fixing Estimates for psi and p

questions concerning analysis/theory using program PRESENCE

fixing Estimates for psi and p

Postby jhubbell072786 » Sun May 14, 2017 1:59 pm

To all,

I have a simple question, which I think I already know the answer to, but I'd like to get some responses to verify my thoughts.
The species I'm working with is a widely distributed darter that lives in small headwater streams (i.e., its movement is likely highly limited). I collected my data using 4 equally sized, and equally spaced, spatial replicates at a site to obtain my detection histories. Initially, I ran the simple, single season model to obtain early estimates of psi and p. Then, I decided to use the spatial dependence model to approximate thetapi due to the fact that I used spatial replicates in my study design and expected detections to be correlated due to the low mobility of my target species. With that being said, early estimates from the simple, single season model indicate that the darter has a high estimate for psi. Therefore, two control for high beta estimates, I fixed this value when running the spatial dependence model for it. With that being said, by fixing psi, you obviously cannot properly estimate this parameter using the spatial dependence model. I would assume that all site covariates relationships to psi would also be spurious due to the fixed nature of the parameter. So, my question is: is it ok to use the simple single season estimates for psi and then simply approximate p and theta using the spatial dependence model? As far as I can tell, this is really my only option.

Thanks,

Josh
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Re: fixing Estimates for psi and p

Postby darryl » Sun May 14, 2017 5:33 pm

Hi Josh,
A few clarification questions.

1. Did you resurvey your spatial replicates at all or where they only surveyed once?
2. What were your estimates (and SE) for psi and p from the simple model?
3. How many detections did you get, and what was naive psi?
4. How many sites in total were surveyed?
5. Do you get any warnings when trying to run the dependence model without fixing parameters?

That you get a high psi estimate isn't necessarily a problem (unless when you say 'high' you mean '1' which might indicate other issues) provided you've got a good-sized data set with sufficient number of detections. In fact, if you're working a widely distributed species, a high psi is exactly what you might expect!

If you happen to get lucky and fix psi to the 'correct' value then you're estimates of p and theta will be unbiased, but their SE's will be too small (won't account for the uncertainty in the psi value). If you're unlucky, and you probably will be, the value for psi will be wrong and then you'll get biased estimates of p and theta.

Darryl
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Re: fixing Estimates for psi and p

Postby jhubbell072786 » Tue May 16, 2017 5:20 pm

Darryl,

Thanks, as always, for the fast reply. To answer your questions:

1. Yes, due to the nature of the study, I was only able to survey each spatial replicate at a site one time ( 4 replicates total per site).
2. I realize I mispoke when I said psi was high (I'm working with 2 species and got the numbers mixed up). For this species, psi was 0.40 with an SE of 0.05.
3&4. My naive estimate was similar (0.37), with 35 detections at 101 sites (so the two estimates seem fairly representative).
5. The problem involves estimates of p (not psi, sorry!). As far as I can tell, I'm not getting any warnings with the spatial model. Without any covariates, the transformed estimates for p for each replicate go to 1.0 using the spatial model. Modeling p with the single season model using my sampling covariates yields an estimate 0.49. Honestly, given the ecology of the species, an estimate of p near 1.0, is probably fairly likely given the disjunct nature of the distribution of this species, and its fairly specific habitat requirements. However, a jump from 0.49 to 1.0 is quite a leap...
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