Study design considerations - counting cones on pines of variable sizes

[teresa...@gmail.com]

I have used distance sampling with animals and am trying to figure out if it will work well for estimating the density of whitebark pine cones in subalpine forests.  We are thinking about using distance sampling to estimate whitebark pine cone density along 200 m transects, somewhat similar to Williams et al. ( 2020; https://esajournals.onlinelibrary.wiley.com/doi/full/10.1002/ecs2.3085).  However, I am concerned that detectability of cones varies as a function of distance from the transect and also tree size. Trees as small as 2 m tall may produce cones in mast years, though most cone producing trees are larger (5-7 m tall).  Large trees will be visible from the transect at greater distances than small trees. 

My question: Do I need to build separate distance functions for large and small trees? (If yes, this introduces many problems for us in how to define small and large trees, and also creates difficulties in placing trees into size categories in the field.)

Thank you!

Teresa

[Eric Rexstad]

Teresa

Thanks for the citation to Williams et al. (2020) and that novel application of distance sampling.  You could use tree size as a covariate in the detection function.  An example of this is in Sections 5.2.2.4 and 5.3.2.3 of Buckland et al. (2015), estimating density of cork oak trees of different sizes.  If your interest is only in estimating density of cones, rather than trees, you might be able to rely upon the pooling robustness property of distance sampling to produce unbiased estimates of cone density even without measuring tree heights or classes.

There are lots of features that likely influence cone detectability in addition to tree height:  time of year, time of day, etc. etc.  The pooling robustness property says estimates will be unbiased even without taking these features into account in your detection function modelling.

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Eric Rexstad
Centre for Ecological and Environmental Modelling
University of St Andrews
St Andrews is a charity registered in Scotland SC013532

[teresa...@gmail.com]

Eric, Thank you for your quick reply. This is very helpful. 

Teresa

[teresa...@gmail.com]

I tried our distance sample protocol with whitebark pine cones at 5 sites, and it worked well but I do have concerns about missing some detections of cones on the transect line (cones on the tops of 10-m tall trees - not really visible from ground). How robust is distance sampling is to violations of the assumption that objects at 0 are detected?  Among 5 transects surveyed, two of them had at least one tree that was within 5 m of the transect line and we could not easily count all of the cones.  In these cases, should we deviate from the transect line in order to get a better view of the tree canopy for counting cones (to minimize chances we will miss cones on the transect line)?  Or is distance sampling robust such that if we see the vast majority of cones on the transect line, we can assume that this assumption is not violated.  In some cases we can get a better view of a tree's crown by moving off the transect line, but in other cases it is not possible to see the cones because of foliage that blocks our view of the crown. One would need a birds-eye view of the canopy to see all of the cones on some trees. 

Teresa

[Eric Rexstad]

Teresa

Density estimate bias is directly proportional to the amount by which detectability at distance 0 deviates from 1; i.e., if 5% of cones on the line are undetected, the density estimate has 5% negative bias.

It is a good idea to depart from the transect to improve the probability of detecting cones on the transect.  You have an advantage with your study organism in that the cones will not "flush" when your crew takes time off the transect to look for cones on the transect.

To view this discussion on the web visit https://groups.google.com/d/msgid/distance-sampling/31f956f0-e41e-4a9f-8e4f-6adcc09967ben%40googlegroups.com.