Abstract
We propose a hierarchical model coupled to geostatistics to deal with a non-gaussian data distribution and take explicitly into account complex spatial structures (i.e. trends, patchiness and random fluctuations). A common characteristic of animal count data is a distribution that is both zero-inflated and heavy tailed. In such cases, empirical variograms are no more robust and most structural analyses result in poor and noisy estimated spatial variogram structures. Thus kriged maps feature a broad variance of prediction. Moreover, due to the heterogeneity of wildlife population habitats, a nonstationary model is often required. To avoid these difficulties, we propose a hierarchical model that assumes that the count data follow a Poisson distribution given a theoretical sighting density which is a latent variable to be estimate. This density is modelled as the product of a positive long range trend by a positive stationary random field, characterized by a unit mean and a variogram function. A first estimate of the drift is used to obtain an estimate of the variogram of residuals including a correction term for variance coming from the Poisson distribution and weights due to the non-constant spatial mean. Then a kriging procedure similar to a modified universal kriging is implemented to directly map the latent density from raw count data. An application on fin whale data illustrates the effectiveness of the method in mapping animal density in a context that is presumably non-stationary.
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Acknowledgements
Concerning the case study, the authors would like to acknowledge Laurent Dubroca (Dubroca et al., 2004) for providing access to a part of the original dataset. The authors are also indebted to all people and organisations who contributed to the sighting data collection and collation: the Centre de Recherche sur les Mammifres Marins (CRMM), the CETUS, the Commission Internationale pour l’Exploration Scientifique de la mer Méditerranée (CIESM), Conservation Information Recherche sur les Cétacés (CIRC), Delphinia Sea Conservation, the Ecole Pratique des Hautes Etudes (EPHE) particularly P.C. Beaubrun, L. David and N. Di-Mglio, the Groupe d’Etude des Cétacés de Méditerranée (GECEM), the Groupe de Recherche sur les Cétacés (GREC), the Institut Franais de Recherche pour l’Exploitation de la Mer (IFREMER), the Muse Océanographique de Monaco, the Réserve Internationale en Mer Méditerranée Occidentale (RIMMO), the Supreme Allied Commander Atlantic Undersea Research Centre (SACLANT), the Société de Navigation Corse Méditerranée (SNCM), the Swiss Cetacean Society (SCS) and the WWF-France.
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Bellier, E., Monestiez, P., Guinet, C. (2010). Geostatistical Modelling of Wildlife Populations: A Non-stationary Hierarchical Model for Count Data. In: Atkinson, P., Lloyd, C. (eds) geoENV VII – Geostatistics for Environmental Applications. Quantitative Geology and Geostatistics, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2322-3_1
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