The SECR book


A handbook of spatially explicit capture–recapture methods
Version 1.0.1


Author
Affiliation

Murray Efford

University of Otago, New Zealand

Published

April 3, 2025

Foreword

This book is about the methods for describing animal populations that have come to be called ‘spatially explicit capture–recapture’ or simply ‘spatial capture–recapture’. We use ‘SECR’ as a general label for these data and models.

SECR data are observations of marked animals at known locations. The observations are from a well-defined regime of spatial sampling, most often with traps, cameras, or some other type of passive detector. SECR models are used to estimate parameters of the animal population, particularly the population density. We focus on ‘closed’ populations whose composition does not change during sampling.

Why SECR?

Non-spatial capture–recapture methods are highly developed and powerful (Cooch & White, 2023; Otis et al., 1978; Williams et al., 2002). SECR plugs some gaps in non-spatial methods (particularly with respect to density estimation), and has some unexpected benefits:

  1. Freedom from edge effects
    Estimation of density with non-spatial capture–recapture is dogged by uncertain edge effects. SECR explicitly accounts for edge effects so density estimates are unbiased.
  2. Reduced individual heterogeneity
    Unmodelled individual heterogeneity of detection is a universal source of bias in capture–recapture (e.g., Laake & Collier, 2024). Spatial sampling is a potent source of heterogeneity, due to differential access to detectors. SECR models this component of heterogeneity, which then ceases to be a problem.
  3. Scalable detection model
    The detection model in SECR is built from components describing the interaction between a single individual and a single detector. Parameter estimates can therefore be used to simulate sampling with novel detector configurations, which is key to designing better studies.
  4. Coherent adjustment for effort
    Known variation in effort, including incomplete use of a detector array, is included directly in the model, without additional covariates or parameters.
  5. Spatial pattern (covariates)
    SECR allows density to be modelled as a function of continuous spatial covariates.

Why this book?

The literature of SECR has grown beyond the attention spans and time budgets of most users. Major SECR publications are Efford (2004), Borchers & Efford (2008), Royle et al. (2014), Borchers & Fewster (2016), Sutherland et al. (2019) and Turek et al. (2021).

This book provides both a gentle introduction, in the spirit of Cooch & White (2023), and more in-depth treatment of important topics. It is software oriented and therefore unashamedly partial and incomplete. Much of the content is drawn from earlier papers and the documentation of R (R Core Team, 2024) packages. Some topics are yet to be included (e.g., acoustic data) but documentation may be found on the DENSITY website. Others such as partial identity models (Augustine et al., 2018) have yet to be considered at all.

SECR has become popular for the potential benefits noted above. But are the results reliable? Understanding the real-world performance of SECR is an active research area with its own questions. Are particular field data adequate? Are results robust when assumptions are not strictly met? How can we design better studies? We assemble the evidence in a form that we hope will be useful to practitioners.

Organisation

Part I introduces the concepts of SECR and walks the reader through a simple example. Part II establishes the necessary theory. Part III provides substantial new material on the performance of SECR: Which assumptions really matter? and How should studies be designed? Part IV is a practical guide to SECR modelling with the R package secr. Appendices provide detail on specialised topics such as area and transect searches, spatial mark-resight and non-Euclidean distances.

We expect that most readers will start with Part I and thereafter jump to topics of interest. Cross-references are provided to fill in relevant detail that may have been missed.

Software

The R package secr (Efford, 2025) provides most of the functionality we will need. It performs maximum likelihood estimation for a range of closed-population SECR models. The Windows application DENSITY (Efford et al., 2004) has been superceded, although its graphical interface can still come in handy.

Bayesian approaches using Markov chain Monte Carlo (MCMC) methods are a flexible, but generally slower, alternative to maximum likelihood (1.8.4 Estimation). The R package nimbleSCR promises to make MCMC methods for SECR more accessible and faster.

Add-on packages extend the capability of secr:

  • ipsecr fits models by simulation and inverse prediction, rather than maximum likelihood; this is a rigorous way to analyse data from single-catch traps (ipsecr-vignette.pdf).

  • secrdesign enables the assessment of alternative study designs by Monte Carlo simulation; scenarios may differ in detector (trap) layout, sampling intensity, and other characteristics (secrdesign-vignette.pdf).

  • openCR implements the open-population models of Efford & Schofield (2020).

These packages are available from the CRAN repository – just open R and type install.packages('xxxx') where xxxx is the package name.

Other R packages for SECR may be found outside CRAN. A distinct maximum-likelihood implementation by Sutherland et al. (2019) is available on GitHub (https://github.com/jaroyle/oSCR).

Feedback

This is work in progress. If you find an error or would like to make a suggestion, please raise an issue on GitHub or contact the author directly.

Acknowledgments

Ian Durbach, Brian Gerber, Dan Linden, Cyril Milleret, Joanne Potts, and Rahel Sollmann gave helpful comments on earlier versions of some chapters. For help with particular chapters I especially thank Rahel (Chapter 6) and Ian (Chapter 8). Errors remain my own. Matt Schofield provided encouragement, answered some theoretical questions, and reviewed several chapters. Thanks to John Boulanger for his collaboration on study design and analysis over many projects, and to Alice Kenney for her snowshoe hare photograph.

Thanks for data -

See also the links in Appendix L — Datasets.

This book is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license.

Murray Efford
Dunedin, April 2025