# Elk River WCT Abundance Analysis 2023

The suggested citation for this analytic appendix is:

*Hill, N.E. & Thorley, J.L. (2024) Elk River WCT Abundance Analysis
2023. A Poisson Consulting Analysis Appendix. URL:
https://www.poissonconsulting.ca/f/1440841288.*

## Background

The Elk River is one of eight upper Kootenay River tributaries (Bull,
Michel, Skookumchuck, St. Mary, upper Kootenay, White and Wigwam) that
are designated as Class II due to the importance of their recreational
fisheries for Westslope Cutthroat Trout (*Oncorhynchus clarkii lewisi*).
The population abundance of Westslope Cutthroat Trout in the Elk River
is relatively uncertain. To reduce the uncertainty, a mark-recapture
analysis using Passive Integrated Transponder (PIT) tags deployed by
both boat electrofishing and guides was recommended (J. L. Thorley 2021).

After a successful pilot study in 2021, data collection via boat electrofishing and guides continued in the Elk River in 2022 and 2023. The goal of the present analysis is to use the additional data to update the annual estimates.

### Data Preparation

The data were provided by Nupqu Limited Partnership. The data were prepared for analysis using R version 4.3.2 (R Core Team 2023) and organized in a SQLite database. All river distances are based on the BC Freshwater Atlas layer.

Key assumptions of the data preparation included:

- PIT tag numbers were recorded correctly in instances where the data was not verifiable by the PIT reader log.
- PIT reader log was taken to be correct in instances where the recorded PIT tag code did not match the PIT reader log.
- GPS coordinates of outing start/end points were extended if they did not overlap locations of fish captured on a given outing using the coordinates of a previous outing to the same zone.

### Statistical Analysis

Model parameters were estimated using Bayesian methods. The estimates were produced using JAGS (Plummer 2003). For additional information on Bayesian estimation the reader is referred to McElreath (2020).

Unless stated otherwise, the Bayesian analyses used weakly informative normal and half-normal prior distributions (Gelman, Simpson, and Betancourt 2017). 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 the potential scale reduction factor \(\hat{R} \leq 1.05\) (Kery and Schaub 2011, 40) and the effective sample size (Brooks et al. 2011) \(\textrm{ESS} \geq 150\) for each of the monitored parameters (Kery and Schaub 2011, 61).

Model adequacy was assessed via posterior predictive checks (Kery and Schaub 2011). More specifically, the proportion of zeros in the data and the first four central moments (mean, variance, skewness and kurtosis) in the deviance residuals were compared to the expected values by simulating new data based on the posterior distribution and assumed sampling distribution and calculating the deviance residuals.

Where computationally practical, the sensitivity of the posteriors to the choice of prior distributions was evaluated by doubling the standard deviations of all normal, half-normal and log-normal priors by an order of magnitude and then using \(\hat{R}\) to evaluate whether the samples were drawn from the same posterior distribution (Joseph L. Thorley and Andrusak 2017).

The parameters are summarised in terms of the point *estimate*, *lower*
and *upper* 95% compatibility limits (Rafi and Greenland 2020) and the
surprisal *s-value* (Greenland 2019). The estimate is the median
(50th percentile) of the MCMC samples while the 95% CLs are the 2.5th
and 97.5th percentiles. The s-value indicates how surprising it would be
to discover that the true value of the parameter is in the opposite
direction to the estimate (Greenland 2019). An s-value of \(>\)
4.32 bits, which is equivalent to a p-value \(<\) 0.05
(Kery and Schaub 2011; Greenland and Poole 2013), indicates that the
surprise would be equivalent to throwing at least 4.3 heads in a row on
a fair coin.

Variable selection was based on the heuristic of directional certainty (Kery and Schaub 2011). Fixed effects were included if their s-value was \(>\) 4.32 bits (Kery and Schaub 2011). Based on a similar argument, random effects were included if their standard deviation had a lower 95% CL \(>\) 5% of the median estimate.

The results are displayed graphically by plotting the modeled
relationships between individual 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 (Kery and Schaub 2011, 77–82). Unless stated otherwise the
typical value is the arithmetic mean. When informative the influence of
particular variables is expressed in terms of the *effect size* (i.e.,
percent change in the response variable) with 95% CLs
(Bradford, Korman, and Higgins 2005).

