A non-technical overview of spatially explicit capture–recapture models


Most capture–recapture studies are inherently spatial in nature, with capture probabilities depending on the location of traps relative to animals. The spatial component of the studies has until recently, however, not been incorporated in statistical capture–recapture models. This paper reviews capture–recapture models that do include an explicit spatial component. This is done in a non-technical way, omitting much of the algebraic detail and focussing on the model formulation rather than on the estimation methods (which include inverse prediction, maximum likelihood and Bayesian methods). One can view spatially explicit capture–recapture (SECR) models as an endpoint of a series of spatial sampling models, starting with circular plot survey models and moving through conventional distance sampling models, with and without measurement errors, through mark–recapture distance sampling (MRDS) models. This paper attempts a synthesis of these models in what I hope is a style accessible to non-specialists, placing SECR models in the context of other spatial sampling models.

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  1. 1.

    Note that the “effective sample area” of Royle et al. (2009a) is not the same thing as the effective sample area of this paper. Their effective sample area is the effective area within which animals might be captured—analogous to the area of the searched region in the SECR movement model but excluding the p(x) of that model.


  1. Alpizar-Jara R (1997) Assessing assumption violation in line transect sampling. PhD thesis, North Carolina State University, Raleigh

  2. Borchers DL (1996) Line transect estimation with uncertain detection on the trackline. PhD thesis, University of Cape Town

  3. Borchers DL, Efford MG (2008) Spatially explicit maximum likelihood methods for capture–recapture studies. Biometrics 64:377–385

    CAS  Article  Google Scholar 

  4. Borchers DL, Zucchini W, Fewster RM (1998) Mark-recapture models for line transect surveys. Biometrics 54:1207–1220

    Article  Google Scholar 

  5. Borchers DL, Buckland ST, Zucchini W (2002) Estimating animal abundance: closed populations. Springer, London

    Book  Google Scholar 

  6. Borchers DL, Pike D, Gunnlaugsson T, Vikingsson GA (2009) Minke whale abundance estimation from the NASS 1987 and 2001 cue counting surveys taking account of distance estimation errors. North Atlantic Marine Mammal Commission Special Issue 7: North Atlantic Sightings Surveys (1987–2001), pp 95–110

  7. Borchers DL, Marques TA, Gunlaugsson T, Jupp P (2010) Estimating distance sampling detection functions when distances are measured with errors. J Agric Biol Environ Stat. doi:https://doi.org/10.1007/s13253-010-0021-y

  8. Buckland ST, Anderson DR, Burnham KP, Laake JL, Borchers DL, Thomas L (2001) Introduction to distance sampling: estimating abundance of biological populations. Oxford University Press, Oxford

    Google Scholar 

  9. Burnham KP, Overton WS (1978) Estimation of the size of a closed population when capture probabilities vary among animals. Biometrika 65:625–633

    Article  Google Scholar 

  10. Chen SX (1998) Measurement errors in line transect surveys. Biometrics 54:899–908

    Article  Google Scholar 

  11. Chen SX, Cowling A (2001) Measurement errors in line transect sampling where detectability varies with distance and size. Biometrics 57:732–742

    CAS  Article  Google Scholar 

  12. Dawson DK, Efford MG (2009) Bird population density estimated from acoustic signals. J Appl Ecol 46:1201–1209

    Article  Google Scholar 

  13. Dorazio RM, Royle JA (2003) Mixture models for estimating the size of a closed population when capture rates vary among individuals. Biometrics 59:351–364

    Article  Google Scholar 

  14. Efford MG (2004) Density estimation in live-trapping studies. Oikos 106:598–610

    Article  Google Scholar 

  15. Efford MG, Dawson DK, Robbins CS (2004) DENSITY: software for analysing capture–recapture data from passive detector arrays. Anim Biodivers Conserv 27:217–228

    Google Scholar 

  16. Efford MG, Warburton B, Coleman MC, Barker RJ (2005) A field test of two methods for density estimation. Wildl Soc Bull 33:731–738

    Article  Google Scholar 

  17. Efford MG, Borchers DL, Byrom AE (2009a) Density estimation by spatially explicit capture–recapture: likelihood-based methods. In: Thompson DL, Cooch EG, Conroy MJ (eds) Modeling demographic processes in marked populations. Springer, New York, pp 255–269

    Google Scholar 

  18. Efford MG, Dawson DK, Borchers DL (2009b) Population density estimated from locations of individuals on a passive detector array. Ecology 90:2676–2682

    Article  Google Scholar 

  19. Hiby L, Ward A, Lovell P (1989) Analysis of the North Atlantic sightings survey 1987: aerial survey results. Rep Int Whaling Comm 39:447–455

    Google Scholar 

  20. Kissling ML, Garton EO, Handel CM (2006) Estimating detection probability and density from point-count surveys: a combination of distance and double-observer sampling. Auk 123:735–752

    Article  Google Scholar 

  21. Manly B, McDonald L, Garner G (1996) Maximum likelihood estimation for the double-count method with independent observers. J Agric Biol Environ Stat 1:170–189

    Article  Google Scholar 

  22. Marques TA (2004) Predicting and correcting bias caused by measurement error in line transect sampling using multiplicative error models. Biometrics 60:757–763

    Article  Google Scholar 

  23. Marques TA, Thomas L, Martin SW, Mellinger DK, Jarvis S, Morrissey RP, Ciminello C, DiMarzio N (2010) Spatially explicit capture recapture methods to estimate minke whale abundance from data collected at bottom mounted hydrophones. J Ornithol. doi:https://doi.org/10.1007/s10336-010-0535-7

  24. Norris JL, Pollock KH (1996) Nonparametric MLE under two closed capture–recapture models with heterogeneity. Biometrics 52:639–649

    Article  Google Scholar 

  25. Obbard ME, Howe EJ, Kyle C (2010) Empirical comparison of density estimates for large carnivores. J Appl Ecol 47:76–84

    Article  Google Scholar 

  26. Pledger S (2000) Unified maximum likelihood estimates for closed capture–recapture models using mixtures. Biometrics 56:434–442

    CAS  Article  Google Scholar 

  27. Royle JA, Dorazio RM (2008) Hierarchical modeling and inference in ecology. Academic, London

    Google Scholar 

  28. Royle JA, Young KV (2008) A hierarchical model for spatial capture–recapture data. Ecology 89:2281–2289

    Article  Google Scholar 

  29. Royle JA, Nichols JD, Karanth KU, Gopalaswamy AM (2009a) A hierarchical model for estimating density in camera-trap studies. J Appl Ecol 46:118–127

    Article  Google Scholar 

  30. Royle JA, Karanth KU, Gopalaswamy AM, Kumar NS (2009b) Bayesian inference in camera-trapping studies for a class of spatial capture–recapture models. Ecology 90:3233–3244

    Article  Google Scholar 

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I would like to thank Andy Royle for inviting me to present this work at the 2009 EURING Meeting, Tiago Marques and Len Thomas for useful feedback on an earlier draft, which led to a much improved manuscript, and to the anonymous reviewers for making suggestions that improved the accessibility and readability of the manuscript.

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Correspondence to David Borchers.

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Communicated by M. Schaub.

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Borchers, D. A non-technical overview of spatially explicit capture–recapture models. J Ornithol 152, 435–444 (2012). https://doi.org/10.1007/s10336-010-0583-z

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  • Spatially explicit capture–recapture
  • Spatial sampling
  • Measurement error
  • Capture function
  • Plot sampling
  • Distance sampling