Extracting a density and abundance by line or camera in LTDS/CTDS

[Benjamin Debetencourt]

Dear all, 

I am working with line transect distance sampling and camera trap distance sampling. I wanted to dissect the outputs that the dht2 function create in R, to obtain a density/abundance by line transect or camera trap, using the sample_res attribute.

For the line transect, it was straightforward, I could use the number of observation corrected by the probability of detection as my abundance at the line, and divide by the covered area (length transect * truncation distance *2) for the density.

I managed to recover from that all the estimates from the region.

When I tried the same thing with CTDS, I stumbled in some discrepancies between what I compute by camera and what the dht2 global estimate is.

I computed for each of the k cameras the density, by using the formula in Howe, 2017, 

For each k, I compute one value that I believe is the density at each k location (Dk). The effort in my data is the value of ek, that takes into account the spatial and temporal effort of each camera.

When I want to obtain the “abundance” at each camera, I multiplied the Dk by my area covered by each camera, which is the (FOV in degree/360) * pi * (truncation distance)^2, if I am not mistaken. 

When I then sum the “abundance” obtained like this of all the cameras and divide it by the sum of the covered area for each camera, I should obtain the density estimate global D. But I do not. 

If I compute with the data extracted from dht2 the formula above for D, I do find the same density.

I fear there is something I am missing, probably linked with the temporal effort but I am not sure what. In the Dk computation I take into account the temporal and spatial effort, so I should be able to retrieve the “abundance” when I multiply the density by the area covered? 

I would be happy to read any input one may have, if anyone else have tried to obtained an “abundance” at the camera location or if I am doing a very obvious mistake.

Best regards, 

Benjamin Debetencourt

[Eric Rexstad]

Benjamin

I'm not very comfortable when folks want to make inference at the level of the transect (whether for lines or points). As a matter of principle, estimates should have associated measures of precision, which are awkward to compute at the level of the transect; as the only uncertainty that can be incorporated is the uncertainty in detection probability. 

Speaking of detection probability, there is seldom sufficient detections to fit a transect-specific detection function. In lieu of this, the detection probability estimated from data from all transects is applied at the transect level for the transect-level abundance estimate. We know that applying a detection function estimated from pooled data, but applied at a lower level of aggregation (the transect) results in biased estimates. See below for statement from Slide 9 of this online lecture https://distancesampling.org/online-course/08-covariates/Mod8-2023-covariates.pdf

For CTDS, I suspect there is an additional complication for estimating density at the transect level. You don't mention your study animal or camera equipment. But from my experience, the truncation distance for most CTDS deployments is smaller than 20m and the camera field of view is less than 50 degrees. This results in a very small covered area or camera "footprint".  For the values in the previous sentence, the covered area is 0.02ha. Doubling both the truncation distance and FOV increases the covered area to 0.14ha. Estimated abundance in areas of this size will be difficult to ecologically interpret. Covered areas of this size are also likely to be highly variable as some cameras will view such things as watering holes while other cameras will view uninteresting bits of habitat.

Theoretical issues aside, you want to know why you don't recover the study area estimated density by summing the transect-specific abundance estimates and dividing the sum by the total covered area. I suspect the answer lies, as you suggest, in the failure to account for transect-specific effort. The summation of the transect-specific abundance estimates should be weighted by the effort expended by each camera.

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From: distance...@googlegroups.com <distance...@googlegroups.com> on behalf of Benjamin Debetencourt <b.debet...@gmail.com>
Sent: 23 January 2026 11:56
To: distance-sampling <distance...@googlegroups.com>
Subject: [distance-sampling] Extracting a density and abundance by line or camera in LTDS/CTDS

 

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[Benjamin Debetencourt]

Dear Eric, 

Thank you very much for your detailed answer. I probably should have explained why I am interested in extracting those values. It is purely theoretical, I was trying to better understand the outputs of dht2 and how to reconstruct the estimates from it. As I managed pretty easily to do so with LTDS, I was bothered by the fact I could not figure it out with CTDS.

Yes, it is definitely not meaningful ecologically, especially for the cameras, the area we sampled is indeed very small (we are working with FOV between 38 and 50 and the truncation distance is 20m). 

Thanks for the suggestion about adding some weight to the abundance, I will try to make it work following that lead.

Many thanks again, 

Benjamin Debetencourt