Lower Columbia River Fish Population Indexing 2021

2022-07-05

The suggested citation for this analytic report is:

Thorley, J.L. & Hussein, N. (2022) Lower Columbia River Fish Population Indexing 2021. A Poisson Consulting Analysis Appendix. URL: https://www.poissonconsulting.ca/f/1314086833.

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 4.2.0 (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 (P. Macdonald 2012) which implements Maximum Likelihood with Expectation Maximization.

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).

The parameters are summarised in terms of the point estimate, lower and upper 95% credible limits (CLs) 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 can be considered a test of directionality. More specifically it indicates how surprising (in bits) it would be to discover that the true value of the parameter is in the opposite direction to the estimate. An s-value (Chow and Greenland 2019) is the Shannon transform (-log to base 2) of the corresponding p-value (Kery and Schaub 2011; Greenland and Poole 2013). A surprisal value of 4.3 bits, which is equivalent to a p-value of 0.05 indicates that the surprise would be equivalent to throwing 4.3 heads in a row. The condition that non-essential explanatory variables have s-values \(\geq\) 4.3 bits provides a useful model selection heuristic (Kery and Schaub 2011).

Model adequacy was assessed via posterior predictive checks (Kery and Schaub 2011). More specifically, the number of zeros and the first four central moments (mean, variance, skewness and kurtosis) for the deviance residuals were compared to the expected values by simulating new residuals. In this context the s-value indicates how surprising each metric is given the estimated posterior probability distribution for the residual variation.

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

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 or n-fold change in the response variable) with 95% credible intervals (CIs, Bradford, Korman, and Higgins 2005).

The analyses were implemented using R version 4.2.0 (R Core Team 2020) and the mbr family of packages.

Model Descriptions

Condition

The expected weight of fish of a given length were estimated from the data using an allometric mass-length model (He et al. 2008).

\[W = \alpha L^{\beta}\]

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.

The growth model was only fitted to Walleye with a fork length at release less than 450 mm.

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.

The estimated probability of being caught at the same site versus a different site was then converted into the site fidelity by assuming that those fish which were recaught at a different site represented just 32 % of those that left the site. The correction factor corresponds to the proportion of the river bank that belongs to index sites.

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 (P. D. M. 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.

Preliminary analysis indicated that only including visits to index sites did not substantially change the results.

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.

Preliminary analyses indicated that the direction of effect of the frequency of the electrofishing current (30, 60 or 120 Hz) was uncertain.

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 fish density varies randomly with site, year and site within year.
The change in fish density with overall abundance varies by site density.
The capture efficiency at a typical fish density is the point estimate for a typical session from the capture efficiency model.
The count efficiency varies from the capture efficiency.
The capture efficiency (but not the count efficiency) varies with density.
The overdispersion varies by visit type (count or catch).
The catches and counts are described by a gamma-Poisson distribution.

Distribution

The distribution was calculated in terms of the Shannon index of evenness in each year for each species and life-stage. The index was calculated using the following formula where \(S\) is the number of sites and \(p_i\) is the proportion of the total density belonging to the ith site

\[ E = \frac{-\sum p_i \log(p_i)}{\log(S)}\]

Survival (Abundance-based)

The subadult (\(S_t\)) and adult (\(A_t\)) abundance estimates were used to calculate the subadult and adult survival (\(\phi_t\)) in year \(t\) based on the relationship

\[\phi_t = \frac{A_t}{S_{t-1} + A_{t-1}}\]

Weight

The weight (\(W_t\)) in year \(t\) was estimated from the expected adult length using the condition model.

Fecundity

Mountain Whitefish

The fecundity-weight relationship for Mountain Whitefish was estimated from data collected by Boyer et al. (2017) for the Madison River, Montana. The data were analysed using an allometric model of the form

\[F = \alpha W^{\beta}\]

Key assumptions of the fecundity model include:

The residual variation in fecundity is log-normally distributed.

