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On the reliability of N-mixture models for count data.

Richard J Barker1, Matthew R Schofield1, William A Link2

  • 1Department of Mathematics and Statistics, University of Otago, P. O. Box 56 Dunedin 9016, New Zealand.

Biometrics
|July 4, 2017
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Summary
This summary is machine-generated.

N-mixture models for wildlife counts are problematic because they cannot reliably estimate abundance (N) and detectability (p) without marking animals. Alternative models produce similar data, suggesting caution when inferring absolute abundance.

Keywords:
Ancillary statisticCapture recaptureLog linear modelN-mixture modelsPartial likelihood

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Area of Science:

  • Ecology
  • Wildlife Biology
  • Statistical Modeling

Background:

  • N-mixture models are widely used for analyzing ecological count data, estimating population size (N) and detection probability (p) without animal marking.
  • These models are popular for their ability to infer abundance while accounting for factors influencing detection.

Purpose of the Study:

  • To critically evaluate the identifiability and reliability of N-mixture models from a capture-recapture perspective.
  • To investigate the impact of unmarked data on the estimation of abundance (N) and detection probability (p).

Main Methods:

  • Utilized a capture-recapture framework to analyze information loss from unmarked animals in N-mixture models.
  • Demonstrated model overspecification issues when detection probabilities vary across repeat visits.
  • Employed counter-examples to show indistinguishable data from alternative models with non-identifiable or absent N parameters.

Main Results:

  • The absence of animal marking critically limits reliable statistical modeling of both N and p using only count data.
  • Models with distinct detection probabilities across repeat visits are overspecified and problematic.
  • Alternative models, even with constant detection probability (p), can generate data indistinguishable from N-mixture models, especially with sparse data.

Conclusions:

  • Reliable inference of absolute abundance using N-mixture models is questionable without marking or auxiliary data, particularly under the constant p assumption.
  • Inference of relative abundance is more feasible using Poisson regression, controlling for covariates affecting p.
  • For absolute abundance estimates, researchers should collect auxiliary data to improve the estimation of detection probability (p).