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Computational aspects of N-mixture models.

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  • 1School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, UK.

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Summary
This summary is machine-generated.

The N-mixture model estimates population size using counts, but can yield infinite abundance estimates. This study introduces diagnostics and methods to avoid underestimation and improve accuracy for ecological abundance estimation.

Keywords:
Abundance estimationMethod of momentsMultivariate PoissonMultivariate negative binomialOptimal designSamplingTemporal replication

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Area of Science:

  • Ecology
  • Statistical Modeling

Background:

  • The N-mixture model is a standard tool for estimating population abundance using count data with unknown detection probability.
  • This model relies on spatial and temporal replication of sampling occasions.

Purpose of the Study:

  • To explore the equivalence between N-mixture models and multivariate Poisson/negative-binomial models.
  • To identify and address issues leading to infinite abundance estimates in N-mixture models.
  • To propose improved methods for fitting N-mixture models and selecting parameters.

Main Methods:

  • Exploiting the mathematical equivalence of N-mixture models with multivariate Poisson and negative-binomial distributions.
  • Developing a sample covariance diagnostic to detect infinite abundance estimates.
  • Investigating the impact of the summation bound (K) on abundance estimates.
  • Proposing an automatic method for selecting an appropriate value for K.

Main Results:

  • Demonstrated the equivalence, enabling new fitting approaches for N-mixture models.
  • Identified conditions (low detection probability, few sampling occasions) prone to infinite estimates.
  • Validated the sample covariance diagnostic for detecting infinite estimates in Poisson models.
  • Showed that default bounds (K) can cause abundance underestimation and proposed an alternative selection method.

Conclusions:

  • The equivalence provides a powerful framework for fitting N-mixture models.
  • Care must be taken to avoid infinite abundance estimates, which can be detected using sample covariance.
  • Default summation bounds in software can lead to biased results; a data-driven approach for selecting K is recommended.
  • The proposed methods improve the reliability of population abundance estimation from count data.