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On the robustness of N-mixture models.

William A Link1, Matthew R Schofield2, Richard J Barker2

  • 1USGS Patuxent Wildlife Research Center, Laurel, Maryland, 20708, USA.

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Summary

N-mixture models estimate population size from counts but are sensitive to assumptions. Violating these assumptions, even slightly, can cause significant estimation bias, making additional data crucial for reliable population size estimates.

Keywords:
Bayesian P-valueN-mixture modelabundance estimationcount datadetection probabilityrobustness

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Area of Science:

  • Ecology
  • Wildlife population monitoring
  • Statistical modeling

Background:

  • N-mixture models offer an alternative to mark-recapture for estimating population size and detection probability using count data.
  • These models do not require individual animal identification, making them appealing for certain wildlife studies.
  • However, N-mixture models are known to be sensitive to their underlying assumptions.

Purpose of the Study:

  • To investigate the impact of common assumption violations on N-mixture model inference.
  • To quantify the bias introduced by specific, realistic violations of N-mixture model assumptions.
  • To provide guidance on data collection for robust population size estimation.

Main Methods:

  • Simulated count data under scenarios with violations of N-mixture model assumptions.
  • Evaluated effects of double counting, unmodeled temporal variation in population size, and unmodeled temporal variation in detection probability.
  • Assessed the detectability of these violations using goodness-of-fit tests.

Main Results:

  • Small, realistic violations of N-mixture model assumptions can lead to substantial biases in population size and detection probability estimates.
  • The considered violations were often qualitatively small and difficult to detect with standard goodness-of-fit tests.
  • Bias in estimates was pronounced even with minor deviations from model assumptions.

Conclusions:

  • N-mixture models require careful consideration of their assumptions due to high sensitivity to violations.
  • Standard goodness-of-fit tests may fail to detect assumption violations that cause significant estimation bias.
  • For reliable population size estimates, especially in critical applications, collecting additional data like marked recaptures for direct detection probability estimation is recommended.