Incoporating abundance data into single-season models

[hf.hwa]

Hi - I'm new to occupancy modeling, but have been working through the online tutorials for PRESENCE and reading the book by MacKenzie et al. I'm hoping someone might provide some advice regarding which modeling approach to use given my question / data.

A bit of background: We are interested in estimating the number of trees (sites) infested with an introduced pest. We sampled ~500 trees for a predetermined amount of time on 3 occasions and noted whether the pest was present or absent. We returned to all trees with at least one detection, fully sampled the tree and determined abundance of the pest (the pest is sedentary and dispersal happens during a narrow window, so we can safely assume populations are closed between surveys).

My question is: how do we incorporate abundance data into our model? We do not wish to estimate abundance, but rather we want to use abundance & corresponding detection histories to provide an estimate of infestation (occupancy) rate and how abundant the pest has to be before we can reliably detect it. To me, this seems a bit different than the models described in Ch.5 of MacKenzie et al. Or I am I missing something?

Many thanks for your help.

[darryl]

You're right, this isn't the sort of situation covered in Ch 5 of the book. In chapter 10 (I think) we wave our arms about ways you might incorporate actual estimates of abundance at a selection of sites into the modelling, but we haven't done much with that ourselves, although perhaps there some others that have (I know Mike Conroy and UGA, Athens, GA had been looking into that a bit at one stage). However, I think the way you've done the sampling may create some additional problems, you've only gone back to those trees where saw the species at least once to try and estimate abundance. What if at some of those trees where you never saw the species, they were there, but perhaps at low abundance? Thats going to create some biases if the modelling isn't done appropriately.

I suggest the first step would be to forget about the abundance data initially and perhaps think about using covariates for occupancy/detection that may explain among tree variation in these probabilities, some of which might be caused by abundance. If you really what to start addressing the abundance issue then you might have to think about how to modify either the models or the sampling to be able to do that.

With your initial surveys, what information were you collecting to detect the pest?

Darryl

[hf.hwa]

Hi Darryl - Many thanks for your help. In the interest of brevity I failed to mention that we are also returning to a subset of trees with zero detections and thoroughly searching them to get a sense of the rate of false negatives. We are also searching the canopies of very tall trees using a lift to get a sense of the relationship between canopy infestation and detections at ground level.

The pest (hemlock woolly adelgid) produces a white woolly covering that is very easy to see against the dark needles of its host tree. For our initial surveys, observers visited trees (3 independent observers per tree), searched the branches for 2 minutes or until they detected the adelgid. So the information we collected to detect the pest was whether or not it was seen by the observer.

The adelgid has no natural enemies, competitors, etc and its distribution at this time is mainly limited by dispersal (wind, birds, humans). It infests hemlock trees only and does not move once settled on a branch. Larger trees are larger targets for dispersal and therefore might influence occupancy - especially at the early stages of an infestation, which is of most interest to us. Tree size may also influence detection probability given that smaller trees are much easier to search thoroughly than tall trees.

Perhaps we could use pest density as a covariate rather than abundance since this would incorporate abundance and tree size at once?

Thanks again for your help & advice,
Matt

[darryl]

Matt,
At worst, you could use the intensive sample as a 4th detection/nondetection survey that is likely to have a higher p than the other 3. Trees that didn't get a 4th survey are just given a missing value.

Perhaps we could use pest density as a covariate rather than abundance since this would incorporate abundance and tree size at once?

When you say abundance, is this the true number or likely an undercount? You could use density, although what value would you use for trees that didn't get a 4th survey? To bring in this information correctly, then really you need to do something that is not currently available in any software (I believe) that I alluded to in my previous post. Basically you formulate an occupancy model similar to the Royle and Nichols approach, but rather than having to fully rely on a spatial distribution for abundance (eg Poisson) at some places you actually have an estimate of abundance that you can plug in. At those places you don't have an estimate you essentially have to integrate across all possible values for abundance (as in Royle and Nichols 2003).
Darryl

[hf.hwa]

Hi Darryl,

When you say abundance, is this the true number or likely an undercount?

For most trees, especially large ones, our abundance value is likely an undercount. But this count represents the number of insects we are able to detect given our surveys.

You could use density, although what value would you use for trees that didn't get a 4th survey?

I should mention that we will monitor changes in the population across several years, so we will resurvey all trees many more times. For this year, any tree that has a 000 detection history, we will assume that either (1) the tree is not infested or (2) the density is currently below that which we can detect. We will use next year's surveys to decipher between these two possibilities.

Does that make sense?

Thanks for your help,
Matt

[darryl]

Hi Darryl,

When you say abundance, is this the true number or likely an undercount?

For most trees, especially large ones, our abundance value is likely an undercount. But this count represents the number of insects we are able to detect given our surveys.

Ok, this is a pet peeve of mine. Rightly or wrongly, I restrict my use of the term 'abundance' to some guesstimate of the population size. All you really have is a count that represents some unknown fraction of the population size. Not worried about semantics, but it's good to clarify for me what exactly you have.

You could use density, although what value would you use for trees that didn't get a 4th survey?

I should mention that we will monitor changes in the population across several years, so we will resurvey all trees many more times. For this year, any tree that has a 000 detection history, we will assume that either (1) the tree is not infested or (2) the density is currently below that which we can detect. We will use next year's surveys to decipher between these two possibilities.

I'm not sure how that is likely to help unless you don't expect any new infestations between years. When you do your main surveys, to you just note detection/nondetection of infestation, or do you score it in terms of severity of apparent infestation?