postHocLM - Attenuation of effects using the full community

[Aaron Skinner]

Hi Jeff and all,

I had a question about the inclusion of rare species and how they influence functional trait inference using `postHocLM()`.

My objective is to understand which functional traits explain species’ responses to local silvopasture implementation. When I include the full community (271 species), many trait effects are strongly attenuated toward 0. However, filtering to species with ≥ 3 observations (n = 188) yields substantially stronger relationships (see 'postHocLM_attenuation' screenshot). In the attached screenshot, the red stars indicate variables that attenuate at 271 species.

Conceptually, this attenuation seems at least partly expected. Species with < 3 observations have very little information, so their species-level responses to silvopasture are heavily shrunk toward the community mean (with high uncertainty). My understanding is that `postHocLM()` will propagate uncertainty from the first stage (the occupancy model), so the contribution from poorly estimated species will be downweighted. However it still seems like including many such species may muddy the relationship between functional traits and species’ responses to silvopasture. Given this, my current inclination is to interpret the model using only species with ≥ 3 observations. Does that seem reasonable?

Importantly, in the attached screenshot, the two blue arrows indicate that the mean estimates of these effects actually switch sign going from 188 to 271, so there may be something going on that I've missed. The species with < 3 observations appear to be roughly randomly distributed in trait space (including on this migration variable), so I don’t think filtering is removing any obvious portion of functional space.

Thanks in advance for any thoughts.

Aaron Skinner

PhD candidate, University of British Columbia

[Jeffrey Doser]

Hi Aaron, 

This is not particularly surprising to me. When using postHocLM to explore the effect of species traits, including many extremely rare species will likely mean that their estimated regression coefficients are both highly uncertain and all very similar (e.g., close to the community mean). Assuming these species represent a breadth of species traits, this would then result in the estimated effect of the traits being closer to 0. The uncertainty in the estimates does not necessarily "downweight" species with large uncertainty, but rather would contribute to their being less support for a strong relationship with the species traits. I think it's reasonable to not use the full community given the rarity of most of the species in your data set. Note that even the threshold you are using (at least three observations) still likely includes some very rare species that have large uncertainty in their estimates (i.e., 3 detections is extremely little information to inform species-specific estimates beyond what is suggested by the community mean). Also note that while the sign of the coefficients does change when dropping the very rare species (based on your plot), they also both have substantial posterior density on the opposite side of 0 (i.e., for the two migration categories).

Jeff

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Jeffrey W. Doser, Ph.D.

Assistant Professor

Department of Forestry and Environmental Resources

North Carolina State University

Statistical Ecology and Forest Science Lab

Pronouns: he/him/his

[Aaron Skinner]

Hi Jeff, 



All good points. I know you have sent a paper on inclusion of rare species in occupancy modeling, which was very helpful, but it was not specific to this context of a post-hoc analysis of functional traits. The goal of this analysis is to understand which functional traits explain species’ responses to local silvopasture implementation. Do you have any suggestion for a cutoff regarding the number of sites? To me, I think it would make sense to try to find the point where shrinkage is minimal, so the data are the predominant thing driving the species-specific response to silvopasture. I understand that finding the point where shrinkage is minimal is subjective and dataset dependent, but maybe there are some general guidelines or tools you have used to investigate this?

Cutoff (# sites w/ an observation):
1+ site: 280 species (All species)
3 sites: 198 species
5 sites: 163 species
10 sites: 128 species
20 sites: 99 species
30 sites: 75 species



Increasing the cutoff for the number of sites changes the focus of the analysis, but that’s OK. 

Thanks,

Aaron
He/him/his