# Lower Columbia River Fish Population Indexing Analysis 2018

The suggested citation for this analytic report is:

*Thorley, J.L. and Dalgarno, S. (2019) Lower Columbia River Fish
Population Indexing Analysis 2018. A Poisson Consulting Analysis
Appendix. URL: https://www.poissonconsulting.ca/f/1169613097.*

## Background

In the mid 1990s BC Hydro began operating Hugh L. Keenleyside (HLK) Dam to reduce dewatering of Mountain Whitefish and Rainbow Trout eggs.

The primary goal of the Lower Columbia River Fish Population Indexing program is to answer two key management questions:

What are the abundance, growth rate, survival rate, body condition, age distribution, and spatial distribution of subadult and adult Whitefish, Rainbow Trout, and Walleye in the Lower Columbia River?

What is the effect of inter-annual variability in the Whitefish and Rainbow Trout flow regimes on the abundance, growth rate, survival rate, body condition, and spatial distribution of subadult and adult Whitefish, Rainbow Trout, and Walleye in the Lower Columbia River?

The inter-annual variability in the Whitefish and Rainbow Trout flow regimes was quantified in terms of the percent egg dewatering as greater flow variability is associated with more egg stranding.

## Methods

### Data Preparation

The fish indexing data were provided by Okanagan Nation Alliance and Golder Associates in the form of an Access database. The discharge and temperature data were obtained from the Columbia Basin Hydrological Database maintained by Poisson Consulting. The Rainbow Trout egg dewatering estimates were provided by CLBMON-46 (Irvine, Baxter, and Thorley 2015) and the Mountain Whitefish egg stranding estimates by Golder Associates (2013).

#### Discharge

Missing hourly discharge values for Hugh-Keenleyside Dam (HLK), Brilliant Dam (BRD) and Birchbank (BIR) were estimated by first leading the BIR values by 2 hours to account for the lag. Values missing at just one of the dams were then estimated assuming \(HLK + BRD = BIR\). Negative values were set to be zero. Next, missing values spanning \(\leq\) 28 days were estimated at HLK and BRD based on linear interpolation. Finally any remaining missing values at BIR were set to be \(HLK + BRD\).

The data were prepared for analysis using R version 3.6.1 (R Core Team 2018).

### Data Analysis

Model parameters were estimated using hierarchical Bayesian methods. The parameters were produced using JAGS (Plummer 2015) and STAN (Carpenter et al. 2017). For additional information on Bayesian estimation the reader is referred to McElreath (2016).

The one exception is the length-at-age estimates which were produced using the mixdist R package (Macdonald 2012) which implements Maximum Likelihood with Expectation Maximization.

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 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). For ML models, the point estimate is the MLE, the standard
deviation is the standard error, the z-score is
\(\mathrm{MLE}/\mathrm{sd}\) and the 95% CLs are the
\(\mathrm{MLE} \pm 1.96 \cdot \mathrm{sd}\). For Bayesian models, the
estimate is the median (50th percentile) of the MCMC samples, the
z-score is \(\mathrm{mean}/\mathrm{sd}\) 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.

Where relevant, model adequacy was confirmed by examination of residual plots for the full model(s).

The results are displayed graphically by plotting the modeled
relationships between particular variables and the response(s) 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). 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% confidence/credible
intervals (CIs, Bradford, Korman, and Higgins 2005).

The analyses were implemented using R version 3.6.1
(R Core Team 2018) and the
`mbr`

family of packages.

### 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 expected weight is allowed to vary with length and date.
- The expected weight is allowed to vary randomly with year.
- The relationship between weight and length is allowed to vary with date.
- The relationship between weight and length is allowed to vary randomly with year.
- The residual variation in weight is log-normally distributed.

Only previously untagged fish were included in models to avoid potential effects of tagging on body condition. Preliminary analyses indicated that the annual variation in weight was not correlated with the annual variation in the relationship between weight and length.

#### Growth

Annual growth of fish were estimated from the inter-annual 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.

Key assumptions of the growth model include:

- The mean maximum length \(L_{\infty}\) is constant.
- The growth coefficient \(k\) is allowed to vary randomly with year.
- The residual variation in growth is normally distributed.

#### Movement

The extent to which sites are closed, i.e., fish remain at the same site between sessions, was evaluated with a logistic ANCOVA (Kery 2010). 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 expected site fidelity is allowed to vary with fish length.
- Observed site fidelity is Bernoulli distributed.

Length as a second-order polynomial was not found to be a significant predictor for site fidelity.

#### Length-At-Age

The expected length-at-age of Mountain Whitefish and Rainbow Trout were estimated from annual length-frequency distributions using a finite mixture distribution model (Macdonald and Pitcher 1979)

There were assumed to be three distinguishable normally-distributed age-classes for Mountain Whitefish (Age-0, Age-1, Age-2 and Age-3+) two for Rainbow Trout (Age-0, Age-1, Age-2+). Initially the model was fitted to the data from all years combined. The model was then fitted to the data for each year separately with the initial values set to be the estimates from the combined values. The only constraints were that the standard deviations of the MW age-classes were identical in the combined analysis and fixed at the initial values in the individual years.

Rainbow Trout and Mountain Whitefish were categorized as Fry (Age-0), Juvenile (Age-1) and Adult (Age-2+) based on their length-based ages. All Walleye were considered to be Adults.

#### Survival

The annual adult survival rate was estimated by fitting a Cormack-Jolly-Seber model (Kery and Schaub 2011, 220–31) to inter-annual recaptures of adults.

Key assumptions of the survival model include:

- Survival varies randomly with year.
- The encounter probability for adults is allowed to vary with the total bank length sampled.

