Issues with model fit and density predictions
Thomas McLaren
Hi all,
I’m a grad student working on a single species study collecting point count transect data with distance sampling methods. I’ve run into a few issues I was hoping you all would be willing to provide feedback on.
We have two years of point count survey data collected. In the first year we collected distances on only visual observations. In year two, however, we collected distances for both visual and auditory detections of our study species. The goal is to use several years of survey data to create a two-stage model of habitat use following the procedure laid out in Buckland et al 2009. In order to perform distance analysis on the data from both years, I’ve decided to only use our visual detections. I also opted to pool the data from both years because the sample size in each year was not very high (year 1: ~80 detections, year 2: ~90 detections). In total I have 176 observations from both years combined.
The upper limit of our distance detections is just beyond 300 meters. After truncating the farthest 10-15% of the data, I still seem to have a long tail of distant detections. Estimating models using this truncation distance results in poor fit in the uniform and half normal models (visual inspection and GOF tests). The hazard rate fits better, presumably because it is more flexible, but produces estimates of N and D that are unrealistically high (density = 479 birds per square km). All models have estimates of detectability below 0.08 which also seems far lower than I’d expect in reality.
After truncating the data at several distances I found that models seem to fit well with a truncation distance of 70 meters. This truncation distance only leaves 69% of the detections for analysis though. Additionally, all models with a truncation distance of 70 meters produce unrealistically high estimates of N. One trend I noticed was that as I decreased truncation distance, density estimates tended to increase across all models.
To summarize the problem, models with far truncation distances produce more reasonable estimates of density and abundance (except for Hazard rate) but they don’t seem to fit the data (from visual inspection and GOF tests). These models also produce very low estimates of detectability. Models with more extreme truncation distances fit the data well but produce unrealistically high estimates of density and abundance.
I guess my questions are:
1) Am I making an error by truncating my data set down to just 70 meters? Is this a case of good fit-bad predictions?
2) Is there any recommended action when a model provides good fit but produces density estimates that seem to be inflated?
3) In one study of Island Scrub Jays, Sillett et al 2012, the authors binned their data into three very wide bins (0-100m, 100-200m, 200-300m) to account for responsive movement of birds during their surveys. Would this be a reasonable approach to use in this situation?
Here is the paper cited: Sillett, T. S., Chandler, R. B., Royle, J. A., Kéry, M., & Morrison, S. A. (2012). Hierarchical distance‐sampling models to estimate population size and habitat‐specific abundance of an island endemic. Ecological Applications, 22(7), 1997-2006.
I'm concerned that there may be issues with the distribution of our detections that could result from a violation of assumptions or lack of visibility in dense forest habitat. Maybe birds are moving responsively or there are instances of recounting. Since we only have single observer data I’m not sure how I can investigate this.
I’m happy to provide more detail on the models. Thanks for any insights you can give!
All the best,
Tommy McLaren
Stephen Buckland
Tommy, when detection probabilities are highly heterogeneous, you can get long-tailed distributions like this, then more severe truncation is sensible. You hint at the problem here – movement. Responsive movement towards the observers would certainly cause the problems you’re seeing. But if your species is very mobile, even if movement is not responsive, it can result in data like these, hence the suggestion of using a snapshot approach in:
Buckland, S.T. 2006. Point transect surveys for songbirds: robust methodologies. The Auk 123, 345-357.
This doesn’t really help you though if the movement is responsive, unless you wait at each point long enough for your study species to ignore you, then record distances to those whose position you know at a snapshot moment. Sample size will then become an issue!
If responsive movement is a major problem, you might want to consider putting microphone arrays at each point, which can give you triangulated distances to calls/songs, and use the cue-count method for analysis. For this, you would need to estimate the mean call rate.
Steve Buckland
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Thomas McLaren
Hello Dr. Buckland,
Thank you for the reply, it certainly helped to clarify some of the problems I am encountering with this analysis. Reflecting on the conditions at our study sites, your point about heterogeneous detection probabilities seems spot-on.
Additionally, the inflated estimates of density I’m getting could very easily arise from movement bias. Our target species is very mobile, so maybe random movement is driving this problem. I have been reading up on cue counts and the snap-shot method and I’ll be bringing up the issue of movement bias with our research team. If you don’t mind, I have a follow up question I was hoping you could answer.
If it is possible, I’d still like to use the existing data for a two-stage distance analysis. Is there any way to account for movement bias in data that is already collected? If not, would it be reasonable to acknowledge that this bias exists when presenting results?
Thanks again for the insight, it’s greatly appreciated.
- Tommy
Stephen Buckland
Tommy, if you can somehow estimate the detection function, e.g. by collecting data by the snapshot method this year, you could apply that estimated detection function to your earlier data. For this to work, you would need to choose as large a truncation distance as you can get away with, so that if there is responsive movement, birds are unlikely to respond from outside the truncation distance. However, you suggest the problem may be a lot of movement independent of the observer, and this would not remove all the bias in that case. If you record the time of detection of each bird, you could try analyses with a shorter time window for each point. E.g. if you record for 15 mins, try analyses with the first 12 mins, then the first 9 mins, the first 6 mins, and the first 3 mins. Hopefully the estimates may appear to asymptote.
I would avoid using the hazard-rate model because it can fit spikes in the data close to the point caused by movement far too well, giving a detection function that falls impossibly rapidly with distance from the point, and impossibly high density estimates. If all else fails, I would simply fit a single parameter model, perhaps the half-normal with no adjustment terms, noting that the poor fit is likely caused by movement. If the true detection function is similar to the half-normal, this will give very much smaller bias than if you try to fit the data better.
Of course whether a journal would accept your analyses depends on who you get as referees! My own view is that I would be unsympathetic if the difficulties were swept under the carpet, but much more sympathetic if the paper is open about the problems, and discusses the measures that might be taken to resolve the problems.
Steve
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Thomas McLaren
Hi Dr. Buckland,
Thank you for the comments! We do indeed have data about time periods within our point count surveys so I’ll look at results from reducing the total survey time as you suggested. I’ll also consult with our research group to see if we can implement a snap shot survey for future seasons.
From previous work on this data set, I’ve had some suspicions about the hazard rate model’s applicability in this scenario. I’ll avoid using it for the reasons you mention and opt for a half normal key function. If all else fails, then we will just have to be explicit about the limitations for inference when writing this study up.
Thanks for the guidance with this analysis,
Tommy