point transect and left truncation

[Marjorie Bison]

Hello Distance list,

I come back to you for a new concern about point transect and left truncation.

5 point-transects have been performed to study ibex population (sampled since 2000, 2 or 3 times a year). Observers are not located physically within the observed population but at distances that vary according to the point-transect. For example, for the observation point n°1, observer is located on the other side of the valley, which allows the observer to see all the other side of the mountain where the population is (the observation points are easily accessible, that's why we chose this design. Going into the population to count them would require a lot of time, people and energy). Distances are calculated on a map from the observer to the clusters of individuals. This observer n°1 is located at  680 m from the first cluster of individuals. The distances between the observers and the closest cluster varies between point transect (e.g. observer n°2 is located at 370m from the closest cluster) and distances are never small or equal to 0.
An important point is that observers are generally separated from the other side of the mountain by the valley and a river where no individuals can be observed (because they never go there, low altitude).
This implies that we have to take into account a left-truncation in our data analysis. Right ?

1- Left-truncation distances varie between point transect, how do we deal with this in the "ds" function with R (as the left-truncation only requires a single number) ? 
2- Should we analyse each point transect individually even if it decreases the power of the analysis ?
3- Should we use left-truncation (assuming g(x) is different to 1 at the truncation point) or substract the truncation distances (different according to point transect) from all the data (assuming that g(x)=1 at the truncation distance) ? The latter case would imply that the location of the observer is not important in the observation, which is not true.

It is not very easy to explain, I hope you will understand my problem !

Thanks a lot for your help

Cheers
Marjorie
 

[Mark Wilson]

Hi Marjorie,

I remember your situation from a previous post. It struck me at the time that it might be possible to justify a distance-based approach if you could reasonably assume that ibex in the nearest portion of the counting area were detected with close to 100% efficiency. I can imagine situations in which this was the case and it might be possible to operate an analysis where your 'zero' started at the nearest distance that you could detect animals (assuming detection probability of 1). However, in the circumstances you described there are a number of complications:

1. I have no idea whether and how strongly you could argue that detection probability of ibex in the nearest distance band was 100%. If it is likely to be less than this, it would likely be a difficult parameter to get a decent estimate of. Something like an intensive study involving remote-tracking of GPS or VHF tagged animals, where you could calibrate survey observations with known positions of marked animals, might provide you with the information you needed... but would probably require a prohibitive level of resourcing!

2. In the situation you are describing, I think it is likely that detectability would vary not only with distance from observer, but also direction. Animals 2km away on a steep slope and straight in front of you would probably be more visible than animals 2km away and off to the side, on less steeply sloping ground. With enough data, you might be able to get around this by assigning animals to different detection zones, and working out detectability for each zone relative to the nearest and most visible zone (where you would assume 100%).

3. Much more problematic, for distance sampling, is the fact that the actual distribution of animals over the area in which you are detecting them is unlikely to be random with respect to distance. This would mean that comparing the densities detected at different distances (or in different detection zones) can't straightforwardly be interpreted in terms of detectability, as you can't distinguish them from real differences in density.

On the plus side, counts from set points, using standardised effort, experience, equipment etc. should be good indices of abundance, even if it's hard or impossible to interpret them in absolute abundance terms.

As you can see, I haven't really offered a solution to you. I am intrigued to see what the more expert distance analysts on the list can recommend!

Cheers,

Mark

[Eric Rexstad]

Marjorie

I concur with Mark's points 1-3.

I'm trying to think of ways this survey design might work, but I'm afraid I identify more challenges this design possesses.  Recognise that even if the design was perfect, drawing inference from 5 transects will limit you ability to accurately estimate encounter rate variability.  The fewer transects, the more suspect is the inference extended from those 5 transects to a broader study area.  You also note "observation points are easily accessible" hence they are not representative of the study area.  Along with the non-representativeness Mark's issue 3 about distribution of animals with respect to distance from the point also arises in your design.

