# Quesnel Lake Large Trout Natural and Fishing Mortality Analysis 2015

Suggested Citation: Thorley, J.L. (2016) Quesnel Lake Large Trout Natural and Fishing Mortality Analysis 2015. A Poisson Consulting Analysis Report. URL: http://www.poissonconsulting.ca/f/1323057218.

## Background

Quesnel Lake supports recreational fisheries for large Bull Trout, Lake Trout and Rainbow Trout. To provide information on the natural and fishing of large trout, acoustic receivers were deployed at key locations in Quesnel Lake. Large trout were caught by angling and tagged with acoustic transmitters and reward tags.

## Methods

### Data Preparation

For the purpose of quantifying movement, Quesnel Lake was divided into 32 sections based on the lake morphology and receiver locations. The lake section, acoustic receiver, fish capture and recapture and hourly detection data were provided by Gary Pavan.

The provided data were then converted into an R data package called qlexdatr. During conversion into an R data package:

• Georeferenced information was projected as UTM zone 10N NAD83 (EPSG: 26910).
• Temporal information was converted to Pacific Standard Time (UTC-8).
• If details were not recorded for a specific recapture, it was assumed to have been caught by the public and released and the T-bar tags removed.
• Two or less detections of a fish at a receiver in a given hour were considered unreliable and were discarded.

The hourly receiver detection data in qlexdatr was then resolved into six hour time intervals by section using the make_detect_data function of the lexr R package. During data resolution:

• The proportional receiver coverage at each section in each interval was calculated assuming a detection radius of 500 m, no overlap between receivers and a maximum coverage of 1.
• Each fish was permitted to be in only one section in each time interval. If a fish was detected in more than one section, the section with the most detections was selected. If sections were tied for detections the section with the least receivers was selected. Failing that, the section with the smaller area was selected.
• Each fish was permitted to move between adjacent sections from one interval to the next. If the distance between detections was greater than the number of intervals then the latter detection was considered a jump.

The six hourly sectional detection data were then aggregated into calendar months periods using the make_analysis_data function of the lexr package. During data aggregation:

• The coverage in each section in each period was the mean coverage across the corresponding time intervals.
• Each fish was permitted to be recaught once in each period. If a fish was recaught twice then the last recapture was chosen.

### Statistical Analysis

Hierarchical Bayesian models were fitted to the data using R version 3.2.3 (R Core Team 2015) and JAGS 4.0.1 (Plummer 2015) which interfaced with each other via jaggernaut 2.3.1 (Thorley 2013). 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 models used prior distributions that were vague in the sense that they did not affect the posterior distributions (Kery and Schaub 2011, 36). The posterior distributions were estimated from a minimum of 1,000 Markov Chain Monte Carlo (MCMC) samples thinned from the second halves of three chains (Kery and Schaub 2011, 38–40). Model convergence was confirmed by ensuring that Rhat (Kery and Schaub 2011, 40) was less than 1.1 for each of the parameters in the model (Kery and Schaub 2011, 61). Model adequacy was confirmed by examination of residual plots.

The posterior distributions of the fixed (Kery and Schaub 2011, 75) parameters are summarised in terms of a point estimate (mean), lower and upper 95% credible limits (2.5th and 97.5th percentiles), the standard deviation (SD), percent relative error (half the 95% credible interval as a percent of the point estimate) and significance (Kery and Schaub 2011, 37, 42).

Variable selection was achieved by dropping insignificant (Kery and Schaub 2011, 37, 42) fixed (Kery and Schaub 2011, 77–82) variables and uninformative random variables. A fixed variables was considered to be insignificant if its significance was $$\geq$$ 0.05 while a random variable was considered to be uninformative if its percent relative error was $$\geq$$ 80%. The Deviance Information Criterion (DIC) was not used because it is of questionable validity when applied to hierarchical models (Kery and Schaub 2011, 469).

The results are displayed graphically by plotting the modeled relationships between particular variables and the response with 95% credible intervals (CRIs) 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% CRIs (Bradford, Korman, and Higgins 2005).

### Natural and Fishing Mortality

Natural and fishing mortality was estimated from the monthly detection data using a Cormack-Jolly-Seber state-space model (Kery and Schaub 2011, 175–77).

Key assumptions of the mortality model include:

• The probability of an angler reporting a fish with T-bar tags is 90% to 100%.
• The probability of an angler removing the T-bar tags is 90% to 100%.
• The handling mortality is 0 to 20%.
• The annual T-bar tag loss rate is 5 to 10%.

