For detection probabilities in the two-species model we have 5 parameters:
pA – prob detection, given only species A is present
pB – prob detection, given only species B is present
rA – prob detection of A, given both species present
rBA – prob detection of B, given both species present and species A detected
rBa – prob detection of B, given both species present and species A not detected
There are two types of dependence here. Detection could depend on whether only one species is present, or both species are present. Alternatively, detection for species B could depend on whether species A is detected when both are present.
The default design matrix which appears has dependence in both occupancy and detection. Detection is different if both species are present versus only one species present, and detection of species B is different when species A is detected versus when species A is not detected.
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,b1,b2,b3,b4,b5
pA[1] 1 0 0 0 0
pB[1] 0 1 0 0 0
rA[1] 0 0 1 0 0
rBA[1] 0 0 0 1 0
rBa[1] 0 0 0 0 1
To make detection of species B
independent of the occupancy of species A, the rows for rBA and rBa would be the same as the rows for pB (rB. = pB).
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b1 b2 b3
pA[1] 1 0 0
pB[1] 0 1 0
rA[1] 0 0 1
rBA[1] 0 1 0
rBa[1] 0 1 0
In the design matrix above, detection for species A when species B is not present is estimated using beta1. Detection for species A when species B is present (rA) is estimated using beta3. Detection of species B, regardless of the occupancy and detection of species A is estimated using beta2.
To make detection of species B independent of detection of species A, it means rBA is the same as rBa, so the rows of the design matrix for rBA should be the same as the rows for rBa.
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b1 b2 b3 b4
pA[1] 1 0 0 0
pB[1] 0 1 0 0
rA[1] 0 0 1 0
rBA[1] 0 0 0 1
rBa[1] 0 0 0 1
In the matrix above, detection of species B is dependent on the occupancy of species A (pB not = rB), but independent on the detection of species A (rBA = rBa). Detection for species A when species B is not present is estimated using beta1. Detection for species A when species B is present (rA) is estimated using beta3. Detection of species B, when species A is present is estimated using beta2. Detection of species B when species A is present is estimated using beta4.
The idea is to arrange the 1’s in the matrix such that parameters which you would like to be different have 1’s in different columns. Parameters which you would like to be the same will have rows which are the same.
See the Presence help file for more info on design matrices.