Cowichan Lake Cuththroat Trout Exploitation Analysis 2023

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, handling and spawning 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 the \(\frac{1}{12}\) 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).

The probability of spawning at estimated fork length \(L\) is determined by

\[S = \frac{L^{S_p}}{L_s^{S_p} + L^{S_p}} \cdot {E_s}\]

where \(L_s\) is the length at which 50% of fish are mature, \(E_s\) is the probability of a mature fish spawning and \(S_p\) is the maturity (as a function of length) power.

Additional key assumptions of the survival model include all but two of the assumptions in Thorley and Andrusak (2017) – the exceptions being 3 (no loss of FLOY tags) and 11 (anglers report all FLOY tags). The survival model also assumes that:

• 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%.
  
• The effect of handling mortality is restricted to the first two monthly periods after initial capture or recapture.
  
• The effect of spawning mortality is restricted to the spawning period.
  
• Acoustic tags are functional over their estimated battery lifespan and are not shed.
  
• Recapture probability varies by month and size class.
  
• Natural mortality varies by month, 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.

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). Since data collection started in October, use of study year instead of calendar year ensured that all months were represented in each year. Observations after study year 4 (i.e., in October 2023) were removed from this year’s analysis.

Size classes are defined as small (\(\le\) 350 mm), medium (351 \(-\) 500 mm) and large (> 500 mm). Size class membership can change in each period depending on the fork length predicted by the growth model.

Preliminary analyses indicated lack of support for variation in recapture probability and spawning 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.

We assumed that fish detected in monitored spawning tributaries represents all spawning tagged fish in the lake. The ‘spawning window’ was defined as February to May given that there was consistent receiver coverage in spawning tributaries across years. Receivers were also placed in spawning tributaries in January in study years 3 and 4. Four fish that were detected in a spawning tributary only in January (all in study year 4) were not assigned a status of ‘spawning’. Two study years had partial coverage in February (starting Feb 10-11 and Feb 17-19). These spawning detections were included because we assumed that most spawning events would occur toward the end of the month.

Survival

.model{
  bMortality ~ dnorm(-3, 3^-2)
  bMortalityHandling ~ dnorm(0, 2^-2)
  bMonthsHandling <- 2
  bMortalitySpawning ~ dnorm(0, 2^-2)
  bLs ~  dunif(100, 1000)
  bSp ~ dexp(1/20)
  bEs ~ dbeta(1,1)

  bDetectedAlive ~ dbeta(1, 1)
  bDieNear ~ dbeta(1, 1)
  bDetectedDeadNear ~ dbeta(10, 1)
  bDetectedDeadFar ~ dbeta(1, 10)
  bDetectedCensus ~ dbeta(1, 1)
  bMovedH ~ dbeta(1, 1)
  bMovedV ~ dbeta(1, 1)
  bRecaptured ~ dnorm(0, 2^-2)
  bReported ~ dbeta(1, 1)
  bReleased ~ dbeta(1, 1)
  bTagLoss <- 0.001

  bMortalityAnnual[1] <- 0
  for (i in 2:nAnnual) {
    bMortalityAnnual[i] ~ dnorm(0, 2^-2)
  }
  bRecapturedSize[1] <- 0
  for (i in 2:nSize) {
    bRecapturedSize[i] ~ dnorm(0, 2^-2)
  }
  bMortalitySize[1] <- 0
  for (i in 2:nSize) {
    bMortalitySize[i] ~ dnorm(0, 2^-2)
  }
  sRecapturedMonth ~ dexp(1)
  for (i in 1:nMonth) {
    bRecapturedMonth[i] ~ dnorm(0, sRecapturedMonth^-2)
  }
  sMortalityMonth ~ dexp(1)
  for (i in 1:nMonth) {
    bMortalityMonth[i] ~ dnorm(0, sMortalityMonth^-2)
  }
  for (i in 1:nCapture){
    eMortalityHandling[i, PeriodCapture[i]] <- ilogit(bMortalityHandling)
    eMonthsSinceCapture[i,PeriodCapture[i]] <- 1-Recaptured[i,PeriodCapture[i]]
    eMortalitySpawning[i, PeriodCapture[i]] <- ilogit(bMortalitySpawning) * SpawningPeriod[PeriodCapture[i]]
    