The analyses were implemented using R version 4.3.2
(R Core Team 2023) and the
`mbr`

family of packages.

### Model Descriptions

#### Growth

Annual growth was estimated with measurement error from the inter-annual PIT tag recaptures using the Fabens method (Fabens 1965) for estimating the von Bertalanffy growth curve (von Bertalanffy 1938). This curve is based on the premise that:

\[ \frac{\text{d}L}{\text{d}t} = k (L_{\infty} - L)\]

where \(L\) is the length of the individual, \(k\) is the growth coefficient and \(L_{\infty}\) is the maximum length.

Integrating the above equation gives:

\[ L_t = L_{\infty} (1 - e^{-k(t - t_0)})\]

where \(L_t\) is the length at time \(t\) and \(t_0\) is the time at which the individual would have had zero length.

The Fabens form allows

\[ L_r = L_c + (L_{\infty} - L_c) (1 - e^{-kT})\]

where \(L_r\) is the length at recapture, \(L_c\) is the length at capture and \(T\) is the time between capture and recapture.

Measurement error was incorporated by using additional variation around the reported fork length measurements to estimate the true lengths for initial captures and recaptures, which were used to estimate the growth model parameters.

Nine fish with very unlikely reported growth increments (as determined by an absolute deviance residual greater than two) were excluded from the final analysis.

Key assumptions of the growth model include:

- The standard deviation of measurement error varies by capture group (guides versus electrofishing) and year.
- The standard deviation of measurement error varies randomly by capture group within year.
- The residual variation in measurement error is normally distributed.
- The residual variation in growth is normally distributed.

#### Capture Efficiency

The data were analysed using a logistic regression model. Guide captures were excluded from this analysis because their sampling effort is unknown.

Key assumptions of the efficiency model include:

- Capture efficiency varies by year, electrofishing effort, and fork length and its squared polynomial.
- There is an increasing asymptotic relationship between electrofishing effort and capture efficiency.
- The residual variation in whether or not a capture was a within-year recapture is Bernoulli-distributed.

#### Movement

The extent to which sites are closed (i.e., fish remain at the same site within a sampling season) was evaluated using a logistic regression model. The model estimates the probability that intra-annual recaptures were caught at the same site versus a different one.

Key assumptions of the site fidelity model include:

- The probability of site fidelity varies by fork length.
- The residual variation in site fidelity is Bernoulli-distributed.

#### Annual Abundance

The data were analysed using a hierarchical Bayesian mark-recapture abundance model. Each zone was split into six kilometre sites, except sites at the end of the zone, which were added to the previous site if the length was less than three kilometres. Captures from sites that had less then 10% of their length surveyed were not included in the analysis.

Fish were divided into two length classes based on the estimated relationship between fork length and capture efficiency. The fish were split into length classes using their mean estimated true length in the year of capture if they were ever recaptured, based on the growth model, and their reported length if they were not recaptured. The small class includes fish between 200 and 299 mm, and the large class includes fish 300 mm and greater. 142 fish under 200 mm, as well as 7 fish missing length measurements were excluded from this analysis.

Key assumptions of the mark-recapture abundance model include:

- 61% of previously marked fish are present at a site when it is resampled.
- There is no mortality of fish within a sampling season.
- The probability of capturing a marked or unmarked fish is the same.
- All recaptured fish are correctly identified as being marked and there is no tag loss.
- Lineal densities of small fish vary randomly by year and site within year.
- Lineal densities of large fish vary randomly by year and site within year.
- Capture efficiency varies by electrofishing effort.
- The effect of electrofishing effort is the same for small and large fish.
- Capture efficiency of small fish varies randomly by site visit.
- Capture efficiency of large fish varies randomly by site visit.
- The number of small and large recaptures (of fish marked at that site in that year) and the total number of small and large fish caught are each binomially distributed.

#### Annual Survival

Preliminary analysis found that the data were insufficient to reliably determine whether non-captures were due to mortality, failure to recapture, or movement out of the study area.

### Model Templates

#### Growth

```
. model{
bK ~ dbeta(1, 1)
bLinf ~ dnorm(400, 100^-2) T(0,)
bErrorIntercept ~ dnorm(0, 2^-2)
bErrorGroup[1] <- 0
for (i in 2:ngroup) {
bErrorGroup[i] ~ dnorm(0, 2^-2)
}
bErrorAnnual[1] <- 0
for (i in 2:nannual) {
bErrorAnnual[i] ~ dnorm(0, 2^-2)
}
sErrorGroupAnnual ~ dexp(1)
for (i in 1:ngroup) {
for (j in 1:nannual) {
bErrorGroupAnnual[i, j] ~ dnorm(0, sErrorGroupAnnual^-2)
}
}
for (i in 1:nfish_id) {
bTrueInitialLength[i] ~ dnorm(300, 100^-2) T(0, 600)
log(eObsInit[i]) = bErrorIntercept + bErrorGroup[initial_group[i]] + bErrorAnnual[initial_annual[i]] + bErrorGroupAnnual[initial_group[i], initial_annual[i]]
obs_initial_length[i] ~ dnorm(bTrueInitialLength[i], eObsInit[i]^-2)
}
for (i in 1:nObs) {
log(eObsRecap[i]) = bErrorIntercept + bErrorGroup[group[i]] + bErrorAnnual[annual[i]] + bErrorGroupAnnual[group[i], annual[i]]
eGrowth[i] = (bLinf - bTrueInitialLength[fish_id[i]]) * (1 - exp(-bK * years[i]))
eTrueFinalLength[i] = ifelse(eGrowth[i] < 0, bTrueInitialLength[fish_id[i]], bTrueInitialLength[fish_id[i]] + eGrowth[i])
recapture_length[i] ~ dnorm(eTrueFinalLength[i], eObsRecap[i]^-2)
}
}
```

Block 1. Model description.

#### Capture Efficiency

```
.model {
bEfficiencyEffort ~ dnorm(0, 2^-2)
bEfficiencyLength ~ dnorm(0, 2^-2)
bEfficiencyLength2 ~ dnorm(0, 2^-2)
for (i in 1:nannual) {
bEfficiencyAnnual[i] ~ dnorm(-3, 10^-2)
}
for (i in 1:nObs){
logit(eEfficiency[i]) <- bEfficiencyAnnual[annual[i]] + bEfficiencyEffort * (log(effort[i]) - log(0.25)) + bEfficiencyLength * length[i] + bEfficiencyLength2 * length[i]^2
recapture[i] ~ dbern(eEfficiency[i])
}
```

Block 2. Model description.

#### Movement

```
.model{
bFidelity ~ dnorm(0, 2^-2)
bLength ~ dnorm(0, 2^-2)
for (i in 1:nObs) {
logit(eFidelity[i]) <- bFidelity + bLength * fork_length[i]
fidelity[i] ~ dbern(eFidelity[i])
}
```

Block 3. Model description.

#### Annual Abundance

```
.model{
sDensitySmallAnnualSiteID ~ dexp(1)
sDensityLargeAnnualSiteID ~ dexp(1)
for (i in 1:nannual) {
bEfficiencySmallAnnual[i] ~ dnorm(-4, 2^-2)
bEfficiencyLargeAnnual[i] ~ dnorm(-4, 2^-2)
bDensitySmallAnnual[i] ~ dnorm(5, 2^-2)
bDensityLargeAnnual[i] ~ dnorm(5, 2^-2)
for (j in 1:nsite_id) {
bDensitySmallAnnualSiteID[i, j] ~ dnorm(0, sDensitySmallAnnualSiteID^-2)
bDensityLargeAnnualSiteID[i, j] ~ dnorm(0, sDensityLargeAnnualSiteID^-2)
}
}
bFidelity ~ dbeta(33, 21)
bEfficiencySecondsPerMetre ~ dnorm(0, 1^-2)
bThetaLarge ~ dexp(10)
bThetaSmall ~ dexp(10)
for (i in 1:nObs) {
log(eDensitySmall[i]) <- bDensitySmallAnnual[annual[i]] + bDensitySmallAnnualSiteID[annual[i], site_id[i]]
logit(eProbSmall[i]) <- bEfficiencySmallAnnual[annual[i]] + bEfficiencySecondsPerMetre * seconds_per_metre[i]
eEfficiencySmall[i] ~ dbeta((2 * eProbSmall[i]) / bThetaSmall, (2 * (1 - eProbSmall[i])) / bThetaSmall)
recaptures_small[i] ~ dbinom(eEfficiencySmall[i] * bFidelity, marked_small[i])
bAbundanceSmall[i] ~ dpois(eDensitySmall[i] * site_length[i] * survey_proportion[i])
count_small[i] ~ dbinom(eEfficiencySmall[i], bAbundanceSmall[i])
}
for (i in 1:nObs) {
log(eDensityLarge[i]) <- bDensityLargeAnnual[annual[i]] + bDensityLargeAnnualSiteID[annual[i], site_id[i]]
logit(eProbLarge[i]) <- bEfficiencyLargeAnnual[annual[i]] + bEfficiencySecondsPerMetre * seconds_per_metre[i]
eEfficiencyLarge[i] ~ dbeta((2 * eProbLarge[i]) / bThetaLarge, (2 * (1 - eProbLarge[i])) / bThetaLarge)
recaptures_large[i] ~ dbinom(eEfficiencyLarge[i] * bFidelity, marked_large[i])
bAbundanceLarge[i] ~ dpois(eDensityLarge[i] * site_length[i] * survey_proportion[i])
count_large[i] ~ dbinom(eEfficiencyLarge[i], bAbundanceLarge[i])
}
```

Block 4. Model description.

## Results

### Tables

#### Growth

Table 1. Parameter descriptions.

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

`annual[i]` |
Year of capture for the `i` ^{th} recapture |

`bErrorAnnual[i]` |
Effect of year of capture on standard deviation of measurement error |

`bErrorGroupAnnual[i, j]` |
Random effect of the `i` ^{th} capture group and `j` ^{th}
year on standard deviation of measurement error |

`bErrorGroup[i]` |
Effect of capture group on standard deviation of measurement error |

`bErrorIntercept` |
Intercept of standard deviation of measurement error |

`bK` |
Von Bertalanffy growth coefficient |

`bLinf` |
Mean maximum length |

`bTrueInitialLength[i]` |
Estimated true initial length of the `i` ^{th} fish |

`eGrowth[i]` |
Expected growth between initial capture and the `i` ^{th}
recapture |

`eObsInit[i]` |
Expected standard deviation of measurement error for the
`i` ^{th} fish’s initial capture |

`eObsRecap[i]` |
Expected standard deviation of measurement error for the
`i` ^{th} recapture |

`eTrueFinalLength[i]` |
Estimated true recapture length of the `i` ^{th} recapture |

`fish_id[i]` |
Unique identifier for the `i` ^{th} recaptured fish |

`group[i]` |
Group of capture for the `i` ^{th} recapture |

`initial_annual[i]` |
Year of initial capture for the `i` ^{th} fish |

`initial_group[i]` |
Group of initial capture for the `i` ^{th} fish |

`obs_initial_length[i]` |
Reported fork length for the initial capture of the
`i` ^{th} fish |

`recapture_length[i]` |
Reported fork length for the `i` ^{th} recapture |

`sErrorGroupAnnual` |
Standard deviation of the random effect of
`bErrorGroupAnnual` |

`years[i]` |
Years between initial capture and recapture of `i` ^{th}
recapture |

Table 2. Model coefficients.

term | estimate | lower | upper | svalue |
---|---|---|---|---|

bErrorAnnual[2] | -0.0174 | -1.280 | 1.420 | 0.0331 |

bErrorAnnual[3] | 0.6110 | -0.742 | 2.360 | 1.8200 |

bErrorGroup[2] | 0.2760 | -0.743 | 1.460 | 0.9800 |

bErrorIntercept | 2.5200 | 1.250 | 3.440 | 7.0900 |

bK | 0.4370 | 0.290 | 0.694 | 10.6000 |

bLinf | 382.0000 | 354.000 | 409.000 | 10.6000 |

sErrorGroupAnnual | 0.5780 | 0.217 | 1.690 | 10.6000 |

Table 3. Model convergence.

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

216 | 7 | 3 | 500 | 150 | 298 | 1.012 | TRUE |

Table 4. Model posterior predictive checks.

moment | observed | median | lower | upper | svalue |
---|---|---|---|---|---|

zeros | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |

mean | -0.0256180 | -0.0017869 | -0.1354568 | 0.1283499 | 0.4896621 |

variance | 0.6106158 | 0.9953261 | 0.8154167 | 1.1949778 | 10.5517083 |

skewness | 0.1529792 | -0.0014757 | -0.3136194 | 0.3158953 | 1.5715687 |

kurtosis | 1.5929545 | -0.0819613 | -0.5248574 | 0.7188016 | 8.9667458 |

Table 5. Model sensitivity.

all | analysis | sensitivity | bound |
---|---|---|---|

all | 1.012 | 1.007 | 1.029 |

#### Capture Efficiency

Table 6. Parameter descriptions.

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

`annual[i]` |
Year of the `i` ^{th} capture |

`bEfficiencyAnnual` |
Effect of `annual[i]` on `logit(eEfficiency)` |

`bEfficiencyEffort` |
The effect of `effort[i]` on `logit(eEfficiency)` |

`bEfficiencyLength2` |
Effect of `length[i]^2` on `logit(eEfficiency)` |

`bEfficiencyLength` |
Effect of `length[i]` on `logit(eEfficiency)` |

`eEfficiency[i]` |
Expected recapture probability for the `i` ^{th} capture |

`effort[i]` |
Electrofishing effort (seconds per metre) during the
visit of the `i` ^{th} capture |

`length[i]` |
Standardized fork length (mm) of the `i` ^{th} capture |

`recapture[i]` |
Binary variable describing whether the `i` ^{th} capture
was a recapture |

Table 7. Model coefficients.

term | estimate | lower | upper | svalue |
---|---|---|---|---|

bEfficiencyAnnual[1] | -12.100 | -27.300 | -5.82000 | 10.60 |

bEfficiencyAnnual[2] | -3.900 | -4.560 | -3.33000 | 10.60 |

bEfficiencyAnnual[3] | -3.590 | -4.100 | -3.16000 | 10.60 |

bEfficiencyEffort | 0.427 | -0.459 | 1.42000 | 1.65 |

bEfficiencyLength | 1.010 | 0.575 | 1.51000 | 10.60 |

bEfficiencyLength2 | -0.361 | -0.850 | -0.00328 | 4.36 |

Table 8. Model convergence.

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

2267 | 6 | 3 | 500 | 2 | 380 | 1.011 | TRUE |

Table 9. Model posterior predictive checks.

moment | observed | median | lower | upper | svalue |
---|---|---|---|---|---|

zeros | 0.9770622 | 0.9770622 | 0.9677989 | 0.9850022 | 0.0057785 |

mean | -0.1190194 | -0.1215632 | -0.1424338 | -0.0993102 | 0.3073444 |

variance | 0.1866252 | 0.1844339 | 0.1266217 | 0.2484169 | 0.0709181 |

skewness | 5.8514346 | 5.8542216 | 4.8672975 | 7.2441536 | 0.0115802 |

kurtosis | 34.7229487 | 35.1168267 | 23.4680286 | 54.6511747 | 0.0528591 |

Table 10. Model sensitivity.

all | analysis | sensitivity | bound |
---|---|---|---|

all | 1.011 | 1.006 | 1.1 |

#### Movement

Table 11. Parameter descriptions.

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

`bFidelity` |
Intercept for `eFidelity` |

`bLength` |
Effect of `fork_length[i]` on `bFidelity` |

`eFidelity[i]` |
Expected value of `fidelity[i]` |

`fidelity[i]` |
Whether or not the `i` ^{th} recapture was encountered at the
same site as the previous encounter |

`fork_length[i]` |
Predicted true underlying fork length of the `i` ^{th}
recapture from the growth model |

Table 12. Model coefficients.

term | estimate | lower | upper | svalue |
---|---|---|---|---|

bFidelity | 0.778000 | -2.21000 | 3.65000 | 0.689 |

bLength | -0.000907 | -0.00954 | 0.00797 | 0.254 |

Table 13. Model convergence.

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

52 | 2 | 3 | 500 | 50 | 770 | 1.004 | TRUE |

Table 14. Model posterior predictive checks.

moment | observed | median | lower | upper | svalue |
---|---|---|---|---|---|

zeros | 0.3846154 | 0.3846154 | 0.2115385 | 0.5769231 | 0.0769883 |

mean | 0.0804083 | 0.0642667 | -0.2635046 | 0.3849839 | 0.1518963 |

variance | 1.3485795 | 1.3433405 | 0.9732261 | 1.4413432 | 0.0449048 |

skewness | -0.4740519 | -0.4683442 | -1.4088217 | 0.3113575 | 0.1035920 |

kurtosis | -1.7742710 | -1.7715779 | -1.9937830 | -0.0034133 | 0.0648732 |

Table 15. Model sensitivity.

all | analysis | sensitivity | bound |
---|---|---|---|

all | 1.004 | 1.005 | 1.037 |

#### Annual Abundance

Table 16. Parameter descriptions.

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

`annual[i]` |
Year of the `i` ^{th} survey visit |

`bAbundanceLarge[i]` |
Expected abundance of 300+ mm fish during `i` ^{th} site
visit |

`bAbundanceSmall[i]` |
Expected abundance of 200-299 mm fish during `i` ^{th}
site visit |

`bDensityLargeAnnualSiteID[i, j]` |
Effect of the `i` ^{th} year and the `j` ^{th} site on
`log(eDensityLarge)` |

`bDensityLargeAnnual[i]` |
Effect of `i` ^{th} year on `log(eDensityLarge)` |

`bDensitySmallAnnualSiteID[i, j]` |
Effect of the `i` ^{th} year and the `j` ^{th} site on
`log(eDensitySmall)` |

`bDensitySmallAnnual[i]` |
Effect of `i` ^{th} year on `log(eDensitySmall)` |

`bEfficiencyLargeAnnual[i]` |
Effect of `i` ^{th} year on `logit(eProbLarge)` |

`bEfficiencySecondsPerMetre` |
Effect of electrofishing seconds per metre travelled
on `logit(eProbSmall)` and `logit(eProbLarge)` |

`bEfficiencySmallAnnual[i]` |
Effect of `i` ^{th} year on `logit(eProbSmall)` |

`bFidelity` |
Probability that intra-annual recaptures were caught at the same site versus a different one |

`bThetaLarge` |
Variation in the random effect of site visit on
`eEfficiencyLarge` |

`bThetaSmall` |
Variation in the random effect of site visit on
`eEfficiencySmall` |

`count_large[i]` |
The number of 300+ mm fish captured during the `i` ^{th}
site visit |

`count_small[i]` |
The number of 200-299 mm fish captured during the
`i` ^{th} site visit |

`eDensityLarge[i]` |
Expected 300+ mm fish density during the `i` ^{th} site
visit |

`eDensitySmall[i]` |
Expected 200-299 mm fish density during the `i` ^{th}
site visit |

`eEfficiencyLarge[i]` |
Expected capture efficiency for 300+ mm fish during
the `i` ^{th} site visit, including additional visit
variation |

`eEfficiencySmall[i]` |
Expected capture efficiency for 200-299 mm fish during
the `i` ^{th} site visit, including additional visit
variation |

`eProbLarge[i]` |
Expected capture efficiency for 300 + mm fish |

`eProbSmall[i]` |
Expected capture efficiency for 200-299 mm fish |

`marked_large[i]` |
Number of 300+ mm fish marked prior to the `i` ^{th}
site visit |

`marked_small[i]` |
Number of 200-299 mm fish marked prior to the `i` ^{th}
site visit |

`recaptures_large[i]` |
Number of marked 300+ mm fish observed during the
`i` ^{th} site visit |

`recaptures_small[i]` |
Number of marked 200-299 mm fish observed during the
`i` ^{th} site visit |

`sDensityLargeAnnualSiteID` |
Standard deviation of the random effect of
`bDensityLargeAnnualSiteID` |

`sDensitySmallAnnualSiteID` |
Standard deviation of the random effect of
`bDensitySmallAnnualSiteID` |

`seconds_per_metre[i]` |
Number of electrofishing seconds per metre on the
`i` ^{th} site visit |

`site_id[i]` |
Site of the `i` ^{th} survey visit |

`site_length[i]` |
Length of the site visited for the `i` ^{th} site visit |

`survey_proportion[i]` |
Proportion of site surveyed during the `i` ^{th} site
visit |