Rainbow Trout

Following (Andrusak and Thorley 2019) the fecundity (\(F_t\)) in year \(t\) of an adult female Rainbow Trout was calculated from the expected weight (\(W_t\)) in grams using the equation:

\[F_t = 3.8 \cdot W_t^{0.9}\]

Egg Deposition

The total egg deposition (\(E_t\)) in year \(t\) was calculated according to the equation \[E_t = F_t * \frac{A_t}{2}\]

Stock-Recruitment

The relationship between the total number of eggs deposited (\(E_t\)) and the resultant number of subadults (age-1 recruits) (\(S_{t+1}\)) was estimated using a Beverton-Holt stock-recruitment model (Walters and Martell 2004):

\[S_{t+1} = \frac{\alpha \cdot E_t}{1 + \beta \cdot E_t}\]

where \(\alpha\) is the egg to age-1 survival at low density and \(\beta\) is the density-dependence.

Key assumptions of the stock-recruitment model include:

The egg to recruit survival at low density (\(\alpha\)) was likely less than 1% (the prior distribution for \(\alpha\) was a zero truncated normal with standard deviation of 0.005.
The expected log number of recruits varies with the proportional egg loss.
The residual variation in the number of recruits is log-normally distributed.

The expected egg survival for a given egg deposition is \(S / E_t\) which is given by the equation

\[\phi_E = \frac{\alpha}{1 + \beta * E}\]

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.

Adjusted Recruitment

The abundance of Age-1 Rainbow Trout was estimated based on the proportion of the Rainbow Trout eggs dewatered the previous year and the abundance of age-1 Mountain Whitefish caught in the same year to account for inter-annual variation in age-1 salmonid abundance and/or capture efficiency.

The relationship(s) were estimated using a Generalized Linear Model (GLM).

Key assumptions of the final model include:

The abundance of Age-1 Rainbow Trout varies with proportion of the eggs dewatered and then number of Age-1 Mountain Whitefish caught in the same year.
The residual variation is log-normally distributed.

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<lower=0> sWeightYear;
  real<lower=0> sWeightLengthYear;

  vector[nYear] bWeightYear;
  vector[nYear] bWeightLengthYear;
  real<lower=0> sWeight;

model {

  vector[nObs] eWeight;

  bWeight ~ normal(5, 4);
  bWeightLength ~ normal(3, 1);

  bWeightDayte ~ normal(0, 1);
  bWeightLengthDayte ~ normal(0, 1);

  sWeightYear ~ normal(0, 1);
  sWeightLengthYear ~ normal(0, 1);

  for (i in 1:nYear) {
    bWeightYear[i] ~ normal(0, sWeightYear);
    bWeightLengthYear[i] ~ normal(0, 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], sWeight);
  }

Block 1.

Growth

.model {
  bK ~ dnorm (0, 5^-2)
  sKYear ~ dnorm(0, 2^-2) T(0,)

  for (i in 1:nYear) {
    bKYear[i] ~ dnorm(0, sKYear^-2)
    log(eK[i]) <- bK + bKYear[i]
  }

  bLinf ~ dunif(200, 1000)
  sGrowth ~ dnorm(0, 25^-2) T(0,)
  for (i in 1:length(Year)) {
    eGrowth[i] <- max(0, (bLinf - LengthAtRelease[i]) * (1 - exp(-sum(eK[Year[i]:(Year[i] + dYears[i] - 1)]))))
    Growth[i] ~ dnorm(eGrowth[i], sGrowth^-2)
  }

Block 2.

Movement

.model {

  bFidelity ~ dnorm(0, 1^-2)
  bLength ~ dnorm(0, 1^-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, 4^-2)
  bEfficiencySampledLength ~ dnorm(0, 4^-2)

  bSurvival ~ dnorm(0, 4^-2)

  sSurvivalYear ~ dnorm(0, 4^-2) T(0,)
  for(i in 1:nYear) {
    bSurvivalYear[i] ~ dnorm(0, 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(-4, 2^-2)

  sEfficiencySessionAnnual ~ dnorm(0, 1^-2) T(0,)
  for (i in 1:nSession) {
    for (j in 1:nAnnual) {
      bEfficiencySessionAnnual[i, j] ~ dnorm(0, 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, 4^-2)
  bDensitySiteAnnual2 ~ dnorm(0, 2^-2)

  sDensityAnnual ~ dnorm(0, 1^-2) T(0,)
  for (i in 1:nAnnual) {
    bDensityAnnual[i] ~ dnorm(0, sDensityAnnual^-2)
  }

