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#### BAYESIAN REGULARISED MODEL FOR MODELLING THE ABUNDANCE AND DETECTION OF ALIEN REPTILES IN cHRISTMAS ISLAND ####
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##### NIMBLE code for running the Bayesian regularised  model for estimating the abundance and probabilities of individual detection of alien reptiles in Christmas Island. 
##### The model was fit independently to the data from each of the five species


model.ci<-nimbleCode({

	### Prior distributions for the abundance part of the model

	
	### Priors for the slopes of the abundance model - for running the Bayesian regularisation approach

	for(i in 1:n.covab){			### n.covab: number of abundance covariates - 8 in our model	
		beta.ab[i]~dnorm(0, var=s.ab)	### Prior for the slopes in the model
	}


	s.ab~dexp(0.5)			### Prior for the variance parameter of the slopes; use of an exponential distribution for obtaining a regularised model


	r~dunif(0, 50)			### Prior for the overdispersion parameter of the Negative Binomial regression
	

	### Prior distributions for the detection part of the model	


	### Multivariate Normal priors for the detection intercepts; time of the survey (day and night) - specific intercepts

	alpha.det[1:2]~dmnorm(alphadet.mean[1:2], prec=tau.day[1:2, 1:2])

	    for (j in 1:2){

	        alphadet.mean[j]<-0

	        }

	    tau.day[1:2,1:2]~dwish(S3.day[1:2, 1:2], 3)

	

	### Priors for the slopes of the detection model - for running the Bayesian regularisation approach

	for (i in 1:n.covdet){			### n.covdet: number of covariates in the detection model, n = 4

		beta.det[i]~dnorm(0, var=s.det)
	}
		

	s.det~dexp(0.5)			### Prior for the variance parameter of the slopes; use of an exponential distribution for obtaining a regularised model		



	### Likelihood for the species abundance model

	for (i in 1:n.sites){			### n.sites: number of surveying sites; n = 34
	
	log(mu[i])<-beta.ab[1]*dist[i]+beta.ab[2]*tree[i]+beta.ab[3]*bush[i]+beta.ab[4]*grass[i]+beta.ab[5]*rocks[i]+beta.ab[6]*human[i]+beta.ab[7]*length[i]+beta.ab[8]*elev[i]
	
	p.nb[i]<-r/(r+mu[i])
	
	
	abundance[i]~dnbinom(p.nb[i], r)        ### Negative Binomial distribution of abundance

	}

	### Likelihood of the species detection model

	for (i in 1:sample.size){	### sample.size: number of sites surveyed for alien reptiles by number of repeated survey occasions (n = 204)

		logit(p[i])<-alpha.det[day[i]]+beta.det[1]*tground[i]+beta.det[2]*t10[i]+beta.det[3]*tunder[i]+beta.det[4]*tair[i]	 ### Probability of detection
		
		
		count[i]~dbin(p[i], abundance[site[i]])		### Binomial distribution of the number of individuals recorded in each site during each repeated survey occasion. 


	}


})