In order to make an estimate of the size of a population of animals at a given time by the Petersen method, use is made of a sample of the fraction of marked animals in the population. However, if some of the animals originally marked lose their marks and thus can not be identified in the sample, a Petersen type estimate will be biased, the magnitude of the bias depending upon the proportion of animals retaining their identity. If an estimate can be made of the animals which have retained their identity at a given time, it is possible to make corrections for this bias. This report presents formulas for estimating the number of marked animals which have retained their identity at a given time from multiple marked animals and shows their derivation, shows their application to the Petersen method, discusses the necessary conditions for them to apply, discusses the errors associated with such estimates and shows how confidence limits can be determined.
