:
859:
837:
805:
803:
794:
783:
782:
781:
779:
776:
775:
769:
734:
702:
700:
691:
680:
679:
678:
676:
673:
672:
658:
620:
618:
602:
600:
586:
585:
583:
580:
579:
573:
538:
536:
522:
521:
519:
516:
515:
485:
472:
470:
467:
466:
441:
436:
433:
432:
413:
408:
405:
404:
397:
365:
363:
349:
348:
346:
343:
342:
325:
319:
277:
272:
271:
270:
267:
264:
255:
252:
243:
237:
228:
222:
211:
210:
186:, populations.
157:
145:medically frail
143:, services for
75:
64:
58:
55:
45:Please help to
44:
28:
24:
17:
12:
11:
5:
3353:
3343:
3342:
3337:
3332:
3327:
3322:
3317:
3303:
3302:
3297:
3290:
3289:External links
3287:
3286:
3285:
3282:
3275:
3262:
3244:(2): 396–405.
3233:
3202:
3199:
3198:
3197:
3157:
3151:
3138:
3104:(4): 945–955.
3086:
3080:
3067:
3061:
3048:
3035:
3006:
2994:Martin-Löf, P.
2990:
2964:(3): 540–547.
2950:
2949:
2939:
2930:
2923:
2905:
2886:(6): 348–352.
2868:
2865:on 2009-07-24.
2850:
2833:"Program MARK"
2824:
2809:
2787:
2765:
2730:
2689:
2682:
2661:
2634:
2607:
2564:
2542:
2535:
2512:
2505:
2487:
2473:
2444:(3): 445–450.
2424:
2376:
2369:
2351:
2325:
2310:
2309:
2307:
2304:
2303:
2302:
2297:
2292:
2287:
2282:
2275:
2274:
2271:Ecology portal
2258:
2255:
2238:
2235:
2206:
2203:
2183:
2182:
2171:
2166:
2163:
2158:
2155:
2141:
2140:
2129:
2126:
2123:
2119:
2115:
2112:
2109:
2106:
2103:
2098:
2095:
2090:
2087:
2082:
2079:
2073:
2030:
2029:
2018:
2015:
2012:
2009:
2006:
2003:
1998:
1995:
1990:
1987:
1983:
1979:
1976:
1973:
1970:
1967:
1962:
1959:
1954:
1951:
1946:
1943:
1937:
1933:
1930:
1911:
1910:
1899:
1896:
1893:
1890:
1887:
1884:
1881:
1878:
1875:
1872:
1869:
1864:
1861:
1856:
1853:
1850:
1845:
1842:
1837:
1834:
1765:
1762:
1743:
1742:
1731:
1728:
1725:
1702:
1699:
1696:
1693:
1690:
1687:
1684:
1681:
1678:
1675:
1670:
1667:
1664:
1661:
1658:
1655:
1652:
1649:
1646:
1643:
1640:
1637:
1634:
1631:
1625:
1622:
1612:
1601:
1598:
1595:
1572:
1569:
1566:
1561:
1558:
1555:
1552:
1549:
1546:
1543:
1540:
1537:
1534:
1528:
1525:
1511:
1510:
1497:
1494:
1489:
1486:
1483:
1480:
1465:
1462:
1449:
1446:
1443:
1440:
1437:
1434:
1431:
1398:
1390:
1387:
1384:
1381:
1378:
1375:
1372:
1369:
1366:
1363:
1360:
1357:
1354:
1351:
1346:
1343:
1340:
1334:
1328:
1325:
1322:
1319:
1316:
1312:
1307:
1301:
1298:
1295:
1292:
1289:
1285:
1280:
1274:
1271:
1268:
1264:
1257:
1252:
1245:
1242:
1223:of a standard
1209:
1205:
1201:
1198:
1195:
1173:
1169:
1165:
1161:
1138:
1135:
1130:
1123:
1120:
1111:
1107:
1103:
1099:
1095:
1092:
1089:
1086:
1080:
1077:
1074:
1071:
1068:
1063:
1060:
1057:
1054:
1051:
1048:
1045:
1042:
1039:
1036:
1033:
1030:
1027:
1024:
1018:
1015:
1012:
1009:
1006:
1003:
1000:
997:
968:
965:
962:
959:
956:
953:
950:
938:
935:
900:
899:
888:
885:
882:
879:
874:
870:
867:
864:
858:
855:
852:
846:
843:
840:
835:
832:
829:
826:
823:
820:
817:
814:
811:
808:
802:
797:
790:
787:
768:
765:
764:
763:
752:
749:
743:
740:
737:
732:
729:
726:
723:
720:
717:
714:
711:
708:
705:
699:
694:
687:
684:
657:
654:
653:
652:
641:
638:
633:
629:
626:
623:
617:
612:
608:
605:
599:
593:
590:
572:
569:
565:
564:
553:
548:
544:
541:
535:
529:
526:
509:
508:
497:
492:
489:
484:
479:
476:
448:
444:
440:
420:
416:
412:
396:
393:
392:
391:
380:
375:
371:
368:
362:
356:
353:
321:Main article:
318:
315:
306:
305:
299:
293:
287:
276:
273:
269:
268:
265:
258:
256:
253:
246:
244:
238:
231:
229:
224:Collar-tagged
223:
216:
213:
212:
208:
207:
206:
156:
153:
102:mark-recapture
77:
76:
31:
29:
22:
15:
9:
6:
4:
3:
2:
3352:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3323:
3321:
3318:
3316:
3313:
3312:
3310:
3301:
3298:
3296:
3293:
3292:
3283:
3280:
3276:
3272:
3268:
3263:
3259:
3255:
3251:
3247:
3243:
3239:
3234:
3230:
3226:
3222:
3218:
3214:
3210:
3205:
3204:
3194:
3190:
3186:
3182:
3178:
3174:
3170:
3166:
3162:
3158:
3154:
3152:0-12-754406-2
3148:
3144:
3139:
3135:
3131:
3127:
3123:
3119:
3115:
3111:
3107:
3103:
3099:
3092:
3087:
3083:
3081:1-930665-55-5
3077:
3073:
3068:
3064:
3058:
3054:
3049:
3046:(2): 111–118.
