Inference based on covariates

[leob...@gmail.com]

Hi all,

I have been working on a 20-year point count distance dataset of Hawaiian forest birds, that includes hundreds of point count stations across 3 separate regions.  I have already achieved the main goal of the analysis which was to estimate annual densities for each species in each region.  

However, my collaborator in this project has notified me that in one of the study regions, an ungulate proof fence was built mid-study, and she is interested to determine if the difference in vegetation cover inside/outside of the fence influenced bird density inside/outside of the fence after the fence was built. There are 84 point count stations in this study region and 25 of them are inside of the fence.

I'm trying to decide the best way to answer this question. Does it makes sense to divide the study region by the fence, into two separate regions and compare densities that way? I might run into sample size issues this way, and also it doesn't make sense to me since there is no geographic separation. 

Instead, I was thinking of creating a categorical inside/outside (the fence) covariate, and running a distance analyses before and after the fence was built for each species.  Then run an AIC between the null model and the model with inside/outside covariate, as well as goodness of fit test. If the model with inside/outside covariate wins AIC and has no lack of fit, then is this evidence that bird densities differed appreciably inside/outside the fence? Can I use the parameter estimates of those covariates to report quantitative differences?

Alternatively, instead of distance analysis I was thinking of running a Poisson or negative binomial generalized linear model with the response variable being bird detections, and using the same covariates.  However I think I'd have to check out zero-inflated models because of the high number of zero counts especially for low density species.

Thanks for any ideas or input.

Best regards,

[Eric Rexstad]

Leo

Thanks for the question. Having a "treatment" imposed after the survey has been designed can lead to difficulties as you note, because effort wasn't allocated to suit that objective. Nevertheless you might still be able to make some statements about the effect upon density correlated (not caused) by the arrival of the fence.

I'm not sure I agree with you that contiguousness of strata (enclosure/not enclosure) represents a problem.  Studies investigating habitat effects (shrub vs grassland vs forest) invariably have contiguous strata.

My first approach to your problem would be to do as you say, separate your stations into "enclosure" and "not enclosure" strata. The cleanest analysis would be to have each stratum "self-sufficient"; i.e. separate encounter rates and detection functions producing independent density estimates. If there are insufficient detections in the "enclosure" stratum because of smaller number of stations, you could think about modelling detectability using stratum as a covariate, assuming both strata share a common key function shape (half normal or hazard rate).

With stratum-specific estimates, you could then estimate differences in density between strata.  There exists a case study on our examples page describing (and providing code) to carry out the test for density differences between strata. Recognise if you take the covariate approach, you are inducing a dependence between the stratum-specific estimates as they share some parameters of the detection function. The code in the case study accommodates this by taking a bootstrapping approach.

http://examples.distancesampling.org/differences/differences.html

Detecting density estimate differences - Distance Sampling Management context. Often ecological questions extend beyond simply wanting an estimate of density in a study region. It is common for inference to extend to differences in density over time or space. examples.distancesampling.org

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What was unstated in your question (hence ignored in my answer) is a temporal effect and accounting for species. If you wish to conduct this comparison on a species-specific basis, you may again struggle with adequate detections. Everything I have described above assumes pre-treatment data will be pooled, likewise post-treatment data; with the comparison made between strata defined in that fashion.  A more thorough way to address the question of interest is a before/after treatment/control (BACI) analysis where inference is based upon the interaction effect (does enclosure density change while outside-enclosure density does not change), but we don't have an off-the-shelf tool for that approach.

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From: distance...@googlegroups.com <distance...@googlegroups.com> on behalf of leob...@gmail.com <leob...@gmail.com>

Sent: 28 July 2022 18:29
To: distance-sampling <distance...@googlegroups.com>
Subject: [distance-sampling] Inference based on covariates

 

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