Alouette Reservoir Kokanee Size-at-Age 2019

Data Preparation

The gillnetting and productivity data were provided by BC Ministry of Forests, Lands and Natural Resource Operations.

Statistical Analysis

Model parameters were estimated using Bayesian methods. The estimates were produced using JAGS (Plummer 2015). For additional information on Bayesian estimation the reader is referred to McElreath (2016).

Unless stated otherwise, the Bayesian analyses used weakly informative normal and half-normal prior distributions (Gelman, Simpson, and Betancourt 2017). The posterior distributions were estimated from 1500 Markov Chain Monte Carlo (MCMC) samples thinned from the second halves of 3 chains (Kery and Schaub 2011, 38–40). Model convergence was confirmed by ensuring that the potential scale reduction factor \(\hat{R} \leq 1.05\) (Kery and Schaub 2011, 40) and the effective sample size (Brooks et al. 2011) \(\textrm{ESS} \geq 150\) for each of the monitored parameters (Kery and Schaub 2011, 61).

The parameters are summarised in terms of the point estimate, standard deviation (sd), the z-score, lower and upper 95% confidence/credible limits (CLs) and the p-value (Kery and Schaub 2011, 37, 42). The estimate is the median (50th percentile) of the MCMC samples, the z-score is \(\mathrm{mean}/\mathrm{sd}\) and the 95% CLs are the 2.5th and 97.5th percentiles. A p-value of 0.05 indicates that the lower or upper 95% CL is 0.

The results are displayed graphically by plotting the modeled relationships between particular variables and the response(s) with the remaining variables held constant. In general, continuous and discrete fixed variables are held constant at their mean and first level values, respectively, while random variables are held constant at their typical values (expected values of the underlying hyperdistributions) (Kery and Schaub 2011, 77–82). When informative the influence of particular variables is expressed in terms of the effect size (i.e., percent change in the response variable) with 95% confidence/credible intervals (CIs, Bradford, Korman, and Higgins 2005).

The analyses were implemented using R version 3.6.2 (R Core Team 2019) and the mbr family of packages.

Model Descriptions

Model Templates

.model{
  bLength ~ dnorm(5, 1^-2)
  bYear ~ dnorm(0, 1^-2)
  bDayte ~ dnorm(0, 1^-2)

  bHabitat[1] <- 0
  for (i in 2:nHabitat) {
      bHabitat[i] ~ dnorm(0, 1^-2)
  }

  sLengthAnnual ~ dnorm(0, 1^-2) T(0,)
  for (i in 1:nAnnual) {
      bAnnual[i] ~ dnorm(0, sLengthAnnual^-2)
  }

  sLocationAnnual ~ dnorm(0, 1^-2) T(0,)
  for (i in 1:nLocation) {
    for(j in 1:nAnnual) {
      bLocationAnnual[i, j] ~ dnorm(0, sLocationAnnual^-2)
    }
  }

  sLength ~ dnorm(0, 1^-2) T(0,)

  for(i in 1:length(Length)){
    log(eLength[i]) <- bLength + bHabitat[Habitat[i]] + bYear * Year[i] + bDayte * Dayte[i] + bAnnual[Annual[i]] + bLocationAnnual[Location[i], Annual[i]]

    Length[i] ~ dlnorm(log(eLength[i]), sLength^-2)
  }
..

Tables

Figures

Size-at-Age