### Model Code

The JAGS model code, which uses a series of naming conventions, is presented below.

#### Natural And Fishing Mortality

Variable/Parameter Description
bAngled Annual probability of being recaught
bDetect Interval probability of being detected if inlake
bHandlingM Probability of dying due to (re)capture
bMove Interval probability of moving if alive
bNaturalM Annual probability of dying due to natural causes
bPublic Probability of recapture by public angler (vs research team)
bReleased[2] Probability of a public angler releasing a fish
bRemoved[2] Probability of a public angler removing T-bar tags
bReported[2] Probability of a public angler reporting a T-bar tagged fish
bTagLoss Annual probability of T-bar tag loss
##### Natural And Fishing Mortality - Model1
model{

bDetect ~ dunif(0, 1)
bMove ~ dunif(0, 1)

bAngled ~ dunif(0, 1)
bPublic ~ dunif(0, 1)
bReported[1] <- 1
bReported[2] ~ dunif(0.9, 1.0)
bRemoved[1] <- 0
bRemoved[2] ~ dunif(0.9, 1)
bReleased[1] <- 1
bReleased[2] ~ dunif(0, 1)
bNaturalM ~ dunif(0, 1)
bHandlingM ~ dunif(0, 0.2)
bTagLoss ~ dunif(0.05, 0.1)

eAngledDaily <- 1-(1-bAngled)^(1/365)
eNaturalMDaily <- 1-(1-bNaturalM)^(1/365)
eTagLossDaily <- 1-(1-bTagLoss)^(1/365)

for (i in 1:nCapture){
eInlake[i,PeriodCapture[i]] <- 1
eAlive[i,PeriodCapture[i]] <- 1

Detected[i,PeriodCapture[i]] ~ dbern(bDetect * eInlake[i,PeriodCapture[i]])
Moved[i,PeriodCapture[i]] ~ dbern(Detected[i,PeriodCapture[i]] * eAlive[i,PeriodCapture[i]] * bMove)

eAngled[i,PeriodCapture[i]] ~ dbern((1-(1-eAngledDaily)^Days[PeriodCapture[i]]) * eAlive[i,PeriodCapture[i]])
Public[i,PeriodCapture[i]] ~ dbern(bPublic)

eTags[i,PeriodCapture[i]] <- step(sum(Tags[i,PeriodCapture[i],1:2])-1)
Reported[i,PeriodCapture[i]] ~ dbern(eAngled[i,PeriodCapture[i]] * eTags[i,PeriodCapture[i]] * bReported[Public[i,PeriodCapture[i]]+1])
Released[i,PeriodCapture[i]] ~ dbern(bReleased[Public[i,PeriodCapture[i]]+1])

eHandlingM[i,PeriodCapture[i]] <- bHandlingM

for(j in (PeriodCapture[i]+1):PeriodTagExpire[i]) {
Removed[i,j-1] ~ dbern(eAngled[i,j-1] * eTags[i,j-1] * bRemoved[Public[i,j-1]+1])
Tags[i,j,1] ~ dbern(Tags[i,j-1,1] * (1-eTagLossDaily)^Days[j-1] * (1-Removed[i,j-1]))
Tags[i,j,2] ~ dbern(Tags[i,j-1,2] * (1-eTagLossDaily)^Days[j-1] * (1-Removed[i,j-1]))

eInlake[i,j] ~ dbern(eInlake[i,j-1] * (1-(eAngled[i,j-1] * (1-Released[i,j-1]))))
eAlive[i,j] ~ dbern(eInlake[i,j] * eAlive[i,j-1] * (1-eNaturalMDaily)^Days[j-1] * (1 - (eAngled[i,j-1] * Released[i,j-1] * eHandlingM[i,j-1])))

Detected[i,j] ~ dbern(bDetect * eInlake[i,j])
Moved[i,j] ~ dbern(Detected[i,j] * eAlive[i,j] * bMove)

eAngled[i,j] ~ dbern((1-(1-eAngledDaily)^Days[j]) * eAlive[i,j])
Public[i,j] ~ dbern(bPublic)
eTags[i,j] <- step(sum(Tags[i,j,1:2])-1)
Reported[i,j] ~ dbern(eAngled[i,j] * eTags[i,j] * bReported[Public[i,j]+1])
Released[i,j] ~ dbern(bReleased[Public[i,j]+1])
eHandlingM[i,j] <- eAngled[i,j] * bHandlingM

}
}
}

## Results

Due to the preliminary nature of the analysis, the results should be considered preliminary and interpreted with caution for management purposes.

