Computational aspects of N-mixture models

Dennis, Emily B. and Morgan, Byron J. T. and Ridout, Martin S. (2015) Computational aspects of N-mixture models. Biometrics, 71 (1). pp. 237-246. ISSN 0006-341X. (doi: (Full text available)

PDF - Author's Accepted Manuscript

Creative Commons Licence
This work is licensed under a Creative Commons Attribution 4.0 International License.
Download (629kB) Preview
Official URL


The N-mixture model is widely used to estimate the abundance of a population in the presence of unknown detection probability from only a set of counts subject to spatial and temporal replication (Royle, 2004, Biometrics 60,105–115). We explain and exploit the equivalence of N-mixture and multivariate Poisson and negative-binomial models, which provides powerful new approaches for fitting these models. We show that particularly when detection probability and the number of sampling occasions are small, infinite estimates of abundance can arise. We propose a sample covariance as a diagnostic for this event, and demonstrate its good performance in the Poisson case. Infinite estimates may be missed in practice, due to numerical optimization procedures terminating at arbitrarily large values. It is shown that the use of a bound, K, for an infinite summation in the N-mixture likelihood can result in underestimation of abundance, so that default values of K in computer packages should be avoided. Instead we propose a simple automatic way to choose K. The methods are illustrated by analysis of data on Hermann’s tortoise Testudo hermanni.

Item Type: Article
Uncontrolled keywords: Abundance estimation;Method of moments;Multivariate negative binomial;Multivariate Poisson;Optimal design;Sampling;Temporal replication
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Q Science > QH Natural history > QH541 Ecology
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Byron Morgan
Date Deposited: 09 Jun 2015 12:49 UTC
Last Modified: 11 Jun 2015 11:36 UTC
Resource URI: (The current URI for this page, for reference purposes)
  • Depositors only (login required):


Downloads per month over past year