SECR with Camera Traps, Binomial count proximity detector VS Poisson count proximity detector

[Benjamin Debetencourt]

Hi all,

We implemented a SECR design with 34 camera traps placed opportunistically in a 2 by 2 km grid (one camera by cell) to estimate the density of an elephant population based on individual identification from video footage. One occasion was defined as 10 days to increase the encounter rate per occasion, and the study period consisted of 27 occasions. Cameras were treated as count proximity detectors. Due to transboundary constraints, the sampled area covers only part of the elephants’ range.

We considered two alternative ways of modelling the data:

1. Poisson Count Proximity Detector

Using:

•  λ₀ (lambda0) as a detection parameter,

•  Detection functions HHN and HEX, parameterised in terms of cumulative hazards,

•  Usage coded as the proportion of time a camera was active during an occasion (e.g., 0.9 for 9 days of operation),

•  Multiple detections of the same individual at the same camera on the same day were allowed if videos were independent (≥30 min apart). Thus, the count for one individual at one camera in one occasion could exceed 10.

2. Binomial Count Proximity Detector

Using:

•  g₀ as a detection parameter,

•  Traditional detection functions HN and EX,

•  Usage coded as the number of days the camera was active during an occasion,

•  All detections of the same individual at the same camera on the same day collapsed to a single detection. Thus, the maximum number of detections for one individual at one camera per occasion equalled the number of active camera days.

Since both approaches produced essentially equivalent results, we would appreciate advice on which modelling framework is more appropriate for our study system. Hence, following questions:

Q1. Which detector type is more suitable for our data: Poisson count proximity or Binomial count proximity? 

Q2. For the Binomial count proximity model, which baseline parameter is appropriate: g₀ or λ₀?

Our understanding is that λ₀ should be used with Poisson count proximity detectors, but the appropriate parameterisation for Binomial count proximity remains unclear to us.

The Binomial count proximity model (and similarly the Poisson model) identified Mk—the model allowing for a change in detection probability after the first capture—as the best model based on AIC. Ecologically, this seems reasonable for elephants, given that cameras were placed along movement paths or near preferred resources.

However, the Mk model produced a noticeably higher density estimate with a wide confidence interval, whose upper bound appears unrealistic. Our hypothesis is that if detection probability is indeed higher after the first capture, this effect may vary greatly across camera locations. Plotting the number of individuals detected per location per occasion (with crosses indicating no detections) shows high variability in post‐first‐capture behaviour.

We initially thought that Mk might capture site‐level heterogeneity—particularly since 13 of the 34 cameras never recorded an elephant—but we are now unsure whether the Mk model is conceptually appropriate for SECR analyses using camera traps.

Q3. Can this model be considered a valid candidate for SECR designs using camera traps?

Thank you in advance for your time ! Any input on our questions will be greatly appreciated !

Best regards, 

Viktor Mertens & Benjamin Debetencourt

[Murray Efford]

Hello Viktor and Benjamin

That's a lot to digest! Here are some comments from my perspective, without pretending to cover everything.

Q1. This is a matter of taste. My preference is for (2) which is exactly equivalent to a daily proximity detector. If you had used daily data with a proximity detector then 'secr' defaults to collapsing the data to binomial across all occasions anyway ('fastproximity', unless the model requires otherwise).

Q2. Either  λ₀ or  g₀ may be used with any detector type. My preference these days is for  λ₀ (see 10.1 in The SECR Book).

Q3. What you call Mk is a model I have not really explored (change in detection probability after first detection at a site, for any individual). Intuitively it does allow heterogeneity of sites, but it's not exactly that. Unless you really believe in the across-animals learned response, I suggest finding a habitat or site covariate that might explain differences. and if the AIC difference is small I would not feel bound to go with Mk. Just my opinion.

Your transboundary point is not a worry in itself, but I hope the overall scale of sampling is enough, and individuals have home ranges smaller than the study.

Murray

[Benjamin Debetencourt]

Dear Murray, 

Thanks a lot for taking the time to answer us, we really appreciate your feedbacks.

You raise one big concern we had, about the size of the study area regarding the home ranges. 

The population definitely has a bigger home range than our study design. However, it seems that there is a seasonality in their usage of territory, they are months when they never come where our cameras are, and months where we capture them often. The survey period only encompasses months when they are present in the survey area. We cannot though confirm if during the study period, they spent most of their time in the area we surveyed. When we raised this concern with a colleague, he advised us to still use an SECR framework to estimate the density of elephants in our survey area, and use a non-spatial capture recapture model to estimate the population size. Does it seem reasonable to you ?

Thank you again for your quick feedback and all the content on the method freely available, that is of tremendous help !

Best regards, 

Viktor & Benjamin

[Murray Efford]

May be a bit of a stretch. Think about the models and their respective state variables. In the SECR model, fixed individual activity centres (and home ranges) are scattered independently over space (within the habitat mask) and the distribution is characterised by density. Your elephant population will violate this because of social cohesion and changing activity centres over time, but there may be a case that the model is nevertheless useful within a temporal window (sociality mostly biases the variance estimates e.g. Bischof et al. 2020 and Efford & Fletcher 2025). However, you raise the possibility that, even within the window, movements may be larger than can be inferred from re-detections within the study area (because animals stray way outside); in that case I think density estimates will be biased high. Using a non-spatial model is fine if your study population is a naturally defined group of animals, and N does not depend on the spatial extent of your sampling (would not increase if you sampled a larger area).

So there are lots of ifs and buts, and how much you can bend the models depends on the spatial dynamics of the population in relation to the time and spatial scale of sampling.

[Benjamin Debetencourt]

Dear Murray,

Thank you for pointing out the overdispersion issue. We looked into the available tests and correction factors to apply to both our non-spatial and spatial models.
Regarding the spatial issue: although we lack direct movement data beyond our sampled area and do not know exactly how far individuals range into the neighboring country during certain time windows, the northern boundary of our study area lies only about 8 km from the southern international border. Published studies on other elephant populations report daily movements of 7–8 km, making it highly likely that individuals travel beyond our sampling frame during at least part of the study period. 

However, looking at the encounter rates we obtain across the years, there are two peaks when we capture more elephants: one in the wet season (June-August) and one in the dry season (December-February). In light of this pattern, would it be advisable to fit two independent SECR models—one for each peak— to limit the time period to the months when the elephants are more likely to spend time in our study area? Or is it preferable to treat these as two separate sessions within a single multi-session model?

Then, given the scale of elephant movements relative to our study area, we hope we could interpret the estimates as conditional densities for the specific time windows and area sampled ? Or do the movement dynamics introduce too much bias for these seasonal density estimates to be meaningful, even in a restricted context?

Thank you in advance for your guidance !

Best regards, 

Viktor & Benjamin

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[Murray Efford]

How to fit SECR models to these data, and whether it's a good idea at all, will depend on sample size (number of individuals) and spatial scale (weekly and seasonal movements relative to sampled area).  Seasonal estimates are good (better fit of model to biology) if the population is plausibly stationary within a season and samples are large enough. I think I've reached the limit of what I can say without seeing all the details, and I'm sorry I don't have time for that.
Murray

[Benjamin Debetencourt]

Dear Murray, 

many thanks for all the feedbacks, it was really helpful to better understand the limitations of our design and of the method.

We have a clearer understanding of what we can and cannot do now !

All the best, 

Viktor & Benjamin