GOF issue with songbird acoustic recording data

[darryl]

Hi Murray,
I think we'll have to agree to disagree on some of these points. You've got some valid points but I don't think it's necessarily as dire as you make out. I wholeheartedly agree it's not an ideal situation for occupancy models, but it's not an unreasonable application of the methods either provided one can accept the limitations on the inference. If you've got some idea about what may affect your detection radius, why not use them as covariates on detection? Admittedly, not as ideal as a design-based solution to try and fix the detection radius, but it may be a step in the right direction.

Without additional information to try and tease out some of the issues your allude to, what else is one to do? Ignore detection completely and use normal logistic regression. Use just the raw counts? How would you suggest this sort of data (and similar data) be analysed?

Cheers
Darryl

[northernbio]

Hi Guys: Was a holiday in Canada yesterday, so am just getting to this today. Murray knows I have been struggling with the definition of "site" for awhile and the applicablility of these methods to point count data, so I will provide a bit more background here. Sorry for it being a long post, but the devil is in the details!

1. I've done experimental playback work to determine the distance at which I can no longer detect a playback made at 80 dB (about the call volume of typical birds). This was stratified by different song frequencies (e.g., high pitched Golden-crowned Kinglet versus American Redstart), and in different habitat types. The 100 m reflected the coarse detection radius for American Redstart in mature conifer. GCKI is about 75 m.

2. The territory size of American Redstart is about 0.5 ha, which equates to a radius of about 40 m. So probably most, but not all of detectable AMRE have territories contained within the detection distance. A few of my species have larger avg. territory size, e.g., Ovenbird with a reported territory size of 1.3 ha, which equates to a 64 m radius of equivalent sized circle.

3. My sampling objective is to estimate if occupancy rate differs, by species, in forested landscapes that arose from natural disturbance versus forest management disturbance. Age-class and overstory type are two major covariates. Landscapes are either a wildfire burn or an area of forest management (e.g., large progressive clear-cut that occurred over about a 5 year period). They tend to be < 10000 ha (often < 1000 ha), and I have at least 2 automated recorders in each landscape (often 4), separated by at least 500 m. I sample at least 30 landscapes, and I analyse 4 recordings from each recording post.

4. I collect covariates at each sample occasion, and these include weather covariates (temperature, humidty, rain, and wind), shrub density, recording quality (ranked 1 - 4), julian date within the season (relative to May 1st). Most species have detection probabilities quite a bit less than 1. An exception is White Throated Sparrow, which never shuts up!

5. I use AIC in the context of ecological knowledge to define and select candidate models. The detection covariates most frequenctly selected are recording quality, temperature, days since May 1st, and shrub density. For only about 1/2 the detection model sets do I get a GOF with values > 0.05 (based on least parsimoniuous model). Hence my desire to explore the 2-group models. I wonder if some sites have birds with territories close to the microphones, and others are further away, hence two detection groups.

6. I interpret occupancy rate primarily from the perspective of whether a landscape is providing usable habitat to a species. I guess I look at the occupancy/detection model as a sort of resource selection probability function rather than as an index related to density based on a snap-shot in time. However, I am also interested in whether overall occupancy rate for species within an ecoregion (say 4 million ha area) is changing from one time period to another (say over a 5 year period).

7. In terms of habitat associated with a species (site variables), I calculate both conditions near the microphones (approx 100 m radius) as well as more landscape level characteristics (e.g., amount of edge, homogeneous forest, wetland extent) over a 5000 ha extent.

8. Even after giving this all a lot of thought, I am still somewhat confused. I agree with Darryl that the analysis perspective is critical, hence me providing the above detail. But I still wonder if or how I am making a critical error by applying the occupancy method to point count data (which I take it to mean any data set where species can move in or out of detection range over the survey period). I also wonder whether I should adopt a 2-group approach, given one can conceive of birds with territories fully contained within detection distance, and those only partially contained within detection distance, as being two groups with different detection probabilities.

Cheers,

Rob Rempel

[murray.efford]

Rob
Mostly in response to your point 8, and with my own apologies for length...

Perhaps it helps if I cast your study in the framework we used in Efford and Dawson (2012):

(1) A point on the landscape is occupied by a species if it is overlapped by the home range or territory of at least one individual (we won’t worry about fuzzy range edges). Any overlap will do. The proportion of such occupied points equals the proportion of area occupied (PAO, using here the terminology we advocate; Darryl calls it ‘usage’). PAO obviously reflects movement, but that is necessary for animals to occupy space (rather than just pin-prick points).

(2) A point recording (no relation to preceding ‘point’) samples the instantaneous presence of vocalising individuals within a circular plot of more-or-less unknown size around the recorder – the set of places from which they can be heard at the centre.