  sDensitySite ~ dnorm(0, 1^-2) T(0,)
  sDensitySiteAnnual ~ dnorm(0, 1^-2) T(0,)
  for (i in 1:nSite) {
    bDensitySite[i] ~ dnorm(0, sDensitySite^-2)
    for (j in 1:nAnnual) {
      bDensitySiteAnnual[i, j] ~ dnorm(0, sDensitySiteAnnual^-2)
    }
  }

  bEfficiencyVisitType[1] <- 0
  bEfficiencyVisitTypeDensity[1] ~ dnorm(0, 2^-2)
  for (i in 2:nVisitType) {
    bEfficiencyVisitType[i] ~ dnorm(0, 2^-2)
    bEfficiencyVisitTypeDensity[i] <- 0
  }

  sDispersion ~ dnorm(0, 1^-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]] + bDensitySiteAnnual2 * exp(bDensity + bDensitySite[Site[i]]) * bDensityAnnual[Annual[i]]

    eAbundance[i] <- eDensity[i] * SiteLength[i]

    logit(eEfficiency[i]) <- logit(Efficiency[i]) + bEfficiencyVisitType[VisitType[i]] + bEfficiencyVisitTypeDensity[VisitType[i]] * (eDensity[i] - exp(bDensity + sDensityAnnual^2/2 + sDensitySite^2/2 + sDensitySiteAnnual^2/2))

    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.

Fecundity

model {
  bFecundity ~ dnorm(0, 5^-2)
  bFecundityWeight ~ dnorm(1, 1^-2) T(0,)

  sFecundity ~ dnorm(0, 1^-2) T(0,)
  for(i in 1:length(Weight)) {
    eFecundity[i] = bFecundity + bFecundityWeight * log(Weight[i])
    Fecundity[i] ~ dlnorm(eFecundity[i], sFecundity^-2)
  }

Block 7.

Stock-Recruitment

.model {
  bAlpha ~ dnorm(0, 0.003^-2) T(0,)
  bBeta ~ dnorm(0, 0.007^-2) T(0, )
  bEggLoss ~ dnorm(0, 100^-2)

  sRecruits ~ dnorm(0, 1^-2) T(0,)
  for(i in 1:length(Recruits)){
    log(eRecruits[i]) <- log(bAlpha * Eggs[i] / (1 + bBeta * Eggs[i])) + bEggLoss * EggLoss[i]
    Recruits[i] ~ dlnorm(log(eRecruits[i]), sRecruits^-2)
  }

Block 8.

Age-Ratios

.model{
  bProbAge1 ~ dnorm(0, 1^-2)
  bProbAge1Loss ~ dnorm(0, 1^-2)

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

Block 9.

Adjusted Recruitment

.model{
  b0 ~ dnorm(0, 10^-2)
  bMw ~ dnorm(0, 2^-2)
  bEggLoss ~ dnorm(0, 2^-2)

  sRb ~ dnorm(0, 2^-2) T(0,)
  for (i in 1:nObs) {
    log(eRb[i]) <- b0 + bMw * Mw[i] + bEggLoss * EggLoss[i]
    Rb[i] ~ dlnorm(log(eRb[i]), sRb^-2)
  }

Block 10. Model description.

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	lower	upper	svalue
bWeight	5.4755067	5.4560069	5.4942465	10.55171
bWeightDayte	-0.0212162	-0.0245880	-0.0176117	10.55171
bWeightLength	3.1655960	3.1217713	3.2065635	10.55171
bWeightLengthDayte	-0.0177076	-0.0270115	-0.0085988	10.55171
sWeight	0.1472061	0.1455043	0.1489253	10.55171
sWeightLengthYear	0.1037495	0.0730413	0.1493594	10.55171
sWeightYear	0.0470375	0.0356170	0.0652866	10.55171

Table 3. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
16015	7	3	500	2	406	1.009	TRUE

Table 4. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.0000735	0.0001773	-0.0153873	0.0157513	0.0154610
variance	0.9967563	0.9999487	0.9786269	1.0219366	0.3880586
skewness	-0.6070306	-0.0022072	-0.0380180	0.0375339	10.5517083
kurtosis	1.7900372	-0.0019176	-0.0739929	0.0788359	10.5517083

Table 5. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
16015	7	3	500	1.009	1.007	1.006	TRUE

Rainbow Trout

Table 6. Model coefficients.