#### Observer Length Correction

The annual bias (inaccuracy) and error (imprecision) in observer’s fish length estimates were quantified from the divergence of the length distribution of their observed fish from the length distribution of the measured fish. More specifically, the length correction that minimised the Jensen-Shannon divergence (Lin 1991) between the two distributions provided a measure of the inaccuracy while the minimum divergence (the Jensen-Shannon divergence was calculated with log to base 2 which means it lies between 0 and 1) provided a measure of the imprecision.

#### Capture Efficiency

The probability of capture was estimated using a recapture-based binomial model (Kery and Schaub 2011, 134–36, 384–88).

Key assumptions of the capture efficiency model include:

- The capture probability varies randomly by session within year.
- The probability of a marked fish remaining at a site is the estimated site fidelity.
- The number of recaptures is described by a binomial distribution.

#### Abundance

The abundance was estimated from the catch and bias-corrected observer count data using an overdispersed Poisson model (Kery and Schaub 2011, 55–56).

Key assumptions of the abundance model include:

- The capture efficiency is the point estimate from the capture efficiency model.
- The efficiency varies by visit type (catch or count).
- The lineal fish density varies randomly with site, year and site within year.
- The overdispersion varies by visit type (count or catch).
- The catches and counts are described by a gamma-Poisson distribution.

#### Stock-Recruitment

The relationship between the adults and the resultant number of age-1 subadults was estimated using a Beverton-Holt stock-recruitment model (Walters and Martell 2004):

\[ R = \frac{\alpha \cdot S}{1 + \beta \cdot S}\]

where \(S\) is the adults (stock), \(R\) is the subadults (recruits), \(\alpha\) is the recruits per spawner at low density (productivity) and \(\beta\) is the density-dependence.

Key assumptions of the stock-recruitment model include:

- The prior for \(\log(\alpha)\) is a truncated normal distribution from \(\log(1)\) to \(\log(5)\).
- The expected log number of recruits is affected by the egg loss.
- The residual variation in the number of recruits is log-normally distributed.

#### Age-Ratios

The proportion of Age-1 Mountain Whitefish \(r^1_t\) from a given spawn year \(t\) is calculated from the relative abundance of Age-1 & Age-2 fish \(N^1_t\) & \(N^2_t\) respectively, which were lead or lagged so that all values were with respect to the spawn year:

\[r^1_t = \frac{N^1_{t+2}}{N^1_{t+2} + N^2_{t+2}}\]

The relative abundances of Age-1 and Age-2 fish were taken from the proportions of each age-class in the length-at-age analysis.

As the number of Age-2 fish might be expected to be influenced by the percentage egg loss \(Q_t\) three years prior, the predictor variable \(\Pi_t\) used is:

\[\Pi_t = \textrm{log}(Q_t/Q_{t-1})\]

The ratio was logged to ensure it was symmetrical about zero (Tornqvist, Vartia, and Vartia 1985).

The relationship between \(r^1_t\) and \(\Pi_t\) was estimated using a Bayesian regression (Kery 2010) loss model.

Key assumptions of the final model include:

- The log odds of the proportion of Age-1 fish varies with the log of the ratio of the percent egg losses.
- The residual variation is normally distributed.

The relationship between percent dewatering and subsequent recruitment is expected to depend on stock abundance (Subbey et al. 2014) which might be changing over the course of the study. Consequently, preliminary analyses allowed the slope of the regression line to change by year. However, year was not a significant predictor and was therefore removed from the final model. The effect of dewatering on Mountain Whitefish abundance was expressed in terms of the predicted percent change in Age-1 Mountain Whitefish abundance by egg loss in the spawn year relative to 10% egg loss in the spawn year. The egg loss in the previous year was fixed at 10%. The percent change could not be calculated relative to 0% in the spawn or previous year as \(\Pi_t\) is undefined in either case.

### Model Templates

#### Condition

```
data {
int nYear;
int nObs;
vector[nObs] Length;
vector[nObs] Weight;
vector[nObs] Dayte;
int Year[nObs];
parameters {
real bWeight;
real bWeightLength;
real bWeightDayte;
real bWeightLengthDayte;
real sWeightYear;
real sWeightLengthYear;
vector[nYear] bWeightYear;
vector[nYear] bWeightLengthYear;
real sWeight;
model {
vector[nObs] eWeight;
bWeight ~ normal(5, 5);
bWeightLength ~ normal(3, 2);
bWeightDayte ~ normal(0, 2);
bWeightLengthDayte ~ normal(0, 2);
sWeightYear ~ normal(0, 2);
sWeightLengthYear ~ normal(0, 2);
for (i in 1:nYear) {
bWeightYear[i] ~ normal(0, exp(sWeightYear));
bWeightLengthYear[i] ~ normal(0, exp(sWeightLengthYear));
}
sWeight ~ normal(0, 5);
for(i in 1:nObs) {
eWeight[i] = bWeight + bWeightDayte * Dayte[i] + bWeightYear[Year[i]] + (bWeightLength + bWeightLengthDayte * Dayte[i] + bWeightLengthYear[Year[i]]) * Length[i];
Weight[i] ~ lognormal(eWeight[i], exp(sWeight));
}
..
```

Block 1.

#### Growth

```
.model {
bK ~ dnorm (0, 5^-2)
sKYear ~ dnorm(0, 5^-2)
for (i in 1:nYear) {
bKYear[i] ~ dnorm(0, exp(sKYear)^-2)
log(eK[i]) <- bK + bKYear[i]
}
bLinf ~ dunif(100, 1000)
sGrowth ~ dnorm(0, 5^-2)
for (i in 1:length(Year)) {
eGrowth[i] <- (bLinf - LengthAtRelease[i]) * (1 - exp(-sum(eK[Year[i]:(Year[i] + dYears[i] - 1)])))
Growth[i] ~ dnorm(max(eGrowth[i], 0), exp(sGrowth)^-2)
}
..
```

Block 2.

#### Movement

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

Block 3.