Now to the matter that the observers are not situated at the centre of the point transect, rather are located at "distance that are never small."  I wonder how much ibex detectability would actually vary as a function of distance from the transect centre under your design.  Central tenet of distance sampling is the existence of information in detection distance to help estimate detection probability through fitting a detection function.  I am sceptical that information content of detection distance in this situation would be of much use in producing a defensible estimate of detection probability.

Independent of the mechanics of performing left-truncation upon the data, I would be reluctant to perform a distance sampling analysis upon these data as I would be dubious of the result.

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[Marjorie Bison]

Thank you for your answers !

Indeed I agree with all the problems you put forward.

I will try to identify different areas with different slopes that could influence detectability.

In this analysis, we do not infer to a broader study area. We only focus on the covered area and compare estimates between years.

One of the aim is to compare those results with CMR data, so we could determine whether distance sampling analysis upon these data is "very bad" or "not so bad" !

Cheers

Marjorie

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Marjorie Bison

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[PABLO PALENCIA MAYORDOMO]

Hi folks!

I’m coming with similar questions that the one initially posted by Marjorie three years ago (probably because my target species is the same: ibex, haha). Marjorie, do you finally analysed your data?

Briefly, I surveyed a high mountain population of ibex by point-transect distance sampling. Because of the practical limitations of these habitats, our sampling points were usually located on one side of the valley, and we surveyed “the other side” of the mountain (see my fancy figure "DesignSM.png", please). Additionally, I would like to note that we sampled around 50 points distributed all over the study area (so some of the limitations highlighted in the previous comments are solved here, I think..).

This design implies that left-truncation should be considered, essentially because the closer distances to the observers locations are blinded. The issue is that this blind area is point-specific, and a specific left truncation distance should be considered for each point location. As it is not possible on the analyses (a general left (and right) truncation distance should be considered during analysis), how can we include this variability?

Here my thoughts:

-          One option could be to apply stratified analyses, and considered in each strata sampling points with similar left truncation distances.

-          Second option, is to subtract the distance between the observer and the closest point of the surveyed zone. Doing that, we assumed perfect detection at the beginning of the surveyed area, and I think that it could be assumed in most of the points because we used binoculars and a telescope on all the points, and left truncation distances are around 200m in most of them. However, I’m wondering about points with longer blind distances (around 500-600m) in which should be necessary to assume perfect detection at 500-600m, that could be contradictory according to the previous lines.

-          Third option is don’t consider left truncation, and then estimate a “correction factor” based on the ratio between surveyed area divided by the theoretical surveyed area.

(See "AnalSM.png")

-          Fourth option?

PD: I would like to note that I didn't found any protocol about that on the bibliography. I just found a brief comment about that on Buckland et al 2001 (section 6.7, pag 215), but I think that these issues should be addressed by someone before... (as this group evidence haha), so please, let me know any paper focused on that.

Thank you very much for your time

Looking forward to your response

All the best

Pablo

[Eric Rexstad]

Pablo

Thanks for the handsome artwork, it makes it easier to understand your field situation.  I understand the difficulty of the mountainous terrain.

When employing point transect distance sampling the quantity that is most critical to the estimation is the slope of the probability density function at distance 0 (h(0)).

Left truncation removes data in the vicinity of the point, making estimation of that fundamental quantity difficult, so recognise your challenges.

Of the options you propose, I would suggest the use of #2 for treating the point-specific left truncation distance.  I don't know what implications this might have for study-wide right truncation you might wish to apply.

Are your figures drawn roughly to scale? Specifically, is the left-truncation distance approximately equal to at least one-half the total detectability distance?  If so, I wonder if distance sampling is appropriate.  Remember, we measure distances because we assume detectability changes as a function of distance.  In the situation you depict, the range of distances where you can detect animals is small (<1/2) relative to the total distance from the observer to the top of the adjacent mountain.  My fear is that detectability of ibex varies only a small amount within your "real area surveyed" distances.  Fitting a detection function to such data would likely result in a very flat detection function; implying detectability really is not a function of distance in your situation.  You can assess this quite easily by simply plotting a histogram of your detection distances.

