# Quesnel Lake Exploitation Analysis 2019

The suggested citation for this analytic report is:

*Dalgarno, S. and Thorley, J.L. (2020) Quesnel Lake Exploitation
Analysis 2019. A Poisson Consulting Analysis Appendix. URL:
https://www.poissonconsulting.ca/f/574898434.*

## Background

Quesnel Lake supports a recreational fishery for large Bull Trout, Lake Trout and Rainbow Trout. To provide information on the natural and fishing mortality, trout were caught by angling and tagged with acoustic transmitters and/or a $100 and $10 reward tag.

## Methods

### Data Preparation

The outing, receiver deployment, detection, fish capture and recapture information were provided by the Ministry of Forests, Lands and Natural Resource Operations and added to a SQLite database.

The data were prepared for analysis using R version 3.6.2 (R Core Team 2019). Receivers were assumed to have a detection range of 500 m. Detections were aggregated daily, where for each transmitter the receiver with the most number of detections was chosen. In the case of a tie, the receiver with the greatest coverage area was chosen. 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.

The Seasons were Winter (December - February), Spring (March - May), Summer (June - August) and Autumn (September - November).

### Data Analysis

Hierarchical Bayesian models were fitted to the data using R version
3.6.2 (R Core Team 2018) 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 Bayesian analyses used normal and uniform prior distributions that were vague in the sense that they did not constrain the posteriors (Kery and Schaub 2011, 36). The posterior distributions were estimated from 1500 Markov Chain Monte Carlo (MCMC) samples thinned from the second halves of 3 chains (Kery and Schaub 2011, 38–40). Model convergence was confirmed by ensuring that \(\hat{R} \leq 1.05\) (Kery and Schaub 2011, 40) and \(\textrm{ESS} \geq 150\) for each of the monitored parameters (Kery and Schaub 2011, 61). Where \(\hat{R}\) is the potential scale reduction factor and \(\textrm{ESS}\) is the effective sample size (Brooks et al. 2011).

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 \(\mathrm{sd}/\mathrm{mean}\) 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

#### 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.

## Results

### Templates

#### 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.

### Tables

#### Recaptures

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

Species | Year | Captured | Recaptured |
---|---|---|---|

Bull Trout | 2013 | 24 | 0 |

Bull Trout | 2014 | 16 | 0 |

Bull Trout | 2015 | 13 | 2 |

Bull Trout | 2016 | 23 | 1 |

Bull Trout | 2017 | 8 | 5 |

Bull Trout | 2018 | 4 | 0 |

Bull Trout | 2019 | 0 | 0 |

Lake Trout | 2013 | 101 | 1 |

Lake Trout | 2014 | 181 | 9 |

Lake Trout | 2015 | 74 | 2 |

Lake Trout | 2016 | 60 | 9 |

Lake Trout | 2017 | 35 | 11 |

Lake Trout | 2018 | 0 | 0 |

Lake Trout | 2019 | 0 | 0 |

Rainbow Trout | 2013 | 55 | 1 |

Rainbow Trout | 2014 | 53 | 13 |

Rainbow Trout | 2015 | 55 | 6 |

Rainbow Trout | 2016 | 140 | 18 |

Rainbow Trout | 2017 | 65 | 13 |

Rainbow Trout | 2018 | 91 | 10 |

Rainbow Trout | 2019 | 92 | 6 |

#### Condition

Table 2. Parameter descriptions.

Parameter | Description |
---|---|

`bWeight` |
Intercept of `eWeight` |

`bWeightLength` |
Effect of `Length` on `bWeight` |

`eWeight` |
Log expected `Weight` |

`LogLength` |
Log-transformed and centered fork length (cm) |

`sWeight` |
Standard deviation of residual variation in `eWeight` |

`Weight` |
Mass (kg) |

##### Bull Trout

Table 3. Model coefficients.

term | estimate | sd | zscore | lower | upper | pvalue |
---|---|---|---|---|---|---|

bWeight | 0.8297757 | 0.1322915 | 6.2471713 | 0.5610818 | 1.0816456 | 0.0006662 |

bWeightLength | 3.1774374 | 0.1870486 | 16.9925909 | 2.7916318 | 3.5496950 | 0.0006662 |

sWeight | 0.0118292 | 0.0174712 | 0.9721239 | 0.0004531 | 0.0645066 | 0.0006662 |