### Model Parameters

The posterior distributions for the fixed (Kery and Schaub 2011 p. 75) parameters in each model are summarised below.

#### Natural And Fishing Mortality - Bull Trout

Parameter Estimate Lower Upper SD Error Significance
bAngled 0.05340 0.01510 0.11570 0.02570 94 0.001
bDetect 0.49499 0.46332 0.52744 0.01692 6 0.001
bHandlingM 0.08950 0.00280 0.19090 0.05590 100 0.001
bMove 0.30025 0.25490 0.34685 0.02349 15 0.001
bNaturalM 0.08360 0.01510 0.18080 0.04450 99 0.001
bPublic 0.23410 0.00540 0.65930 0.19170 140 0.001
bReleased[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
bReleased[2] 0.53420 0.02940 0.97840 0.29010 89 0.001
bRemoved[2] 0.95139 0.90262 0.99749 0.02889 5 0.001
bReported[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
bReported[2] 0.95017 0.90280 0.99772 0.02931 5 0.001
bTagLoss 0.07383 0.05115 0.09851 0.01406 32 0.001
Convergence Iterations
1.08 10000

#### Natural And Fishing Mortality - Lake Trout

Parameter Estimate Lower Upper SD Error Significance
bAngled 0.02588 0.00561 0.05922 0.01400 100 0.001
bDetect 0.83534 0.81670 0.85365 0.00943 2 0.001
bHandlingM 0.09280 0.00500 0.19370 0.05700 100 0.001
bMove 0.68859 0.65982 0.71729 0.01472 4 0.001
bNaturalM 0.14420 0.07390 0.22730 0.03990 53 0.001
bPublic 0.79100 0.43930 0.99520 0.16960 35 0.001
bReleased[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
bReleased[2] 0.49350 0.09790 0.90960 0.21750 82 0.001
bRemoved[2] 0.95165 0.90312 0.99782 0.02899 5 0.001
bReported[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
bReported[2] 0.95107 0.90277 0.99707 0.02867 5 0.001
bTagLoss 0.07331 0.05106 0.09842 0.01415 32 0.001
Convergence Iterations
1.07 20000

#### Natural And Fishing Mortality - Rainbow Trout

Parameter Estimate Lower Upper SD Error Significance
bAngled 0.14670 0.08790 0.21640 0.03280 44 0.001
bDetect 0.60447 0.57992 0.62940 0.01241 4 0.001
bHandlingM 0.06340 0.00160 0.17930 0.04980 140 0.001
bMove 0.84495 0.82145 0.86869 0.01236 3 0.001
bNaturalM 0.18350 0.09260 0.28000 0.04880 51 0.001
bPublic 0.73240 0.50070 0.89790 0.10060 27 0.001
bReleased[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
bReleased[2] 0.80520 0.58910 0.95470 0.09790 23 0.001
bRemoved[2] 0.91152 0.90037 0.93840 0.01035 2 0.001
bReported[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
bReported[2] 0.95927 0.90530 0.99837 0.02834 5 0.001
bTagLoss 0.07330 0.05105 0.09843 0.01403 32 0.001
Convergence Iterations
1.08 10000

## Acknowledgements

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

## References

Bradford, Michael J, Josh Korman, and Paul S Higgins. 2005. “Using Confidence Intervals to Estimate the Response of Salmon Populations (Oncorhynchus Spp.) to Experimental Habitat Alterations.” Canadian Journal of Fisheries and Aquatic Sciences 62 (12): 2716–26. https://doi.org/10.1139/f05-179.

Kery, Marc, and Michael Schaub. 2011. Bayesian Population Analysis Using WinBUGS : A Hierarchical Perspective. Boston: Academic Press. http://www.vogelwarte.ch/bpa.html.

Plummer, Martyn. 2015. “JAGS Version 4.0.1 User Manual.” http://sourceforge.net/projects/mcmc-jags/files/Manuals/4.x/.

R Core Team. 2015. “R: A Language and Environment for Statistical Computing.” Vienna, Austria: R Foundation for Statistical Computing. http://www.R-project.org/.

Thorley, J. L. 2013. “Jaggernaut: An R Package to Facilitate Bayesian Analyses Using JAGS (Just Another Gibbs Sampler).” Nelson, B.C.: Poisson Consulting Ltd. https://github.com/poissonconsulting/jaggernaut.