model { for (i in 1:N.site) { # Observation Fish[i] ~ dbern(p.fish[i]) BiomassZP[i] ~ dnorm(bzp[i], tau.err[1]) Chl.a[i] ~ dnorm(chl.a[i], tau.err[2]) log.din[i] ~ dnorm(log.DIN[i], tau.err[3]) log.dtp[i] ~ dnorm(log.DTP[i], tau.err[4]) W.temp[i] ~ dnorm(w.temp[i], tau.err[5]) w.temp[i] ~ dnorm(0.0, tau.err[6]) # log.density -> mean[i] p.fish[i] <- 1 - exp(-exp(log.density[i, 1])) log(bzp[i]) <- log.density[i, 2] log(chl.a[i]) <- log.density[i, 3] log.density[i, 1:N.level] ~ dmnorm(mu[i,], inv.vc[,]) # Means mu[i,1] <- ( # log(fish density) beta.f[1] + beta.f[2] * w.temp[i] + beta.f[3] * log.Area[i] ) mu[i,2] <- ( # log(biomass of zoo plankton) beta.z[1] + beta.z[2] * w.temp[i] ) mu[i,3] <- ( # log(density of Chl-a) beta.c[1] + beta.c[2] * w.temp[i] + beta.c[3] * log.din[i] + beta.c[4] * log.dtp[i] ) } # parameters for (k in 1:N.beta.f) { beta.f[k] ~ dnorm(0, Tau.noninformative) } for (k in 1:N.beta.z) { beta.z[k] ~ dnorm(0, Tau.noninformative) } for (k in 1:N.beta.c) { beta.c[k] ~ dnorm(0, Tau.noninformative) } # hyper priors for (k in 1:N.err) { tau.err[k] ~ dgamma(Err.gamma, Err.gamma) } inv.vc[1:N.level,1:N.level] ~ dwish(R[,], Deg.freedom) vc[1:N.level,1:N.level] <- inverse(inv.vc[,]) for (l1 in 1:N.level) { for (l2 in 1:N.level) { rho[l1, l2] <- vc[l1,l2] / sqrt(vc[l1, l1] * vc[l2, l2]) } } }