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Estimating population size with imperfect detection using a parametric bootstrap

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  • Lisa Madsen
  • Dan Dalthorp
  • Manuela Maria Patrizia Huso
  • Andy Aderman

Abstract

We develop a novel method of estimating population size from imperfectly detected counts of individuals and a separate estimate of detection probability. Observed counts are separated into classes within which detection probability is assumed constant. Within a detection class, counts are modeled as a single binomial observation X with success probability p where the goal is to estimate index N. We use a Horvitz–Thompson‐like estimator for N and account for uncertainty in both sample data and estimated success probability via a parametric bootstrap. Unlike capture–recapture methods, our model does not require repeated sampling of the population. Our method is able to achieve good results, even with small X. We show in a factorial simulation study that the median of the bootstrapped sample has small bias relative to N and that coverage probabilities of confidence intervals for N are near nominal under a wide array of scenarios. Our methodology begins to break down when P(X=0)>0.1 but is still capable of obtaining reasonable confidence coverage. We illustrate the proposed technique by estimating (1) the size of a moose population in Alaska and (2) the number of bat fatalities at a wind power facility, both from samples with imperfect detection probabilities, estimated independently.

Suggested Citation

  • Lisa Madsen & Dan Dalthorp & Manuela Maria Patrizia Huso & Andy Aderman, 2020. "Estimating population size with imperfect detection using a parametric bootstrap," Environmetrics, John Wiley & Sons, Ltd., vol. 31(3), May.
  • Handle: RePEc:wly:envmet:v:31:y:2020:i:3:n:e2603
    DOI: 10.1002/env.2603
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    Cited by:

    1. Staci A. Hepler & Robert J. Erhardt, 2021. "A spatiotemporal model for multivariate occupancy data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.
    2. Matt Higham & Jay Ver Hoef & Lisa Madsen & Andy Aderman, 2021. "Adjusting a finite population block kriging estimator for imperfect detection," Environmetrics, John Wiley & Sons, Ltd., vol. 32(1), February.

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