Fixing p in in correlated detection models

[bnewkirk]

Hi,

I am trying to build occupancy models to describe the environmental associations of some rare fish species. I am trying to use the correlated detection models because I had to use a space-for-time design due to logistical constraints. Going through the modeling process, I have encountered some issues with detection probability that I think are being caused by the rarity of the species. I am curious if there is a method I could use to fix the detection probability in my models, or if there is a way that I could model detection probability based on sites where the species have been detected. Any help with this would be greatly appreciated.

Thank you in advance for any help!

[jhines]

You can easily fix parameters in RPresence by adding the argument, “fixed=xyz”, where xyz is a dataframe containing two variables: “param” and “value”. The “param” variable should contain the labels of the parameters you’d like to fix and the “value” variable should contain the values to fix them to. For example,

fixedvals = data.frame(param=c(‘p(1)’,’p(2)’)), value=c(1,1))

Then, include this in the occMod function call:

mod1 <- occMod(list(psi~1, p~1, theta~1), data=mypao, type=”so.cd”, fixed=fixedvals)

However, the whole point of occupancy modeling is to estimate occupancy, accounting for detection. So, by fixing the p’s, you’re estimating the product of occupancy and detection.

Even with rare species, as long as you have some detections, you should be able to get estimates for the simplest of models, which would be better than just computing the proportion of sites with detection (naïve occupancy). If you’d like to send me the dataset, I’d be happy to make a recommendation.

[sbonner]

Hi Braxton,

Out of curiosity, what is the distribution of the number of detections across the space-for-time replicates at each site?

A student of mine has been working on occupancy models for rare species. We have found that the models breakdown when the species is detected at only 1 or at most 2 of the replicates at each site. This is not surprising. The detection probability is essentially estimated by modelling the number of repeat detections (i.e., total number of detection minus 1) at each site at which the species is detected at least once. If the majority of sites have no repeat detections (i.e., the species is seen at most once) then the estimates become very unstable. Even with a few sites with 2 or three detections, the estimated detection probability will be very close to 0 and the abundance estimate will be very high.

Cheers,

Simon

[bnewkirk]

Thank you both for your replies to this post.

Jim, I appreciate your help with how to fix detection probability. I have been getting some estimates from my intercept-only models, however, confidence intervals have ranged from 0-1 and some of my estimates of occupancy have been high relative to the rarity of the species. I will pass along a dataset for one or two of my species. Thank you being willing to take a look at this.

Simon, that likely could be the problem we're running into. Many of our species were detected in only 1 or 2 of the space-for-time replicates. Thank you for your insight to this.

Best,
Braxton

[jhines]

Hi Braxton,

For the first species, NR.., you only have 3 unique histories and either all were non-detections (or non-detections and missing value) or all were detections. Your idea of fixing p to the value for sites with detections is actually what happened in the model anyway. In this case, the 3 sites with all detections indicate that p=1.0 and that is what the model estimates. As that estimate is on a boundary, no standard error can be computed. With 3 of the 46 sites containing detections, the estimated occupancy probability is 3/46, or 0.0652, which is what the model estimated. If the occupancy and detection estimates for this species seem unreasonable, I suspect that the detections are not independent over surveys. The correlated-detections model would account for this, but there isn't enough data for this model.

The 2nd species, PL.., has only 1 detection, so not enough data to estimate anything except the product of occupancy and detection, 1/(46*3) = .0073.

The 3rd species has more data and the model did produce estimates which look reasonable (to me). For this species you have some sites with detections, but not in all 3 surveys. Of the sites with detections (5 of them), you have 12 total detections, giving a detection probability of 12/15 = .80 which is close to the model estimate.

One suggestion I have is to combine the 3 species into a single analysis so that you can share parameters. For example, with the combined data, you could estimate a different occupancy probability for each species, assuming the detection probabilities are the same. I know nothing about the species you have, so this might not be reasonable, but it is probably better than fixing detection to an arbitrary value. When I ran this model with the combined data, I got psi(nr)=0.0657, psi(pl)=0.0219, psi(ws)=0.1095 and p=0.8088. Again, this assumes detection among the 3 surveys is independent. If they are not independent, then you would need the correlated detections model, which would require more surveys.

So, it doesn't seem like there is much we can do with such sparse data, unless we can combine it with something else. If you plan future studies, I suggest using the "genpres" functions in RPresence to gauge how many sites and surveys are necessary in order to get reasonable estimates from these models.

Jim