Table 4. Model summary.

n | K | nchains | niters | nthin | ess | rhat | converged |
---|---|---|---|---|---|---|---|

60 | 3 | 3 | 500 | 10 | 1449 | 1.001 | TRUE |

##### Lake Trout

Table 5. Model coefficients.

term | estimate | sd | zscore | lower | upper | pvalue |
---|---|---|---|---|---|---|

bWeight | 0.8883430 | 0.0597298 | 14.8820968 | 0.7750009 | 1.003225 | 0.0006662 |

bWeightLength | 3.1668007 | 0.1780803 | 17.7944419 | 2.8348505 | 3.493468 | 0.0006662 |

sWeight | 0.0025467 | 0.0040909 | 0.9431764 | 0.0000702 | 0.015168 | 0.0006662 |

Table 6. Model summary.

n | K | nchains | niters | nthin | ess | rhat | converged |
---|---|---|---|---|---|---|---|

263 | 3 | 3 | 500 | 10 | 1256 | 1.002 | TRUE |

##### Rainbow Trout

Table 7. Model coefficients.

term | estimate | sd | zscore | lower | upper | pvalue |
---|---|---|---|---|---|---|

bWeight | 0.8824793 | 0.0462303 | 19.079068 | 0.7895845 | 0.9735769 | 0.0006662 |

bWeightLength | 3.1620721 | 0.1618839 | 19.530999 | 2.8450008 | 3.4759539 | 0.0006662 |

sWeight | 0.0015623 | 0.0021732 | 1.010563 | 0.0000530 | 0.0082513 | 0.0006662 |

Table 8. Model summary.

n | K | nchains | niters | nthin | ess | rhat | converged |
---|---|---|---|---|---|---|---|

470 | 3 | 3 | 500 | 10 | 1184 | 1.002 | TRUE |

#### Tag Loss

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

Species | Loss100 | Loss10 |
---|---|---|

Bull Trout | 0 | 5 |

Lake Trout | 1 | 1 |

Rainbow Trout | 0 | 9 |

Table 10. Parameter descriptions.

Parameter | Description |
---|---|

`bTagLossIntercept` |
Intercept for logit(eTagLoss) |

`eTagLoss[i]` |
Predicted probability of single tag loss for the ith recapture |

`TagsRecap[i]` |
Tags remaining on ith recapture |

##### Bull Trout

Table 11. Model coefficients.

term | estimate | sd | zscore | lower | upper | pvalue |
---|---|---|---|---|---|---|

bTagLoss | 0.1947323 | 0.0693181 | 2.895183 | 0.0807137 | 0.3509004 | 0.0006662 |

Table 12. Model summary.

n | K | nchains | niters | nthin | ess | rhat | converged |
---|---|---|---|---|---|---|---|

14 | 1 | 3 | 500 | 10 | 1500 | 1 | TRUE |

##### Lake Trout

Table 13. Model coefficients.

term | estimate | sd | zscore | lower | upper | pvalue |
---|---|---|---|---|---|---|

bTagLoss | 0.0300305 | 0.0166965 | 1.98645 | 0.0088054 | 0.0761053 | 0.0006662 |

Table 14. Model summary.

n | K | nchains | niters | nthin | ess | rhat | converged |
---|---|---|---|---|---|---|---|

60 | 1 | 3 | 500 | 10 | 1500 | 1 | TRUE |

##### Rainbow Trout

Table 15. Model coefficients.

term | estimate | sd | zscore | lower | upper | pvalue |
---|---|---|---|---|---|---|

bTagLoss | 0.063162 | 0.0177743 | 3.643769 | 0.034354 | 0.1055982 | 0.0006662 |

Table 16. Model summary.

n | K | nchains | niters | nthin | ess | rhat | converged |
---|---|---|---|---|---|---|---|

100 | 1 | 3 | 500 | 10 | 1364 | 1.002 | TRUE |

#### Survival

Table 17. Parameter descriptions.

