Royle point-count survey for territorial birds

[atsw2]

Hi,

I would like to ask a few questions about the Royle point-count survey. We are currently working on an endangered specie, Todiramphus godeffroyi (Marquesan Kingfisher), which is a territorial bird that only exists in Tahuata Island (Marquesas archipelago). We chose to use the program Presence, and we would like to use the Royle biometrics to estimate the abundance of this specie on this island.

For this project, we decided to do point-count survey, with 3 visits minimum. These points are separated by 300 m, during a given time 10 minutes. We only had 3 weeks and we were only able to do 66 sites, since a lot of the island is difficult to access (some parts are only accessible by boat!). Plus, there are missing observations since the roads are not in good conditions and were not easily accessible.

Basically, I don't have a lot of data to work with, and when I tried to run the Royle point-count model, the 95% confidence interval is too large. I am not sure if I am supposed to modify parameters or not (often kingfishers are in couple). I am wondering if I am doing something wrong, or that there is just not enough sites and I should just use the naive occupancy estimate to estimate myself the total abundance. Does the Royle model take into account the size of the area sampled? In my case the island? Here is the ouput of Royle point-count model, without covariates or changing any parameters:

********* Input Data summary *******
Number of sites = 66
Number of sampling occasions = 3
Number of missing observations = 20
Data checksum = 19788

Naive occupancy estimate = 0.2424

NSiteCovs-->0
NSampCovs-->0
Primary periods=3 Secondary periods: 1 1 1
- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
essaie
- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
modtype=4 N=66 T=3 Groups=1 bootstraps=0

-->3-1
Matrix 1: rows=3, cols=3
-,a1,a2,
p 1 0
lambda 0 1
========================

Matrix 2: rows=0, cols=0
========================

Matrix 3: rows=0, cols=0
========================

Matrix 4: rows=0, cols=0
========================

Matrix 5: rows=0, cols=0
========================

Matrix 6: rows=0, cols=0
========================


Royle Model w/ species counts (k=200)
Number of sites = 66
Number of sampling occasions = 3
Number of missing observations = 20

Number of parameters = 2

Number of parameters = 2

Number of parameters = 2
Number of function calls = 71
-2log(likelihood) = 167.7554
AIC = 171.7554

varcov: nsig=6 eps=1.000000e-002

Untransformed Estimates of coefficients for covariates (Beta's)
======================================================================
estimate std.error
A1 p : -3.038199 1.626439
A2 lambda : 1.197502 1.544142

============================================================

Individual Site estimates of <p>
Site estimate Std.err 95% conf. interval
p 1 site 1 : 0.0457 0.0710 0.0020 - 0.5373

============================================================

Individual Site estimates of <lambda>
Site estimate Std.err 95% conf. interval
lambda 1 site 1 : 3.3118 5.1139 0.1606 -68.3076

============================================================

MODEL PARAMETERS:
Estimated parameter estimate std.err 95% confidence interval
-------------------------- -------- ------- ------------------------
Detection probability (c) = 0.0457 0.0710 -0.0934 - 0.1848
Avg. abundance/sample unit(lambda) = 3.31 5.11 -6.71 - 13.34

Derived parameter estimate std.err 95% confidence interval
-------------------------- -------- ------- ------------------------
Occupancy (psi) = 0.9636 0.1864 0.5982 - 1.3289
Total Abundance (N) = 218.58 337.52 -442.96 - 880.12

[darryl]

Hi Adara,
Firstly, you might want to review the basic assumptions of the Royle model. One of them is that individuals are detected independently of one another. If you tend to detect pairs (so if you see the male you're also more likely to see the female) then this basic assumption may be getting violated. Your counts will also tend to have more even numbers (2, 4, 6, ...) that what you'd expect if birds were being detected independently. There's also a number of other assumptions that you should review to make sure they're reasonable for your situation.

How sparse is you're data? From your output I'd guess you detected kingfishers at about 16 sites. Did you tend to redetect individuals in subsequent surveys of the same site, or only really see them in 1 of the 3 surveys (if at all). The estimated per-individual detection rate is very low which makes me think that you're data is quite sparse.

