The Annals of Applied Statistics

Simultaneous modelling of movement, measurement error, and observer dependence in mark-recapture distance sampling: An application to Arctic bird surveys

Paul B. Conn and Ray T. Alisauskas

Full-text: Open access

Abstract

Mark-recapture distance sampling is a promising method for surveying bird populations from aircraft in open landscapes. However, commonly available distance sampling estimators require that distances to target animals are made without error and that animals are stationary while sampling is being conducted. Motivated by a recent bird survey where these requirements were routinely violated, we describe a marginal likelihood framework for estimating abundance from double-observer data that can accommodate movement and measurement error when observations are made consecutively (as with front and rear observers), when animals are uniformly distributed during detection by the first observer, and when detections consist of both moving and stationary animals. Assuming that all animals are subject to measurement error and that some animals can move between detections, we integrate over unknown animal locations to construct a marginal likelihood for detection, movement, and measurement error parameters. Estimates of animal abundance are then obtained using a modified Horvitz–Thompson-like estimator. In addition, unmodelled heterogeneity in detection probability can be accommodated through observer dependence parameters. Using simulation, we show that our approach yields low bias compared to approaches that ignore movement and/or measurement error, including in cases where there is considerable detection heterogeneity. Applying our approach to data from a double-observer waterfowl helicopter survey in northern Canada, we are able to estimate bird density accounting for movement and measurement error and corrected for observer heterogeneity. Our approach appears promising for generating unbiased estimates of bird abundance necessary for reliable conservation and management.

Article information

Source
Ann. Appl. Stat., Volume 12, Number 1 (2018), 96-122.

Dates
Received: April 2017
Revised: October 2017
First available in Project Euclid: 9 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1520564466

Digital Object Identifier
doi:10.1214/17-AOAS1108

Mathematical Reviews number (MathSciNet)
MR3773387

Zentralblatt MATH identifier
06894700

Keywords
Aerial survey double-observer mark-recapture distance sampling measurement error movement point independence

Citation

Conn, Paul B.; Alisauskas, Ray T. Simultaneous modelling of movement, measurement error, and observer dependence in mark-recapture distance sampling: An application to Arctic bird surveys. Ann. Appl. Stat. 12 (2018), no. 1, 96--122. doi:10.1214/17-AOAS1108. https://projecteuclid.org/euclid.aoas/1520564466


