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Copy pathM1_variant_Hardangervidda_fall2018.R
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M1_variant_Hardangervidda_fall2018.R
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### JAGS-model 'M1_variant - for Hardangervidda using data available at Oct. 19th 2018':
###
### Total counts in summer until 2018 [although last count was performed 2014]
### Total counts in winter until 2018 [last count performed 2018]
### Harvest data unti 2017
### Calf census data until 2018
### Structural surveys until 2017
### ie. last data for estimation: N[2018] and X[2018], SU[2018] & J[2018];
### NOTE THAT FOR HARDANGERVIDDA, MINIMUM COUNTS ARE AVAILABLE BOTH SUMMER (n) AND WINTER (x). IN
### THIS VERSION, BOTH ARE INCLUDED
sink("jagsMod_M1_HV_variant_fall2018.bug")
cat("
model {
############################################################
# Define the priors for the parameters
############################################################
# Initial pre-harvest population sizes
N0f[1] ~ dnorm(500, 0.0001)I(0,) # calves
N0m[1] ~ dnorm(500, 0.0001)I(0,) # calves
N1f[1]~ dnorm(300, 0.0001)I(0,) # yearling females
N1m[1]~ dnorm(300, 0.0001)I(0,) # yearling males
Nadf[1]~dnorm(500, 0.0001)I(0,) # adult females
Nadm[1]~dnorm(500, 0.0001)I(0,) # adult females
# Survival probabilites and productivity-estimates
for(t in 1:T){
p1[t]~ dunif(0,1)
}
for(t in 1:T){
p2[t]~ dunif(0,1)
}
## Vital rates
phi3 ~ dunif(0, 1)
mean.f ~ dunif(-5,5)
mean.phi1 ~ dunif(-5,5)
tau_f <- 1/(sd_f*sd_f)
sd_f ~ dunif(0,2)
tau_phi1 <- 1/(sd_phi1*sd_phi1)
sd_phi1 ~ dunif(0,2)
##############################
# DERIVED PARAMETERS
#############################
fert <- exp(mean.f)/(1+exp(mean.f))
Sjuv <- exp(mean.phi1)/(1+exp(mean.phi1))
#############################
# SYSTEM PROCESS
#############################
for (t in 1:(T-1)){
logit(f[t]) <- mean.f+eps_f[t]
eps_f[t]~dnorm(0, tau_f)
logit(phi1[t]) <- mean.phi1+eps_phi1[t]
eps_phi1[t]~dnorm(0, tau_phi1)
N0f[t+1] ~dbin(phi1[t]*f[t]/2, max(50, Nadf[t+1]))
N0m[t+1] ~dbin(phi1[t]*f[t]/2, max(50, Nadf[t+1]))
N1f[t+1] ~ dbin(phi3, max(50, round(N0f[t]-H0f[t])))
N1m[t+1] ~ dbin(phi3, max(50, round(N0m[t]-H0m[t])))
Nadf[t+1] ~ dbin(phi3, max(50, round(N1f[t]+Nadf[t]-H1f[t]-Hadf[t])))
Nadm[t+1] ~ dbin(phi3, max(50, round(N1m[t]+Nadm[t]-H1m[t]-Hadm[t])))
}
for (t in 1:T){
Ntot[t] <- round(N0f[t] + N0m[t] + N1f[t] + N1m[t] + Nadf[t] + Nadm[t]) # summing up population vector to population size
}
for (t in 1:(T-1)){
Xtot[t] <- round(N0f[t]+N0m[t]+N1f[t]+N1m[t]+Nadf[t]+Nadm[t]-H0f[t]-H0m[t]-H1f[t]-H1m[t]-Hadf[t]-Hadm[t]) # summing up population vector to population size
}
#################################################################
# OBSERVATION PROCESS: COUNT DATA
#################################################################
##
for(t in 1:T){
y_s[t]~dpois(Ntot[t])
}
for(t in 1:(T-1)){
y_w[t]~dpois(Xtot[t])
}
############################################################
# OBSERVATION PROCESS: STRUCTURE SURVEY DATA
############################################################
# Last year - with no phi1[t] estimate available - use
J[T] ~ dbin(p1[T], round((N0f[T]+N0m[T])/ilogit(mean.f)))
SU[T] ~ dbin(p1[T], round(N1m[T]+N1f[T]+Nadf[T]))
