Camera trap monitoring of unmarked animals: a map of the relationships between population size estimators
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Abstract
The use of camera traps to monitor unmarked animal populations has expanded during the last decade, leading to the development of several density estimation methods. This plethora of methods may be confusing for the newcomer to the field. Some methods, such as the random encounter model, require the knowledge of the mean travel speed of the animals, while others, such as camera trap distance sampling, do not rely on such assumptions. Different methods, like instantaneous sampling, camera trap distance sampling, and the association model, rely on similar types of data, but do not seem identical. In this article, I explore the relationships between different density estimators, including the random encounter model, the random encounter and staying time model, the time in front of camera approach, the time-to-event model, camera-trap distance sampling, the association model, and the space-to-event model. I show how these different estimators are related under two simplifying assumptions (perfect detectability, and animals moving as molecules in an ideal gas). I develop a map of mathematical relationships between these estimators. This framework helps readers understand how these methods are interconnected, providing a clearer conceptual foundation for selecting and implementing density estimation studies.
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Estimating population size over a given area, i.e., estimating population density, has historically been done using capture-recapture methods for marked animals or distance sampling. However, over the last decades, the rise of camera trap data has led to the development of numerous methods estimating population density from photographs of unmarked animals recorded by camera traps. While many of these methods have different data requirements and could appear unrelated, Calenge (2026) describes how the various methods connect mathematically to each other under the assumption that animals move according to the ideal gas model (Hutchinson & Waser 2007, 2009). He focuses on methods that use the field of view of the camera rather than an effective sampling area of the traps (Gilbert et al. 2021). There was a previous indication in the …
Estimating population size over a given area, i.e., estimating population density, has historically been done using capture-recapture methods for marked animals or distance sampling. However, over the last decades, the rise of camera trap data has led to the development of numerous methods estimating population density from photographs of unmarked animals recorded by camera traps. While many of these methods have different data requirements and could appear unrelated, Calenge (2026) describes how the various methods connect mathematically to each other under the assumption that animals move according to the ideal gas model (Hutchinson & Waser 2007, 2009). He focuses on methods that use the field of view of the camera rather than an effective sampling area of the traps (Gilbert et al. 2021). There was a previous indication in the literature that some of the former methods might be connected (Palencia et al. 2021) but no comprehensive map of the relationships between the diverse estimators, even under this simple movement model.
In addition to providing such a map, the paper carefully dissects why the estimators are linked, which might have otherwise remained hidden to many practitioners. The standardized notation and pedagogical approach employed by Calenge (2026) will no doubt help to understand better these links. Which links may hold or not under more general assumptions or different movement models is a natural follow-up question. As the author sketches in the discussion, it is also a challenging one.
References
Calenge, C. (2026) Camera trap monitoring of unmarked animals: a map of the relationships between population size estimators. bioRxiv, ver.4 peer-reviewed and recommended by PCI Ecology https://doi.org/10.1101/2025.02.28.640755
Gilbert, N. A., Clare, J. D., Stenglein, J. L., & Zuckerberg, B. (2021). Abundance estimation of unmarked animals based on camera‐trap data. Conservation Biology, 35(1), 88-100. https://doi.org/10.1111/cobi.13517
Hutchinson, J. M., & Waser, P. M. (2007). Use, misuse and extensions of “ideal gas” models of animal encounter. Biological Reviews, 82(3), 335-359. https://doi.org/10.1111/j.1469-185X.2007.00014.x
Hutchinson, J. M., & Waser, P. M. (2009), Corrigendum. Biological Reviews, 84: 347-347. https://doi.org/10.1111/j.1469-185X.2008.00072.x
Palencia, P., Rowcliffe, J. M., Vicente, J., & Acevedo, P. (2021). Assessing the camera trap methodologies used to estimate density of unmarked populations. Journal of Applied Ecology, 58(8), 1583-1592. https://doi.org/10.1111/1365-2664.13913
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