Kootenay Lake Piscivorous Trout Inlake Abundance Estimation 2015

Data Preparation

The parameters used for the analysis must be provided as two files located in the folder .\input\. The abdunace parameters used in this analysis, which must be in the file .\input\parameters.csv, are:

The von Bertalanffy growth parameters used in this analysis, which must be in the file .\input\vB.csv, are:

These files may be modified at will, with parameters added or removed as appropriate; the code will check that the structure is correct for each species and for both sets of spawner and catch parameters, and will run the analysis and produce plots for each valid combination. Additional fish species may also be added to the end of the input files, provided the structure is identical to the above.

Statistical Analysis

Bayesian models were fitted to the data using R version 3.2.1 (Team 2013) and JAGS 3.4.0 (Plummer 2012) which interfaced with each other via jaggernaut 2.3.0 (Thorley 2013). For additional information on Bayesian modelling in the BUGS language, of which JAGS uses a dialect, the reader is referred to Kery and Schaub (2011, 41–44).

Unless indicated otherwise, the models use prior distributions in the form of a normal distribution defined by the parameters provided for the analysis, truncated by the lower and upper credible limits. The posterior distributions were estimated from a minimum of 1,000 Markov Chain Monte Carlo (MCMC) samples thinned from the second halves of three chains (Kery and Schaub 2011, 38–40). Model convergence was confirmed by ensuring that Rhat (Kery and Schaub 2011, 40) was less than 1.1 for each of the parameters in the model (Kery and Schaub 2011, 61).

The posterior distributions of the parameters are summarised in terms of a point estimate (mean), lower and upper 95% credible limits (2.5th and 97.5th percentiles), the standard deviation (SD), percent relative error (half the 95% credible interval as a percent of the point estimate) and significance (Kery and Schaub 2011, 37, 42).

The results are displayed graphically by plotting the modeled relationships between particular variables and the response with 95% credible intervals (CRIs) with the remaining variables held constant.

Model Code

The JAGS model code, which uses a series of naming conventions, is presented below.

model{

    bN ~ dnorm(N.mean, N.sd^-2) T(N.lower, N.upper)
    bP ~ dnorm(p.mean, p.sd^-2) T(p.lower, p.upper)

    N_A <- bN/bP

    bOmega_A ~ dnorm(omega_A.mean, omega_A.sd^-2) T(omega_A.lower, omega_A.upper)

    N_4 <- N_A * ((bOmega_A - 1) * bOmega_A^3)/(bOmega_A^iLambda - bOmega_A^3)

    for(i in 4:iLambda){
      N[i] <- N_4 * bOmega_A^(i-4)
    }

    N_1 ~ dnorm(N_1.mean, N_1.sd^-2) T(N_1.lower, N_1.upper)

    bOmega_J <- ifelse(N_1 == 1, 0, (N_4/N_1)^(1/3))

    for(i in 1:3){
      N[i] <- ifelse(N_1 == 1, 0, N_1 * bOmega_J^(i-1))
    }
}

Model Parameters

The posterior distributions for the fixed (Kery and Schaub 2011 p. 75) parameters in each model are summarised below.

Figures

Abundance - Rainbow Trout - Catch

Abundance - Bull Trout - Catch

Length - Rainbow Trout - Catch

Length - Bull Trout - Catch