#State-space surplus production model for albacore tuna with lognormal errors
#Process equation extended for prediction
#############################################################################
model StateSpaceTuna;
{
######distribution of I's#####
for (i in 1:N) { Imean[i] <- log(Q*P[i]);
                      I[i] ~ dlnorm(Imean[i],itau2);}

######distribution of P's######
Pmean[1] <- 0;
P[1] ~ dlnorm(Pmean[1],isigma2)I(0.5,2.0)
for(i in 2:N) {
    Pmean[i] <- log(max(P[i-1] + r*P[i-1]*(1-P[i-1]) - k*C[i-1],0.01));
    P[i] ~ dlnorm(Pmean[i],isigma2);
    }

#####Prediction: M-year extension to process equation#####
for(i in (N+1):(N+M)) {
    Pmean[i] <- log(max(P[i-1] + r*P[i-1]*(1-P[i-1]) - k*TAC,0.01));
    P[i] ~ dlnorm(Pmean[i],isigma2);
    }
collapse <- 1-step(P[N+M]-0.1) #Here, collapse defined as less than 10% of virgin

#####Prior on r######
#Lognormal prior corresponding to 10% and 90% of r at 0.13 and 0.48 
r~dlnorm(-1.38,3.845);

#####Prior on k######
#Lognormal prior corresponding to 10% and 90% of k at 1/300 and 1/80
k ~ dlnorm(-5.042905,3.7603664);
K <- 1/k;

#####Prior on Q#####
iq ~ dgamma(0.001,0.001);
q <- 1/iq;
Q <- q*K;

#######Priors on isigma2 and itau2#####
a0<-3.785518;  b0<-0.010223; 
c0<-1.708603; d0<-0.008613854;
isigma2 ~ dgamma(a0,b0);
itau2   ~ dgamma(c0,d0);
Sigma2<-1/isigma2; Tau2<-1/itau2;

#Parameters to monitor
Pars[1]<-K; Pars[2]<-r; Pars[3]<-Sigma2; Pars[4]<-q; Pars[5]<-Tau2

}