Parameter | Description |
---|---|

`bDetectedAlive` |
Monthly probability of detection if in-lake |

`bDetectedDeadFar` |
Monthly probability of detection if in-lake and dead far from a receiver |

`bDetectedDeadNear` |
Monthly probability of detection if in-lake and dead near a receiver |

`bDieNear` |
Lifetime probability of dying near versus far from a receiver |

`bMonthsHandling` |
Duration of handling effect in months |

`bMortality` |
Log odds monthly probability of dying of natural causes |

`bMortalityHandling` |
Effect of capture and handling on `bMortality` |

`bMoved` |
Monthly probability of being detected moving between sections if alive |

`bRecaptured` |
Monthly probability of being recaptured if alive |

`bRelease` |
Probability of being released if recaptured and untagged |

`bReported` |
Probability of being reported if recaptured with one or more T-bar tags |

`TagLoss` |
Monthly probability of loss of a single tag (estimate from tag loss model divided by 24) |

##### Bull Trout

Table 18. Model coefficients.

term | estimate | sd | zscore | lower | upper | pvalue |
---|---|---|---|---|---|---|

bDetectedAlive | 0.6972246 | 0.0120973 | 57.630457 | 0.6744240 | 0.7204530 | 0.0006662 |

bDetectedDeadFar | 0.0078189 | 0.0023078 | 3.523863 | 0.0042600 | 0.0132538 | 0.0006662 |

bDetectedDeadNear | 0.9200423 | 0.0253973 | 36.155798 | 0.8641472 | 0.9624430 | 0.0006662 |

bDieNear | 0.0843894 | 0.0377185 | 2.384809 | 0.0300552 | 0.1726160 | 0.0006662 |

bMortality | -3.3233576 | 0.1495587 | -22.220999 | -3.6311573 | -3.0311040 | 0.0006662 |

bMortalityHandling | 0.9861377 | 0.3373141 | 2.875253 | 0.2658565 | 1.5993282 | 0.0059960 |

bMoved | 0.1810338 | 0.0101336 | 17.866241 | 0.1619431 | 0.2011515 | 0.0006662 |

bRecaptured | 0.0049417 | 0.0017100 | 3.010898 | 0.0024426 | 0.0089347 | 0.0006662 |

bReported | 0.9591577 | 0.0286618 | 33.365097 | 0.9037297 | 0.9981237 | 0.0006662 |

Table 19. Model summary.

n | K | nchains | niters | nthin | ess | rhat | converged |
---|---|---|---|---|---|---|---|

7040 | 9 | 3 | 500 | 50 | 344 | 1.017 | TRUE |

##### Lake Trout

Table 20. Model coefficients.

term | estimate | sd | zscore | lower | upper | pvalue |
---|---|---|---|---|---|---|

bDetectedAlive | 0.9191034 | 0.0043094 | 213.240013 | 0.9108973 | 0.9271175 | 0.0006662 |

bDetectedDeadFar | 0.0100367 | 0.0046652 | 2.304728 | 0.0040527 | 0.0211195 | 0.0006662 |

bDetectedDeadNear | 0.6638272 | 0.0316303 | 21.058508 | 0.6107534 | 0.7367335 | 0.0006662 |

bDieNear | 0.2451305 | 0.0490172 | 5.034022 | 0.1579986 | 0.3493860 | 0.0006662 |

bMortality | -3.9735965 | 0.1199373 | -33.186915 | -4.2262362 | -3.7612736 | 0.0006662 |

bMortalityHandling | 0.4278720 | 0.3892762 | 1.045451 | -0.3753722 | 1.1179428 | 0.3044637 |

bMoved | 0.4542085 | 0.0078283 | 58.026192 | 0.4385143 | 0.4691766 | 0.0006662 |

bRecaptured | 0.0034530 | 0.0005093 | 6.820299 | 0.0025209 | 0.0045225 | 0.0006662 |

bReported | 0.9865066 | 0.0174399 | 56.272839 | 0.9351863 | 0.9993338 | 0.0006662 |

Table 21. Model summary.

n | K | nchains | niters | nthin | ess | rhat | converged |
---|---|---|---|---|---|---|---|

36080 | 9 | 3 | 500 | 50 | 27 | 1.275 | FALSE |

##### Rainbow Trout

Table 22. Model coefficients.

