Two species design matrix

questions concerning analysis/theory using program PRESENCE

Two species design matrix

Postby jasniyas » Sat Apr 08, 2017 3:56 am

Hello,

Apologies for the long post and if my question is silly. I could really use some help here.

I am trying to do a Single season two-species analysis to study the co-occurrence patterns of two species. I have camera trap presence/absence data from 5 macro areas and within each macro area are approximately 25 camera stations. These cameras were deployed at different dates across 5 years as they were not initially deployed for co-occurrence analysis specifically. Therefore, some of the cameras were active for almost a year whereas some for 5-6 weeks. So my sampling occasions were 15 day periods. My hypothesis is that the co-occurrence patterns may vary based on the macro site, the habitat and the year.
In order to avoid overparameterizing my model, I decided to do individual analyses for every macro-site. I had 25 sites, 17 surveys occasions, 2 site-specific covariates (habitat 1 and habitat 2) for my first model for Macro area 1. My design matrix was as follows, (assuming independence based on the biology of the species)

Code: Select all
          a1     a2       a3        a4       a5       a6
psiA       1   habitat1 habitat2     0       0         0
psiB       0       0        0         1     habitat1 habitat2
phi        0       0        0         1     habitat1 habitat2


Code: Select all
-,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,
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pB[8]         0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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I intended to add year as another covariate in the next model. However, I understand that it will add more parameters to the model and I am worried that it will affect my analysis. I've probably got the design matrix wrong.

My question is would it be a better way to go if I take all the cameras from all the macro sites and have macro site as a covariate in addition to the habitat and year covariates? It would be great if someone could help me with setting up the design matrix.

Thanks in advance,
Jasni
jasniyas
 
Posts: 2
Joined: Wed Feb 22, 2017 7:25 pm

Re: Two species design matrix

Postby jhines » Sat Apr 08, 2017 1:45 pm

To answer your question, yes, in general it's better to combine the data and use macro area as a covariate so you can possibly share parameters among macro areas. You can also combine years of data (with each year as a set of new sites) and include year as a covariate. You'd be able to test if occupancy differs among years. Of course, you could include years as additional surveys, then test the multi-season model vs. the single-season model to see if occupancy varies among years.

I see that you've made detection probabilities survey-specific, in addition to being different for the two species and different based on whether the other species is there. So, you're trying to estimate 91 parameters (6 occupancy and 85 detection) with only 25 sites. I doubt that you can get that many estimates from such a small dataset. I suggest starting with a very restrictive model (constant detection and detection equal among species), then add complexity, instead of starting with a very complex model.

You mentioned that some areas had nearly a year of surveys in one year. You have to be careful that occupancy doesn't change during the sampling surveys. If your survey for a year, then your second season starts immediately after the last survey in the first year, some sites which were occupied and detected in the beginning of the first year could have gone locally extinct during the year, while others which were detected near the end of the year have little chance to go locally extinct. To avoid this, you may need to subset the data such that the survey period is short, relative to the interval between seasons.

If you have combined the data with each macro-site/year combination as a set of sites, with year and macro-site as covariates, the design matrix for occupancy could be something like this (for yr+macro-area w/ 3 yrs, 2 macro-area):

Code: Select all
       
psiA       1  0  0 yr2  0     0   yr3  0    0    mac2   0       0
psiB       0  1  0  0   yr2   0    0   yr3  0       0     mac2  0
phi        0  0  1   0   0   yr2  0    0    yr3    0       0      mac2


An important note here is that you don't want the row for phi to be the same as either of the other rows since phi is a quotient of a couple of parameters and you don't want the effect of covariates on phi to be the same as on the Psi's.
jhines
 
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Location: Laurel, MD, USA


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