Help with two-species models

questions concerning analysis/theory using program PRESENCE

Help with two-species models

Hi, 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 36 sites with 10 surveys. I'm a little bit confuse about how to put the models in the design matrix in the program. There are not many tutorials on how to do this "tecnic" work with two-species models.This is one of the models that i'm currently trying:

PSIA, PSIBA = PSIBa, pB = rB

I am also working with habitat covariates (for sites) obtained from a PCA. This covariates are only applicable to ocupation. This is one of the models with covariates: PSIA (Pc1), PSIBA (Pc1), PSIBa (Pc1), pB = rB

I would appreciate if you could guide me on how to put these models in the program and run them.Thanks.
cMILA89

Posts: 2
Joined: Fri Jul 03, 2020 4:24 am

Re: Help with two-species models

Hi,

Although the help file in Presence doesn't explicitly show how to build design matrices for every model, the procedure is the same for all models. If you look in the help section, "User-defined custom models", it shows how to build design matrices for detection probabilities in the single-season model.

To summarize the help section, it says to build a model, you list each real parameter in the model as an equation using optimization parameters (beta's). To set real parameters equal to each other, make the equations for those parameters equal. Once you have the equations, just use the coefficients of the beta's in the design matrix.

For the model you're currently trying, the equations would be:

psiA = 1 * beta1 + 0 * beta2
psiBA = 0 * betea1 + 1 * beta2
psiBa = 0 * betea1 + 1 * beta2

So, the design matrix for occupancy would be:

Code: Select all
`           beta1   beta2psiA       1         0        psiBA      0         1          psiBa      0         1`

For detection, assuming all detection probabilities constant across surveys and pA not = rA, the design matrix would be:

Code: Select all
`          b1  b2 b3pA(1)      1  0  0pA(2)      1  0  0  :pA(10)     1  0  0pB(1)      0  1  0pB(2)      0  1  0  :pB(10)     0  1  0rA(1)      0  0  1rA(2)      0  0  1  :rA(10)     0  0  1rBA(1)     0  1  0rBA(2)     0  1  0  :rBA(10)    0  1  0rBa(1)     0  1  0rBa(2)     0  1  0  :rBa(10)    0  1  0`

From the detection design matrix, pB, rBA and rBa all have the same equation which only involves beta2, so they will all be equal.

For a model with a parameter as a function of a covariate, you still write each parameter as an equation. You have psiA(Pc1), meaning psiA is a function of the covariate, Pc1. The equations would be:

Code: Select all
`psiA = 1*beta1 + Pc1*beta2psiBA = 1*beta1 + Pc1*beta2psiBa = 1*beta1 + Pc1*beta2`

Note that we need an "intercept" beta (1*beta1) in the equation so that the real parameters are not forced to be zero when the covariate (Pc1) is zero.

That set of equations becomes this design matrix:
Code: Select all
`           beta1   beta2psiA       1         Pc1        psiBA      1        Pc1          psiBa      1         Pc1`

In that design matrix, all 3 psi's are equal to each other (but still depend on the covariate). To make them different, you just need a different intercept (beta1) and effect (beta2) for each real parameter:

psiA = 1*beta1 + Pc1*beta2
psiBA = 1*beta3 + Pc1*beta4
psiBa = 1*beta5 + Pc1*beta6
jhines

Posts: 587
Joined: Fri May 16, 2003 9:24 am
Location: Laurel, MD, USA

Re: Help with two-species models

Thank you so much!! I understand better!!
cMILA89

Posts: 2
Joined: Fri Jul 03, 2020 4:24 am

Re: Help with two-species models

Hi everyone
I also need help with my two-species models. I ran a model for two species single season analysis with 65 sites, 7 sampling occasion, 1 method, and 4 site covariates (elevation, distance to nearest forest, roughness, and slope). It ended up had the same estimate values for all sampling site. Please, does anyone have a clue?
restiacn

Posts: 2
Joined: Thu Apr 07, 2022 2:38 am

Re: Help with two-species models

Hi, I'm glad to help, but need more info. Are you using the Windows program Presence, or the R package RPresence? What does your design matrix look like? Can you post the "beta" estimates from the model?
jhines

Posts: 587
Joined: Fri May 16, 2003 9:24 am
Location: Laurel, MD, USA

Re: Help with two-species models

Thank you for your response. Sorry I'm late to login again

I'm using the one on Windows. Here's my matrix for occupancy :
psiA 1 0 0
psiB 0 1 0
phi 0 0 1

and this one for detection
pA[1] 1 0 0 0 0
pA[2] 1 0 0 0 0
pA[3] 1 0 0 0 0
pA[4] 1 0 0 0 0
pA[5] 1 0 0 0 0
pA[6] 1 0 0 0 0
pA[7] 1 0 0 0 0
pB[1] 0 1 0 0 0
pB[2] 0 1 0 0 0
pB[3] 0 1 0 0 0
pB[4] 0 1 0 0 0
pB[5] 0 1 0 0 0
pB[6] 0 1 0 0 0
pB[7] 0 1 0 0 0
rA[1] 0 0 1 0 0
rA[2] 0 0 1 0 0
rA[3] 0 0 1 0 0
rA[4] 0 0 1 0 0
rA[5] 0 0 1 0 0
rA[6] 0 0 1 0 0
rA[7] 0 0 1 0 0
rB[1] 0 0 0 1 0
rB[2] 0 0 0 1 0
rB[3] 0 0 0 1 0
rB[4] 0 0 0 1 0
rB[5] 0 0 0 1 0
rB[6] 0 0 0 1 0
rB[7] 0 0 0 1 0
delta[1] 0 0 0 0 1
delta[2] 0 0 0 0 1
delta[3] 0 0 0 0 1
delta[4] 0 0 0 0 1
delta[5] 0 0 0 0 1
delta[6] 0 0 0 0 1
delta[7] 0 0 0 0 1
restiacn

Posts: 2
Joined: Thu Apr 07, 2022 2:38 am

Re: Help with two-species models

Without site-specific covariates, all sites will have the same estimated occupancy and detection parameters. Models with site-specific covariates will produce different estimates for different sites.
jhines

Posts: 587
Joined: Fri May 16, 2003 9:24 am
Location: Laurel, MD, USA

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