#### Survival

```
.model{
bEfficiency ~ dnorm(0, 5^-2)
bEfficiencySampledLength ~ dnorm(0, 5^-2)
bSurvival ~ dnorm(0, 5^-2)
sSurvivalYear ~ dnorm(0, 5^-2)
for(i in 1:nYear) {
bSurvivalYear[i] ~ dnorm(0, exp(sSurvivalYear)^-2)
}
for(i in 1:(nYear-1)) {
logit(eEfficiency[i]) <- bEfficiency + bEfficiencySampledLength * SampledLength[i]
logit(eSurvival[i]) <- bSurvival + bSurvivalYear[i]
eProbability[i,i] <- eSurvival[i] * eEfficiency[i]
for(j in (i+1):(nYear-1)) {
eProbability[i,j] <- prod(eSurvival[i:j]) * prod(1-eEfficiency[i:(j-1)]) * eEfficiency[j]
}
for(j in 1:(i-1)) {
eProbability[i,j] <- 0
}
}
for(i in 1:(nYear-1)) {
eProbability[i,nYear] <- 1 - sum(eProbability[i,1:(nYear-1)])
}
for(i in 1:(nYear - 1)) {
Marray[i, 1:nYear] ~ dmulti(eProbability[i,], Released[i])
}
..
```

Block 4.

#### Capture Efficiency

```
.model {
bEfficiency ~ dnorm(0, 5^-2)
sEfficiencySessionAnnual ~ dnorm(0, 2^-2)
for (i in 1:nSession) {
for (j in 1:nAnnual) {
bEfficiencySessionAnnual[i, j] ~ dnorm(0, exp(sEfficiencySessionAnnual)^-2)
}
}
for (i in 1:length(Recaptures)) {
logit(eEfficiency[i]) <- bEfficiency + bEfficiencySessionAnnual[Session[i], Annual[i]]
eFidelity[i] ~ dnorm(Fidelity[i], FidelitySD[i]^-2) T(FidelityLower[i], FidelityUpper[i])
Recaptures[i] ~ dbin(eEfficiency[i] * eFidelity[i], Tagged[i])
}
..
```

Block 5.

#### Abundance

```
.model {
bDensity ~ dnorm(5, 5^-2)
sDensityAnnual ~ dnorm(0, 2^-2)
for (i in 1:nAnnual) {
bDensityAnnual[i] ~ dnorm(0, exp(sDensityAnnual)^-2)
}
sDensitySite ~ dnorm(0, 2^-2)
sDensitySiteAnnual ~ dnorm(0, 2^-2)
for (i in 1:nSite) {
bDensitySite[i] ~ dnorm(0, exp(sDensitySite)^-2)
for (j in 1:nAnnual) {
bDensitySiteAnnual[i, j] ~ dnorm(0, exp(sDensitySiteAnnual)^-2)
}
}
bEfficiencyVisitType[1] <- 0
for (i in 2:nVisitType) {
bEfficiencyVisitType[i] ~ dnorm(0, 2^-2)
}
sDispersion ~ dnorm(0, 2^-2)
sDispersionVisitType[1] <- 0
for(i in 2:nVisitType) {
sDispersionVisitType[i] ~ dnorm(0, 2^-2)
}
for (i in 1:length(Fish)) {
log(eDensity[i]) <- bDensity + bDensitySite[Site[i]] + bDensityAnnual[Annual[i]] + bDensitySiteAnnual[Site[i],Annual[i]]
eAbundance[i] <- eDensity[i] * SiteLength[i]
logit(eEfficiency[i]) <- logit(Efficiency[i]) + bEfficiencyVisitType[VisitType[i]]
log(esDispersion[i]) <- sDispersion + sDispersionVisitType[VisitType[i]]
eDispersion[i] ~ dgamma(esDispersion[i]^-2 + 0.1, esDispersion[i]^-2 + 0.1)
eFish[i] <- eAbundance[i] * ProportionSampled[i] * eEfficiency[i]
Fish[i] ~ dpois(eFish[i] * eDispersion[i])
}
..
```

Block 6.

#### Stock-Recruitment

```
.model {
bAlpha ~ dnorm(1, 2^-2) T(log(1), log(5))
bBeta ~ dnorm(-10, 5^-2)
bEggLoss ~ dnorm(0, 2^-2)
sRecruits ~ dnorm(0, 1^-2) T(0,)
for(i in 1:length(Stock)){
log(eAlpha[i]) <- bAlpha
log(eBeta[i]) <- bBeta
eLogRecruits[i] <- log((eAlpha[i] * Stock[i]) / (1 + eBeta[i] * Stock[i])) + bEggLoss * EggLoss[i]
Recruits[i] ~ dlnorm(eLogRecruits[i], sRecruits^-2)
}
..
```

Block 7.

#### Age-Ratios

```
.model{
bProbAge1 ~ dnorm(0, 2^-2)
bProbAge1Loss ~ dnorm(0, 2^-2)
sProbAge1 ~ dunif(0, 2)
for(i in 1:length(Age1Prop)){
eAge1Prop[i] <- bProbAge1 + bProbAge1Loss * LossLogRatio[i]
Age1Prop[i] ~ dnorm(eAge1Prop[i], sProbAge1^-2)
}
..
```

Block 8.

## Results

### Tables

#### Condition

Table 1. Parameter descriptions.