Export citation

References

  • Alho, J. M. (1990). Logistic regression in capture-recapture models. Biometrics 46 623–635.
  • Alisauskas, R. T. and Conn, P. B. (2018). Evaluating detectability of Arctic waterfowl populations in double-observer helicopter surveys. To be submitted to the Euring 2017 Proceedings.
  • Borchers, D. L. and Efford, M. G. (2008). Spatially explicit maximum likelihood methods for capture-recapture studies. Biometrics 64 377–385.
  • Borchers, D. L. and Marques, T. A. (2017). From distance sampling to spatial capture–recapture. AStA Adv. Stat. Anal. 101 475–494.
  • Borchers, D. L., Zucchini, W. and Fewster, R. M. (1998). Mark-recapture models for line transect surveys. Biometrics 54 1207–1220.
  • Borchers, D. L., Laake, J. L., Southwell, C. and Paxton, C. G. M. (2006). Accomodating unmodeled heterogeneity in double-observer distance sampling surveys. Biometrics 62 372–378.
  • Borchers, D., Marques, T., Gunnlaugsson, T. and Jupp, P. (2010). Estimating distance sampling detection functions when distances are measured with errors. J. Agric. Biol. Environ. Stat. 15 346–361.
  • Borchers, D. L., Stevenson, B. C., Kidney, D., Thomas, L. and Marques, T. A. (2015). A unifying model for capture-recapture and distance sampling surveys of wildlife populations. J. Amer. Statist. Assoc. 110 195–204.
  • Buckland, S. T., Laake, J. L. and Borchers, D. L. (2010). Double-observer line transect methods: Levels of independence. Biometrics 66 169–177.
  • Buckland, S. T. and Turnock, B. J. (1992). A robust line transect method. Biometrics 901–909.
  • Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L. and Thomas, L. (2001). Introduction to Distance Sampling: Estimating the Abundance of Biological Populations. Oxford Univ. Press, Oxford, United Kingdom.
  • Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L. and Thomas, L. (2004). Advanced Distance Sampling. Oxford Univ. Press, Oxford, United Kingdom.
  • Burnham, K. P., Anderson, D. R. and Laake, J. L. (1980). Estimation of density for line transect sampling of biological populations. Wildl. Monogr. 72 7–202.
  • Burnham, K. P., Anderson, D. R., White, G. C., Brownie, C. and Pollock, K. H. (1987). Design and analysis methods for fish survival experiments based on release-recapture. Am. Fish. Soc. Monogr. 5 1–437.
  • Burnham, K. P., Buckland, S. T., Laake, J. L., Borchers, D. L., Marques, T. A., Bishop, J. R. B. and Thomas, L. (2004). Further topics in distance sampling. 307–392. Oxford Univ. Press, Oxford, United Kingdom.
  • Burt, M. L., Borchers, D. L., Jenkins, K. J. and Marques, T. A. (2014). Using mark–recapture distance sampling methods on line transect surveys. Methods Ecol. Evol. 5 1180–1191.
  • Conn, P. B., Laake, J. L. and Johnson, D. S. (2012). A hierarchical modeling framework for multiple observer transect surveys. PLoS ONE 7 e42294.
  • Conn, P. B., Ver Hoef, J. M., McClintock, B. T., Moreland, E. E., London, J. M., Cameron, M. F., Dahle, S. P. and Boveng, P. L. (2014). Estimating multi-species abundance using automated detection systems: Ice-associated seals in the eastern Bering Sea. Methods Ecol. Evol. 5 1280–1293.
  • Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2014). Bayesian Data Analysis, 3rd ed. Taylor & Francis, London.
  • Glennie, R., Buckland, S. T. and Thomas, L. (2015). The effect of animal movement on line transect estimates of abundance. PLoS ONE 10 e0121333.
  • Hiby, L. and Lovell, P. (1998). Using aircraft in tandem formation to estimate abundance of harbour porpoise. Biometrics 54 1280–1289.
  • Huggins, R. M. (1989). On the statistical analysis of capture-recapture experiments. Biometrika 76 133–140.
  • Huggins, R. M. (1990). Some practical aspects of a conditional likelihood approach to capture experiments. Biometrics 47 725–732.
  • Koneff, M. D., Royle, J. A., Otto, M. C., Wortham, J. S. and Bidwell, J. K. (2008). A double-observer method to estimate detection rate during aerial waterfowl surveys 72 1641–1649.
  • Laake, J. L. (2013). RMark: An R interface for analysis of capture-recapture data with MARK. AFSC Processed Rep. No. 2013-01, Alaska Fish. Sci. Cent., NOAA, Natl. Mar. Fish. Serv., Seattle, WA.
  • Laake, J. L. and Borchers, D. L. (2004). Methods for incomplete detection at distance zero. In Advanced Distance Sampling (S. T. Buckland, D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers and L. Thomas, eds.) 108–189. Oxford Univ. Press, Oxford, United Kingdom.
  • MacKenzie, D. I. and Clement, D. (2016). Accounting for lack of independence and partial overlap of observation zones in line-transect mark-recapture distance sampling. J. Agric. Biol. Environ. Stat. 21 41–57.
  • R Development Core Team (2016). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
  • Royle, J. A., Dorazio, R. M. and Link, W. A. (2007). Analysis of multinomial models with unknown index using data augmentation. J. Comput. Graph. Statist. 16 1–19.
  • Royle, J. A., Chandler, R. B., Sollmann, R. and Gardner, B. (2013). Spatial Capture-Recapture. Academic Press, San Diego.
  • Schweder, T., Skaug, H. J., Langaas, M. and Dimakos, X. K. (1999). Simulated likelihood methods for complex double-platform line transect surveys. Biometrics 55 678–687.
  • White, G. C. and Burnham, K. P. (1999). Program MARK: Survival estimation from populations of marked animals. Bird Study 46 Supplement, 120–138.