Bayesian spatial modeling of data from avian point count surveys

We present a unified framework for modeling bird survey data collected at spatially replicated survey sites in the form of repeated counts or detection history counts, through which we model spatial dependence in bird density and variation in detection probabilities due to changes in covariates across the landscape. The models have a complex hierarchical structure that makes them suited to Bayesian analysis using Markov chain Monte Carlo (MCMC) algorithms. For computational efficiency, we use a form of conditional autogressive model for modeling spatial dependence. We apply the models to survey data for two bird species in the Great Smoky Mountains National Park. The algorithms converge well for the more abundant and easily detected of the two species, but some simplification of the spatial model is required for convergence for the second species. We show how these methods lead to maps of estimated relative density which are an improvement over those that would follow from past approaches that ignored spatial dependence. This work also highlights the importance of good survey design for bird species mapping studies.

[1]  C. S. Robbins,et al.  Managing and Monitoring Birds Using Point Counts: Standards and Applications , 1995 .

[2]  W. Link,et al.  NONLINEARITY AND SEASONAL BIAS IN AN INDEX OF BRUSHTAIL POSSUM ABUNDANCE , 2005 .

[3]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[4]  T. Simons,et al.  Spatial autocorrelation and autoregressive models in ecology , 2002 .

[5]  P. Diggle,et al.  Model-based geostatistics (with discussion). , 1998 .

[6]  N. Cressie,et al.  Hierarchical modeling of count data with application to nuclear fall-out , 2003, Environmental and Ecological Statistics.

[7]  P. Gustafson,et al.  Conservative prior distributions for variance parameters in hierarchical models , 2006 .

[8]  Theodore R. Simons,et al.  Comparison of breeding bird and vegetation communities in primary and secondary forests of Great Smoky Mountains National Park , 2006 .

[9]  Sw. Banerjee,et al.  Hierarchical Modeling and Analysis for Spatial Data , 2003 .

[10]  David R. Anderson,et al.  Statistical inference from capture data on closed animal populations , 1980 .

[11]  A. Gelfand,et al.  Proper multivariate conditional autoregressive models for spatial data analysis. , 2003, Biostatistics.

[12]  J. Besag Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[13]  A. Munk,et al.  On Identifiability in Capture–Recapture Models , 2006, Biometrics.

[14]  J. Andrew Royle,et al.  Hierarchical models of animal abundance and occurrence , 2006 .

[15]  J. D. White,et al.  The relationships between vegetation type and topography in Lassen Volcanic National Park , 1997, Plant Ecology.

[16]  Tapabrata Maiti,et al.  Bayesian Data Analysis (2nd ed.) (Book) , 2004 .

[17]  Shirley Pledger,et al.  The Performance of Mixture Models in Heterogeneous Closed Population Capture–Recapture , 2005, Biometrics.

[18]  P. Diggle,et al.  Model‐based geostatistics , 2007 .

[19]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  G. Seber The estimation of animal abundance and related parameters , 1974 .

[21]  David J. Spiegelhalter,et al.  WinBUGS user manual version 1.4 , 2003 .

[22]  A. Gelman Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[23]  C. Wikle Spatial Modelling of Count Data: A Case Study in Modelling Breeding Bird Survey Data on Large Spatial Domains , 2002 .

[24]  J. Andrew Royle,et al.  Statistical mapping of count survey data , 2002 .

[25]  J. Nichols,et al.  Statistical inference for capture-recapture experiments , 1992 .

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

[27]  Susan A. Shriner,et al.  Distribution of Breeding Birds in Great Smoky Mountains National Park , 2002 .

[28]  J. Alho Logistic regression in capture-recapture models. , 1990, Biometrics.

[29]  R. Huggins On the statistical analysis of capture experiments , 1989 .

[30]  S. Pledger Unified Maximum Likelihood Estimates for Closed Capture–Recapture Models Using Mixtures , 2000, Biometrics.

[31]  T. C. Haas,et al.  Model-based geostatistics. Discussion. Authors' reply , 1998 .

[32]  Kenneth H. Pollock,et al.  TIME-OF-DETECTION METHOD FOR ESTIMATING ABUNDANCE FROM POINT-COUNT SURVEYS , 2007 .

[33]  W. Link Nonidentifiability of Population Size from Capture‐Recapture Data with Heterogeneous Detection Probabilities , 2003, Biometrics.

[34]  Michael Krawczak,et al.  Statistical Inference from , 1999 .

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

[36]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[37]  Robert M Dorazio,et al.  Improving Removal‐Based Estimates of Abundance by Sampling a Population of Spatially Distinct Subpopulations , 2005, Biometrics.

[38]  Theodore R. Simons,et al.  Evaluating Great Smoky Mountains National Park as a Population Source for the Wood Thrush , 2000 .

[39]  K. Pollock,et al.  EXPERIMENTAL ANALYSIS OF THE AUDITORY DETECTION PROCESS ON AVIAN POINT COUNTS , 2007 .

[40]  J. Norris,et al.  NONPARAMETRIC MLE UNDER TWO CLOSED CAPTURE-RECAPTURE MODELS WITH HETEROGENEITY , 1996 .

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

[42]  A. Agresti,et al.  The Use of Mixed Logit Models to Reflect Heterogeneity in Capture‐Recapture Studies , 1999, Biometrics.

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

[44]  J. Andrew Royle N‐Mixture Models for Estimating Population Size from Spatially Replicated Counts , 2004, Biometrics.

[45]  J. Andrew Royle,et al.  Mixture Models for Estimating the Size of a Closed Population When Capture Rates Vary among Individuals , 2003, Biometrics.

[46]  A. Brix Bayesian Data Analysis, 2nd edn , 2005 .

[47]  Kenneth H. Pollock,et al.  A REMOVAL MODEL FOR ESTIMATING DETECTION PROBABILITIES FROM POINT-COUNT SURVEYS , 2002 .