The width of the confidence interval is a consequence of the data, and also the model used. The Royle count model is about the only option in PRESENCE for estimating abundance (though involves a number of assumptions), but if you want to move away from abundance you could use some of the other occupancy models. Sparse data could also be adding to the problem, could you post it so we can see what it looks like? Adding covariates may help, for example if you think there's variation in abundance among sites due to habitat type.

What's labelled as 'Total Abundance' is the estimated total at the 66 sites you surveyed, it doesn't account for the area of the island that you a haven't surveyed. You could do that yourself though if you know what fraction of the island you surveyed, or if you know the area of a 'site' and the total area of the island. An important consideration to keep in mind however is that what the model is giving you is an estimate of the average abundance per site (3.31 in your output). If you're going to scale-up to get a total abundance, you have to consider whether those individuals are fully restricted to each point count site or not. If not, then you're potentially going to overestimate total abundance because the 3 birds (say) that were at a site, actually came from a larger area that just the point count station.

I also note a bit of inconsistency in how Jim Hines has calculated confidence intervals in the output that I''l contact him about off-list.

Cheers
Darryl

[jhines]

Hi Adara, Darryl,

A while ago, PRESENCE computed confidence limits by adding +/- 1.96 * std. error of the real parameter estimates. I changed it to compute them by adding +/- 1.96* std. error of the beta parameters and transforming those. The first few lines in the output don't appear in your post, so I can't tell what version of PRESENCE you used, but I suspect it is an old one. If you download and install the current version, the confidence intervals on the real parameters (c, lambda) will be computed using the transformed beta SE's.

Jim

[jhines]

Hi Adara, Darryl,

Oops. I was looking at the Royle point-count output. The Royle-Nichols model still computes the SE's using the real parameter SE's in some places. I'll correct this today.

Jim

[jhines]

I've uploaded a new version of PRESENCE which has the conf. intervals computed from the Beta SE's for the Royle and Royle/Nichols models. Thanks for pointing this out to me.

Jim

[atsw2]

Hi,

The male and female are alike, so when individuals were detected, it can't be assumed that there were a couple in a territory. And not a lot of couples were detected, but when 2 were together, it was assumed that it was a couple since they defend a large territory of 5-6 hectares. I was not sure if I could use this info for the model without going against the assumptions, but I was trying all sorts of things to reduce this interval.

Yes, the data is really sparse, and often were detected only once or not at all. Here is the raw data

Sites 1 2 3
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 0
5 0 0 0
6 0 0 0
7 0 0 0
8 0 0 0
9 0 0 0
10 0 0 0
11 0 0 0
12 0 0 0
13 0 0 0
14 0 0 0
15 0 1 0
16 0 0 0
17 2 0 0
18 0 0 0
19 0 0 0
20 0 0 0
21 0 1 0
22 0 1 0
23 0 2 2
24 0 1 0
25 0 0 0
26 0 0 0
27 0 0 0
28 0 0 0
29 0 0 0
30 0 0 0
31 1 0 0
32 2 0 0
33 2 0 0
34 0 0 0
35 0 0 0
36 0 0 0
37 0 0 0
38 0 0 0
39 0 0 0
40 0 0 0
41 0 0 0
42 0 2 0
43 0 0 0
44 1 0 0
45 0 0
46 0 0
47 0 0
48 0 0
49 0 0
50 0 0
51 0 0
52 0 0
53 0 0
54 0 0
55 0 0
56 0 2
57 0 0
58 0 0
59 0 0
60 0 1
61 0 0
62 0 0
63 2 0
64 0 0
65 0 1 0
66 0 1 2

The naive occupancy estimate is 0.2424, could I use this, with the island area, to estimate the abundance? I don't think 3.31 birds per site is possible. I tried to fix the parameter p=0.0457 (detection probability from the Royle Count model without fixed parameters) and it really reduced the confidence interval. But I don't know if I am allowed to do that. I will download the new version of Presence and try again to see if it changes anything. Thank you a lot for you're help!

