Sampling design for a clustered population

[Joseph Clark]

We are studying an elk population that tends to be clustered around forest openings.  We are planning to use line transect sampling to collect and genotype elk scats for secr analysis.  Most of the elk fecal samples will be in these openings (fields) so we want to adequately sample those areas.  However, a random or systematic sampling design across elk range would result in us spending a lot of time in areas where there are few if any elk.  We have run some simulations with different sampling intensities in grid cells that we have designated as high density and low density, with greater sampling intensity in the high density cells.  The estimates seem okay with little bias.  However, my question is what if we are wrong in assigning the high density and low density cells?  For example, if high elk densities in reality extend further into the low density cells than we thought, will this present a bias?  So far, our simulations suggest no, but I was looking to see if there was a theoretical reason why this sampling approach might be flawed.

Alternatively, we were interested in estimating elk densities as a linear or quadratic function of the distance from fields.  I know that could be done, but would there be a bias if we adjusted our sampling effort the same way?  I know there are adaptive sampling approaches that might be used but I figured that since we have a pretty good idea that elk densities are going to be positively related to the fields, using that information to develop a sampling regime would be preferred.  Thanks!

Joe 

[Murray Efford]

Hi Joe

I'm cautious on this because I suspect/believe that increasing sampling intensity in high density areas causes bias unless handled carefully (I opened a file on this a few years ago but haven't progressed it). However, stratification does make sense. From my amateur understanding of classical stratification, poor definition of strata just reduces the benefit (variance reduction) rather than causing bias. Nor do I see a risk of bias in estimating a density gradient with arbitrarily placed samples - again it's a matter of efficiency.

Murray

[Joseph Clark]

Thanks for your response Murray.  However, I’m a little confused…  Stratification implies higher sampling intensity in areas where density is higher, and you say stratification makes sense, but also say that it could create a bias.  I agree that using different sampling intensities without a corresponding density covariate might cause problems but, as long as the densities are assumed to vary with sampling intensity and modeled as such, will there still be a bias?  Our simulations suggest no…

[Murray Efford]

"[As] long as the densities are assumed to vary with sampling intensity and modeled as such" is the key. Conversely, in my old file I find "A naive, pooled SECR analysis of data from such stratified sampling gives biased estimates of overall attributes such as average density and total population size."

There are subtleties here that I'm sure you are onto. If you really care about density in the low density areas then to pin that down you need all the samples you can get... And poorly estimated density across a large low density area might screw up estimates of total number... And detection parameters may vary with density...

[Joseph Clark]

That helps.  Thanks Murray!