Table 17. Model coefficients.

term | estimate | lower | upper | svalue |
---|---|---|---|---|

bDensityLargeAnnual[1] | 4.55000 | 3.91000 | 5.2800 | 10.6 |

bDensityLargeAnnual[2] | 3.99000 | 3.58000 | 4.3900 | 10.6 |

bDensityLargeAnnual[3] | 4.46000 | 4.01000 | 4.9000 | 10.6 |

bDensitySmallAnnual[1] | 4.81000 | 3.49000 | 6.1300 | 10.6 |

bDensitySmallAnnual[2] | 5.16000 | 4.51000 | 5.7800 | 10.6 |

bDensitySmallAnnual[3] | 5.47000 | 4.81000 | 6.1000 | 10.6 |

bEfficiencyLargeAnnual[1] | -4.19000 | -4.88000 | -3.5800 | 10.6 |

bEfficiencyLargeAnnual[2] | -3.18000 | -3.60000 | -2.7700 | 10.6 |

bEfficiencyLargeAnnual[3] | -3.83000 | -4.32000 | -3.3500 | 10.6 |

bEfficiencySecondsPerMetre | 0.33300 | 0.23700 | 0.4340 | 10.6 |

bEfficiencySmallAnnual[1] | -5.64000 | -6.68000 | -4.5300 | 10.6 |

bEfficiencySmallAnnual[2] | -4.67000 | -5.30000 | -4.0300 | 10.6 |

bEfficiencySmallAnnual[3] | -4.75000 | -5.37000 | -4.1600 | 10.6 |

bFidelity | 0.59100 | 0.45900 | 0.7310 | 10.6 |

bThetaLarge | 0.02100 | 0.01260 | 0.0345 | 10.6 |

bThetaSmall | 0.00873 | 0.00458 | 0.0163 | 10.6 |

sDensityLargeAnnualSiteID | 0.08550 | 0.00348 | 0.2790 | 10.6 |

sDensitySmallAnnualSiteID | 0.32200 | 0.09190 | 0.5610 | 10.6 |

Table 18. Model convergence.

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

120 | 18 | 3 | 500 | 4000 | 219 | 1.007 | TRUE |

Table 19. Model posterior predictive checks.

moment | observed | median | lower | upper | svalue |
---|---|---|---|---|---|

zeros | 0.1166667 | 0.0666667 | 0.0166667 | 0.1250000 | 3.7062182 |

mean | -0.8909700 | -0.8335360 | -0.9486094 | -0.7205455 | 1.4937165 |

variance | 0.3764958 | 0.4056427 | 0.2994116 | 0.5294532 | 0.7109303 |

skewness | -0.8745223 | -0.8920879 | -1.3344141 | -0.5199066 | 0.1035920 |

kurtosis | 0.0051542 | 0.1724347 | -0.7801863 | 1.9973080 | 0.3144983 |

Table 20. Model sensitivity.

all | analysis | sensitivity | bound |
---|---|---|---|

all | 1.007 | 1.027 | 1.018 |

Table 21. The estimated abundance in zones 2 to 6 of the Elk River, by year and size class (with 95% CIs).

annual | size class | estimate | lower | upper |
---|---|---|---|---|

2021 | Large | 8309.180 | 4427.252 | 17297.009 |

2022 | Large | 4747.317 | 3192.296 | 7011.152 |

2023 | Large | 7584.234 | 4861.441 | 11663.058 |

2021 | Small | 11280.741 | 3187.544 | 40969.043 |

2022 | Small | 15967.947 | 8678.823 | 29435.537 |

2023 | Small | 21695.348 | 12170.150 | 40448.027 |

### Figures

#### Maps

#### Size

#### Captures

#### Growth

#### Capture Efficiency

#### Movement

#### Annual Abundance

#### Outing

#### Codes

## Acknowledgements

The organizations and individuals whose contributions have made this analytic appendix possible include:

- Nupqu Limited Partnership
- Mark Fjeld
- Dominique Nicholas
- Rebecca Kuzek
- Rafael Acosta

- Teck Coal Ltd.
- Bronwen Lewis
- Jessy Dubnyk
- Dorian Turner

- BC Government
- Matt Neufeld
- Will Warnock

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