Natural Resource BiometricsMark and Recapture MethodsSchnabel Method: (Multiple marking)The Schnabel method is an extension of the Petersen method to a series of samples. Each sampling event includes capture, examination for previous marks, marking and then release. The marking time is not need so only one type of mark is needed. For each sample we need to record the following data:
Marks accumulate over time. So
or as a formula: where
Schnabel (1938) proposed the following weighted average of Petersen estimates as a estimate of population density. If the each sample catch and the marked population are less that 10 % of the population size the following is a better estimator of the population size. where:
The variance estimator is calculated on the reciprocal of the population density 1/N as: And the standard error of the reciprocal population density is: Schumacher and Eschmeyer (1943) pointed out that one could use a regression a slope of 1/N passing through th origin. A formula using the regression methodology is: The variance of this density estimate can be estimated from the variance estimator or the slope parameter estimate (Zar, 1996) as: And the standard error of the population density estimate can be determined by: Confidence Intervals: If the total number of recapture in < 50 the confidence limits for the population estimate should be obtained from a Poisson distribution (Krebs 1989, Appendix 1.2). If the number of recaptures is >50 use the normal approximation as follows: where:
t alpha is the value from Student's ttable for (100  alpha) % confidence limits.
Also See: Chapter 2  Estimating Abundance: MarkandRecapture pages 3037 in:

Natural Resources Biometrics by David R. Larsen is licensed under a Creative Commons AttributionShareAlike 4.0 International License . Author: Dr. David R. Larsen Created: November 5, 1997 Last Updated: October 13, 2014 