3045:
3041:
3036:
3032:
3028:
3024:
3020:
3016:
3012:
3007:
3003:
2999:
2995:
2991:
2987:
2983:
2979:
2975:
2971:
2967:
2963:
2959:
2954:
2953:
2943:
2934:
2926:
2924:0-521-47815-4
2920:
2916:
2909:
2901:
2897:
2893:
2889:
2885:
2881:
2880:
2872:
2864:
2860:
2854:
2838:
2834:
2828:
2820:
2813:
2798:
2791:
2776:
2769:
2754:
2741:
2734:
2726:
2722:
2717:
2712:
2708:
2704:
2700:
2693:
2685:
2683:9781400840908
2679:
2675:
2668:
2666:
2657:
2653:
2649:
2645:
2638:
2630:
2626:
2622:
2618:
2611:
2603:
2599:
2595:
2591:
2587:
2583:
2579:
2575:
2568:
2560:
2553:
2551:
2549:
2547:
2538:
2536:9780321021731
2532:
2528:
2527:
2519:
2517:
2508:
2506:1-930665-55-5
2502:
2498:
2491:
2483:
2477:
2469:
2465:
2460:
2455:
2451:
2447:
2443:
2439:
2435:
2428:
2420:
2416:
2412:
2408:
2404:
2400:
2396:
2392:
2391:
2386:
2380:
2372:
2366:
2362:
2355:
2347:
2340:
2338:
2336:
2334:
2332:
2330:
2321:
2315:
2311:
2301:
2298:
2296:
2293:
2291:
2288:
2286:
2283:
2280:
2277:
2276:
2272:
2261:
2254:
2252:
2248:
2244:
2234:
2232:
2227:
2225:
2221:
2217:
2213:
2202:
2200:
2196:
2192:
2188:
2169:
2164:
2161:
2156:
2153:
2146:
2145:
2144:
2127:
2124:
2121:
2117:
2110:
2107:
2104:
2096:
2093:
2088:
2085:
2080:
2077:
2071:
2063:
2062:
2061:
2059:
2055:
2051:
2047:
2043:
2039:
2035:
2016:
2010:
2007:
2004:
1996:
1993:
1988:
1985:
1981:
1974:
1971:
1968:
1960:
1957:
1952:
1949:
1944:
1941:
1935:
1931:
1928:
1921:
1920:
1919:
1917:
1897:
1891:
1888:
1885:
1876:
1873:
1870:
1862:
1859:
1854:
1851:
1848:
1843:
1840:
1835:
1832:
1825:
1824:
1823:
1821:
1817:
1813:
1809:
1804:
1800:
1795:
1793:
1785:
1781:
1777:
1776:
1770:
1761:
1759:
1755:
1752:The example (
1750:
1748:
1729:
1726:
1723:
1697:
1694:
1691:
1682:
1679:
1676:
1665:
1662:
1659:
1656:
1653:
1644:
1641:
1638:
1635:
1632:
1623:
1620:
1613:
1599:
1596:
1593:
1570:
1567:
1564:
1556:
1553:
1550:
1541:
1538:
1535:
1526:
1523:
1516:
1515:
1514:
1495:
1492:
1487:
1484:
1481:
1478:
1471:
1470:
1469:
1461:
1441:
1438:
1435:
1429:
1420:
1418:
1414:
1411:The example (
1409:
1396:
1385:
1382:
1379:
1376:
1373:
1364:
1361:
1358:
1355:
1352:
1344:
1341:
1338:
1332:
1326:
1323:
1320:
1317:
1314:
1310:
1305:
1299:
1296:
1293:
1290:
1287:
1283:
1278:
1272:
1269:
1266:
1262:
1255:
1250:
1240:
1228:
1226:
1222:
1207:
1203:
1199:
1196:
1193:
1171:
1167:
1163:
1159:
1149:
1136:
1128:
1118:
1109:
1105:
1101:
1097:
1093:
1087:
1084:
1075:
1072:
1069:
1058:
1055:
1052:
1049:
1046:
1037:
1034:
1031:
1028:
1025:
1016:
1013:
1010:
1007:
1004:
1001:
998:
995:
987:
985:
981:
960:
957:
954:
948:
934:
932:
928:
924:
920:
916:
912:
908:
903:
886:
883:
880:
877:
872:
868:
865:
862:
856:
853:
850:
844:
841:
838:
830:
827:
824:
815:
812:
809:
800:
795:
785:
774:
773:
772:
750:
747:
741:
738:
735:
727:
724:
721:
712:
709:
706:
697:
692:
682:
671:
670:
669:
667:
663:
639:
636:
631:
627:
624:
621:
615:
610:
606:
603:
597:
588:
578:
577:
576:
568:
551:
546:
542:
539:
533:
524:
514:
513:
512:
495:
490:
487:
482:
477:
474:
465:
464:
463:
460:
446:
442:
438:
418:
414:
410:
401:
378:
373:
369:
366:
360:
351:
341:
340:
339:
336:
334:
333:Lincoln index
330:
324:
323:Lincoln index
314:
312:
303:
300:
297:
294:
291:
288:
285:
282:
281:
280:
262:
257:
250:
245:
242:
235:
230:
227:
220:
215:
214:
205:
202:
198:
195:
190:
187:
185:
184:
179:
174:
166:
161:
152:
150:
146:
142:
138:
134:
129:
127:
123:
119:
118:band recovery
115:
111:
107:
106:sight-resight
103:
99:
95:
91:
87:
83:
73:
70:
62:
52:
48:
42:
41:
35:
30:
21:
20:
3320:Epidemiology
3278:
3270:
3266:
3241:
3237:
3212:
3208:
3168:
3164:
3142:
3101:
3097:
3071:
3055:. Elsevier.
3052:
3043:
3039:
3017:(2): 85–94.
3014:
3010:
3001:
2997:
2961:
2957:
2942:
2933:
2914:
2908:
2883:
2877:
2871:
2863:the original
2853:
2841:. Retrieved
2837:the original
2827:
2812:
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2790:
2779:. Retrieved
2768:
2756:. Retrieved
2743:. Retrieved
2733:
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2647:
2643:
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2427:
2394:
2388:
2379:
2360:
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2240:
2228:
2208:
2195:optimization
2190:
2184:
2142:
2057:
2053:
2049:
2045:
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2037:
2033:
2031:
1915:
1912:
1819:
1815:
1811:
1807:
1802:
1798:
1796:
1792:epidemiology
1789:
1773:
1760:≈ 42 ± 21.5
1757:
1753:
1751:
1744:
1512:
1467:
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1416:
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914:
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462:In symbols,
461:
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310:
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301:
295:
289:
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239:Ring-tagged
203:
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171:Typically a
170:
133:epidemiology
130:
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2859:"Logiciels"
2709:(3): 71–2.
2253:estimates.
2251:uncertainty
1772:Bank vole,
51:introducing
3309:Categories
3281:, 6, 5–84.
3238:Biometrics
2958:Biometrics
2803:2016-09-02
2781:2016-09-02
2306:References
395:Derivation
226:rock hyrax
173:researcher
137:estimating
90:population
59:March 2008
34:references
3215:: 28–40.
2602:205556773
2594:0361-0918
2247:parameter
2108:−
2089:−
2008:−
1972:−
1953:−
1889:−
1874:−
1695:−
1680:−
1657:−
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1496:ϵ
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1200:α
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3134:43172823
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2411:11590637
2385:Chao, A.
2257:See also
1221:quantile
275:Notation
3258:2533383
3229:3768264
3161:Chao, A
3106:Bibcode
3019:Bibcode
2900:2304025
2716:5518027
2644:Ecology
2459:6366498
2361:Ecology
2224:E-SURGE
1754:n, K, k
1413:n, K, k
241:Jackdaw
86:ecology
47:improve
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2843:29 May
2758:19 Nov
2745:19 Nov
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1151:where
194:sample
124:, and
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3254:JSTOR
3193:78437
3189:S2CID
3130:S2CID
3094:(PDF)
2982:S2CID
2896:JSTOR
2598:S2CID
2419:78437
2415:S2CID
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3225:PMID
3181:PMID
3147:ISBN
3122:PMID
3076:ISBN
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2974:PMID
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2760:2014
2747:2014
2721:PMID
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