term	estimate	lower	upper	svalue
bWeight	6.0273022	6.0157058	6.0375840	10.55171
bWeightDayte	-0.0035791	-0.0058187	-0.0015225	10.55171
bWeightLength	2.9243024	2.9020301	2.9481417	10.55171
bWeightLengthDayte	0.0393561	0.0327095	0.0462931	10.55171
sWeight	0.1005880	0.0995274	0.1016662	10.55171
sWeightLengthYear	0.0524848	0.0379964	0.0772029	10.55171
sWeightYear	0.0252582	0.0189860	0.0352581	10.55171

Table 7. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
17171	7	3	500	2	321	1.007	TRUE

Table 8. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.0001685	-0.0001032	-0.0153414	0.0149919	0.0389678
variance	0.9968564	0.9997184	0.9802061	1.0197653	0.3705560
skewness	-0.6822971	0.0001985	-0.0366285	0.0361468	10.5517083
kurtosis	2.3959339	-0.0004343	-0.0706962	0.0709834	10.5517083

Table 9. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
17171	7	3	500	1.007	1.016	1.008	TRUE

Walleye

Table 10. Model coefficients.

term	estimate	lower	upper	svalue
bWeight	6.2882814	6.2743650	6.3025910	10.551708
bWeightDayte	0.0155997	0.0132817	0.0183091	10.551708
bWeightLength	3.2275879	3.1929829	3.2629158	10.551708
bWeightLengthDayte	-0.0056988	-0.0211123	0.0097076	1.223033
sWeight	0.0917645	0.0905086	0.0930050	10.551708
sWeightLengthYear	0.0748556	0.0527848	0.1091235	10.551708
sWeightYear	0.0340421	0.0257027	0.0467774	10.551708

Table 11. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
10302	7	3	500	2	318	1.005	TRUE

Table 12. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.0005407	0.0001909	-0.0191359	0.0192184	0.0588536
variance	0.9962830	1.0000676	0.9719750	1.0277542	0.3337506
skewness	-0.0352659	0.0003738	-0.0481119	0.0452778	2.8582213
kurtosis	0.9527777	-0.0023943	-0.0967035	0.1012277	10.5517083

Table 13. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
10302	7	3	500	1.005	1.012	1.01	TRUE

Growth

Table 14. 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 15. Model coefficients.

term	estimate	lower	upper	svalue
bK	-0.9334122	-1.1668308	-0.7389528	10.55171
bLinf	397.3922591	391.5009401	402.2493079	10.55171
sGrowth	11.3399966	10.4331213	12.4180163	10.55171
sKYear	0.3923854	0.2529341	0.6175770	10.55171

Table 16. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
287	4	3	500	50	1010	1.004	TRUE

Table 17. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.0420761	0.0023630	-0.1115548	0.1251557	0.9536558
variance	0.9359583	0.9982861	0.8356099	1.1615095	1.0861419
skewness	-0.1955005	-0.0002373	-0.2871447	0.2859367	2.4589511
kurtosis	0.5620973	-0.0403186	-0.4640294	0.7078076	3.4121569

Table 18. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
287	4	3	500	1.004	1.002	1.001	TRUE

Rainbow Trout

Table 19. Model coefficients.

term	estimate	lower	upper	svalue
bK	-0.1337746	-0.2734122	0.0052791	4.01255
bLinf	481.2234816	476.4854765	485.9129576	10.55171
sGrowth	29.8435671	28.7802542	30.9230946	10.55171
sKYear	0.2927230	0.2135052	0.4179306	10.55171

Table 20. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
1432	4	3	500	50	930	1.005	TRUE

Table 21. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.0095261	0.0005153	-0.0507503	0.0487427	0.4134365
variance	0.9869659	0.9991168	0.9269479	1.0745174	0.3981562
skewness	0.2811677	-0.0016016	-0.1259689	0.1229332	10.5517083
kurtosis	0.6640704	-0.0158381	-0.2248422	0.2548556	8.9667458

Table 22. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
1432	4	3	500	1.005	1.005	1.004	TRUE

Walleye

Table 23. Model coefficients.

term	estimate	lower	upper	svalue
bK	-2.495586	-3.023231	-2.0519073	10.55171
bLinf	729.536867	620.143076	946.6953696	10.55171
sGrowth	17.540309	16.158432	19.2634101	10.55171
sKYear	0.322550	0.195136	0.5140263	10.55171

Table 24. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
286	4	3	500	50	188	1.006	TRUE

