############################################################################### # # # This file accompanies: # # # # Price, Freytag, Bonner, Drayer, Muncy, Hutton and Barton (2018) Mountaintop # # removal mining alters stream salamander population dynamics. Diversity # # and Distributions. # # # ############################################################################### ## Notes: ## S indexes species ## s indexes site ## y indexes year ## v indexes visit model{ ##### Likelihood ##### ##### Occupancy ##### for(S in 1:nspecies){ ## 1) Mean parameters for(mtr in 0:1){ ## a) Initial occupancy eta.psi0[S,mtr+1] <- beta.occ[1,mtr+1,S] logit(psi0.pop[S,mtr+1]) <- eta.psi0[S,mtr+1] ## b) Colonization eta.gamma[S,mtr+1] <- beta.occ[2,mtr+1,S] logit(gamma.pop[S,mtr+1]) <- eta.gamma[S,mtr+1] ## c) Survival eta.phi[S,mtr+1] <- beta.occ[3,mtr+1,S] logit(phi.pop[S,mtr+1]) <- eta.phi[S,mtr+1] } ## 2) Site specific parameters for(s in 1:nsite){ ## Initial occupancy logit(psi[S,s,1]) <- eta.psi0[S,MTR[s]+1] Occupancy[S,s,1] ~ dbern(psi[S,s,1]) ## Occupancy in subsequent years for(y in 2:nyear){ ## Colonization logit(gamma[S,s,y-1]) <- eta.gamma[S,MTR[s]+1] ## Survival logit(phi[S,s,y-1]) <- eta.phi[S,MTR[s]+1] ## Occupancy psi[S,s,y] <- (1-Occupancy[S,s,y-1]) * gamma[S,s,y-1] + Occupancy[S,s,y-1] * phi[S,s,y-1] Occupancy[S,s,y] ~ dbern(psi[S,s,y]) } } } ## Abundance given occupancy for(S in 1:nspecies){ log(lambda.pop[S,1]) <- beta.abund[1,S] log(lambda.pop[S,2]) <- beta.abund[2,S] for(s in 1:nsite){ for(y in 1:nyear){ log(lambda[S,s,y]) <- beta.abund[1,S] * (1-MTR[s]) + beta.abund[2,S] * MTR[s] Abundance.tmp[S,s,y] ~ dpois(lambda[S,s,y])T(1,) Abundance[S,s,y] <- Abundance.tmp[S,s,y]*Occupancy[S,s,y] } } } ## Detection for(S in 1:nspecies){ for(s in 1:nsite){ for(y in 1:nyear){ for(v in 1:nvisit[y]){ logit(p[S,s,y,v]) <- beta.det[1,S] + beta.det[2,S] * CoverObjects[s,y] + beta.det[3,S] * Precip[s,y,v] } } } } ## Observations for(i in 1:nobs){ for(S in 1:nspecies){ Y[i,S] ~ dbinom(p[S,Site[i],Year[i],Visit[i]], Abundance[S,Site[i],Year[i]]) } } ##### Priors ##### ## Parameters for half-t priors on variance df <- 3 tau <- .25 ## Occupancy for(i in 1:3){ # 1=Initial, 2=Colonization, 3=Survival for(k in 1:2){ # 1=Intercept, 2=MTR for(S in 1:nspecies){ xi.occ[i,k,S] ~ dnorm(0,tau.beta.occ[i,k]) beta.occ[i,k,S] <- mu.beta.occ[i,k] + alpha.beta.occ[i,k] * xi.occ[i,k,S] } mu.beta.occ[i,k] ~ dnorm(0,.36) tau.beta.occ[i,k] ~ dgamma(df/2,df/2/tau) sigma.beta.occ[i,k] <- abs(alpha.beta.occ[i,k])/sqrt(tau.beta.occ[i,k]) alpha.beta.occ[i,k] ~ dnorm(0,1) } } ## Abundance for(i in 1:2){ for(S in 1:nspecies){ xi.abund[i,S] ~ dnorm(0,tau.beta.abund[i]) beta.abund[i,S] <- mu.beta.abund[i] + alpha.beta.abund[i] * xi.abund[i,S] } mu.beta.abund[i] ~ dnorm(0,.001) tau.beta.abund[i] ~ dgamma(df/2,df/2/tau) sigma.beta.abund[i] <- abs(alpha.beta.abund[i])/sqrt(tau.beta.abund[i]) alpha.beta.abund[i] ~ dnorm(0,1) } ## Detection for(i in 1:3){ for(S in 1:nspecies){ xi.det[i,S] ~ dnorm(0,tau.beta.det[i]) beta.det[i,S] <- mu.beta.det[i] + alpha.beta.det[i] * xi.det[i,S] } mu.beta.det[i] ~ dnorm(0,.36) tau.beta.det[i] ~ dgamma(df/2,df/2/tau) sigma.beta.det[i] <- abs(alpha.beta.det[i])/sqrt(tau.beta.det[i]) alpha.beta.det[i] ~ dnorm(0,1) } ##### Derived Values ##### ## Percent occupancy for(S in 1:nspecies){ for(s in 1:nsite){ OccSum[S,s] <- sum(Occupancy[S,s,]) } PercOcc[S,1] <- 100*inprod(OccSum[S,],(1-MTR[]))/(sum(1-MTR[])*nyear) PercOcc[S,2] <- 100*inprod(OccSum[S,],MTR[])/(sum(MTR[])*nyear) } ## Mean abundance given occupancy for(S in 1:nspecies){ for(s in 1:nsite){ AbundMean.tmp[S,s] <- mean(Abundance[S,s,]) } AbundMean[S,1] <- inprod(AbundMean.tmp[S,],(1-MTR[]))/(sum(1-MTR[])*nyear) AbundMean[S,2] <- inprod(AbundMean.tmp[S,],MTR[])/(sum(MTR[])*nyear) } }