One other issue that occurs to me as a non-ibex biologist.  Are ibex equally likely to be at all elevations depicted in your figure?  If they have elevational preferences (either likely to be on the tops or avoid the tops) then that will cause difficulties in your analysis as it assumes animals are equally likely to be at all distances from the points.

To view this discussion on the web visit https://groups.google.com/d/msgid/distance-sampling/97053efd-aa3a-4938-9356-fd47ed85c8b2n%40googlegroups.com.

-- 
Eric Rexstad
Centre for Ecological and Environmental Modelling
University of St Andrews
St Andrews is a charity registered in Scotland SC013532

[PABLO PALENCIA MAYORDOMO]

Dear Eric,

Thank you very much for your helpful response. I understand your ideas.

My figures weren't on scale (just an example), I understand the need for a wide range of distances in the surveyed area.

Regarding the distribution of ibex, yes they prefer tops, but we surveyed tops of the mountain in all the points, so I think that we controlled this factor.

Now, I have two more questions:

- It is possible to include different angles in point-transect DS? I'm using package "Distance", and the argument "sample_fraction" of the function "dht2" must be a single number. So it is not possible to set a specific angle (or sample fraction) to each point?

- Regarding the re-scalation of detection distance to solve the blind areas close to the observer, I'm wondering about the fact that NOT all the area within a given sector was sampled, and we just sampled a fraction of the sector because of the irregular terrain and blind areas (see attached figure). If I'm right, a bias will be expected on estimated densities; we will underestimate density because we assumed that we effectively sampled all the sector. However, we only sampled an irregular part of the sector. To solve that, I have thought on estimate a correction factor (see attached figure) in which we estimated the proportion of the survey area in relation to the area of the circular sector. In this respect, I've also thought that this correction factor should be only considered if the effectively surveyed areas are regularly distributed through the sector, if not, bias is expected (e.g. if the effective areas are overrepresented close to the observer, and underrepresented far away from the observer, the number of detections at a high distance will be lower than expected because of the low probability of detection, but also because of the low area surveyed). It is right? How can I handle this issue?

Thank you very much for your help

All the best

Pablo

[Eric Rexstad]

Pablo

Your Q1:  if each point has a different angle of view, you can make station-specific adjustments to your data by altering the Effort field.  Rather than setting this field to "1", you can set it to the proportion of the circle you sampled for that point.

Your Q2:  You provided this figure in your earlier email.  I can't work out how you would apply your point-specific correction factor to the overall density estimate.  You won't be producing point-specific density estimates from your survey, but rather a single density estimate for the entire survey.

To view this discussion on the web visit https://groups.google.com/d/msgid/distance-sampling/2a4f28a8-17c8-415f-9606-26fe2caaba70n%40googlegroups.com.

[PABLO PALENCIA MAYORDOMO]

Thank you very much, Eric :)

Regarding the correction factor to the single density estimate, my proposal is to estimate an average correction factor considering all the points sampled. The background is similar to the activity period estimates when working with camera trap distance sampling. In that case, we estimate a global activity rate (and not point-specific) to take into account the "availability" for the detection of animals by the cameras. I fully understand the distance sampling results are never at point level.

All the best

Pablo

[Eric Rexstad]

Pablo

I understand the analogy with animal activity camera trap distance sampling.  If you pursue that course, you will need to propagate the variability in your correction factor by not only including the correction factor as a multiplier, but also the standard error of that mean correction factor.

The propagation of uncertainty is described in the lecture material

https://workshops.distancesampling.org/online-course/lecturepdfs/Ch6/L6-2%20Multipliers.pdf

To view this discussion on the web visit https://groups.google.com/d/msgid/distance-sampling/ce36ffd5-9c39-48bd-8bd9-5a3624dbce6cn%40googlegroups.com.

[PABLO PALENCIA MAYORDOMO]

Yes! thank you for your response :)

Best

Pablo