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mod3.txt
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mod3.txt
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model{
###########################################
### Spatial Dynamic Co-Occurrence Model ###
###########################################
# State 1= Unoccupied(U), State 2= rodent(A), State 3 = mustelid(B), State 4 = rodent & mustelid(AB)
###########################################
##############
## Priors ##
##############
for(i in 1:2){
beta0_gamA[i] ~ dnorm(0,1)
beta0_gamAB[i] ~ dnorm(0,1)
beta0_gamB[i] ~ dnorm(0,1)
beta0_gamBA[i] ~ dnorm(0,1)
beta0_epsA[i] ~ dnorm(0,1)
beta0_epsAB[i] ~ dnorm(0,1)
beta0_epsB[i] ~ dnorm(0,1)
beta0_epsBA[i] ~ dnorm(0,1)
# interscept det prob
alphaA0[i] ~ dnorm(0,1)
alphaB0[i] ~ dnorm(0,1)
} # end loop
beta0_GamA ~ dnorm(0,1)
beta0_GamAB ~ dnorm(0,1)
beta0_GamB ~ dnorm(0,1)
beta0_GamBA ~ dnorm(0,1)
beta0_EpsA ~ dnorm(0,1)
beta0_EpsAB ~ dnorm(0,1)
beta0_EpsB ~ dnorm(0,1)
beta0_EpsBA ~ dnorm(0,1)
# prior for the seasonal covariat on block level
for(b in 1:nblock){
for(t in 1:(nseason-1)){
for(j in 1:nsite){
seas[j,b,t] ~ dbern(0.5)
}
}
}
# initial state parameters
for(b in 1:nblock){
for(i in 1:3){
psi[b,i] ~ dunif(0,0.5) # site
}
# for block, which is just a function of the states of the sites within each block
x[b,1] <- ifelse(sum(z[,b,1]==1) == nsite, 1,
ifelse(sum(z[,b,1]==2) + sum(z[,b,1]==1) == nsite, 2,
ifelse(sum(z[,b,1]==3) + sum(z[,b,1]==1) == nsite, 3, 4) ) )
#site
for(j in 1:nsite){
fsm[j, b, 1] <- 1-psi[b,1]-psi[b,2]-psi[b,3] #-----------|U
fsm[j, b, 2] <- psi[b,1] #-----------|A
fsm[j, b, 3] <- psi[b,2] #-----------|B
fsm[j, b, 4] <- psi[b,3] #-----------|AB
# first season latent state
# for sites
z[j, b, 1] ~ dcat( fsm[j, b, ( 1:nout )])
