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MAPR_IPM_v6.jags
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MAPR_IPM_v6.jags
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model {
#-------------------------------------------------
# - population model for the MacGillivray's Prion population
# - age structured model with 4 age classes
# - adult survival based on CMR ringing data
# - productivity based on Prion Cave nest monitoring data
# - TWO future scenarios to project population growth with and without eradication
# -------------------------------------------------
#-------------------------------------------------
# 1. PRIORS FOR ALL DATA SETS
#-------------------------------------------------
# -------------------------------------------------
# 1.1. Priors and constraints FOR FECUNDITY
# -------------------------------------------------
mean.fec ~ dunif(0,0.5) ## uninformative prior for CURRENT FECUNDITY
orig.fec ~ dunif(0.33,0.37) ## uninformative prior for ORIGINAL FECUNDITY
full.fec ~ dnorm(0.519,100) T(0.1,1) ## prior for full fecundity without predation from Nevoux & Barbraud (2005) - very high precision
fec.decrease <- (mean.fec-orig.fec)/(66-1)
# -------------------------------------------------
# 1.2. Priors and constraints FOR SURVIVAL
# -------------------------------------------------
phi ~ dunif(0.7, 1)
p ~ dunif(0, 1)
juv.surv <- juv.surv.prop*phi
juv.surv.prop ~ dnorm(mean.juv.surv.prop,1000) T(0,1)
#-------------------------------------------------
# 2. LIKELIHOODS AND ECOLOGICAL STATE MODEL
#-------------------------------------------------
# -------------------------------------------------
# 2.1. System process: female based matrix model
# -------------------------------------------------
for (scen in 1:2){
### INITIAL VALUES FOR COMPONENTS FOR YEAR 1 - based on stable stage distribution from previous model
JUV[1,scen]<-round(Ntot.breed[1,scen]*0.5*(orig.fec))
N1[1,scen]<-round(Ntot.breed[1,scen]*0.5*(orig.fec)*juv.surv)
N2[1,scen]<-round(Ntot.breed[1,scen]*0.5*(orig.fec)*juv.surv*phi)
N3[1,scen]<-round(Ntot.breed[1,scen]*0.5*(orig.fec)*juv.surv*phi*phi)
#Ntot.breed[1,scen] ~ dunif(2000000,5000000) # initial value of population size
Ntot.breed[1,scen] ~ dnorm(Ntot.obs[1,scen],tau.obs[scen]) # initial value of population size
for (tt in 2:66){
## DECREASING FECUNDITY FROM UNKNOWN ORIGINAL in 1956 to known current fecundity in 2015
fec.proj[scen,tt]<-orig.fec + fec.decrease*tt ## models linear decrease of fecundity
## THE PRE-BREEDERS ##
JUV[tt,scen] ~ dbin(fec.proj[scen,tt],round(0.5 * Ntot.breed[tt,scen])) ### number of locally produced FEMALE chicks
N1[tt,scen] ~ dbin(juv.surv, max(2,round(JUV[tt-1,scen]))) ### number of 1-year old survivors
N2[tt,scen] ~ dbin(phi, max(2,round(N1[tt-1,scen]))) ### number of 2-year old survivors
N3[tt,scen] ~ dbin(phi, max(2,round(N2[tt-1,scen]))) ### number of 3-year old survivors
## THE BREEDERS ##
Ntot.breed[tt,scen] ~ dbin(phi, max(2,round(N3[tt-1,scen]+Ntot.breed[tt-1,scen]))) ### the annual number of breeding birds is the sum of old breeders and recent recruits
} # tt
for (tt in 67:PROJ){
## SELECT CURRENT OR RODENT FREE FECUNDITY FOR FUTURE
fec.proj[scen,tt]<-max(mean.fec,(scen-1)*full.fec) ## takes current fecundity for scenario 1 and full fecundity for scenario 2
## THE PRE-BREEDERS ##
JUV[tt,scen] ~ dbin(fec.proj[scen,tt],round(0.5 * Ntot.breed[tt,scen])) ### need a discrete number otherwise dbin will fail, dpois must be >0
N1[tt,scen] ~ dbin(juv.surv, max(2,round(JUV[tt-1,scen]))) ### number of 1-year old survivors
N2[tt,scen] ~ dbin(phi, max(2,round(N1[tt-1,scen]))) ### number of 2-year old survivors
N3[tt,scen] ~ dbin(phi, max(2,round(N2[tt-1,scen]))) ### number of 3-year old survivors
## THE BREEDERS ##
Ntot.breed[tt,scen] ~ dbin(phi, max(2,round(N3[tt-1,scen]+Ntot.breed[tt-1,scen]))) ### the annual number of breeding birds is the sum of old breeders and recent recruits
} # tt
### CONSTRAINT ON COUNT DATA IN YEAR 2000
sigma.obs[scen] ~ dunif(200000,2000000)
tau.obs[scen]<-pow(sigma.obs[scen],-2)
#Ntot.obs[1,scen] ~ dnorm(Ntot.breed[1,scen],tau.obs[scen])
Ntot.obs[2,scen] ~ dnorm(Ntot.breed[46,scen],tau.obs[scen])
} # scen
# -------------------------------------------------
# 2.2. Likelihood for fecundity: Poisson regression from the number of surveyed broods
# -------------------------------------------------
for (t in 1:(T.fec)){ ### T-1 or not
J[t] ~ dpois(rho.fec[t])
rho.fec[t] <- R[t]*mean.fec
} # close loop over every year in which we have fecundity data
# -------------------------------------------------
# 2.3. Likelihood for adult and juvenile survival from CMR
# -------------------------------------------------
for (i in 1:nind){
# Define latent state at first capture
z[i,f[i]] <- 1
for (t in (f[i]+1):n.occasions){
# State process
z[i,t] ~ dbern(mu1[i,t])
mu1[i,t] <- phi * z[i,t-1]
# Observation process
y[i,t] ~ dbern(mu2[i,t])
mu2[i,t] <- p * z[i,t]
} #t
} #i
# -------------------------------------------------
# 4. DERIVED POPULATION GROWTH RATE
# -------------------------------------------------
## DERIVED POPULATION GROWTH RATE
for (scen in 1:2){
for (tt in 1:33){
lambda[tt,scen]<-Ntot.breed[tt+67,scen]/max(1,Ntot.breed[tt+66,scen])
loglam[tt,scen]<-log(lambda[tt,scen])
} ## end of tt
growth.rate[scen] <- exp((1/(33))*sum(loglam[1:(33),scen])) ### geometric mean growth rate
} ## end of scen
} ## END MODEL LOOP