Quesnel Lake Exploitation Analysis 2019

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 weight varies with length according to an allometric relationship.
• 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).

Across all species, of the fish that were reported with only one tag, 15 had the $100 tag while only 1 had the $10 tag, suggesting that anglers were underreporting fish that had lost their $100 tag.

Survival

The natural mortality and recapture probability were estimated using a Bayesian individual state-space survival model (Thorley and Andrusak 2017) with monthly intervals. The survival model incorporated handling mortality, acoustic detections, inter-section movement, T-bar tag loss and reporting. In addition to assumptions 1 to 2 and 4 to 10, in Thorley and Andrusak (2017), the model also assumes that:

• The effect of handling on mortality lasts up to two months after (re)capture.
• The monthly probability of T-bar tag loss is 1/24 of that estimated by the tag loss model.
• The probability of detection depends on whether a fish is alive or has died near or far from a receiver
• All recaptured fish are released.
• All recaptured fish have their tags removed.
• Reporting of recaptured fish with one or more T-bar tags is between 90 and 100%.

Yield-Per-Recruit

The optimal recapture rate (to maximize biomass of individuals caught) 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 < 500 mm are retained.
• All captured individuals \(\geq\) 500 mm are released.
• Handling mortality is 10%.
• The life-history parameters are fixed.
• There are no Allee effects.
• There are no limitations on prey species.

The optimal yield was also calculated with no slot limit.

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)
  bMonthsHandling <- 2
  bDetectedAlive ~ dunif(0, 1)
  bDieNear ~ dunif(0, 1)
  bDetectedDeadNear ~ dunif(0.5, 1)
  bDetectedDeadFar ~ dunif(0, 0.5)
  bMoved ~ dunif(0, 1)
  bRecaptured ~ dunif(0, 1 - (1 - 0.50)^(1/12))
  bReleased <- 1
  bReported ~ dunif(0.9, 1.00)

  for (i in 1:nCapture){
    logit(eMortality[i,PeriodCapture[i]]) <- bMortality + bMortalityHandling
    
    eDetectedAlive[i] <- bDetectedAlive
    eDieNear[i] ~ dbern(bDieNear)
    eDetectedDeadNear[i] <- bDetectedDeadNear
    eDetectedDeadFar[i] <- bDetectedDeadFar
    
    eDetected[i,PeriodCapture[i]] <- Alive[i,PeriodCapture[i]] * eDetectedAlive[i] + (1-Alive[i,PeriodCapture[i]]) * (eDieNear[i] * eDetectedDeadNear[i] + (1 - eDieNear[i]) * eDetectedDeadFar[i])

    eMoved[i,PeriodCapture[i]] <- bMoved
    eRecaptured[i,PeriodCapture[i]] <- bRecaptured
    eReleased[i,PeriodCapture[i]] <- bReleased
    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-TagLoss)
    TBarTag10[i,PeriodCapture[i]] ~ dbern(1-TagLoss)
    
    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]] - 1))
    Released[i,PeriodCapture[i]] ~ dbern(Recaptured[i,PeriodCapture[i]] * (1-Reported[i,PeriodCapture[i]]) * eReleased[i,PeriodCapture[i]])
    
    eMonthsSinceCapture[i,PeriodCapture[i]] <- 1-Recaptured[i,PeriodCapture[i]]

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

    eDetected[i,j] <- Alive[i,j] * eDetectedAlive[i] + (1-Alive[i,j]) * (eDieNear[i] * eDetectedDeadNear[i] + (1 - eDieNear[i]) * eDetectedDeadFar[i])

    eMoved[i,j] <- bMoved
    eRecaptured[i,j] <- bRecaptured
    eReleased[i,j] <- bReleased
    eReported[i,j] <- bReported
    
    InLake[i,j] ~ dbern(InLake[i,j-1] * (1 - Recaptured[i,j-1] * (1 - Released[i,j-1])))
    Alive[i,j] ~ dbern(Alive[i,j-1] * InLake[i,j] * (1-eMortality[i,j]))
    TBarTag100[i,j] ~ dbern(TBarTag100[i,j-1] * (1-Recaptured[i,j-1]) * (1-TagLoss))
    TBarTag10[i,j] ~ dbern(TBarTag10[i,j-1] * (1-Recaptured[i,j-1]) * (1-TagLoss))
    
    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] - 1))
    Released[i,j] ~ dbern(Recaptured[i,j] * (1-Reported[i,j]) * eReleased[i,j])
    
    eMonthsSinceCapture[i,j] <- (1-Recaptured[i,j]) * (eMonthsSinceCapture[i,j-1] + 1)
  }
  }
..

Block 3. Survival model description.

Recaptures

Table 1. Summary of the captures and recaptures from the survival dataset by species and year.

Condition

Table 2. Parameter descriptions.

Tag Loss

Table 9. The number of recaptured fish that were reported without their $100 versus $10 reward tag by species.

Table 10. Parameter descriptions.

Survival

Table 17. Parameter descriptions.

Yield-per-Recruit

Captures

Sections

Coverage

Detections

Section Use

Condition

Tag Loss

Survival

Yield-per-Recruit