for (t in 2:T){
J[t] ~ dbin(p1[t], round((N0f[t]+N0m[t])/phi1[t-1]))
SU[t] ~ dbin(p1[t], round(N1m[t]+N1f[t]+Nadf[t]))
}
for(t in 1:(T-1)){
C0[t] ~ dbin(p2[t], round(N0f[t]+N0m[t]-H0f[t]-H0m[t]))
Cf[t] ~ dbin(p2[t], round(N1f[t]+Nadf[t]-H1f[t]-Hadf[t]))
Cm[t] ~ dbin(p2[t], round(N1m[t]+Nadm[t]-H1m[t]-Hadm[t]))
}
############################################################
### Ending model;
###########################################################
} # End Model
",fill = TRUE)
sink()
####################################################################
########### ONLY WINTER COUNTS
sink("jagsMod_M1_HV_variant2_fall2018.bug")
cat("
model {
############################################################
# Define the priors for the parameters
############################################################
# Initial pre-harvest population sizes
N0f[1] ~ dnorm(500, 0.0001)I(0,) # calves
N0m[1] ~ dnorm(500, 0.0001)I(0,) # calves
N1f[1]~ dnorm(300, 0.0001)I(0,) # yearling females
N1m[1]~ dnorm(300, 0.0001)I(0,) # yearling males
Nadf[1]~dnorm(500, 0.0001)I(0,) # adult females
Nadm[1]~dnorm(500, 0.0001)I(0,) # adult females
# Survival probabilites and productivity-estimates
for(t in 1:T){
p1[t]~ dunif(0,1)
}
for(t in 1:T){
p2[t]~ dunif(0,1)
}
## Vital rates
phi3 ~ dunif(0, 1)
mean.f ~ dunif(-5,5)
mean.phi1 ~ dunif(-5,5)
tau_f <- 1/(sd_f*sd_f)
sd_f ~ dunif(0,2)
tau_phi1 <- 1/(sd_phi1*sd_phi1)
sd_phi1 ~ dunif(0,2)
##############################
# DERIVED PARAMETERS
#############################
fert <- exp(mean.f)/(1+exp(mean.f))
Sjuv <- exp(mean.phi1)/(1+exp(mean.phi1))
#############################
# SYSTEM PROCESS
#############################
for (t in 1:(T-1)){
logit(f[t]) <- mean.f+eps_f[t]
eps_f[t]~dnorm(0, tau_f)
logit(phi1[t]) <- mean.phi1+eps_phi1[t]
eps_phi1[t]~dnorm(0, tau_phi1)
N0f[t+1] ~dbin(phi1[t]*f[t]/2, max(50, Nadf[t+1]))
N0m[t+1] ~dbin(phi1[t]*f[t]/2, max(50, Nadf[t+1]))
N1f[t+1] ~ dbin(phi3, max(50, round(N0f[t]-H0f[t])))
N1m[t+1] ~ dbin(phi3, max(50, round(N0m[t]-H0m[t])))
Nadf[t+1] ~ dbin(phi3, max(50, round(N1f[t]+Nadf[t]-H1f[t]-Hadf[t])))
Nadm[t+1] ~ dbin(phi3, max(50, round(N1m[t]+Nadm[t]-H1m[t]-Hadm[t])))
}
for (t in 1:T){
Ntot[t] <- round(N0f[t] + N0m[t] + N1f[t] + N1m[t] + Nadf[t] + Nadm[t]) # summing up population vector to population size
}
for (t in 1:(T-1)){
Xtot[t] <- round(N0f[t]+N0m[t]+N1f[t]+N1m[t]+Nadf[t]+Nadm[t]-H0f[t]-H0m[t]-H1f[t]-H1m[t]-Hadf[t]-Hadm[t]) # summing up population vector to population size
}
#################################################################
# OBSERVATION PROCESS: COUNT DATA
#################################################################
for(t in 1:(T-1)){
y_w[t]~dpois(Xtot[t])
}
############################################################
# OBSERVATION PROCESS: STRUCTURE SURVEY DATA
############################################################
# Last year - with no phi1[t] estimate available - use
J[T] ~ dbin(p1[T], round((N0f[T]+N0m[T])/ilogit(mean.f)))
SU[T] ~ dbin(p1[T], round(N1m[T]+N1f[T]+Nadf[T]))
for (t in 2:T){
J[t] ~ dbin(p1[t], round((N0f[t]+N0m[t])/phi1[t-1]))
SU[t] ~ dbin(p1[t], round(N1m[t]+N1f[t]+Nadf[t]))
}
for(t in 1:(T-1)){
C0[t] ~ dbin(p2[t], round(N0f[t]+N0m[t]-H0f[t]-H0m[t]))
Cf[t] ~ dbin(p2[t], round(N1f[t]+Nadf[t]-H1f[t]-Hadf[t]))