term | estimate | sd | zscore | lower | upper | pvalue |
---|---|---|---|---|---|---|

bDetectedAlive | 0.9560250 | 0.0029198 | 327.402875 | 0.9500273 | 0.9615393 | 0.0006662 |

bDetectedDeadFar | 0.0226848 | 0.0023388 | 9.731491 | 0.0183249 | 0.0273173 | 0.0006662 |

bDetectedDeadNear | 0.7105362 | 0.0228101 | 31.109424 | 0.6626384 | 0.7508247 | 0.0006662 |

bDieNear | 0.1123618 | 0.0184284 | 6.148080 | 0.0812937 | 0.1514553 | 0.0006662 |

bMortality | -2.7171286 | 0.0588120 | -46.189771 | -2.8318430 | -2.6070036 | 0.0006662 |

bMortalityHandling | 0.1555180 | 0.1518917 | 1.034297 | -0.1373809 | 0.4470858 | 0.2951366 |

bMoved | 0.6876527 | 0.0064453 | 106.708660 | 0.6756463 | 0.7002395 | 0.0006662 |

bRecaptured | 0.0102242 | 0.0012017 | 8.557276 | 0.0080528 | 0.0127336 | 0.0006662 |

bReported | 0.9897656 | 0.0131974 | 74.702370 | 0.9493788 | 0.9995983 | 0.0006662 |

Table 23. Model summary.

n | K | nchains | niters | nthin | ess | rhat | converged |
---|---|---|---|---|---|---|---|

44080 | 9 | 3 | 500 | 50 | 837 | 1.054 | FALSE |

#### Yield-per-Recruit

##### Slot Limit

Table 24. Bull Trout yield-per-recruit calculations including the capture probability (pi), exploitation rate (u), and average age, length and weight of fish harvested.

Type | pi | u | Yield | Age | Length | Weight | Effort |
---|---|---|---|---|---|---|---|

actual | 0.0577148 | 0.0577148 | 0.0643621 | 6.112073 | 53.01551 | 1810.651 | 0.5642278 |

optimal | 0.4431592 | 0.4431592 | 0.2377927 | 5.441708 | 49.34771 | 1430.195 | 5.5568812 |

Table 25. Bull Trout yield-per-recruit model parameters.

Parameter | Value | Description | Source |
---|---|---|---|

tmax | 30.0000000 | The maximum age (yr). | Professional Judgement |

k | 0.1300000 | The VB growth coefficient (yr-1). | Professional Judgement |

Linf | 100.0000000 | The VB mean maximum length (cm). | Default |

t0 | 0.0000000 | The (theoretical) age at zero length (yr). | Default |

k2 | 0.1300000 | The VB growth coefficient after length L2 (yr-1). | Default |

Linf2 | 100.0000000 | The VB mean maximum length after length L2 (cm). | Default |

L2 | 1000.0000000 | The length (or age if negative) at which growth switches from the first to second phase (cm or yr). | Default |

Wb | 3.1774374 | The weight (as a function of length) scaling exponent. | Current Study |

Ls | 65.0000000 | The length (or age if negative) at which 50 % mature (cm or yr). | Professional Judgement |

Sp | 100.0000000 | The maturity (as a function of length) power. | Default |

es | 0.5000000 | The annual probability of a mature fish spawning. | Professional Judgement |

Sm | 0.0000000 | The spawning mortality probability. | Professional Judgement |

fb | 1.0000000 | The fecundity (as a function of weight) scaling exponent. | Default |

tR | 1.0000000 | The age from which survival is density-independent (yr). | Default |

BH | 1.0000000 | Recruitment follows a Beverton-Holt (1) or Ricker (0) relationship. | Default |

Rk | 22.9500000 | The lifetime spawners per spawner at low density. | (Chudnow, van Poorten, and McAllister 2018) |

n | 0.3460813 | The annual interval natural mortality rate from age tR. | Current Study |

nL | 0.3000000 | The annual interval natural mortality rate from length Ln. | Default |

Ln | 1000.0000000 | The length (or age if negative) at which the natural mortality rate switches from n to nL (cm or yr). | Constant Mortality |

Lv | 40.0000000 | The length (or age if negative) at which 50 % vulnerable to harvest (cm or yr). | Professional Judgement |

Vp | 20.0000000 | The vulnerability to harvest (as a function of length) power. | Professional Judgement |

