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Fitting and Interpreting Occupancy Models

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  • Alan H Welsh
  • David B Lindenmayer
  • Christine F Donnelly

Abstract

We show that occupancy models are more difficult to fit than is generally appreciated because the estimating equations often have multiple solutions, including boundary estimates which produce fitted probabilities of zero or one. The estimates are unstable when the data are sparse, making them difficult to interpret, and, even in ideal situations, highly variable. As a consequence, making accurate inference is difficult. When abundance varies over sites (which is the general rule in ecology because we expect spatial variance in abundance) and detection depends on abundance, the standard analysis suffers bias (attenuation in detection, biased estimates of occupancy and potentially finding misleading relationships between occupancy and other covariates), asymmetric sampling distributions, and slow convergence of the sampling distributions to normality. The key result of this paper is that the biases are of similar magnitude to those obtained when we ignore non-detection entirely. The fact that abundance is subject to detection error and hence is not directly observable, means that we cannot tell when bias is present (or, equivalently, how large it is) and we cannot adjust for it. This implies that we cannot tell which fit is better: the fit from the occupancy model or the fit ignoring the possibility of detection error. Therefore trying to adjust occupancy models for non-detection can be as misleading as ignoring non-detection completely. Ignoring non-detection can actually be better than trying to adjust for it.

Suggested Citation

  • Alan H Welsh & David B Lindenmayer & Christine F Donnelly, 2013. "Fitting and Interpreting Occupancy Models," PLOS ONE, Public Library of Science, vol. 8(1), pages 1-21, January.
  • Handle: RePEc:plo:pone00:0052015
    DOI: 10.1371/journal.pone.0052015
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    Cited by:

    1. De Cubber, Lola & Trenkel, Verena M. & Diez, Guzman & Gil-Herrera, Juan & Novoa Pabon, Ana Maria & Eme, David & Lorance, Pascal, 2023. "Robust identification of potential habitats of a rare demersal species (blackspot seabream) in the Northeast Atlantic," Ecological Modelling, Elsevier, vol. 477(C).
    2. Kenneth F Kellner & Robert K Swihart, 2014. "Accounting for Imperfect Detection in Ecology: A Quantitative Review," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-8, October.
    3. Gurutzeta Guillera-Arroita & José J. Lahoz-Monfort, 2017. "Species occupancy estimation and imperfect detection: shall surveys continue after the first detection?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 381-398, October.

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