Multi capture traps and N-mixture models

[Daniel Dornan]

I hope this message finds everyone well.

Question: I have count data for different species of mosquito over 3 trap nights, however they were captured using a device which does not allow for independence of capture. I would like to use N-mixture model with multinomial distribution to account for removal sampling. However, I understand one of the fundamental assumptions of these models is the independence of capture.  I would be interested on people's opinions.

Thank you in advance.

Daniel Dornan

Postdoc at University of Helsinki. 

[Marc Kery]

Dear Daniel,

'independence' is such a difficult concept and term .... what exactly do you mean by it in your case ?

Two comments right now:

• if these traps are retaining the individuals over the three days or killing them, then what you have is called a 'removal design'. This is perfectly amenable to analysis using a multinomial Nmix model; see chapter 7 in the AHM1 book, and many other sources, starting with Wyatt (2002), Royle (ABC, 2004), Dorazio et al. (2005). In this case, the removal of the individual from the population induces a non-independence of the resulting counts, but we account for this, or indeed use this for estimation.
• Whenever I head "Nmix model" and "insects" I immediately grow a bit wary ... these models are not good for very large counts and/or small sampling fractions. That is, re the latter, when you're likely to catch less than 1-10% of the total population, then your abundance estimates will likely become so huge, and so uncertain, as to be practically meaningless.

Best regards  ---- Marc

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[Daniel Dornan]

Hi Marc, 

Thank you for your speedy reply.

Independence like their captured at the same time and in the same trap.

Yes I usually use these models for rodents… I understand what you are saying about the numbers of mosquitoes. The aim of this work is to test the impact of habitat restoration on mosquito numbers. Do you suggest using another type of model?

All the best 

Daniel 

[Marc Kery]

Dear Daniel,

re. independence: that is not a problem. (But, again, I think that we biologists don't typically understand what independence means in a statistical analysis. Perhaps someone ought to write a review paper an publish in MEE or JAE or Ecology/StatInno).

Re. the multimix not (necessarily) being a suitable model for insect data: what's the frequency distribution of the counts ?

Overall, I'd probably try to fit some simple models and then do the "commonsense GoF test". This asks whether "results make sense". There is a risk of being circular here (i.e., only accepting a model that tells me something which I believe a priori), but I don't think we can ever do statistical modeling without doing this test.

If formal estimation and modeling of p and N doesn't work for your case, my usual plan B would typically be a Poisson GLM or GLMM or perhaps one with another discrete-valued distribution, such as the Negbin, to model simply the expected count,

Best regards ---- Marc

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[Daniel Dornan]

Hi Marc, 

Yes 100%, a review would be nice.

The frequency distribution of the counts varies between species, but can range between 0-200 per trap, and per occurrence.

I will play around with a few models and see if things make sense.

 Thank you for your help

All the best

Daniel