Llo | 0.0000000 | The lower harvest slot length (cm). | Default |

Lup | 50.0000000 | The upper harvest slot length (cm). | Fishery Regulation |

Nc | 0.0000000 | The slot limits non-compliance probability. | Default |

pi | 0.0577148 | The annual capture probability. | Current Study |

rho | 0.0000000 | The release probability. | Default |

Hm | 0.1000000 | The hooking mortality probability. | Professional Judgement |

Rmax | 1.0000000 | The number of recruits at the carrying capacity (ind). | Default |

Wa | 0.0051225 | The (extrapolated) weight of a 1 cm individual (g). | Current Study |

fa | 1.0000000 | The (theoretical) fecundity of a 1 g female (eggs). | Default |

q | 0.1000000 | The catchability (annual probability of capture) for a unit of effort. | Default |

Table 26. Lake Trout yield-per-recruit calculations including the capture probability (pi), exploitation rate (u), and average age, length and weight of fish harvested.

Type | pi | u | Yield | Age | Length | Weight | Effort |
---|---|---|---|---|---|---|---|

actual | 0.0406584 | 0.0406584 | 0.3274836 | 6.036071 | 53.16049 | 2466.341 | 0.3939626 |

optimal | 0.2434739 | 0.2434739 | 0.9276079 | 5.049155 | 47.55524 | 1861.784 | 2.6482241 |

Table 27. Lake Trout yield-per-recruit model parameters.

Parameter | Value | Description | Source |
---|---|---|---|

tmax | 30.0000000 | The maximum age (yr). | Professional Judgement |

k | 0.1500000 | The VB growth coefficient (yr-1). | Professional Judgement |

Linf | 100.0000000 | The VB mean maximum length (cm). | Default |

t0 | 0.0000000 | The (theoretical) age at zero length (yr). | Default |

k2 | 0.1500000 | The VB growth coefficient after length L2 (yr-1). | Default |

Linf2 | 100.0000000 | The VB mean maximum length after length L2 (cm). | Default |

L2 | 1000.0000000 | The length (or age if negative) at which growth switches from the first to second phase (cm or yr). | Default |

Wb | 3.1668007 | The weight (as a function of length) scaling exponent. | Current Study |

Ls | 65.0000000 | The length (or age if negative) at which 50 % mature (cm or yr). | Professional Judgement |

Sp | 100.0000000 | The maturity (as a function of length) power. | Default |

es | 0.5000000 | The annual probability of a mature fish spawning. | Professional Judgement |

Sm | 0.0000000 | The spawning mortality probability. | Professional Judgement |

fb | 1.0000000 | The fecundity (as a function of weight) scaling exponent. | Default |

tR | 1.0000000 | The age from which survival is density-independent (yr). | Default |

BH | 1.0000000 | Recruitment follows a Beverton-Holt (1) or Ricker (0) relationship. | Default |

Rk | 24.1000000 | The lifetime spawners per spawner at low density. | (Myers, Bowen, and Barrowman 1999) |

n | 0.2003430 | The annual interval natural mortality rate from age tR. | Current Study |

nL | 0.1500000 | The annual interval natural mortality rate from length Ln. | Default |

Ln | 1000.0000000 | The length (or age if negative) at which the natural mortality rate switches from n to nL (cm or yr). | Constant Mortality |

Lv | 25.0000000 | The length (or age if negative) at which 50 % vulnerable to harvest (cm or yr). | Professional Judgement |

Vp | 20.0000000 | The vulnerability to harvest (as a function of length) power. | Professional Judgement |

Llo | 0.0000000 | The lower harvest slot length (cm). | Default |

Lup | 50.0000000 | The upper harvest slot length (cm). | Fishery Regulation |

Nc | 0.0000000 | The slot limits non-compliance probability. | Default |

pi | 0.0406584 | The annual capture probability. | Current Study |

rho | 0.0000000 | The release probability. | Default |

Hm | 0.1000000 | The hooking mortality probability. | Professional Judgement |

Rmax | 1.0000000 | The number of recruits at the carrying capacity (ind). | Default |

Wa | 0.0055748 | The (extrapolated) weight of a 1 cm individual (g). | Current Study |

fa | 1.0000000 | The (theoretical) fecundity of a 1 g female (eggs). | Default |

q | 0.1000000 | The catchability (annual probability of capture) for a unit of effort. | Default |

Table 28. Rainbow Trout yield-per-recruit calculations including the capture probability (pi), exploitation rate (u), and average age, length and weight of fish harvested.

