Cowichan Lake Cuththroat Trout Exploitation Analysis 2022

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 natural and handling mortality, acoustic detections and movements from a fixed receiver array and quarterly lake census, vertical movements from acoustic tags equipped with depth sensors, FLOY tag loss, recapture, reporting and release.

The expected fork length at monthly period \(t\) was estimated from length at capture (\(L_{i,fi}\)) plus the length increment expected under a Von Bertalanffy Growth Curve (Walters and Martell 2004) \[L_{i,t} = L_{i,fi} + (L_{∞} − L_{i,fi} )(1 − e^{(−\frac{1}{12} \cdot k(t −fi))})\] where \(fi\) is the period at capture and \(\frac{1}{12}\) in the exponent adjusts for the fact that there are 12 periods per year.Linf was fixed to a biologically plausible value of 775 mm based on prior information (personal communication, R. Ptolemy); k of 0.23 was estimated from 88 aged Cutthroat Trout in Cowichan Lake (personal communication, Brendan Andersen).

In addition to assumptions 1, 4 to 10, and 13 in Thorley and Andrusak (2017), the survival model assumes that:

• The effect of handling mortality is restricted to the first two monthly periods after initial capture or recapture.
• Recapture probability varies by bi-monthly period and fork length.
  
• Natural mortality varies by season, study year and size class.
  
• The probability of detection depends on whether a fish is alive or has died near or far from a receiver and whether a census has occurred.
• The monthly interval probability of FLOY tag loss is 0.001.
• All recaptured fish that are released have their FLOY tags removed.
• Reporting of a recaptured fish with a FLOY tag is likely greater than 90%.
  
• Survival of fish tagged with a FLOY tag only is the same as those tagged with acoustic tags and a FLOY tag.
  
• Acoustic tags are functional over their estimated battery lifespan and are not shed.

Seasons are defined as winter (December-February), spring (March-May), summer (June-August), and fall (September-November).

Study years span from October 01 to September 30 of the following year (i.e., study year 1 is 2019-10-01 to 2020-09-30). This was used instead of calendar year to ensure that each year group includes all months.

Size classes are defined as small (\(\le\) 350 mm), medium (350 \(-\) 500 mm) and large (> 500 mm).

Preliminary analyses indicated lack of support for variation in recapture probability by study year.

We assumed that the monthly interval probability of FLOY tag loss was 0.001 (0.012 annual probability) based on tag loss estimates from double-tagged Lake Trout in Horse Lake.

Preliminary attempts to estimate tag loss in the model using an uninformative prior confirmed that this assumption was consistent with the available information, although we had to fix tag loss in the model to avoid poor convergence.

Survival

.model{
  bMortality ~ dnorm(-3, 3^-2)
  bMortalityHandling ~ dnorm(0, 2^-2)
  bMonthsHandling <- 2

  bDetectedAlive ~ dnorm(0, 2^-2)
  bDetectedAliveCensus ~ dnorm(0, 2^-2)
  bDieNear ~ dbeta(1, 1)
  bDetectedDeadNear ~ dnorm(1, 1^-2)
  bDetectedDeadNearCensus ~ dnorm(0, 2^-2)
  bDetectedDeadFar ~ dnorm(-1, 1^-2)
  bDetectedDeadFarCensus ~ dnorm(0, 2^-2)
  bMovedH ~ dbeta(1, 1)
  bMovedV ~ dbeta(1, 1)
  bRecaptured ~ dnorm(0, 2^-2)
  bReported ~ dbeta(1, 1)
  bReleased ~ dbeta(1, 1)
  # mode of 0.001
  bTagLoss <- 0.001
  bRecapturedLength ~ dnorm(0, 2^-2)

  sMortalitySizeSeason ~ dexp(1)
  for (i in 1:nSize){
    for(j in 1:nSeason){
      bMortalitySizeSeason[i,j] ~ dnorm(0, sMortalitySizeSeason^-2)
    }
  } 
  bMortalitySeason[1] <- 0
  for (i in 2:nSeason) {
    bMortalitySeason[i] ~ dnorm(0, 2^-2)
  }
  bMortalitySize[1] <- 0
  for (i in 2:nSize) {
    bMortalitySize[i] ~ dnorm(0, 2^-2)
  }
  bMortalityAnnual[1] <- 0
  for (i in 2:nAnnual) {
    bMortalityAnnual[i] ~ dnorm(0, 2^-2)
  }
  bRecapturedBiMonth[1] <- 0
  for (i in 2:nBiMonth) {
    bRecapturedBiMonth[i] ~ dnorm(0, 2^-2)
  }
  for (i in 1:nCapture){
    eMortalityHandling[i, PeriodCapture[i]] <- ilogit(bMortalityHandling)
    eMonthsSinceCapture[i,PeriodCapture[i]] <- 1-Recaptured[i,PeriodCapture[i]]
    
    logit(eDetectedAlive[i, PeriodCapture[i]]) <- bDetectedAlive 
    eDieNear[i] ~ dbern(bDieNear)
    logit(eDetectedDeadNear[i, PeriodCapture[i]]) <- bDetectedDeadNear 
    logit(eDetectedDeadFar[i, PeriodCapture[i]]) <- bDetectedDeadFar 
    eDetectedDead[i, PeriodCapture[i]] <- eDieNear[i] * eDetectedDeadNear[i, PeriodCapture[i]] + 
      (1 - eDieNear[i]) * eDetectedDeadFar[i, PeriodCapture[i]]
    
