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# Bayesian growth curve analysis (Modified from Eaton & Link 2011 and Connette et al. 2005)
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#### Data inputs
## NInd - number of individuals in dataset 
## f - index of first capture
## l - index of last capture
## y - matrix of size data (mm)
## intervals - matrix of time interval data (days)

model {
# Prior Specification (Growth Model)
# lambda ~ dunif(0.001,20)
  # loglambda ~ dunif(0.01,20)
  loglambda ~ dnorm(0.0,0.001)
  log(lambda) <- loglambda
  
  #  a ~ dunif(25,35)
  loga ~ dnorm(0.0,0.001)
  log(a) <- loga
  

tau.eps ~ dgamma(0.01,0.01)
sd.eps <- 1/sqrt(tau.eps)

logk ~ dnorm(0,1.0E-6)
log(k) <- logk

# Likelihood
for (i in 1:NInd){ # Loop through individuals
for (t in f[i]:f[i]){ # Survey of first capture 
y[i,t] ~ dnorm(H[i,t],tau.eps) # Measured size is the expected size +/- measurement error
H[i,t] ~ dgamma(P[i,t],lambda) # True size at first capture is gamma distributed with shape=P[i,t], rate=lambda
P[i,t] <- lambda*H.m[i,t] # Shape of gamma distribution is a product of lambda and the expected size at first capture
H.m[i,t] ~ dunif(7,40) # Prior: Expected size at first capture
}
for (t in (f[i]+1):l[i]){ # Loop through surveys (from subsequent captures)
y[i,t] ~ dnorm(H[i,t],tau.eps)
H[i,t] <- H[i,t-1]+increment[i,t] # True size = previous size plus a random gamma increment
increment[i,t] ~ dgamma(P[i,t],lambda)
P[i,t] <- lambda*abs(H.m[i,t]-H.m[i,t-1])
H.m[i,t] <- H.m[i,t-1]+(a-H.m[i,t-1])*(1-exp(-k*intervals[i,t]/1000)) # Expected size at time t
		} #t
	} #i
} #model