Type | pi | u | Yield | Age | Length | Weight | Effort |
---|---|---|---|---|---|---|---|

actual | 0.1160205 | 0.1160205 | 0.0771597 | 2.780121 | 41.37692 | 1005.9005 | 1.170470 |

optimal | 0.3971217 | 0.3971217 | 0.1501503 | 2.530436 | 38.80338 | 796.1728 | 4.802937 |

Table 29. Rainbow Trout yield-per-recruit model parameters.

Parameter | Value | Description | Source |
---|---|---|---|

tmax | 30.0000000 | The maximum age (yr). | Professional Judgement |

k | 0.2000000 | The VB growth coefficient (yr-1). | Professional Judgement |

Linf | 100.0000000 | The VB mean maximum length (cm). | Default |

t0 | 0.0000000 | The (theoretical) age at zero length (yr). | Default |

k2 | 0.2000000 | The VB growth coefficient after length L2 (yr-1). | Default |

Linf2 | 100.0000000 | The VB mean maximum length after length L2 (cm). | Default |

L2 | 1000.0000000 | The length (or age if negative) at which growth switches from the first to second phase (cm or yr). | Default |

Wb | 3.1620721 | The weight (as a function of length) scaling exponent. | Current Study |

Ls | 65.0000000 | The length (or age if negative) at which 50 % mature (cm or yr). | Professional Judgement |

Sp | 100.0000000 | The maturity (as a function of length) power. | Default |

es | 0.5000000 | The annual probability of a mature fish spawning. | Professional Judgement |

Sm | 0.5000000 | The spawning mortality probability. | Professional Judgement |

fb | 1.0000000 | The fecundity (as a function of weight) scaling exponent. | Default |

tR | 1.0000000 | The age from which survival is density-independent (yr). | Default |

BH | 1.0000000 | Recruitment follows a Beverton-Holt (1) or Ricker (0) relationship. | Default |

Rk | 12.5000000 | The lifetime spawners per spawner at low density. | (???) |

n | 0.5359126 | The annual interval natural mortality rate from age tR. | Current Study |

nL | 0.5000000 | The annual interval natural mortality rate from length Ln. | Default |

Ln | 1000.0000000 | The length (or age if negative) at which the natural mortality rate switches from n to nL (cm or yr). | Constant Mortality |

Lv | 30.0000000 | The length (or age if negative) at which 50 % vulnerable to harvest (cm or yr). | Professional Judgement |

Vp | 20.0000000 | The vulnerability to harvest (as a function of length) power. | Professional Judgement |

Llo | 0.0000000 | The lower harvest slot length (cm). | Default |

Lup | 50.0000000 | The upper harvest slot length (cm). | Fishery Regulation |

Nc | 0.0000000 | The slot limits non-compliance probability. | Default |

pi | 0.1160205 | The annual capture probability. | Current Study |

rho | 0.0000000 | The release probability. | Default |

Hm | 0.1000000 | The hooking mortality probability. | Professional Judgement |

Rmax | 1.0000000 | The number of recruits at the carrying capacity (ind). | Default |

Wa | 0.0061207 | The (extrapolated) weight of a 1 cm individual (g). | Current Study |

fa | 1.0000000 | The (theoretical) fecundity of a 1 g female (eggs). | Default |

q | 0.1000000 | The catchability (annual probability of capture) for a unit of effort. | Default |

### Figures

#### Captures

#### Sections

#### Coverage

#### Detections

#### Section Use

#### Condition

#### Tag Loss

#### Survival

#### Yield-per-Recruit

##### Slot Limit

##### No Slot Limit

### Recommendations

Recommendations include:

- Record the lengths and weights of all captured fish.
- 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.

## Acknowledgements

The organisations and individuals whose contributions have made this analysis report possible include:

- Quesnel Lake anglers for reporting their catches
- Habitat Conservation Trust Foundation (HCTF)
- and the anglers, hunters, trappers and guides who contribute to the Trust

- Ministry of Forests, Lands and Natural Resource Operations
- Lee Williston
- Mike Ramsay
- Greg Andrusak

- Reel Adventures
- Kerry Reed

- Vicky Lipinski

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