} #close site loop
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
###############################################
# btpm = block transition probability matrix. #
# All columns sum to 1. #
###############################################
for(t in 1:(nseason-1)){
# U to ...
btpm[b,t, 1, 1] <- (1-GamA[b,t]) * (1-GamB[b,t]) #--|U
btpm[b,t, 2, 1] <- GamA[b,t] * (1-GamB[b,t]) #--|A
btpm[b,t, 3, 1] <- (1-GamA[b,t]) * GamB[b,t] #--|B
btpm[b,t, 4, 1] <- GamA[b,t] * GamB[b,t] #--|AB
# A to ...
btpm[b,t, 1, 2] <- EpsA[b,t] * (1-GamBA[b,t]) #--|U
btpm[b,t, 2, 2] <- (1-EpsA[b,t]) * (1-GamBA[b,t]) #--|A
btpm[b,t, 3, 2] <- EpsA[b,t] * GamBA[b,t] #--|B
btpm[b,t, 4, 2] <- (1-EpsA[b,t]) * GamBA[b,t] #--|AB
# B to ...
btpm[b,t, 1, 3] <- (1-GamAB[b,t]) * EpsB[b,t] #--|U
btpm[b,t, 2, 3] <- GamAB[b,t] * EpsB[b,t] #--|A
btpm[b,t, 3, 3] <- (1-GamAB[b,t]) * (1-EpsB[b,t]) #--|B
btpm[b,t, 4, 3] <- GamAB[b,t] * (1-EpsB[b,t]) #--|AB
# AB to ..
btpm[b,t, 1, 4] <- EpsAB[b,t] * EpsBA[b,t] #--|U
btpm[b,t, 2, 4] <- (1-EpsAB[b,t]) * EpsBA[b,t] #--|A
btpm[b,t, 3, 4] <- EpsAB[b,t] * (1-EpsBA[b,t]) #--|B
btpm[b,t, 4, 4] <- (1-EpsAB[b,t]) * (1-EpsBA[b,t]) #--|AB
# latent block state for the rest of the seasons
x[b, t+1] ~ dcat(btpm[b, t, (1:nout), x[b, t]])
####################################################
## stpm = site transition probability matrix. ##
## These are dependent on the block level state ##
## All columns sum to 1. ##
####################################################
## Logit links for col and ext probabilities
logit(GamA[b,t]) <- beta0_GamA
logit(GamAB[b,t]) <- beta0_GamAB
logit(GamB[b,t]) <- beta0_GamB
logit(GamBA[b,t]) <- beta0_GamBA
logit(EpsA[b,t]) <- beta0_EpsA
logit(EpsAB[b,t]) <- beta0_EpsAB
logit(EpsB[b,t]) <- beta0_EpsB
logit(EpsBA[b,t]) <- beta0_EpsBA
for(j in 1:nsite){
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# logit links
logit(gamA[b, j, t]) <- beta0_gamA[hab[b, j]]
logit(gamAB[b, j, t]) <- beta0_gamAB[hab[b, j]]
logit(gamB[b, j, t]) <- beta0_gamB[hab[b, j]]
logit(gamBA[b, j, t]) <- beta0_gamBA[hab[b, j]]
logit(epsA[b, j, t]) <- beta0_epsA[hab[b, j]]
logit(epsAB[b, j, t]) <- beta0_epsAB[hab[b, j]]
logit(epsB[b, j, t]) <- beta0_epsB[hab[b, j]]
logit(epsBA[b, j, t]) <- beta0_epsBA[hab[b, j]]
# site transition matrix
# blocks state (x) = U
# U to ...
stpm[b, j, t, 1, 1, 1] <- 1 #--|U
stpm[b, j, t, 2, 1, 1] <- 0 #--|A
stpm[b, j, t, 3, 1, 1] <- 0 #--|B
stpm[b, j, t, 4, 1, 1] <- 0 #--|AB
# A to ...
stpm[b, j, t, 1, 2, 1] <- 1 #--|U
stpm[b, j, t, 2, 2, 1] <- 0 #--|A
stpm[b, j, t, 3, 2, 1] <- 0 #--|B
stpm[b, j, t, 4, 2, 1] <- 0 #--|AB
# B to ...
stpm[b, j, t, 1, 3, 1] <- 1 #--|U
stpm[b, j, t, 2, 3, 1] <- 0 #--|A
stpm[b, j, t, 3, 3, 1] <- 0 #--|B
stpm[b, j, t, 4, 3, 1] <- 0 #--|AB
# AB to ..
stpm[b, j, t, 1, 4, 1] <- 1 #--|U
stpm[b, j, t, 2, 4, 1] <- 0 #--|A
stpm[b, j, t, 3, 4, 1] <- 0 #--|B
stpm[b, j, t, 4, 4, 1] <- 0 #--|AB
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# blocks state (x) = A
# U to ...
stpm[b, j, t, 1, 1, 2] <- (1-gamA[b, j, t]) #--|U
stpm[b, j, t, 2, 1, 2] <- gamA[b, j, t] #--|A
stpm[b, j, t, 3, 1, 2] <- 0 #--|B
stpm[b, j, t, 4, 1, 2] <- 0 #--|AB
# A to ...
stpm[b, j, t, 1, 2, 2] <- epsA[b, j, t] #--|U
stpm[b, j, t, 2, 2, 2] <- (1-epsA[b, j, t]) #--|A
stpm[b, j, t, 3, 2, 2] <- 0 #--|B
stpm[b, j, t, 4, 2, 2] <- 0 #--|AB
# B to ...
stpm[b, j, t, 1, 3, 2] <- (1-gamAB[b, j, t]) #--|U
stpm[b, j, t, 2, 3, 2] <- gamAB[b, j, t] #--|A
stpm[b, j, t, 3, 3, 2] <- 0 #--|B
stpm[b, j, t, 4, 3, 2] <- 0 #--|AB
# AB to ..
stpm[b, j, t, 1, 4, 2] <- epsAB[b, j, t] #--|U
stpm[b, j, t, 2, 4, 2] <- (1-epsAB[b, j, t]) #--|A
stpm[b, j, t, 3, 4, 2] <- 0 #--|B
stpm[b, j, t, 4, 4, 2] <- 0 #--|AB
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# blocks state (x) = B
# U to ...
stpm[b, j, t, 1, 1, 3] <- (1-gamB[b, j, t]) #--|U
stpm[b, j, t, 2, 1, 3] <- 0 #--|A
stpm[b, j, t, 3, 1, 3] <- gamB[b, j, t] #--|B
stpm[b, j, t, 4, 1, 3] <- 0 #--|AB
# A to ...
stpm[b, j, t, 1, 2, 3] <- (1-gamBA[b, j, t]) #--|U
stpm[b, j, t, 2, 2, 3] <- 0 #--|A
stpm[b, j, t, 3, 2, 3] <- gamBA[b, j, t] #--|B
stpm[b, j, t, 4, 2, 3] <- 0 #--|AB
# B to ...
stpm[b, j, t, 1, 3, 3] <- epsB[b, j, t] #--|U
stpm[b, j, t, 2, 3, 3] <- 0 #--|A
stpm[b, j, t, 3, 3, 3] <- (1-epsB[b, j, t]) #--|B
stpm[b, j, t, 4, 3, 3] <- 0 #--|AB
# AB to ..
stpm[b, j, t, 1, 4, 3] <- epsBA[b, j, t] #--|U
stpm[b, j, t, 2, 4, 3] <- 0 #--|A
stpm[b, j, t, 3, 4, 3] <- (1-epsBA[b, j, t]) #--|B
stpm[b, j, t, 4, 4, 3] <- 0 #--|AB
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# blocks state (x) = AB
# U to ...
stpm[b, j, t, 1, 1, 4] <- (1-gamA[b, j, t]) * (1-gamB[b, j, t]) #--|U
stpm[b, j, t, 2, 1, 4] <- gamA[b, j, t] * (1-gamB[b, j, t]) #--|A
stpm[b, j, t, 3, 1, 4] <- (1-gamA[b, j, t]) * gamB[b, j, t] #--|B
stpm[b, j, t, 4, 1, 4] <- gamA[b, j, t] * gamB[b, j, t] #--|AB
# A to ...
stpm[b, j, t, 1, 2, 4] <- epsA[b, j, t] * (1-gamBA[b, j, t]) #--|U
stpm[b, j, t, 2, 2, 4] <- (1-epsA[b, j, t]) * (1-gamBA[b, j, t]) #--|A
stpm[b, j, t, 3, 2, 4] <- epsA[b, j, t] * gamBA[b, j, t] #--|B
stpm[b, j, t, 4, 2, 4] <- (1-epsA[b, j, t]) * gamBA[b, j, t] #--|AB
# B to ...
stpm[b, j, t, 1, 3, 4] <- (1-gamAB[b, j, t] ) * epsB[b, j, t] #--|U
stpm[b, j, t, 2, 3, 4] <- gamAB[b, j, t] * epsB[b, j, t] #--|A
stpm[b, j, t, 3, 3, 4] <- (1-gamAB[b, j, t] ) * (1-epsB[b, j, t]) #--|B
stpm[b, j, t, 4, 3, 4] <- gamAB[b, j, t] * (1-epsB[b, j, t]) #--|AB
# AB to ..
stpm[b, j, t, 1, 4, 4] <- epsAB[b, j, t] * epsBA[b, j, t] #--|U
stpm[b, j, t, 2, 4, 4] <- (1-epsAB[b, j, t]) * epsBA[b, j, t] #--|A
stpm[b, j, t, 3, 4, 4] <- epsAB[b, j, t] * (1-epsBA[b, j, t]) #--|B
stpm[b, j, t, 4, 4, 4] <- (1-epsAB[b, j, t]) * (1-epsBA[b, j, t]) #--|AB
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# latent site state for the rest of the seasons
z[j, b, t+1] ~ dcat( stpm[b, j, t, ( 1:nout ) , z[ j, b, t], x[b,t+1]] + 0.01) # +0.01 to avoide giving the dcat a prob of 0
for(day in 1:nsurvey) {
y[j, b, t, day] ~ dcat( dpm[b, j, t, ( 1:nout ) , z[j, b, t]] + 0.01) # +0.01 to avoide giving the dcat a prob of 0
} #end survey loop
#############################################################
## detection matrix (OS = observed state, TS = true state) ##
#############################################################
# TS = U
dpm[b, j, t, 1, 1] <- 1 #--|OS = U
dpm[b, j, t, 2, 1] <- 0 #--|OS = A
dpm[b, j, t, 3, 1] <- 0 #--|OS = B
dpm[b, j, t, 4, 1] <- 0 #--|OS = AB
# TS = A
dpm[b, j, t, 1, 2] <- 1-pA[b, j, t] #--|OS = U
dpm[b, j, t, 2, 2] <- pA[b, j, t] #--|OS = A
dpm[b, j, t, 3, 2] <- 0 #--|OS = B
dpm[b, j, t, 4, 2] <- 0 #--|OS = AB
# TS = B
dpm[b, j, t, 1, 3] <- 1-pB[b, j, t] #--|OS = U
dpm[b, j, t, 2, 3] <- 0 #--|OS = A
dpm[b, j, t, 3, 3] <- pB[b, j, t] #--|OS = B
dpm[b, j, t, 4, 3] <- 0 #--|OS = AB
# TS = AB
dpm[b, j, t, 1, 4] <- (1-pA[b, j, t]) * (1-pB[b, j, t]) #--|OS = U
dpm[b, j, t, 2, 4] <- pA[b, j, t] * (1-pB[b, j, t]) #--|OS = A
dpm[b, j, t, 3, 4] <- (1-pA[b, j, t]) * pB[b, j, t] #--|OS = B
dpm[b, j, t, 4, 4] <- pA[b, j, t] * pB[b, j, t] #--|OS = AB
## logit links for detection probs
logit(pA[b, j, t]) <- alphaA0[seas[j, b, t]+1]
logit(pB[b, j, t]) <- alphaB0[seas[j, b, t]+1]
} # end site loop
} # end time loop
} #close block loop
## Derived parameters
diff_gamA[1:2] <- gamA[1, c(1,10), 1] - gamAB[1, c(1,10), 1]
diff_gamB[1:2] <- gamB[1, c(1,10), 1] - gamBA[1, c(1,10), 1]
diff_epsA[1:2] <- epsA[1, c(1,10), 1] - epsAB[1, c(1,10), 1]
diff_epsB[1:2] <- epsB[1, c(1,10), 1] - epsBA[1, c(1,10), 1]
diff_GamA <- GamA[1,1] - GamAB[1,1]
diff_GamB <- GamB[1,1] - GamBA[1,1]
diff_EpsA <- EpsA[1,1] - EpsAB[1,1]
diff_EpsB <- EpsB[1,1] - EpsBA[1,1]
ratio_gamA[1:2] <- gamA[1, c(1,10), 1] / gamAB[1, c(1,10), 1]
ratio_gamB[1:2] <- gamB[1, c(1,10), 1] / gamBA[1, c(1,10), 1]
ratio_epsA[1:2] <- epsAB[1, c(1,10), 1] / epsA[1, c(1,10), 1]
ratio_epsB[1:2] <- epsB[1, c(1,10), 1] / epsBA[1, c(1,10), 1]
ratio_GamA <- GamA[1,1] / GamAB[1,1]
ratio_GamB <- GamBA[1,1] / GamB[1,1]
ratio_EpsA <- EpsAB[1,1] / EpsA[1,1]
ratio_EpsB <- EpsB[1,1] / EpsBA[1,1]
}# end