Pcount for hypothesis testing

[Jelaine Gan]

Hi everyone,

I am new to Applied Hierarchical Modelling, and I am reading up papers and the AHM book currently. I have been stuck for quite a while and would really be grateful for advice.

I have conducted 10-min bird point counts at 130 points, with a total of 3 repeats conducted within a few days of each other (assumed closed population given that the repeats were not far apart). My objective is to test bird-habitat associations and not really interested in the abundance estimates themselves, i.e., how are bird species responding to forest amount and edge density. From what I understood, it is important to account for the imperfect detection in models to prevent wrong interpretation of the patterns in the abundance. 

Hence, I wanted to use pcount() to account for varying detection probabilities in testing the following hypothesis for each species:

Null: ~ timesun ~ 1 + (1|site)
A1: ~ timesun ~ %forest + (1|site)
A2: ~ timesun ~ ED + (1|site)
A3:  ~ timesun ~ %forest + ED + (1|site)
A4:  ~ timesun ~ %forest * ED + (1|site)

timesun : number of hours since sunrise/sunset, because birds are usually more active closer to dawn and dusk.
%forest : percentage of the surrounding buffer that is forest
ED : edge density
site : random effect, because the points were placed in 6 different sites.
*I have chosen the family (P, ZIP, or NB) based on the best AIC model for each species.

Problems:
1. Estimates were not stabilizing with increasing K (tried until 2000).
2. Related to the unstable K, my abundance estimates are unrealistically big.

Question:
Since I am interested in using pcount as a hypothesis testing method, rather than obtain abundance estimates for my species, would it be alright to use the model results (the effect of the abundance covar - sig/not; positive/negative) despite the unstable K and very high estimates?

I have read papers that used such abundance estimates as relative abundance or "truncated abundances". So, I am wondering if I can still use the models for my purpose, and use a high enough K (=1000) where the pattern of covar effects does not change anymore.

Thank you in advance,

Jelaine

[Ken Kellner]

Hi Jelaine,

It's unusual to see that kind of problem with K especially given that you are dealing with birds, so presumably the true abundance is not *that* high. What is the range of values in the raw counts? In the encounter histories, do you find that for most sites, you detected >1 bird in only one of the three repeat counts? Do you still have similar problems with K and abundance estimates if you do not include the random effect?

Ken

[Jelaine Gan]

Hi Ken,

Thanks for your reply. It is different for each species, so I will give some examples below: 

Hypsipetes philippinus (Common species) - Philippine Bulbul

130 sites Maximum number of observations per site: 3 Mean number of observations per site: 3 Sites with at least one detection: 114 Tabulation of y observations: 0 1 2 3 4 5 6 7 8 163 72 62 41 28 12 7 3 2

It has stable K if I exclude the random effect. Abundance estimate was 12.18 per 50m-radius point count. This is a bit high, but it not outrageously so. 

Elegant Tit (common species)

130 sites Maximum number of observations per site: 3 Mean number of observations per site: 3 Sites with at least one detection: 28 Tabulation of y observations: 0 1 2 3 359 20 7 4

(this is what the raw data looks like; just a subset)  

A B C 0 0 1 0 0 2 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 3 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3

mod = pcount(~ timesun ~ scale(forest_pland500) + scale(ED500) , K=300, umf, mixture="P")

 

This one did not stabilize with increasing K despite changing the mixture, the covariates, and random effect (removal/addition). Average abundance was estimated as 25 individuals per point (K=300), which is unrealistically high. However, the effect of the two covariates are consistent (i.e., not changing significance (0.05 threshold) and direction of the relationship) even if K is increased up to 2000. 

From what I understand, changing the abundance covariates expectedly affects the intercept / estimate. Since I am using pcount() for hypothesis testing (not to get abundance estimates for the sites), I restricted the models to only have 2 covars (%forest and Edge density). This simple model with two explanatory var obviously is not enough to explain the variation in the data, could this be causing the unusually high intercepts?

Thank you for looking into this!

Jelaine

[Ken Kellner]

Jelaine,

For the 2nd species the most likely explanation is simply that there isn't enough information in the data to support the model complexity (and/or the detection probability is too low) given that the vast majority of counts are 0. For species 1 you do have a lot of detections so it's less clear what the issue is. My guess is TMB is struggling to get good estimates of the random effects, which leads to high uncertainty and perhaps the issues with K. You can look at the estimates of with randomTerms(model). You may find the confidence intervals are incredibly wide which would make me not want to use the model. You might try fitting the model in a Bayesian framework instead - you could do so with the ubms package or (I think) the spAbundance package without much extra work.

Ken