species interaction model

[spitale]

Hi everybody,
I'm exploring interaction models between two species of ungulates (pairwise comparisons). I'm assuming that detection probabilities for the species are independent, since I have not plausible ecological hypotheses explaining this kind of interaction. In order to account for habitat preference and differences in occupancy among sites, I fitted at first a set of single season models with covariates. Then, I would use the same covariates for the best single models in the interaction models. Basically, I have to compare two models, with phi set equal to 1 and the full model, that is:
1) psiA(covA+covB),psiB(covC),phi(.),pA(.),pB(.),rA(.),rB(.),delta(1) = full model
2) psiA(covA+covB),psiB(covC),phi(1),pA(.),pB(.),rA(.),rB(.),delta(1) = reduced model

I'm unsure about the other parameters pA(.),pB(.),rA(.),rB(.). Should they freely estimated as in 1 and 2? Or should they fixed equal to 1 as delta? or we have to impose the same value for all?

Many thanks!
Daniel

[jhines]

Hi Daniel,

Setting delta to 1 will take care of making the detection probabilities independent, since delta=rAB/(rA*rB). Since pA and pB are detection probabilities when the other species is not present, you don't have to worry about them being independent and you can just estimate them. You'll also want to estimate rA and rB as they are the probabilities of detection for species A and B when both species are present. You wouldn't want to set these parameters to 1, unless you know that you can detect the species perfectly.

Jim

[spitale]

Hi Jim, many thanks, now it is clearer!
Daniel

[spitale]

An additional question: in the output of Presence we have 1) untransformed estimates of phi and 2) individual site estimates of phi. Which is the correct one in order to interpret the SIF (phi<1 suggests avoidance; phi>1 means attraction)? Thanks
Daniel

[jhines]

The transformation function for phi is the exponential, so you could test if the transformed phi is significantly different from 1.0, or test if the untransformed beta estimate for phi is significantly different from 0.0.

Jim

[darryl]

Hi Daniel,
It looks like you might be using the first parameterization of this model? Generally I'd recommend either the 2nd or 3rd parameterizations because they are more reliable when you've got covariates. How you set up particular models and how you should interpret the resulting estimates is slightly different in each case, you just need to take you time and not rush through them.
Darryl

[spitale]

Hi Darryl,
yes, I'm using the first parameterization. I'm using that only because it is explained more clearly in the Book. I tried the 2nd parameterization setting up the following models (in my mind they should be identical to those explained above)
1) psiA(covA+covB),psiBA(.),psiBa(covC),pA(.),pB(.),rA(.),rBA=rBa (full model with det prob independent between A and B; no parameters fixed)
2) psiA(covA+covB),psiBA=psiBa(covC),pA(.),pB(.),rA(.),rBA=rBa (reduced model with psiA and psiB independent; det prob independent; again no parameters fixed)
Are they correct? And how SIF (called phi in the 1st parameterization) should be calculated? May be as explained in Richmond et al (2010 Ecol Appl)?
Thanks,
Daniel

[spitale]

Hi, are there someone able to suggest me how to calculate SIF with the second parameterization? Thanks
Daniel

[Alan Dextrase]

From the "Overview" in the Presence drop-down help menu, the SIF for the alternate parameterization is calculated as:

φ = psiA*psiBA/(psiA*psiB)

Al

[spitale]

Thanks, I forgot to read again the Overview. I see that the equations by Richmond et al (2010 Ecol Appl) give the same results as those suggested in the Overview
Another question: as I written above I would like to model occupancy for species B with a covariable. However, with the second parameterization, we have not psiB but we have psiBA and psiBa. Which one is the correct factor to include with the covariable? Both? Thanks
Daniel