(3) Repeated sampling, with the application of single-season occupancy models, estimates _asymptotic_ occupancy of the plot i.e. whether or not it is overlapped by the territory of any individual of the species. Another way of saying this is that the standard estimate is (largely) robust to temporary emigration. The larger the plot, the more likely it is to be occupied.

So we have the relationships:
- Territory size (plus density and dispersion of territories) determines PAO
- Loudness, transmission and reception of acoustic cues determine plot size

In this framework, territory, the set of points from which a bird sings, is quite separate from plot size. Territory size may possibly affect the instantaneous probability at least one individual is present within the plot, and hence species detection probability at a given density, but this is a subtle and marginal point.

The key problem is that the plot is our ruler for occupancy. The size of our ruler is unknown and depends on several things we have been taught to fear (specifically, confounding of detection with effects of interest – habitat etc.). Once you use the term ‘occupancy’ I think readers are entitled to know what it means, and to be disappointed if it is just another index made obscure by some numerical manipulation.

It sounds like you’ve gone to some trouble to pin down the acoustic factors, which does somewhat deflect my point. However, I’m sure we could still have a good argument! A one-off calibration is nice, but doesn’t protect from hidden variation in detectability (the mantra of the detectability fiends). By all means throw in covariates, but you can do that in any linear model where the response is an index.

Of course, we could also estimate density from these data. Density just might be a better metric than PAO for comparing species because it depends neither on territory size nor on the acoustic detection function. Unfortunately, the technology is not quite there yet

Murray

[northernbio]

Thanks for your reply Murray.

I downloaded a copy of Efford and Dawson (2012), but it will take a little while to digest it. It seems to me that much of the analysis is from the perspective of whether occupancy is a good estimate of proportion of area occuppied (PAO), and its value as a surrogate of density (state variable). But what if the question was focused on probability of site occupancy (in the sense of a resource selection function), where "site" is admitedly variable among species, and in part a function of the species vocal characteristics, singing frequency, and territory size? Effects of environmental variables and site vegetation on detection prob would be included as covariates. In particular, the effects of site vegetation could induce bias in the analysis if it is not accounted for.

Even though site definition ("the ruler") is variable among species, would not probability of site occupancy still be useful as a measure of habitat selection and the relative effects of forest management on use of habitat? I think it would be helpful if you cast your Efford and Dawson (2012) simulation results in terms of how best to use occupancy/detection modeling for different management applications, including habitat modelling. I guess I am still having trouble understanding how in my case relative differences in site definition among species would cause invalid estimates of habitat selection.

Just as an added piece of context, in our forest management planning we apply species specific spatial RSPF models to future forest conditions to predict (and create maps) of expected habitat occupancy. The models were developed using logistic regression applied to point count data and habitat information. We bracket these expectaions using natural disturbance models based on the simulated range of natural variation. The monitoring objectives are to determine: if habitat occupancy is occuring at the expected rate, if occupancy rate is differing among managed versus unmanaged forest, and if occupancy rate is changing over time. In my mind, the occupancy estimates are not used as a surrogate of density.

Rob

[murray.efford]

Rob
Certainly that paper was motivated by the surrogacy issue, but the concepts carry over.

I guess I am still having trouble understanding how in my case relative differences in site definition among species would cause invalid estimates of habitat selection.

Maybe we're talking at cross purposes here: the issue is between habitats, within species. It's simply that any differences in detection (and therefore detection distance) between habitats are confounded with real between-habitat variation in PAO. If external evidence allows you to exclude the possibility that detection varies between habitats, fine, but the models will not fix that for you.

The unavoidable effect of territory size on PAO is a different issue, unrelated to site definition.
Murray

[northernbio]

Hmmm....am slowly catching on (I think). I guess if territory size changes with habitat quality (larger territories required in poorer habitat), then detection probability can change in an undetectable manner. Just a random thought (hopefully not off topic), but maybe it is better to use a kind of 3 point cluster sampling to better capture occupancy under such situations. One would need to simulate movement patterns and play with different sample designs and analysis assumptions. Its seems this goodness of fit issue has multiple dimensions (feable attempt to bring this back on topic...lol). Murray, I would be most interested in any simulation studies you and Deanna might conduct on optimal design and spatial configuration of point plots for monitoring songbird occupancy in continous habitat. Cheers, Rob

[murray.efford]

I think the better approach is to combine presence/absence data with acoustic SECR (perhaps using clusters of microphones) to estimate density. The statistical technology for this is on the way, but not quite there yet. We should discuss this elsewhere!
Murray