How to determine if sampling method is less biased.

[sixtystrat]

We are doing a DNA study on black bears and we noticed large bears (most likely males) stepping over our wire to enter the trap site withou leaving a hair sample. We have high capture heterogeneity in the data and p for males is very low. Consequently, the last 3 years (6-year study) we used 2 wires to try to catch these bears that we might have been missing. We use a sampling design whereby we submit a constant number of samples to the lab each year for analysis (32 samples per week over 8 weeks each of the past 6 years).

We are trying to evaluate the effect of the change in our wire setup using mixture models in a robust design framework. Our hypotheses are:
H(0): If there was no effect resulting from the change in sampling protocol, then p would stay the same because we are sampling the same bears as before.
H(A): If there was an effect due to the change, then we would see a decrease in overall p because of the increased number of individuals captured given the constant number of samples analyzed.

Does this approach make sense? We tried looking for a change in capture heterogeneity for the 2 sexes but that was confusing because one does not really know what the source of the heterogeneity represents in Pledger models. Does anyone have any other ideas for testing this effect?
Thank you in advance for your time and input,
Joe

[murray.efford]

Joe
If I have understood you correctly -

- It seems fairly regressive these days to dwell on heterogeneity without addressing spatial effects

- Your test is very indirect, probably has little power, and won't tell you if the estimate is less biased - for that (and to assess power) I would attempt to simulate the process (not hard).

- At least with the finite mixture (Pledger) method you can get an estimate of the quantity you are hanging this on (heterogeneity) that might itself be used in simulations to determine change in bias.

- Your test is useless if density is variable as that will drive temporal (between-year) variation in p under your constant-sample-number protocol. I suspect that even with constant density any year-to-year variation in p (or population structure) will also mess things up.

Murray

[sixtystrat]

Thanks Murray. We wanted to look at heterogeneity caused by the wire before we got into the spatial aspects (which we intend to do) but we wanted to keep things simple at first.

I agree with everything you said wrt the confounding due to changes in p and N, which is my reason for the post. However, I am not sure I understand about the simulations. Yes we could simulate less heterogeneity caused by the second wire and it's effect on bias, but that still doesn't tell is if heterogeneity was really reduced in the field. We think so but we may have just collected more samples from the same bears as before. We are looking into some sort of index for heterogeneity (e.g., Carothers 1973) but the relative amount of heterogeneity in 1 model compared to another is hard to quantify.

[murray.efford]

We wanted to look at heterogeneity caused by the wire before we got into the spatial aspects

But if 'spatial aspects' are a major cause of heterogeneity, and possibly the major cause, this is not as tidy as it sounds, and may be a waste of time.

everything you said wrt the confounding due to changes in p and N

I deliberately did not mention N, because you would only have a well-defined N if you were in fact dealing with an isolated population (Efford & Fewster Oikos in press may help).

the relative amount of heterogeneity in 1 model compared to another is hard to quantify

It's true that measuring heterogeneity per se has got rather little attention, but it's not impossible. I pointed you at the fact that once you have fitted a mixture model you have in your hand a measure of heterogeneity (CV or eta - see Pledger and Dorazio & Royle literature) that can be used in simulation to assess bias. DENSITY provides CV(p) and eta(p) routinely for single-session datasets (see MLE(N) tab).

I was suggesting simulation not as a magical way to know what happens in the field (I hope I would never be caught implying that!) , but as a means of evaluating your proposed test, which was your question, I think.
Murray

[sixtystrat]

I see what you are saying. We'll give the secr approach a try. Thanks!
Joe

[murray.efford]

Trying to understand the effect of capping the number of samples does make my head hurt, hence my recourse to simulation. I'll send some simulation code & results offline.
Murray