    logit(eMortality[i,PeriodCapture[i]]) <- bMortality + bMortalitySeason[Season[PeriodCapture[i]]] + bMortalityAnnual[Annual[PeriodCapture[i]]] + bMortalityHandling + bMortalitySize[Size[i, PeriodCapture[i]]] + bMortalitySizeSeason[Size[i, PeriodCapture[i]], Season[PeriodCapture[i]]]

    eMovedH[i,PeriodCapture[i]] <- bMovedH
    eMovedV[i,PeriodCapture[i]] <- bMovedV
    eDetected[i,PeriodCapture[i]] <- Alive[i,PeriodCapture[i]] * eDetectedAlive[i,PeriodCapture[i]] +
      (1-Alive[i,PeriodCapture[i]]) * eDetectedDead[i,PeriodCapture[i]]
      
    logit(eRecaptured[i,PeriodCapture[i]]) <- bRecaptured + bRecapturedBiMonth[BiMonth[PeriodCapture[i]]] + bRecapturedLength * Length[i, PeriodCapture[i]] 
    eReported[i,PeriodCapture[i]] <- bReported
    eReleased[i,PeriodCapture[i]] <- bReleased

    InLake[i,PeriodCapture[i]] <- 1
    Alive[i,PeriodCapture[i]] ~ dbern((1-eMortality[i,PeriodCapture[i]]) * (1-eMortalityHandling[i,PeriodCapture[i]]))
    TBarTag[i,PeriodCapture[i]] ~ dbern(1-bTagLoss)

    Detected[i,PeriodCapture[i]] ~ dbern(Monitored[i,PeriodCapture[i]] * eDetected[i,PeriodCapture[i]])
    MovedH[i,PeriodCapture[i]] ~ dbern(Alive[i,PeriodCapture[i]] * Detected[i,PeriodCapture[i]] * eMovedH[i,PeriodCapture[i]])
    MovedV[i,PeriodCapture[i]] ~ dbern(Alive[i,PeriodCapture[i]] * Sensor[i,PeriodCapture[i]] * Detected[i,PeriodCapture[i]] * eMovedV[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]] * TBarTag[i,PeriodCapture[i]])
    Released[i,PeriodCapture[i]] ~ dbern(Recaptured[i,PeriodCapture[i]] * eReleased[i,PeriodCapture[i]])

  for(j in (PeriodCapture[i]+1):nPeriod) {
    
    eMortalityHandling[i,j] <- ilogit(bMortalityHandling) * step(bMonthsHandling - eMonthsSinceCapture[i,j-1] - 1)
    eMonthsSinceCapture[i,j] <- (1-Recaptured[i,j]) * (eMonthsSinceCapture[i,j-1] + 1)
    
    logit(eDetectedAlive[i,j]) <- bDetectedAlive + bDetectedAliveCensus * Census[j]
    logit(eDetectedDeadNear[i,j]) <- bDetectedDeadNear + bDetectedDeadNearCensus * Census[j]
    logit(eDetectedDeadFar[i,j]) <- bDetectedDeadFar + bDetectedDeadFarCensus * Census[j]
    eDetectedDead[i,j] <- eDieNear[i] * eDetectedDeadNear[i,j] + (1 - eDieNear[i]) * eDetectedDeadFar[i,j]
    eDetected[i,j] <- Alive[i,j] * eDetectedAlive[i,j] + (1-Alive[i,j]) * eDetectedDead[i,j]

    logit(eMortality[i,j]) <- bMortality + bMortalityAnnual[Annual[j]] + bMortalitySize[Size[i,j]] + bMortalitySeason[Season[j]] + bMortalitySizeSeason[Size[i, j], Season[j]]

    eMovedH[i,j] <- bMovedH
    eMovedV[i,j] <- bMovedV
    logit(eRecaptured[i,j]) <-  bRecaptured + bRecapturedBiMonth[BiMonth[j]] + bRecapturedLength * Length[i,j]  
    eReported[i,j] <- bReported
    eReleased[i,j] <- bReleased

    InLake[i,j] ~ dbern(InLake[i,j-1] * ((1 - (Recaptured[i,j-1])) + Recaptured[i,j-1] * Released[i,j-1])) 
    Alive[i,j] ~ dbern(InLake[i,j] * Alive[i,j-1] * (1-eMortality[i,j]) * (1-eMortalityHandling[i,j])) 
    TBarTag[i,j] ~ dbern(TBarTag[i,j-1] * (1-Recaptured[i,j-1]) * (1-bTagLoss))

    Detected[i,j] ~ dbern(InLake[i,j] * Monitored[i,j] * eDetected[i,j])
    MovedH[i,j] ~ dbern(Alive[i,j-1] * Detected[i,j] * eMovedH[i,j])
    MovedV[i,j] ~ dbern(Alive[i,j] * Sensor[i,j] * Detected[i,j] * eMovedV[i,j])
    
    Recaptured[i,j] ~ dbern(Alive[i,j] * eRecaptured[i,j])
    Reported[i,j] ~ dbern(Recaptured[i,j] * eReported[i,j] * TBarTag[i,j])
    Released[i,j] ~ dbern(Recaptured[i,j] * eReleased[i,j])
  }
  }

Block 1. Survival model description.

Survival

Table 1. Parameter descriptions.

Table 2. Model coefficients.

Table 3. Model convergence.

Table 4. The estimated annual interval probabilities (with 95% CIs). Natural mortalities for each size class are the average across study year. Handling mortality is the probability of mortality from handling, assuming that the effect of handling lasts for two months and occurs once in a year. Harvest mortality is the recapture probability multiplied by the probability of being harvested if recaptured, assuming that recapture can only occur once in a year. Release is the probability of being released if recaptured.

Growth

Survival