Cm[t] ~ dbin(p2[t], round(N1m[t]+Nadm[t]-H1m[t]-Hadm[t]))
}
############################################################
### Ending model;
###########################################################
} # End Model
",fill = TRUE)
sink()
########################################################################
###### ONLY SUMMER COUNTS
sink("jagsMod_M1_HV_variant3_fall2018.bug")
cat("
model {
############################################################
# Define the priors for the parameters
############################################################
# Initial pre-harvest population sizes
N0f[1] ~ dnorm(500, 0.0001)I(0,) # calves
N0m[1] ~ dnorm(500, 0.0001)I(0,) # calves
N1f[1]~ dnorm(300, 0.0001)I(0,) # yearling females
N1m[1]~ dnorm(300, 0.0001)I(0,) # yearling males
Nadf[1]~dnorm(500, 0.0001)I(0,) # adult females
Nadm[1]~dnorm(500, 0.0001)I(0,) # adult females
# Survival probabilites and productivity-estimates
for(t in 1:T){
p1[t]~ dunif(0,1)
}
for(t in 1:T){
p2[t]~ dunif(0,1)
}
## Vital rates
phi3 ~ dunif(0, 1)
mean.f ~ dunif(-5,5)
mean.phi1 ~ dunif(-5,5)
tau_f <- 1/(sd_f*sd_f)
sd_f ~ dunif(0,2)
tau_phi1 <- 1/(sd_phi1*sd_phi1)
sd_phi1 ~ dunif(0,2)
##############################
# DERIVED PARAMETERS
#############################
fert <- exp(mean.f)/(1+exp(mean.f))
Sjuv <- exp(mean.phi1)/(1+exp(mean.phi1))
#############################
# SYSTEM PROCESS
#############################
for (t in 1:(T-1)){
logit(f[t]) <- mean.f+eps_f[t]
eps_f[t]~dnorm(0, tau_f)
logit(phi1[t]) <- mean.phi1+eps_phi1[t]
eps_phi1[t]~dnorm(0, tau_phi1)
N0f[t+1] ~dbin(phi1[t]*f[t]/2, max(50, Nadf[t+1]))
N0m[t+1] ~dbin(phi1[t]*f[t]/2, max(50, Nadf[t+1]))
N1f[t+1] ~ dbin(phi3, max(50, round(N0f[t]-H0f[t])))
N1m[t+1] ~ dbin(phi3, max(50, round(N0m[t]-H0m[t])))
Nadf[t+1] ~ dbin(phi3, max(50, round(N1f[t]+Nadf[t]-H1f[t]-Hadf[t])))
Nadm[t+1] ~ dbin(phi3, max(50, round(N1m[t]+Nadm[t]-H1m[t]-Hadm[t])))
}
for (t in 1:T){
Ntot[t] <- round(N0f[t] + N0m[t] + N1f[t] + N1m[t] + Nadf[t] + Nadm[t]) # summing up population vector to population size
}
for (t in 1:(T-1)){
Xtot[t] <- round(N0f[t]+N0m[t]+N1f[t]+N1m[t]+Nadf[t]+Nadm[t]-H0f[t]-H0m[t]-H1f[t]-H1m[t]-Hadf[t]-Hadm[t]) # summing up population vector to population size
}
#################################################################
# OBSERVATION PROCESS: COUNT DATA
#################################################################
##
for(t in 1:T){
y_s[t]~dpois(Ntot[t])
}
############################################################
# OBSERVATION PROCESS: STRUCTURE SURVEY DATA
############################################################
# Last year - with no phi1[t] estimate available - use
J[T] ~ dbin(p1[T], round((N0f[T]+N0m[T])/ilogit(mean.f)))
SU[T] ~ dbin(p1[T], round(N1m[T]+N1f[T]+Nadf[T]))
for (t in 2:T){
J[t] ~ dbin(p1[t], round((N0f[t]+N0m[t])/phi1[t-1]))
SU[t] ~ dbin(p1[t], round(N1m[t]+N1f[t]+Nadf[t]))
}
for(t in 1:(T-1)){
C0[t] ~ dbin(p2[t], round(N0f[t]+N0m[t]-H0f[t]-H0m[t]))
Cf[t] ~ dbin(p2[t], round(N1f[t]+Nadf[t]-H1f[t]-Hadf[t]))
Cm[t] ~ dbin(p2[t], round(N1m[t]+Nadm[t]-H1m[t]-Hadm[t]))
}
############################################################
### Ending model;
###########################################################
} # End Model
",fill = TRUE)
sink()