Greater glider GG population

Sue Mckinnon

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Two surveyors go through the forest independently. Each surveyor detects 1 in 5 of the other surveyors sightings of GG's. After they have surveyed, they compare locations to determine how many actual GG's were seen. (excluding the double counts where they both saw the same one) . The result is 7 separate GG's seen. How many total detections were there ?
 

Dr.Peterson

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I assumed Greater Gliders would be birds, but I see that they are marsupials. I'm guessing that you were told more in the context, some of which might be relevant to the problem.

I must be misinterpreting something, if the problem is valid.

I made a Venn diagram, with set A being GGs sighted by A, set B being those sighted by B, and the intersection therefore being those that are sighted by both. If the intersection contains x GGs, how many are in each other region? I find that x can't be a whole number, which doesn't make sense.

What is your understanding of the problem? How have you tried to solve it?
 

Sue Mckinnon

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The 7.33 number is the average number of individual Greater Gliders actually seen over 3 nights, so not being a whole number is ok. This figure is found by the 2 surveyors getting together after each survey and determining which ones they both detected so that those ones weren't counted twice.

Yes, i have tried to solve it, and i have an answer of 8.1444 ( i.e. 7.33 x 10/9) . My rationale is that if person 1 detected 5 gliders, and person 2 detected 5 gliders, then 1 glider would have been seen by both, so only 9 gliders actually present even though number of detections is 10. (i.e.the one seen by both has to be counted as one, not 2)
Working backwards then, if the conclusion was there was 9 gliders, then the number of detections would have been 10 , therefore the multiplier is 10/9, therefore the answer is 7.33 x 10 / 9 ( or 7.33 x 1.1111)
The trouble is, my colleague believes that the multiplier is 1.25 We can not agree , despite several attempts by both of us to explain our maths. As far as i understand, he bases this multiplier on his contention that a total detection of 10 would suggest 8 individual gliders seen. I think that a total detection of 10 would suggest 9 individual gliders seen- i.e.the one seen by both has to be counted as one, not 2)

(Another complicating factor is that each surveyor only detects one in 5 gliders actually present - i am not sure if this is relevant in my problem...ii think it isn't relevant to this part of my problem)

Thank you !
 

Dr.Peterson

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Where is 7.33 mentioned? I'm confused. I guess you mean the 7.33 you calculate later. But it appears that you have left out information, which may be relevant.

Are you saying this is a real situation, not a made-up problem? What is the context? I don't see how you could know each sees 20% of what the other sees; and since that implies each necessarily sees the same number, the whole thing seems unrealistic.

As I said, I let x be the number that were seen twice, so 4x are seen only by A and 4x are seen only by B, so the total number of gliders is 9x. Therefore, 1/9 of the gliders are seen by both, and the number of detections is 10/9 of the number of gliders. So I agree with you.

What is the reason given for the claim that 8 would be seen if there are 10 detections? What we've seen is that out of 10 detections, 8 would be seen only once.
 

Sue Mckinnon

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Thanks Dr Peterson
yes , this is a real situation.
The rationale for the assumption that each person detects 1 in 5 GG's that the another person detects is in the attached research.
specifically " Only 21% of all Greater Gliders detected during surveys were seen by both observers, indicating a low detection probability." ( results, page 1)
I find the survey very difficult to understand and I query if all the information is provided:
I have had to separately find out the area of the coupes (I have found this to be :Total area coupes = 135; Barjarg Flat 61 Ha/Mr Hat 36 Ha/Tartan 38 Ha)
Table 1 show 57 individual Greater Gliders seen total over the three coupes ( presumeably after the surveyors determined which ones that they both detected and cancelled out the double count).
Section 3.3 speaks of 121 detections total.
Given the conclusion that they made that only 21% of all Greater Gliders detected during surveys were seen by both observers, then one would expect that a detection of 121 gliders would coincide with a result that 121 - (0.21x121) + (0.5 x 0.21 x121) indivdual greater gliders seen after the surveyors had cancelled out the double counts.
Perhaps on a side issue; I don't understand why they eliminated all detections closer than 15 m. ...While they provide the rationale that there were few detections closer than 15 m, it apears otherwise from figure 2( the histogram).
I don't follow how they got from the number of detections to the number of Gliders estimated over the 3 coupes
 

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Dr.Peterson

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I take it you were assigned to analyze this paper? It's not easy for me to follow, either, in part because there are a lot of terms that may be special to your field and/or your location. (I see the term "logging coupe" used only in Australia, for example.) But I think I figured out the parts you are asking about.

