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Methods exist for estimating the size of a population of imperfectly detected individuals, yet problems arise when the detection probability and the observed count of individuals are both small. 

Researchers from Oregon State University, USGS, and the USFWS developed a novel method to estimate population size with imperfect detection using what’s known as a parametric bootstrap. This allows researchers to account for both the uncertainty in estimating detection probability and variation in the number of observed individuals. Their method involves using two parametric bootstraps, first from the asymptotic distribution of detection probability, then from a binomial with index derived from the first bootstrap. They illustrate the proposed technique by estimating the size of a moose population in Alaska and the number of bat fatalities at a wind power facility, both from samples with imperfect detection probabilities estimated independently. Authors point out both limitations and benefits of this method.


Madsen, L., Dalthorp, D.H., Huso, M.M., Aderman, A., 2019, Estimating population size with imperfect detection using a parametric bootstrap: Environmetrics, p. e2603,

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