[darryl]

I've seen worse, but that data is pretty sparse. I've tried fitting some of the occupancy models in PRESENCE and pretty unsatisfactory results with estimates having large confidence intervals. I believe this is due to low detection rates. Unfortunately the only way to improve the situation would have been to have a greater number of surveys per unit, even if that meant going to fewer sites. Is this work planned to be repeated next year?

If the basic question you're trying to address is 'how many birds are on the island?', I have to admit that I'm really struggling to see how you're going to do that with the design you've used. It would only be possible if you're willing to assume that (on average) the number of birds at a point count station are restricted to an area (e.g., 9ha) around each point count station. Then if you've got 3.3 birds per 'site' and the island is 9000 ha (say), it would be reasonable to guess you've got 3300 birds. However if the actual area associated with each point count station is more or less than 9ha then you will end up over- or under-estimating the total population size. Why did you decide upon this method as opposed to other options for estimating abundance?

Sorry if any of the above is a bit of a downer.

Darryl

[atsw2]

Hi,

I was indeed worried that the low detection rate would be a problem, but at that time, covering most of the island seemed to be important since these birds were really hard to find. Also, lot of the island was not visited in 2003, and that is why there were a lot of sites to visits.

This method was suggested by Dylan Kesler, which is an expert of kingfisher. He said it was because the territories were large, and that transect counts (that was the method used in 2003) are not likely to make good estimates of density or occurrence. Fixed distance or variable distance point transects are likely to be ineffective for the same reasons, so program Distance is not likely to converge on a reliable or useful detection function. That is why he said we should consider occupancy modeling. That would help with the development of a detection probability, which would help correct for detection biases at the site/point level. He then suggested a point-count survey, 8-10 min, separated by min 200m (we did a separation of 300m), which is a standard method for detecting kingfishers.

I know it might be a really basic question, but I thought an area of a 'site' = point-count station area. Is it really possible to expand that site to 9 ha ? The largest territory possible for a kingfisher is 6 hectares, should not we restrict the birds to 6 hectares then(or maybe I'm confused, 9ha is only an example?). This kind of calculation was already suggested by my supervisor, it was just that 3 birds per point-count station seemed unrealistic, but if it is on a larger area, it might work.

So basically, because the data is too sparse, I cannot use the Royle models? Can I still calculate with Presence the occupancy probability, or is that not possible too?

Thank you very much for your help. I think that they are planning to go next year, since the population trend seems to be declining (when compared to 2003).

[darryl]

When using a point detection method like this (e.g., point counts, camera trapping, etc), the number of individuals at the point (over some time period) is the number of individuals whose home ranges (over the same time period) overlap that point. So unless those home ranges are fully encompassed within the point count detection radius, the effective area to which those individuals belong will be greater than the nominal size of your station. The million dollar question is how much greater.

9 ha was a number I just picked based on your 300m separation distance, I have absolutely no idea whether that would be reasonable or not. Really that would be up to you and your team to come up with something that seems reasonable (if you can) and defendable. Things you'd want to consider though is degree of home range overlap, what was you effective detection radius, etc.

The data is also pretty sparse for an occupancy analysis. I fitted a simple psi(.)p(.) model and the estimate of occupancy was about 0.8 with a confidence interval of 0.006-0.996! The estimated p (which I'd be nervous of also) was 0.12, and if it really is that low it would suggest that you need to have way more than 3 surveys; I'd recommend at least doubling the number of surveys next year if you want to persist with these type of approaches, or think of alternative protocols to increase the per-visit detection probability.

[atsw2]

Hi,

I discussed with my supervisor and he wants to ask:

Can we use ,instead of the average abundance per sample unit, the detection probability to estimate the population of this specie on the island ? The detection probability seems to be more realistic compared to have 3.3 birds per site (especially if you look at how sparse the data is).

Thank you very much for you're help