A Model‐Based Approach for Making Ecological Inference from Distance Sampling Data

We consider a fully model-based approach for the analysis of distance sampling data. Distance sampling has been widely used to estimate abundance (or density) of animals or plants in a spatially explicit study area. There is, however, no readily available method of making statistical inference on the relationships between abundance and environmental covariates. Spatial Poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process. A model-based spatial approach to distance sampling data has three main benefits: it allows complex and opportunistic transect designs to be employed, it allows estimation of abundance in small subregions, and it provides a framework to assess the effects of habitat or experimental manipulation on density. We demonstrate the model-based methodology with a small simulation study and analysis of the Dubbo weed data set. In addition, a simple ad hoc method for handling overdispersion is also proposed. The simulation study showed that the model-based approach compared favorably to conventional distance sampling methods for abundance estimation. In addition, the overdispersion correction performed adequately when the number of transects was high. Analysis of the Dubbo data set indicated a transect effect on abundance via Akaike's information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function.

[1]  A. Baddeley,et al.  Practical Maximum Pseudolikelihood for Spatial Point Patterns , 1998, Advances in Applied Probability.

[2]  S. Wood.  Generalized Additive Models: An Introduction with R , 2006 .

[3]  H. Skaug.  Markov Modulated Poisson Processes for Clustered Line Transect Data , 2006, Environmental and Ecological Statistics.

[4]  Tapan K. Nayak.  Rao–Cramer Type Inequalities for Mean Squared Error of Prediction , 2002 .

[5]  Stephen T. Buckland,et al.  Spatial models for line transect sampling , 2004 .

[6]  L. Eberhardt.  Some developments in 'distance sampling'. , 1967, Biometrics.

[7]  D. Cox.  Some Statistical Methods Connected with Series of Events , 1955 .

[8]  S. T. Buckland,et al.  Line Transect Methods for Plant Surveys , 2007, Biometrics.

[9]  S. T. Buckland,et al.  Incorporating Covariates into Standard Line Transect Analyses , 2003, Biometrics.

[10]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[11]  D L Borchers,et al.  Accommodating Unmodeled Heterogeneity in Double‐Observer Distance Sampling Surveys , 2006, Biometrics.

[12]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .

[13]  J. Barlow,et al.  DISTRIBUTION AND ABUNDANCE OF THE AMAZON RIVER DOLPHIN ( INIA GEOFFRENSIS ) AND THE TUCUXI ( SOTALIA FLUVIATILIS ) IN THE UPPER AMAZON RIVER , 1997 .

[14]  Fred L. Ramsey,et al.  A closer look at detectability , 2004, Environmental and Ecological Statistics.

[15]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[16]  J. Andrew Royle,et al.  MODELING ABUNDANCE EFFECTS IN DISTANCE SAMPLING , 2004 .

[17]  A H Welsh,et al.  Line Transect Sampling in Small Regions , 2001, Biometrics.

[18]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[19]  Eberhardt Ll,et al.  Some developments in 'distance sampling'. , 1967 .

[20]  J. Laake,et al.  Coping with variation in aerial survey protocol for line-transect sampling , 2008 .

[21]  Adrian Baddeley,et al.  spatstat: An R Package for Analyzing Spatial Point Patterns , 2005 .

[22]  G. Oehlert.  A note on the delta method , 1992 .

[23]  Tore Schweder,et al.  Likelihood-based inference for clustered line transect data , 2006 .

[24]  Don W. Hayne,et al.  An Examination of the Strip Census Method for Estimating Animal Populations , 1949 .

[25]  S. Buckland.  Introduction to distance sampling : estimating abundance of biological populations , 2001 .

[26]  Mark Berman,et al.  Approximating Point Process Likelihoods with Glim , 1992 .

[27]  J. Møller,et al.  Statistical Inference and Simulation for Spatial Point Processes , 2003 .

[28]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[29]  Len Thomas,et al.  Estimating the Encounter Rate Variance in Distance Sampling , 2009, Biometrics.

[30]  David L. Borchers,et al.  Horvitz-Thompson Estimators for Double-Platform Line Transect Surveys , 1998 .

[31]  Alan Y. Chiang,et al.  Generalized Additive Models: An Introduction With R , 2007, Technometrics.

[32]  E. Slooten,et al.  Small-boat surveys for coastal dolphins: line-transect surveys for Hector's dolphins (Cephalorhynchus hectori) , 2004 .

[33]  David R. Anderson,et al.  Distance Sampling: Estimating Abundance of Biological Populations , 1995 .

[34]  J. Symanzik.  Statistical Analysis of Spatial Point Patterns (2nd ed.) , 2005 .

[35]  T. Schweder.  Advanced Distance Sampling: Estimating Abundance of Biological Populations , 2007 .

[36]  S. T. Buckland,et al.  ESTIMATED POPULATION SIZE OF THE CALIFORNIA GRAY WHALE , 1993 .

[37]  David R. Anderson,et al.  Estimation of Density from Line Transect Sampling of Biological Populations. , 1982 .

[38]  Yongtao Guan,et al.  A Thinned Block Bootstrap Variance Estimation Procedure for Inhomogeneous Spatial Point Patterns , 2007 .