Quesnel Lake Exploitation Analysis 2018

Condition

The expected weight of fish of a given length were estimated from the data using a mass-length model (He et al. 2008). Key assumptions of the condition model include:

• The expected weight is allowed to vary with length and date.
• The residual variation in weight is log-normally distributed.

Tag Loss

T-bar tag loss was estimated from the number of tags reported from recaught double-tagged individuals (Fabrizio et al. 1999).

Key assumptions of the tag loss model include:

• The probability of tag loss is independent between tags on a fish.
• Reported tag numbers are described by a zero-truncated binomial distribution (as fish that had lost both tags were not reportable).

Survival

The natural mortality and exploitation were estimated using a Bayesian individual state-space survival model (Thorley and Andrusak 2017) with monthly intervals. The survival model incorporated natural and handling mortality, acoustic detection, inter-section movement, T-bar tag loss, recapture and reporting. In addition to assumptions 1 to 10, in Thorley and Andrusak (2017), the model also assumes that:

• The effect of handling on mortality lasts up to two months after capture.
• Annual T-bar tag-loss is as estimated by the tag loss model.
• All recaptured fish are retained.
• Reporting of recaptured fish with one or more T-bar tags is between 90 and 100%.

Yield-Per-Recruit

The optimal fishing mortality (to maximize number of individuals harvested) was calculated using a yield-per-recruit approach (Bison, O’Brien, and Martell 2003). Key assumptions include:

• The population is at equilibrium.
• All captured individuals are retained.
• There are no Allee effects.
• There are no limitations on prey species.
• The life-history parameters are fixed.

The values of the vulnerability of capture parameters assume that all fish captured during the study are recorded irrespective of length.

Condition

.model {
               bWeight ~ dnorm(0, 1^-2) 
               bWeightLength ~ dnorm(3.18, 0.19^-2)
               
               sWeight ~ dnorm(0, 1^-2) T(0,) 
               for(i in 1:length(LogLength)) {
               eWeight[i] <- bWeight + bWeightLength * LogLength[i]
               Weight[i] ~ dlnorm(eWeight[i], exp(sWeight)^-2)
               }
               }

Block 1. Condition model description.

Tag Loss

model {
  bTagLoss ~ dunif(0,1)
  for (i in 1:nObs) {
    TagsRecap[i] ~ dbin(1 - bTagLoss, 2) T(1, )
  }
..

Block 2. Model description.

Survival

.model{
  bMortality ~ dnorm(-3, 3^-2)
  bMortalityHandling ~ dnorm(0, 2^-2)
  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){
    eTagLoss[i] ~ dbern(TagLoss^2)

    logit(eMortality[i,PeriodCapture[i]]) <- bMortality + bMortalityHandling
    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]])
    
    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]] * eTagLoss[i])
  for(j in (PeriodCapture[i]+1):nPeriod) {
    logit(eMortality[i,j]) <- bMortality + bMortalityHandling * step(PeriodCapture[i] - j + 2)
    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]))
    
    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] * eTagLoss[i])}}
  }

Block 3. Survival model description.

Recaptures

Table 1. Summary of recaptures by species and year.

Condition

Table 2. Parameter descriptions.

Tag Loss

Table 9. Parameter descriptions.

Survival

Table 16. Parameter descriptions.

Yield-per-Recruit

Captures

Sections

Coverage

Detections

Section Use

Condition

Tag Loss

Survival

Yield-per-Recruit