Quesnel Exploitation Analysis 2016

Data Preparation

The outing, receiver deployment and fish capture and recapture information were provided by the Ministry of Forests, Lands and Natural Resource Operations and entered by Vicky Lipinski and databased by Gary Pavan.

The data were prepared for analysis using R version 3.4.0 (R Core Team 2017). Receivers were assumed to have a detection range of 500 m. Only individuals with a fork length (FL) \(\geq\) 450 mm, an acoustic tag life \(\geq\) 365 days (if acoustically tagged) and a $100 and $10 reward tags were included in the survival analysis.

Data Analysis

Hierarchical Bayesian models were fitted to the data using R version 3.4.0 (R Core Team 2017) and JAGS 4.2.0 (Plummer 2015) which interfaced with each other via the jmbr package. For additional information on hierarchical 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 used prior distributions that were vague in the sense that they did not affect the posterior distributions (Kery and Schaub 2011, 36). The posterior distributions were estimated from 2,000 Markov Chain Monte Carlo (MCMC) samples thinned from the second halves of four chains (Kery and Schaub 2011, 38–40). Model convergence was confirmed by ensuring that \(\hat{R} < 1.1\) (Kery and Schaub 2011, 40) for each of the monitored parameters in the model(Kery and Schaub 2011, 61).

The posterior distributions of the fixed (Kery and Schaub 2011, 75) 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 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). Where informative the influence of particular variables is expressed in terms of the effect size (i.e., percent change in the response variable) with 95% CIs (Bradford, Korman, and Higgins 2005).

Model Descriptions

Templates

Survival

model{
  bMortality ~ dnorm(-3, 3^-2)
  bMortalityHandling ~ dnorm(0, 2^-2)
  bTagLoss ~ dunif(1 - (1 - 0.01)^(1/12), 1 - (1 - 0.30)^(1/12))
  bDetected ~ dunif(0, 1)
  bMoved ~ dunif(0, 1)
  bRecaptured ~ dunif(0, 1 - (1 - 0.50)^(1/12))
  bReported ~ dunif(0.9, 1.00)

  for (i in 1:nCapture){
    logit(eMortality[i,PeriodCapture[i]]) <- bMortality + bMortalityHandling
    eTagLoss[i,PeriodCapture[i]] <- bTagLoss
    eDetected[i,PeriodCapture[i]] <- bDetected
    eMoved[i,PeriodCapture[i]] <- bMoved
    eRecaptured[i,PeriodCapture[i]] <- bRecaptured
    eReported[i,PeriodCapture[i]] <- bReported

    InLake[i,PeriodCapture[i]] <- 1
    Alive[i,PeriodCapture[i]] ~ dbern(1-eMortality[i,PeriodCapture[i]])

    TBarTag100[i,PeriodCapture[i]] ~ dbern(1-eTagLoss[i,PeriodCapture[i]])
    TBarTag10[i,PeriodCapture[i]] ~ dbern(1-eTagLoss[i,PeriodCapture[i]])

    Detected[i,PeriodCapture[i]] ~ dbern(Monitored[i,PeriodCapture[i]] * eDetected[i,PeriodCapture[i]])
    Moved[i,PeriodCapture[i]] ~ dbern(Alive[i,PeriodCapture[i]] * Monitored[i,PeriodCapture[i]] * eMoved[i,PeriodCapture[i]])

    Recaptured[i,PeriodCapture[i]] ~ dbern(Alive[i,PeriodCapture[i]] * eRecaptured[i,PeriodCapture[i]])
    Reported[i,PeriodCapture[i]] ~ dbern(Recaptured[i,PeriodCapture[i]] * eReported[i,PeriodCapture[i]] * step(TBarTag100[i,PeriodCapture[i]] + TBarTag10[i,PeriodCapture[i]] - 1))

    for(j in (PeriodCapture[i]+1):nPeriod) {
      logit(eMortality[i,j]) <- bMortality + bMortalityHandling * step(PeriodCapture[i] - j + 2)
      eTagLoss[i,j] <- bTagLoss
      eDetected[i,j] <- bDetected
      eMoved[i,j] <- bMoved
      eRecaptured[i,j] <- bRecaptured
      eReported[i,j] <- bReported

      InLake[i,j] ~ dbern(InLake[i,j-1] * (1-Recaptured[i,j-1]))
      Alive[i,j] ~ dbern(Alive[i,j-1] * (1-Recaptured[i,j-1]) * (1-eMortality[i,j-1]))

      TBarTag100[i,j] ~ dbern(TBarTag100[i,j-1] * (1-Recaptured[i,j-1]) * (1-eTagLoss[i,j]))
      TBarTag10[i,j] ~ dbern(TBarTag10[i,j-1] * (1-Recaptured[i,j-1]) * (1-eTagLoss[i,j]))

      Detected[i,j] ~ dbern(InLake[i,j] * Monitored[i,j] * eDetected[i,j])
      Moved[i,j] ~ dbern(Alive[i,j] * Monitored[i,j] * eMoved[i,j])

      Recaptured[i,j] ~ dbern(Alive[i,j] * eRecaptured[i,j])

      Reported[i,j] ~ dbern(Recaptured[i,j] * eReported[i,j] * step(TBarTag100[i,j] + TBarTag10[i,j] - 1))
    }
  }
..

Template 1.

Condition

model {
  bWeight ~ dnorm(0, 2^-2)
  bWeightLength ~ dnorm(3, 2^-2)
  bWeightDayte ~ dnorm(0, 2^-2)

  sWeight ~ dnorm(0, 5^-2)
  for(i in 1:length(Length)) {
    eWeight[i] <- bWeight + bWeightDayte * Dayte[i] + bWeightLength * Length[i]
    Weight[i] ~ dlnorm(eWeight[i], exp(sWeight)^-2)
  }
  W_p <- bWeightLength
  W_500 <- exp(bWeight)
..

Template 2.

Tables

Survival

Table 1. Parameter descriptions.

Condition

Table 8. Parameter descriptions.

Yield-Per-Recruit

Table 18. Assumed life-history parameters values in yield-per-recruit calculation by trout species.

Table 19. Yield-per-recruit calculations.

Figures

Capture

Sections

Coverage

Detections

Section Use

Survival

Yield-Per-Recruit

Recommendations

Recommendations include:

• Develop webpage animating individual fish movements.
• Incorporate recaptures by research crew into survival model.
• Add growth component to survival model to estimate growth parameters and adjust lengths.
• Explore seasonal, annual and length-based variation in natural and fishing mortality.
• Review life-history parameters, in particular \(R_k\), used in the yield-per-recruit calculations.