Mapping the abundance of riverine fish populations: integrating hierarchical Bayesian models with a geographic information system (GIS)

A hierarchical Bayesian model is described for mapping the abundance of fish throughout a watershed from single- and multiple-pass removal sampling. A geographic information system (GIS) was used to generate a raster-based model of the river network, which provided three benefits for estimating fish density. Firstly, the horizontal resolution of the raster (50 m) provided an approximation to the statistical sampling frame and allowed correction for the finite number of potential sampling sites in a reach. Secondly, the modelled river network generated explanatory variables for every site in the network, facilitating the mapping of predicted densities and providing the basis for stratified or regression estimators for reach-specific densities. Finally, the spatial autocorrelation of fish densities was modelled in terms of the distance along the river network. A similar Bayesian model was also developed for the wetted width of the river network, and this was combined with the density model to provide estima...

[1]  Wayne A. Hubert,et al.  Integrating New Technologies into Fisheries Science: The Application of Geographic Information Systems , 1997 .

[2]  Paul G. Fernandes,et al.  Geostatistics for Estimating Fish Abundance , 2000 .

[3]  Russell B. Millar,et al.  BUGS in Bayesian stock assessments , 1999 .

[4]  A Multistage Approach to Estimate Fish Abundance in Streams Using Geographic Information Systems , 2000 .

[5]  Calvin Zippin,et al.  An Evaluation of the Removal Method of Estimating Animal Populations , 1956 .

[6]  David G. Hankin,et al.  Multistage Sampling Designs in Fisheries Research: Applications in Small Streams , 1984 .

[7]  Stephen P. Brooks,et al.  Markov chain Monte Carlo method and its application , 1998 .

[8]  P. Burrough.  GIS and geostatistics: Essential partners for spatial analysis , 2001, Environmental and Ecological Statistics.

[9]  Anthony O'Hagan,et al.  Kendall's Advanced Theory of Statistics: Vol. 2B, Bayesian Inference. , 1996 .

[10]  M. Stein,et al.  A Bayesian analysis of kriging , 1993 .

[11]  Russell B. Millar,et al.  Bayesian state-space modeling of age-structured data: fitting a model is just the beginning , 2000 .

[12]  D. Rubin.  Using the SIR algorithm to simulate posterior distributions , 1988 .

[13]  M. Mcallister,et al.  Bayesian stock assessment: a review and example application using the logistic model , 1998 .

[14]  Bradley P. Carlin,et al.  BAYES AND EMPIRICAL BAYES METHODS FOR DATA ANALYSIS , 1996, Stat. Comput..

[15]  Mike R. Strub,et al.  A New Methodfor Estimating Population Size from Removal Data , 1978 .

[16]  J. Zidek,et al.  Interpolation with uncertain spatial covariances: a Bayesian alternative to Kriging , 1992 .

[17]  Alan E. Gelfand,et al.  Bayesian statistics without tears: A sampling-resampling perspective , 1992 .

[18]  P. A. P. Moran,et al.  A MATHEMATICAL THEORY OF ANIMAL TRAPPING , 1951 .

[19]  Walter R. Gilks,et al.  A Language and Program for Complex Bayesian Modelling , 1994 .

[20]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[21]  R. Hilborn,et al.  Fisheries stock assessment and decision analysis: the Bayesian approach , 1997, Reviews in Fish Biology and Fisheries.

[22]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[23]  Robin J Wyatt,et al.  Estimating riverine fish population size from single- and multiple-pass removal sampling using a hierarchical model , 2002 .

[24]  Vic Barnett,et al.  Comparative Statistical Inference , 1974, Technometrics.

[25]  A. W. Kemp,et al.  Kendall's Advanced Theory of Statistics. , 1994 .

[26]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .