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model_cov_reduced_crit_tl_shared.txt
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model_cov_reduced_crit_tl_shared.txt
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# Critical factors expected to reflect moose population best.
# Changed to share coefficients between theta and lambda, to reduce parameter space
# 7 betas
model
{
# Priors
p00 ~ dunif(0,1)
pInt = log(p00/(1-p00)) # Intercept for p on logit scale
theta00 ~ dunif(-20,5) #prior for theta intercept
lambda0 ~ dunif(-20,5) #prior for lambda intercept
# Priors for landscape fixed effects
beta_hab_softwood ~ dnorm(0,0.01) # prior for habitat effect
beta_hab_hardwood = 0 # prior for habitat effect, made to be reference category, since it has the most observations.
beta_hab_wetland ~ dnorm(0,0.01) # prior for habitat effect
beta_hab_mixed ~ dnorm(0,0.01) # prior for habitat effect
beta_elev ~ dnorm(0,0.01) # prior for elevation effect
#beta_highway ~ dnorm(0,0.01) # prior for highway effect
#beta_minor_road ~ dnorm(0,0.01) # prior for an index of human effect, local road density
beta_northing ~ dnorm(0,0.01) # prior for northing effect
#beta_easting ~ dnorm(0,0.01) # prior for easting effect
# Priors for detection fixed effects
#beta_detect_skye ~ dnorm(0,0.01) # prior for dog effect
#beta_detect_scooby ~ dnorm(0,0.01) # prior for dog effect
#beta_detect_ranger ~ dnorm(0,0.01) # prior for dog effect
#beta_detect_max ~ dnorm(0,0.01) # prior for dog effect
#beta_detect_hiccup ~ dnorm(0,0.01) # prior for dog effect
#beta_detect_suzie ~ dnorm(0,0.01) # prior for suzie effect
#beta_detect_jennifer ~ dnorm(0,0.01) # prior for suzie effect
#beta_detect_justin ~ dnorm(0,0.01) # prior for suzie effect
beta_detect_dist ~ dnorm(0,0.01) # prior for distance effect
for(i in 1:nSites){
# Model for deposition ---------------------------------------------------------------------------------------------------------------------------------------
# This iteration of the model has a slightly different structure for N due to changes in simulation.
# Before, y_t ~ Bin(N_t-1, p)
# Now, y_t ~ Bin(N_t, p)
# Initial deposition is Poisson random, and occurs on June 1, 2016 (arbitrary selection, but is the first visit to any site).
N1[i] ~ dpois(lambda[i])
# Time 1 is visit 1, but indexed by 2, since we need to model the initial N. I choose to call that period before any visits time 0.
# Linear model for lambda. Include fixed/random effects here later
lambda[i] = exp(lambda0 * gridCovariates[i,1] +
beta_northing * gridCovariates[i,2] +
#beta_easting * gridCovariates[i,3] +
beta_elev * gridCovariates[i,4] +
#beta_highway * gridCovariates[i,5] +
#beta_minor_road * gridCovariates[i,6] +
beta_hab_softwood * gridCovariates[i,7] +
beta_hab_hardwood * gridCovariates[i,8] + # Made to be reference category
beta_hab_mixed * gridCovariates[i,9] +
beta_hab_wetland * gridCovariates[i,10]
) # somewhat immaterial except for mechanistic model of deposition process and observation.
# Initial deposition of scats. There are no collections, and assumed to be no degradation until we visit, so N[i,1,v] is equal over all v.
for(v in 1:maxV){
N[i,1,v] = N1[i]
}
# Deposition between time 0 and first visit is found in days[i,1]
for(t in 1:(maxT - 1)){
R[i,t] ~ dpois(theta[i]*days[i,t]) # Every round has some added deposition after we leave. It is dependent upon the DAYS in between visits.
# For instance, R[i,2] ~ dpois(theta[i]*days[i,2]), where days[i,2] is the intervening time
}
# Linear model for theta. Include fixed/random effects here later
theta[i] = exp(theta00 * gridCovariates[i,1] +
beta_northing * gridCovariates[i,2] +
#beta_easting * gridCovariates[i,3] +
beta_elev * gridCovariates[i,4] +
#beta_highway * gridCovariates[i,5] +
#beta_minor_road * gridCovariates[i,6] +
beta_hab_softwood * gridCovariates[i,7] +
beta_hab_hardwood * gridCovariates[i,8] + # Made to be reference category
beta_hab_mixed * gridCovariates[i,9] +
beta_hab_wetland * gridCovariates[i,10]
)
# Proceeding N's add new recruits and remove current counts from the previous time step's N.
# Recruits are random poisson variates with mean theta.
# Mechanism for scat removals/deposition ------------------------------------------------------------------------------------------
for(t in 2:maxT){
# First time going to a sampling unit what's there is what was there last time, minus what we picked up last time, plus what deposition happened last time.
N[i,t,1] = N[i,t-1,maxV] - y[i,t-1,maxV] + R[i,t-1]
# On subsequent visits within a sample occasion to a sampling unit, what's there is what was there after the first visit, minus what we picked up, all the way to maxV (20 in 2016).
for(v in 2:maxV){
N[i,t,v] = N[i,t,v-1] - y[i,t,v-1]
}
}
# Observation likelihood. Counts are conditional on population size at previous time step (after recruits and removals), and detection (which also depends on having visited the site). ------------------
for(t in 2:maxT){
for(v in 1:maxV){
# Covariates on detection
logit(p0[i,t,v]) = pInt +
Dcov[i,t-1,v]*beta_detect_dist #+
#dogCov[i,t-1,1]*beta_detect_skye +
#dogCov[i,t-1,2]*beta_detect_scooby +
#dogCov[i,t-1,3]*beta_detect_ranger +
#dogCov[i,t-1,4]*beta_detect_max +
#dogCov[i,t-1,5]*beta_detect_hiccup +
#humCov[i,t-1,1]*beta_detect_suzie +
#humCov[i,t-1,2]*beta_detect_jennifer +
#humCov[i,t-1,3]*beta_detect_justin
# adjust p0 such that those sites not visited are set to 0. Initially, all sites are p0[i,t] = 0.8
# vis is a matrix of binary indicators with '1' being 'visited', and '0' being 'not visited'. Multiply by p0 to fix 'not visited' sites to p = 0, and obtain a new matrix.
p[i,t,v] = p0[i,t,v] * vis[i,t,v]
y[i,t,v] ~ dbin(p[i,t,v], N[i,t,v])
}
}
#density[i] = (theta[i] / per_moose_deposition) / 2500 # density of moose per grid cell (50m x 50m = 2500m)
}
}