300
282
65.46
0.1667
0.2
300
282
65.46
0.1667
0.2
The Mark-Recapture Calculator estimates the total size of a closed population using the Lincoln-Petersen method and its bias-corrected Chapman modification. In this method, a sample of animals is captured, marked, and released. Later, a second sample is captured and the number of previously marked individuals is counted. The ratio of marked to unmarked animals in the second sample estimates the total population.
Enter the number marked in the first capture (M), the total caught in the second capture (C), and the number of recaptured marked individuals (R). The calculator provides both the classic Lincoln-Petersen estimate and the Chapman bias-corrected estimate with standard error.
The Lincoln-Petersen estimator assumes that the proportion of marked animals in the second sample equals the proportion in the total population:
N = (M x C) / R
The Chapman modification reduces bias, especially when R is small:
N_Chapman = ((M + 1)(C + 1) / (R + 1)) - 1
The standard error of the Chapman estimate is:
SE = sqrt((M+1)(C+1)(M-R)(C-R) / ((R+1)²(R+2)))
Assumptions: closed population (no births, deaths, immigration, or emigration between captures), equal capture probability for all individuals, marks are not lost, and marked and unmarked animals mix randomly.
Inputs
Results
50 fish were tagged, and in a later sample of 60, 10 were recaptured with tags. The Lincoln-Petersen estimate is 300 fish, with the Chapman estimate of 278 and SE of about 64.
Inputs
Results
With 30 marked and 8 recaptured out of 40, the estimated population is about 137-150 individuals, with considerable uncertainty (SE = 35).
The key assumptions are: (1) the population is closed (no births, deaths, or movement in/out between samples), (2) all individuals have equal probability of being captured, (3) marks are not lost or overlooked, and (4) marking does not affect behavior or survival. Violation of these assumptions can lead to biased estimates. For example, trap-shy animals lead to underestimation of recaptures and overestimation of N.
The classic Lincoln-Petersen estimator is biased, especially when the number of recaptures (R) is small relative to M and C. It tends to overestimate N. The Chapman modification adds 1 to each count and subtracts 1 from the result, which reduces this bias. It is nearly unbiased when R is greater than about 7, and is the standard recommendation for most applications.
Generally, you should aim for at least 7-10 recaptures to get a reasonably precise estimate. This means marking enough animals relative to the population size. As a rule of thumb, marking 10-20% of the estimated population and having a second sample of similar size gives adequate precision. The confidence interval narrows as R increases.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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