    eDetectedAlive[i] <- bDetectedAlive 
    eDieNear[i] ~ dbern(bDieNear)
    eDetectedDeadNear[i] <- bDetectedDeadNear 
    eDetectedDeadFar[i] <- bDetectedDeadFar 
    eDetectedDead[i] <- eDieNear[i] * eDetectedDeadNear[i] + 
      (1 - eDieNear[i]) * eDetectedDeadFar[i]
    
    logit(eMortality[i,PeriodCapture[i]]) <- bMortality + bMortalityAnnual[Annual[PeriodCapture[i]]] + bMortalitySize[Size[i, PeriodCapture[i]]] + bMortalityMonth[Month[PeriodCapture[i]]]

    eMovedH[i,PeriodCapture[i]] <- bMovedH
    eMovedV[i,PeriodCapture[i]] <- bMovedV
    eDetected[i,PeriodCapture[i]] <- Alive[i,PeriodCapture[i]] * eDetectedAlive[i] +
      (1-Alive[i,PeriodCapture[i]]) * eDetectedDead[i]
    eDetectedCensus[i,PeriodCapture[i]] <- bDetectedCensus
    logit(eRecaptured[i,PeriodCapture[i]]) <- bRecaptured + bRecapturedMonth[Month[PeriodCapture[i]]] + bRecapturedSize[Size[i,PeriodCapture[i]]] 
    eReported[i,PeriodCapture[i]] <- bReported
    eReleased[i,PeriodCapture[i]] <- bReleased

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

    Detected[i,PeriodCapture[i]] ~ dbern(Monitored[i,PeriodCapture[i]] * eDetected[i,PeriodCapture[i]])
    DetectedCensus[i,PeriodCapture[i]] ~ dbern(InLake[i,PeriodCapture[i]] * Monitored[i,PeriodCapture[i]] * eDetectedCensus[i,PeriodCapture[i]] * Census[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(a in (AnnualCapture[i]):nAnnual){
      eSpawning[i,a] <- (((LengthSpawned[i,a]^bSp) / (bLs^bSp + LengthSpawned[i,a]^bSp)) * bEs) 
    }
  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)
    eMortalitySpawning[i,j] <- ilogit(bMortalitySpawning) * Spawned[i,j]
    logit(eMortality[i,j]) <- bMortality + bMortalityAnnual[Annual[j]] + bMortalitySize[Size[i, j]] * (1 - Spawned[i,j]) + bMortalityMonth[Month[j]] * (1 - Spawned[i,j])
    Spawned[i,j] ~ dbern(Monitored[i,j] * SpawningPeriod[j] * eSpawning[i,Annual[j]])
    
    eDetected[i,j] <- Alive[i,j] * eDetectedAlive[i] + (1-Alive[i,j]) * eDetectedDead[i] 
    eDetectedCensus[i,j] <- bDetectedCensus

    eMovedH[i,j] <- bMovedH
    eMovedV[i,j] <- bMovedV
    logit(eRecaptured[i,j]) <-  bRecaptured + bRecapturedMonth[Month[j]] + bRecapturedSize[Size[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]) * (1-eMortalityHandling[i,j-1]) * (1-eMortalitySpawning[i,j-1])) 
    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])
    DetectedCensus[i,j] ~ dbern(InLake[i,j] * Monitored[i,j] * eDetectedCensus[i,j] * Census[j])
    MovedH[i,j] ~ dbern(Alive[i,j-1] * Monitored[i,j] * eMovedH[i,j])
    MovedV[i,j] ~ dbern(Alive[i,j] * Sensor[i,j] * Monitored[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 Mortality’ is the natural mortality averaged across study year and the three size classes for a non-spawning fish. ‘Natural Mortality Spawned’ is the natural mortality for a fish that spawns. ‘Spawning Mortality’ is the probability of mortality from spawning, assuming that the effect of spawning lasts for fourth months (i.e., the spawning window). ‘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. ‘Release’ is the probability of being released if recaptured. ‘Recapture’ is the probability of recapture as the average of the three size classes. ‘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.

Spawning

Table 5. The estimated parameters from the spawning by fork length sub-model. ‘Es’ is the probability of a mature fish spawning. ‘Ls’ is the fork length (mm) at which 50% of fish are mature. ‘Sp’ is the maturity power (as a function of fork length).

Growth

Survival

Spawning