Multi-method with spatial replication

[Pavlacky]

Hello all,

I am interested in applying the multi-method model to estimate avian occupancy from spatially replicated point counts. This approach was suggested as a way to estimate an availabilty parameter (theta) over the spatially replicated occurrence data.

The sample unit is a 1 square kilometer cell. Within each sample unit, there are 16 sytematically located point counts (K=16). The point counts were divided into five one-minute samples (L=5). Each one-minute sample was sampled without replacement.

I ran a multi-method model holding p(.) and theta(.) constant. Then I ran a model alowing p to vary by time p(t) and holding theta(.) constant.

The estimate of Psi was identical for these two models. In fact, no matter what structure I put on p, the estimate of Psi is invariant. Moreover, I get the same estimate of Psi when I run a single season model with spatial replication of the point counts.

I was wondering whether someone could help me troubleshoot my application of the multi-method model.

With thanks,

David Pavlacky

[darryl]

RTFP!

Nichols et al. (2008) J. App. Ecol where the model is described. Last paragraph before the first example...

[Pavlacky]

Hello darryl,

I read Nichols et al. (2008) In the robust design encounter history, I set the spatial replicates as the primary occasions (K=16) and the point count intervals as the secondary occasions (L=5). The No. Occ/season was 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5

However, I am getting some decidedly weird model behaviour. I'm not sure why Psi is invariant when I change the structure on p. I get exactly the same estimate of Psi when I collapse the encounter history and run a single season model with spatial replication (T=16).

Do you have any idea what could be going wrong?

As always your advice is appreciated,

David

[darryl]

To quote from the paragraph I indicated:

"We note that this new parameterization is not required in
order to obtain unbiased estimates of large-scale occupancy,
ψ. In the above example, it is possible to simply collapse
the detection data from the three devices at each sampling
occasion to reflect detection by at least one device or nondetection
by all devices. The example detection history used
above, 010 000, would simply be rewritten as: 1 0. The first
three device-specific detection entries are collapsed to yield
1 for the first occasion, whereas the second three entries are
collapsed to yield 0 for the second occasion. Analysis of data
collapsed in this manner provides unbiased estimates of ψ
and pt, with the caveat that detection probability for
occasion t is now redefined as the product of the probabilities
of presence in the immediate sample location and detection
conditional on presence in the immediate sample location, [... equation here that didn't paste from pdf ...]. The utility of the modelling approach described here is to provide efficient inference about θt and device-specific detection."

Bottom line: nothing is wrong when you collapse things down, everything is behaving as it should

[Pavlacky]

Hello,

Thanks heaps for pointing that out to me. It seems I didn't read the fine print. It is a relief that the model is behaving properly. However, I hoped the multi-model would address the spatial replication bias that Gary found in his simulation. I suppose it allows inference on occupancy among the spatially replicated points, but correct me if I am wrong, theta does not function as an availability parameter in the sense of estimating Psi corrected for availability.

In your opinion, is there is an advantage of the multi-method model over the spatially replicated single season model?

Cheers,

David

[darryl]

It does function as an availability parameter, but (at least from my understanding) that's not the cause of the bias Gary has helped identify when you use spatial replicates. Here's the way i think about it (not claiming I have this 100% correct either by the way):

When you have a limited number of sub-units that could be selected, and not all of the sub-units are occupied if the larger unit is occupied, when you sample sub-units without replacement then you're introducing a form of dependence among surveys. For example, if I have a total of 10 sub-units but only 5 are occupied, the probability of the first unit will be 0.5. However, the probability for the second unit depends upon whether the first one I selected was occupied, 4/9 if it was or 5/9 if it wasn't. That is, the probability depends upon the outcome of previous surveys.

Now if I sample with replacement, then every time the probability I select an occupied unit is 0.5 regardless of what has happened before.

If all sub-units are occupied, then regardless of previous outcomes, even when sampling without replacement, the probability will be 1, so again no problem.

If you have a large number of potential sub-units, then sampling without might not create too much of a bias; eg if 50 out of 100 initially, for the next unit it's either going to be 49/99=0.494949 or 0.505050. I suspect any bias at that scale would get swamped by the SE.

It only has an advantage if you have interest (and it's biologically relevant) in those final level details. If you're really interested in the higher level occupancy, then probably not.

Cheers
Darryl