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

`bWeight` |
Intercept of `log(eWeight)` |

`bWeightDayte` |
Effect of `Dayte` on `bWeight` |

`bWeightLength` |
Intercept of effect of `Length` on `bWeight` |

`bWeightLengthDayte` |
Effect of `Dayte` on `bWeightLength` |

`bWeightLengthYear[i]` |
Effect of `i` ^{th} `Year` on `bWeightLength` |

`bWeightYear[i]` |
Effect of `i` ^{th} `Year` on `bWeight` |

`Dayte[i]` |
Standardised day of year `i` ^{th} fish was captured |

`eWeight[i]` |
Expected `Weight` of `i` ^{th} fish |

`Length[i]` |
Log-transformed and centered fork length of `i` ^{th} fish |

`sWeight` |
Log standard deviation of residual variation in `log(Weight)` |

`sWeightLengthYear` |
Log standard deviation of `bWeightLengthYear` |

`sWeightYear` |
Log standard deviation of `bWeightYear` |

`Weight[i]` |
Recorded weight of `i` ^{th} fish |

`Year[i]` |
Year `i` ^{th} fish was captured |

##### Mountain Whitefish

Table 2. Model coefficients.

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

bWeight | 5.4481708 | 0.0099010 | 550.217864 | 5.4277038 | 5.4674031 | 0.0007 |

bWeightDayte | -0.0176867 | 0.0018633 | -9.517441 | -0.0213734 | -0.0141445 | 0.0007 |

bWeightLength | 3.1579282 | 0.0233766 | 135.080079 | 3.1093590 | 3.2040653 | 0.0007 |

bWeightLengthDayte | -0.0122878 | 0.0050029 | -2.457204 | -0.0221361 | -0.0026500 | 0.0093 |

sWeight | -1.9095091 | 0.0060218 | -317.076006 | -1.9208347 | -1.8977600 | 0.0007 |

sWeightLengthYear | -2.2657732 | 0.1913599 | -11.805313 | -2.6206595 | -1.8801177 | 0.0007 |

sWeightYear | -3.1215164 | 0.1734585 | -17.942536 | -3.4339287 | -2.7488788 | 0.0007 |

Table 3. Model summary.

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

14178 | 7 | 3 | 500 | 2 | 393 | 1.011 | TRUE |

##### Rainbow Trout

Table 4. Model coefficients.

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

bWeight | 5.9948771 | 0.0062049 | 966.160917 | 5.9819110 | 6.0072682 | 7e-04 |

bWeightDayte | -0.0044249 | 0.0012834 | -3.475668 | -0.0069787 | -0.0019914 | 7e-04 |

bWeightLength | 2.9215460 | 0.0125398 | 232.960088 | 2.8962627 | 2.9453204 | 7e-04 |

bWeightLengthDayte | 0.0377059 | 0.0038700 | 9.744408 | 0.0301796 | 0.0451479 | 7e-04 |

sWeight | -2.2655650 | 0.0058125 | -389.785952 | -2.2774300 | -2.2545811 | 7e-04 |

sWeightLengthYear | -2.9060607 | 0.1892851 | -15.342687 | -3.2594914 | -2.5229922 | 7e-04 |

sWeightYear | -3.6317633 | 0.1684327 | -21.507633 | -3.9415447 | -3.2894396 | 7e-04 |

Table 5. Model summary.

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

14589 | 7 | 3 | 500 | 2 | 374 | 1.009 | TRUE |

##### Walleye

Table 6. Model coefficients.

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

bWeight | 6.2919286 | 0.0080132 | 785.139922 | 6.2739150 | 6.3064459 | 0.0007 |

bWeightDayte | 0.0161593 | 0.0014148 | 11.389367 | 0.0134151 | 0.0188725 | 0.0007 |

bWeightLength | 3.2304215 | 0.0191397 | 168.779806 | 3.1904598 | 3.2675943 | 0.0007 |

bWeightLengthDayte | -0.0107375 | 0.0083310 | -1.277545 | -0.0272052 | 0.0058224 | 0.1947 |

sWeight | -2.3681131 | 0.0073079 | -324.012600 | -2.3819666 | -2.3535583 | 0.0007 |

sWeightLengthYear | -2.5323101 | 0.1992700 | -12.680344 | -2.8975376 | -2.1164227 | 0.0007 |

sWeightYear | -3.3305458 | 0.1668623 | -19.908489 | -3.6302314 | -2.9748845 | 0.0007 |

Table 7. Model summary.

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

9205 | 7 | 3 | 500 | 2 | 393 | 1.014 | TRUE |

#### Growth

Table 8. Parameter descriptions.

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

`bK` |
Intercept of `log(eK)` |

`bKYear[i]` |
Effect of `i` ^{th} `Year` on `bK` |

`bLinf` |
Mean maximum length |

`dYears[i]` |
Years between release and recapture of `i` ^{th} recapture |

`eGrowth` |
Expected `Growth` between release and recapture |

`eK[i]` |
Expected von Bertalanffy growth coefficient from `i-1` ^{th} to `i` ^{th} year |

`Growth[i]` |
Observed growth between release and recapture of `i` ^{th} recapture |

`LengthAtRelease[i]` |
Length at previous release of `i` ^{th} recapture |

`sGrowth` |
Log standard deviation of residual variation in `Growth` |

`sKYear` |
Log standard deviation of `bKYear` |

`Year[i]` |
Release year of `i` ^{th} recapture |

##### Mountain Whitefish

Table 9. Model coefficients.

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

bK | -0.9259595 | 0.1086078 | -8.559326 | -1.149029 | -0.7297757 | 7e-04 |

bLinf | 392.6903086 | 3.2148232 | 122.202222 | 386.888094 | 399.3993119 | 7e-04 |

sGrowth | 2.4601904 | 0.0443263 | 55.511488 | 2.377194 | 2.5493541 | 7e-04 |

sKYear | -1.0848023 | 0.2570075 | -4.222173 | -1.557970 | -0.5837363 | 7e-04 |

Table 10. Model summary.

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

259 | 4 | 3 | 500 | 20 | 543 | 1.013 | TRUE |

##### Rainbow Trout

Table 11. Model coefficients.

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

bK | -0.1744708 | 0.0762919 | -2.306990 | -0.3307308 | -0.0225079 | 2e-02 |

bLinf | 487.0687845 | 2.7075093 | 179.890601 | 481.9086684 | 492.4080715 | 7e-04 |

sGrowth | 3.3811271 | 0.0206856 | 163.459867 | 3.3411191 | 3.4218987 | 7e-04 |

sKYear | -1.2416744 | 0.1924957 | -6.405807 | -1.5677043 | -0.8305064 | 7e-04 |

Table 12. Model summary.

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

1158 | 4 | 3 | 500 | 20 | 400 | 1.011 | TRUE |

##### Walleye

Table 13. Model coefficients.

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

bK | -2.539502 | 0.2502549 | -10.147884 | -3.001751 | -2.0618755 | 7e-04 |

bLinf | 754.315450 | 84.3008026 | 9.083864 | 628.631688 | 949.4953241 | 7e-04 |

sGrowth | 2.866226 | 0.0460119 | 62.295651 | 2.778109 | 2.9608715 | 7e-04 |

sKYear | -1.157805 | 0.2545813 | -4.530802 | -1.636968 | -0.6447953 | 7e-04 |

Table 14. Model summary.

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

263 | 4 | 3 | 500 | 40 | 222 | 1.006 | TRUE |

#### Movement

Table 15. Parameter descriptions.

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

`bFidelity` |
Intercept of `logit(eFidelity)` |

`bLength` |
Effect of length on `logit(eFidelity)` |

`eFidelity[i]` |
Expected site fidelity of `i` ^{th} recapture |

`Fidelity[i]` |
Whether the `i` ^{th} recapture was encountered at the same
site as the previous encounter |

`Length[i]` |
Length at previous encounter of `i` ^{th} recapture |

##### Mountain Whitefish

Table 16. Model coefficients.

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

bFidelity | -0.1552880 | 0.1792936 | -0.8567948 | -0.4959377 | 0.1981948 | 0.388 |

bLength | -0.1105809 | 0.1946158 | -0.5319073 | -0.4760564 | 0.2944789 | 0.592 |

Table 17. Model summary.

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

117 | 2 | 3 | 500 | 1 | 847 | 1.002 | TRUE |

##### Rainbow Trout

Table 18. Model coefficients.

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

bFidelity | 0.7654122 | 0.0796299 | 9.626364 | 0.6143531 | 0.9178480 | 7e-04 |

bLength | -0.3300007 | 0.0769163 | -4.272205 | -0.4739996 | -0.1766411 | 7e-04 |

Table 19. Model summary.

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

756 | 2 | 3 | 500 | 1 | 774 | 1.001 | TRUE |

##### Walleye

Table 20. Model coefficients.

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

bFidelity | 0.7258183 | 0.1486066 | 4.9023664 | 0.4342957 | 1.0092428 | 0.0007 |

bLength | -0.0188939 | 0.1390122 | -0.1504418 | -0.2987952 | 0.2483826 | 0.8800 |

Table 21. Model summary.

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

220 | 2 | 3 | 500 | 1 | 942 | 1.003 | TRUE |

#### Length-At-Age

##### Mountain Whitefish

Table 22. The estimated upper length cutoffs (mm) by age and year.

Year | Age0 | Age1 | Age2 |
---|---|---|---|

1990 | 163 | 275 | NA |

1991 | 144 | 226 | 296 |

2001 | 141 | 257 | 344 |

2002 | 163 | 260 | 343 |

2003 | 159 | 263 | 353 |

2004 | 158 | 249 | 342 |

2005 | 168 | 263 | 362 |

2006 | 175 | 284 | 357 |

2007 | 171 | 279 | 337 |

2008 | 170 | 248 | 341 |

2009 | 169 | 265 | 355 |

2010 | 177 | 272 | 353 |

2011 | 163 | 269 | 349 |

2012 | 162 | 268 | 347 |

2013 | 185 | 282 | 350 |

2014 | 178 | 283 | 362 |

2015 | 167 | 278 | 366 |

2016 | 165 | 283 | 352 |

2017 | 158 | 269 | 354 |

2018 | 177 | 262 | 346 |

##### Rainbow Trout

Table 23. The estimated upper length cutoffs (mm) by age and year.

Year | Age0 | Age1 |
---|---|---|

1990 | 155 | 358 |

1991 | 127 | 342 |

2001 | 133 | 324 |

2002 | 155 | 349 |

2003 | 161 | 342 |

2004 | 142 | 332 |

2005 | 164 | 346 |

2006 | 170 | 364 |

2007 | 166 | 375 |

2008 | 146 | 339 |

2009 | 147 | 338 |

2010 | 143 | 337 |

2011 | 156 | 343 |

2012 | 152 | 344 |

2013 | 169 | 354 |

2014 | 154 | 337 |

2015 | 167 | 334 |

2016 | 154 | 336 |

2017 | 133 | 316 |

2018 | 139 | 306 |

#### Survival

Table 24. Parameter descriptions.

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

`bEfficiency` |
Intercept for `logit(eEfficiency)` |

`bEfficiencySampledLength` |
Effect of `SampledLength` on `bEfficiency` |

`bSurvival` |
Intercept for `logit(eSurvival)` |

`bSurvivalYear[i]` |
Effect of `Year` on `bSurvival` |

`eEfficiency[i]` |
Expected recapture probability in `i` ^{th} year |

`eSurvival[i]` |
Expected survival probability from `i-1` ^{th} to `i` ^{th} year |

`SampledLength` |
Total standardised length of river sampled |

`sSurvivalYear` |
Log SD of `bSurvivalYear` |

##### Mountain Whitefish

Table 25. Model coefficients.

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

bEfficiency | -4.1804013 | 0.1042621 | -40.087541 | -4.3845229 | -3.9700036 | 0.0007 |

bEfficiencySampledLength | 0.3721012 | 0.1235324 | 3.044773 | 0.1361591 | 0.6260196 | 0.0027 |

bSurvival | 0.8463913 | 0.4231537 | 2.100816 | 0.1262261 | 1.8068358 | 0.0253 |

sSurvivalYear | 0.2442526 | 0.3452415 | 0.739245 | -0.4118839 | 0.9193125 | 0.4587 |

Table 26. Model summary.

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

17 | 4 | 3 | 500 | 100 | 1052 | 1.005 | TRUE |

##### Rainbow Trout

Table 27. Model coefficients.

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

bEfficiency | -2.5293162 | 0.0910345 | -27.7736502 | -2.7044300 | -2.3480069 | 0.0007 |

bEfficiencySampledLength | 0.0111727 | 0.0715640 | 0.1401614 | -0.1288650 | 0.1565815 | 0.8907 |

bSurvival | -0.4348034 | 0.1118249 | -3.8860616 | -0.6559384 | -0.2061208 | 0.0007 |

sSurvivalYear | -1.2570805 | 1.0270840 | -1.4226367 | -4.9922516 | -0.6119388 | 0.0007 |

Table 28. Model summary.

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

17 | 4 | 3 | 500 | 100 | 261 | 1.017 | TRUE |

##### Walleye

Table 29. Model coefficients.

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

bEfficiency | -3.3757879 | 0.1030395 | -32.8019436 | -3.5811971 | -3.1708020 | 0.0007 |

bEfficiencySampledLength | 0.0587105 | 0.0826296 | 0.7621854 | -0.0929374 | 0.2316543 | 0.4440 |

bSurvival | 0.0628850 | 0.1358752 | 0.5602158 | -0.1683843 | 0.3885211 | 0.5440 |

sSurvivalYear | -1.0997005 | 1.9896128 | -0.9160875 | -8.2747079 | -0.2785067 | 0.0040 |

Table 30. Model summary.

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

17 | 4 | 3 | 500 | 200 | 285 | 1.012 | TRUE |

#### Capture Efficiency

Table 31. Parameter descriptions.

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

`Annual[i]` |
Year of `i` ^{th} visit |

`bEfficiency` |
Intercept for `logit(eEfficiency)` |

`bEfficiencySessionAnnual` |
Effect of `Session` within `Annual` on
`logit(eEfficiency)` |

`eEfficiency[i]` |
Expected efficiency on `i` ^{th} visit |

`eFidelity[i]` |
Expected site fidelity on `i` ^{th} visit |

`Fidelity[i]` |
Mean site fidelity on `i` ^{th} visit |

`FidelitySD[i]` |
SD of site fidelity on `i` ^{th} visit |

`Recaptures[i]` |
Number of marked fish recaught during `i` ^{th} visit |

`sEfficiencySessionAnnual` |
Log SD of effect of `Session` within `Annual` on
`logit(eEfficiency)` |

`Session[i]` |
Session of `i` ^{th} visit |

`Tagged[i]` |
Number of marked fish tagged prior to `i` ^{th} visit |

##### Mountain Whitefish

###### Subadult

Table 32. Model coefficients.

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

bEfficiency | -4.9972025 | 0.2168087 | -23.144160 | -5.50063 | -4.6570936 | 0.0007 |

sEfficiencySessionAnnual | -0.9461967 | 1.1534489 | -1.110064 | -4.39114 | 0.0966403 | 0.0907 |

Table 33. Model summary.

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

1359 | 2 | 3 | 500 | 100 | 172 | 1.011 | TRUE |

###### Adult

Table 34. Model coefficients.

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

bEfficiency | -5.254932 | 0.1430929 | -36.755286 | -5.550742 | -4.9969882 | 7e-04 |

sEfficiencySessionAnnual | -2.049795 | 1.1473121 | -1.939951 | -5.029096 | -0.5983976 | 7e-04 |

Table 35. Model summary.

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

1545 | 2 | 3 | 500 | 200 | 356 | 1.01 | TRUE |

##### Rainbow Trout

###### Subadult

Table 36. Model coefficients.

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

bEfficiency | -3.3923810 | 0.0654085 | -51.880249 | -3.524317 | -3.2695877 | 7e-04 |

sEfficiencySessionAnnual | -0.9259046 | 0.1647731 | -5.624789 | -1.263903 | -0.6153031 | 7e-04 |

Table 37. Model summary.

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

1558 | 2 | 3 | 500 | 100 | 1214 | 1.005 | TRUE |

###### Adult

Table 38. Model coefficients.

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

bEfficiency | -4.019309 | 0.0710880 | -56.58399 | -4.162507 | -3.8854350 | 7e-04 |

sEfficiencySessionAnnual | -1.805271 | 0.8881719 | -2.28053 | -4.395410 | -0.9157114 | 7e-04 |

Table 39. Model summary.

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

1629 | 2 | 3 | 500 | 100 | 244 | 1.009 | TRUE |

##### Walleye

Table 40. Model coefficients.

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

bEfficiency | -4.5702137 | 0.1218943 | -37.523799 | -4.8186384 | -4.3526356 | 0.0007 |

sEfficiencySessionAnnual | -0.5577893 | 0.2079586 | -2.704928 | -0.9992889 | -0.1707303 | 0.0013 |

Table 41. Model summary.

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

1673 | 2 | 3 | 500 | 100 | 1191 | 1.004 | TRUE |

#### Abundance

Table 42. Parameter descriptions.

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

`Annual` |
Year |

`bDensity` |
Intercept for `log(eDensity)` |

`bDensityAnnual` |
Effect of `Annual` on `bDensity` |

`bDensitySite` |
Effect of `Site` on `bDensity` |

`bDensitySiteAnnual` |
Effect of `Site` within `Annual` on `bDensity` |

`bEfficiencyVisitType` |
Effect of `VisitType` on `Efficiency` |

`eDensity` |
Expected density |

`Efficiency` |
Capture efficiency |

`esDispersion` |
Overdispersion of `Fish` |

`Fish` |
Number of fish captured or counted |

`ProportionSampled` |
Proportion of site surveyed |

`sDensityAnnual` |
Log SD of effect of `Annual` on `bDensity` |

`sDensitySite` |
Log SD of effect of `Site` on `bDensity` |

`sDensitySiteAnnual` |
Log SD of effect of `Site` within `Annual` on `bDensity` |

`sDispersion` |
Intercept for `log(esDispersion)` |

`sDispersionVisitType` |
Effect of `VisitType` on `sDispersion` |

`Site` |
Site |

`SiteLength` |
Length of site |

`VisitType` |
Survey type (catch versus count) |

##### Mountain Whitefish

###### Subadult

Table 43. Model coefficients.

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

bDensity | 5.4406580 | 0.1874181 | 29.013274 | 5.0405099 | 5.7930340 | 0.0007 |

bEfficiencyVisitType[2] | 1.4556995 | 0.0806910 | 18.040699 | 1.2955386 | 1.6214112 | 0.0007 |

sDensityAnnual | -0.3775397 | 0.1736743 | -2.125087 | -0.6879389 | -0.0297508 | 0.0387 |

sDensitySite | -0.2804839 | 0.1087247 | -2.544630 | -0.4863189 | -0.0637620 | 0.0120 |

sDensitySiteAnnual | -0.8244691 | 0.0611086 | -13.458192 | -0.9419095 | -0.7030915 | 0.0007 |

sDispersion | -0.7661634 | 0.0449215 | -17.069776 | -0.8547301 | -0.6842493 | 0.0007 |

sDispersionVisitType[2] | 0.6067664 | 0.0927844 | 6.551051 | 0.4258833 | 0.7808791 | 0.0007 |

Table 44. Model summary.

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

2551 | 7 | 3 | 500 | 200 | 242 | 1.009 | TRUE |

###### Adult

Table 45. Model coefficients.

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

bDensity | 6.3926287 | 0.1626779 | 39.271714 | 6.0770985 | 6.7111804 | 0.0007 |

bEfficiencyVisitType[2] | 1.7286939 | 0.0804946 | 21.492578 | 1.5693144 | 1.8887179 | 0.0007 |

sDensityAnnual | -1.0772117 | 0.1991107 | -5.379547 | -1.4486766 | -0.6795237 | 0.0007 |

sDensitySite | 0.1034875 | 0.0951208 | 1.059008 | -0.0796085 | 0.2881605 | 0.2853 |

sDensitySiteAnnual | -0.9089343 | 0.0653335 | -13.926549 | -1.0397152 | -0.7879970 | 0.0007 |

sDispersion | -0.6528188 | 0.0346453 | -18.859430 | -0.7171653 | -0.5855589 | 0.0007 |

sDispersionVisitType[2] | 0.4805907 | 0.0803911 | 5.973736 | 0.3199828 | 0.6406288 | 0.0007 |

Table 46. Model summary.

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

2551 | 7 | 3 | 500 | 200 | 285 | 1.008 | TRUE |

##### Rainbow Trout

###### Subadult

Table 47. Model coefficients.

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

bDensity | 4.8366559 | 0.1161441 | 41.651809 | 4.6119463 | 5.0539153 | 7e-04 |

bEfficiencyVisitType[2] | 1.4215737 | 0.0776402 | 18.346412 | 1.2804333 | 1.5847675 | 7e-04 |

sDensityAnnual | -1.1758941 | 0.2012193 | -5.774457 | -1.5226979 | -0.7263475 | 7e-04 |

sDensitySite | -0.3802453 | 0.0972301 | -3.875574 | -0.5617739 | -0.1774587 | 7e-04 |

sDensitySiteAnnual | -0.8930931 | 0.0557025 | -16.052414 | -1.0040788 | -0.7882411 | 7e-04 |

sDispersion | -0.9650807 | 0.0398708 | -24.228399 | -1.0473340 | -0.8914979 | 7e-04 |

sDispersionVisitType[2] | 0.6569666 | 0.0897573 | 7.266721 | 0.4830828 | 0.8315600 | 7e-04 |

Table 48. Model summary.

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

2551 | 7 | 3 | 500 | 200 | 494 | 1.008 | TRUE |

###### Adult

Table 49. Model coefficients.

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

bDensity | 5.4942462 | 0.1140338 | 48.164683 | 5.2728280 | 5.7120537 | 7e-04 |

bEfficiencyVisitType[2] | 1.2869357 | 0.0602682 | 21.380955 | 1.1664900 | 1.4055163 | 7e-04 |

sDensityAnnual | -1.0927513 | 0.1848807 | -5.862344 | -1.4319721 | -0.7008315 | 7e-04 |

sDensitySite | -0.4651834 | 0.0931610 | -4.958562 | -0.6378218 | -0.2822007 | 7e-04 |

sDensitySiteAnnual | -1.2089195 | 0.0693396 | -17.453081 | -1.3503149 | -1.0796723 | 7e-04 |

sDispersion | -1.0166974 | 0.0437112 | -23.290154 | -1.1051124 | -0.9356607 | 7e-04 |

sDispersionVisitType[2] | 0.5491976 | 0.0927775 | 5.949737 | 0.3708907 | 0.7335595 | 7e-04 |

Table 50. Model summary.

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

2551 | 7 | 3 | 500 | 200 | 538 | 1.006 | TRUE |

##### Walleye

Table 51. Model coefficients.

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

bDensity | 5.4321978 | 0.1158070 | 46.940936 | 5.2043312 | 5.6606843 | 7e-04 |

bEfficiencyVisitType[2] | 1.1735932 | 0.0756155 | 15.543691 | 1.0203961 | 1.3285330 | 7e-04 |

sDensityAnnual | -0.8466866 | 0.1806938 | -4.642299 | -1.1679495 | -0.4744504 | 7e-04 |

sDensitySite | -1.0459901 | 0.1388762 | -7.514605 | -1.3137513 | -0.7765578 | 7e-04 |

sDensitySiteAnnual | -1.3244656 | 0.0846409 | -15.702992 | -1.5117795 | -1.1702710 | 7e-04 |

sDispersion | -0.8224011 | 0.0390031 | -21.050567 | -0.8956316 | -0.7446447 | 7e-04 |

sDispersionVisitType[2] | 0.5073740 | 0.0931255 | 5.432866 | 0.3154596 | 0.6789489 | 7e-04 |

Table 52. Model summary.

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

2551 | 7 | 3 | 500 | 200 | 682 | 1.008 | TRUE |

#### Stock-Recruitment

Table 53. Parameter descriptions.

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

`bAlpha` |
Intercept for `log(eAlpha)` |

`bBeta` |
Intercept for `log(eBeta)` |

`bEggLoss` |
Effect of `EggLoss` on `bBeta` |

`eAlpha` |
`eRecruits` per `Stock` at low `Stock` density |

`eBeta` |
Expected density-dependence |

`EggLoss` |
Calculated proportional egg loss |

`eRecruits` |
Expected `Recruits` |

`Recruits` |
Number of Age-1 recruits |

`sRecruits` |
Log SD of residual variation in `Recruits` |

`Stock` |
Number of Age-2+ spawners |

##### Mountain Whitefish

Table 54. Model coefficients.

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

bAlpha | 0.9003438 | 0.4528069 | 1.9298312 | 0.0575934 | 1.5750652 | 0.0007 |

bBeta | -9.6517720 | 0.5478618 | -17.7067921 | -10.7832662 | -8.8115021 | 0.0007 |

bEggLoss | -0.1312203 | 0.1693046 | -0.7867717 | -0.4716888 | 0.2092525 | 0.4187 |

sRecruits | 0.6146288 | 0.1334134 | 4.7609870 | 0.4290761 | 0.9387169 | 0.0007 |

Table 55. Model summary.

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

16 | 4 | 3 | 500 | 50 | 1262 | 1.002 | TRUE |

##### Rainbow Trout

Table 56. Model coefficients.

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

bAlpha | 1.0563379 | 0.3949465 | 2.567620 | 0.1819702 | 1.5837393 | 0.0007 |

bBeta | -9.1223234 | 0.5321613 | -17.294711 | -10.4142573 | -8.4729122 | 0.0007 |

bEggLoss | 0.1661576 | 0.0742890 | 2.248995 | 0.0252849 | 0.3241453 | 0.0280 |

sRecruits | 0.2746352 | 0.0594218 | 4.793799 | 0.1976847 | 0.4334546 | 0.0007 |

Table 57. Model summary.

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

17 | 4 | 3 | 500 | 50 | 532 | 1.006 | TRUE |

#### Age-Ratios

Table 58. Parameter descriptions.

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

`Age1[i]` |
The number of Age-1 fish in the `i` ^{th} year |

`Age1and2[i]` |
The number of Age-1 and Age-2 fish in the `i` ^{th} year |

`bProbAge1` |
Intercept for `logit(eProbAge1)` |

`bProbAge1Loss` |
Effect of `LossLogRatio` on `bProbAge1` |

`eProbAge1[i]` |
The expected proportion of Age-1 fish in the `i` ^{th} year |

`LossLogRatio[i]` |
The `log` of the ratio of the percent egg losses |

`sDispersion` |
SD of extra-binomial variation |

Table 59. Model coefficients.

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

bProbAge1 | 0.2409373 | 0.2021096 | 1.155502 | -0.1779642 | 0.6160426 | 0.2400 |

bProbAge1Loss | -0.3070399 | 0.2870403 | -1.052766 | -0.8735155 | 0.2271430 | 0.2920 |

sProbAge1 | 0.8203105 | 0.1706548 | 4.943255 | 0.5839656 | 1.2571520 | 0.0007 |

Table 60. Model summary.

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

18 | 3 | 3 | 500 | 1 | 668 | 1.006 | TRUE |

### Figures

#### Condition

##### Subadult

###### Mountain Whitefish

###### Rainbow Trout

##### Adult

###### Mountain Whitefish

###### Rainbow Trout

###### Walleye

#### Growth

##### Mountain Whitefish

##### Rainbow Trout

##### Walleye

#### Movement

#### Length-At-Age

##### Mountain Whitefish

##### Rainbow Trout

#### Survival

##### Adult

###### Mountain Whitefish

###### Rainbow Trout

###### Walleye

#### Observer Length Correction

#### Capture Efficiency

##### Mountain Whitefish

###### Subadult

###### Adult

##### Rainbow Trout

###### Subadult

###### Adult

##### Walleye

#### Abundance

##### Mountain Whitefish

###### Subadult

###### Adult

##### Rainbow Trout

###### Subadult

###### Adult

##### Walleye

#### Stock-Recruitment

##### Mountain Whitefish

##### Rainbow Trout

#### Age-Ratios

## Acknowledgements

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

- BC Hydro
- Okanagan Nation Alliance
- Amy Duncan
- Bronwen Lewis
- Golder Associates
- Demitria Burgoon
- Dustin Ford
- David Roscoe
- Sima Usvyatsov
- Dana Schmidt
- Larry Hildebrand

## References

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Brooks, Steve, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng, eds. 2011. *Handbook for Markov Chain Monte Carlo*. Boca Raton: Taylor & Francis.

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Fabens, A J. 1965. “Properties and Fitting of the von Bertalanffy Growth Curve.” *Growth* 29 (3): 265–89.

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