Species-Presence exercise 6 - Two-species-single-season example

This exercise is designed to show how to run programs PRESENCE to compute species presence, detectability, and co-occurrence estimates from 'presence-absence' data which includes covariates.

Input data consists of 'detection-histories' of two individual species at potential owl territories. Sample covariates have also been included.

Running the program

Start a new project in program PRESENCE.

You're now presented with a 'Results Browser' window where a summary of each model will be saved. To run our first model:

When the 'Setup Numerical Estimation Run' window appears, a design matrix window will appear. The parameters are grouped by 'Occupancy' or 'Detection'. The Occuancy tab will contain 3 parameters: Another way of parameterizing this model is to estimate these parameters: By default, the design matrix is set up to estimate these 3 parameters independently. This would allow an interaction in occupancy of the two species (non-independent occupancy). To change the model such that occupancy of the two species is independent, simply constrain psiBA=psiBa (or fix phi=1.0).

The Detection tab will contain 5 sets of parameters (indexed by sample):

if the 2nd parameterization is chosen, the following 2 parameters would be estimated in place of the last 2 above:

Run model, "psiA(.),psiBA(.)=psiBa(.),pA(.)=rA(.),pB(.)=rBA(.)=rBa(.)"

This model is one where occupancy and detection of the two species are independent (no interaction). Since we'll be setting psiBA=psiBa, that library(fatalityCMR); ?example.search.csv means occupancy of species B is the same whether species A is present or not. To do this in PRESENCE we need to delete the last column in the Occupancy design matrix, and enter a '1' in the last row, 2nd column. The design matrix should look like this:

The design matrix for detection should look like this:

Before running this model, change the model name to "psiA(.),psiBA(.)=psiBa(.),pA(.)=rA(.),pB(.)=rBA(.)=rBa(.)". Click 'OK to Run' to run this model.

After the analysis is complete, click 'yes' to append the output to the results browser. The output from this model should match the output you would get if you ran each species separately in a single-season model.

Which parameterization to use?

The answer to this will depend on the issue you're trying to address. Both parameterizations will (usually) give the same results. Using some algebra, estimates from one parameterization can be converted to estimates in the other. For example, if the 1st parameterization is used, the psiB parameter in the 2nd parameterization can be computed as:
psiB = psiA*psiBA + (1-psiA)*psiBa
and the phi parameter can be computed as:
phi = psiA*psiB/psiAB (where psiAB=psiA*psiBA)
So, if the parameters from the 2nd parameterization can be computed using estimates from the 1st parameterization, why even bother with the 2nd parameterization? The main reason would be that you may be interested in modeling one of those parameters in the 2nd parameterization directly as a function of covariates. This cannot be done if the 1st parameterization is used.

Note about the word 'usually' above: With the first parameterization, all parameters are estimated as probabilities (range= 0 - 1). Regardless of the values taken by the parameters, (psiA, psiBA, psiBa), valid values of the parameters, (psiA, psiB, phi) will result. However, there are values of (psiA, psiB, phi) which will result in implausible values of (psiA, psiBA, psiBa). For example, if

psiA=.6  psiB=.6  phi=.278
then
psiAB=phi*psiA*psiB = 0.1
psiBA=psiAB/psiA = 0.1667
psiBa=(psiB-psiA*psiBA)/(1-psiA)  = 1.25
So, the 2nd parameterization might produce estimates which have a higher likelihood, but have parameter estimates which are out of range. PRESENCE will take steps to try to avoid this, but some data-sets may be problematic due to this.