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A novel method for quantifying overdispersion incount data and its application to farmland birds

Authors: 

BARRY MCMAHON, GORDON PURVIS, HELEN SHERIDAN, GAVIN SIRIWARDENA, ANDREW PARNELL

Publication Type: 
Refereed Original Article
Abstract: 
The statist ical modelling of count data permeates the discipline of ecology. Such dataoften exhibit overdispersion compared with a standard Poisson distribution, so that thevariance of the counts is greater than that of the mean. Whereas modelling to reveal theeffects of explanatory variables on the mean is commonplace, overdispersion is generallyregarded as a nuisance parameter to be accounted for and subsequently ignored. Instead,we propose a method that models the overdispersion as a biologically interesting prop-erty of a data set and show how novel inference is prov ided as a result. We adapted thedouble hierarchical generalized linear model approach to create an easily extendiblemodel structure that quanti fies the influence of explanatory variables on the overdisper-sion of count data, and apply it to farmland birds. These data were from a study withinIrish agricultural ecosystems, in which total bird species abundance and the abundanceof farmland indicat or species were compared on dairy and non-dairy farms in the winterand breeding seasons. In general, overdispersion in bird counts was greater on dairy farmsthan on non-dairy farms, and for total bird numbers, overdispersion was greatest on dairyfarms in winter. Our code is fitted using the Bayesian package Rstan, and we make allcode and data available in a GitHub repository. Within a Bayesian framework, thisapproach facilitates a meaningful quantification of the effects of categorical expl anatoryvariables on any response variable with a tenden cy to overdispersion that has a meaning-ful biological or ecological explanation
Digital Object Identifer (DOI): 
10.1111/ibi.12450
Publication Status: 
Published
Publication Date: 
02/02/2017
Journal: 
Ibis: International Journal of Avian Science
Institution: 
National University of Ireland, Dublin (UCD)
Open access repository: 
No