The way I read the bit you quoted, "Only 21% of all Greater Gliders detected during surveys were seen by both observers, indicating a low detection probability," is not that each person detects 21% of the GG's that the other person detected, but that 21% of the total number of GG's that were detected at all were detected by both. That is very different. For example, it is possible that A detected 100 GG's and B detected 21 of those, and no others. Then 21% of the detected GG's were detected by both, but A detected 100% of those that B detected, while B detected 21% of those detected by A. There are many other possibilities. There is no reason to assume both observers saw the same number.

But given the total number observed, you can determine the total number of detections, which was your question. If N were observed (after taking duplicate observations into account), then 0.21N were detected twice and 0.79N were detected once. The total number of detections was therefore 2*0.21N + 0.79N = 1.21N. (That makes sense, if you think about it.) This is closer to your colleague's 1.25 than to your 1.11.

Another point to make is that they didn't assume that 21% were seen twice; they carefully compared their observations to determine which were duplicates: "On completion of the survey the observers walked back along the transect line together, comparing observations on each individual seen. The two observers’ data were then combined to determine which gliders had been seen only by observer one or observer two, or by both observers. In almost all cases it was straightforward to determine whether each glider had been seen by observer one, observer two, or by both observers. Where it was not obvious, duplicate observations were determined by carefully comparing the coordinates collected by each observer combined with perpendicular distances of gliders from each sighting using GIS. Individual observers alternated between being observer 1 or observer 2." (section 2.3)

As for section 3.3, I think it says that 121 GG's were detected, not that there were 121 detections before eliminating duplicates: "the total set of 121 gliders detected". But if it were 121 detections, then I would say that there were 100 individual GG's detected, based on what I said above.

Finally, I'd say that "the apparent deficit of detections at distances <15 m" means that in theory they would expect the histogram to be decreasing everywhere, indicating that the closer it is, the easier it is to detect; the peak around 15 m suggests, as they say, that it is in fact harder to detect animals almost directly above you, because the numbers there are lower than expected (not low in an absolute sense, but compared to the model). Apparently their analysis (which I didn't try to examine) is based on a model (MRDS) that assumes that detection probability is inversely proportional to distance, or something like that; so they chose to fake it by essentially cutting out the region with 15 m of the path, and the region more than 75 m, so that the model can be applied to that region. (What I am curious about is the big notch around 50 m in the histogram, which they ignore; that seems more noticeable than the drop-off after 75 m.)
 

Sue Mckinnon

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Thank you ...this is very helpful.

I am attempting to understand the survey better as i want to use the findings from this survey ( in the Strathbogies) to extrapolate an estimate of the number of Greater Gliders present in another coupe (in Kinglake) that was suveyed separately and we only have the results from the transect count in Kinglake. This is an actual situation - not an assignment.

You have clarified the relationship between the number of detections and the number of Gliders detected, how then did they get from this point to the determination that there were 503 Gliders in the 3 coupes ? ( The area of the coupes is :Total area coupes = 135 Hectares; Barjarg Flat 61 Hectares/Mr Hat 36 Hectares/Tartan 38 Hectares)

Thanks again
Sue
 

Dr.Peterson

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The mention of 503 gliders in section 3.3.2 refers to table 7, which shows 503 in the three coupes; that would be expected to be the sum of 258+142+115 in table 6, but that sum is 515, off by 12. You'd also expect the Total lines in the two tables to be the same, but they differ by even more (157)! What's going on here?

Table 6 sums correctly; table 7 doesn't. I don't understand some other things about these tables, either; for example, I'd expect the confidence intervals to be centered on the point estimates, but they are not. Probably this somehow relates to the MRDS model they're using, which I know nothing about. I'd have to read a lot more deeply than I am able to in order to fully understand that.

So, I can't answer your question. Maybe someone else with broader experience with statistics might be able to see what they're doing.
 
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