Table 25. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.0388840	-0.0048799	-0.1132172	0.1185114	1.082066
variance	0.9423009	0.9956184	0.8484579	1.1806375	1.002886
skewness	0.1957728	-0.0060292	-0.2955888	0.2718196	2.858221
kurtosis	1.6030601	-0.0597657	-0.4696239	0.5864294	8.966746

Table 26. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
286	4	3	500	1.006	1.002	1.004	TRUE

Movement

Table 27. 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 28. Model coefficients.

term	estimate	lower	upper	svalue
bFidelity	-0.2011430	-0.5550301	0.1564674	1.948082
bLength	-0.0807911	-0.4625010	0.2761610	0.598967

Table 29. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
122	2	3	500	1	910	1.003	TRUE

Table 30. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	-0.0298757	-0.0359115	-0.2575027	0.1729537	0.0769883
variance	1.3848284	1.3695164	1.2229456	1.4119391	0.5960584
skewness	0.1978280	0.2238480	-0.2985772	0.7653002	0.0291267
kurtosis	-1.9570150	-1.9201014	-1.9978107	-1.3937389	0.5989670

Table 31. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
122	2	3	500	1.003	1.002	1.003	TRUE

Rainbow Trout

Table 32. Model coefficients.

term	estimate	lower	upper	svalue
bFidelity	0.7138601	0.5686991	0.8517508	10.55171
bLength	-0.3290639	-0.4717737	-0.1795488	10.55171

Table 33. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
841	2	3	500	1	843	1.004	TRUE

Table 34. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.1072010	0.1048707	0.0255954	0.1767160	0.0749621
variance	1.2372963	1.2386030	1.1558223	1.3089670	0.0389678
skewness	-0.7040137	-0.7043062	-0.9051847	-0.4998678	0.0019236
kurtosis	-1.4424554	-1.4366826	-1.6916828	-1.0999950	0.0369942

Table 35. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
841	2	3	500	1.004	1.001	1.001	TRUE

Walleye

Table 36. Model coefficients.

term	estimate	lower	upper	svalue
bFidelity	0.6639859	0.4076977	0.9368174	10.551708
bLength	-0.1006183	-0.3748077	0.1445717	1.200769

Table 37. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
236	2	3	500	1	912	1.003	TRUE

Table 38. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.1056183	0.1018887	-0.0411419	0.2426967	0.0449048
variance	1.2729612	1.2682990	1.1131400	1.3755984	0.0851219
skewness	-0.6804434	-0.6802602	-1.0740261	-0.3086979	0.0193523
kurtosis	-1.5310395	-1.5188014	-1.8973838	-0.8360514	0.0389678

Table 39. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
236	2	3	500	1.003	1.003	1.002	TRUE

Length-At-Age

Mountain Whitefish

Table 40. The estimated upper length cutoffs (mm) by age and year.

Year	Age0	Age1	Age2
1990	163	274	NA
1991	144	226	296
2001	141	258	344
2002	163	261	344
2003	159	263	354
2004	158	249	342
2005	168	263	363
2006	175	284	357
2007	171	280	337
2008	170	247	340
2009	169	265	355
2010	177	272	352
2011	163	269	348
2012	162	268	347
2013	185	282	349
2014	178	284	362
2015	167	278	366
2016	164	283	352
2017	158	270	354
2018	177	262	346
2019	188	282	363
2020	166	291	365
2021	165	275	349

Rainbow Trout

Table 41. The estimated upper length cutoffs (mm) by age and year.

Year	Age0	Age1
1990	155	355
1991	129	347
2001	133	326
2002	154	352
2003	161	345
2004	142	335
2005	164	349
2006	170	367
2007	166	377
2008	145	342
2009	147	341
2010	143	339
2011	156	346
2012	152	346
2013	169	357
2014	155	340
2015	166	337
2016	154	340
2017	133	320
2018	139	312
2019	160	317
2020	154	349
2021	169	349

Survival

Table 42. 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 43. Model coefficients.

term	estimate	lower	upper	svalue
bEfficiency	-4.2529469	-4.4528223	-4.0614532	10.551708
bEfficiencySampledLength	0.4117789	0.1925864	0.6459047	10.551708
bSurvival	0.8752047	0.3323207	1.7463371	7.744353
sSurvivalYear	1.2564585	0.7112041	2.2848184	10.551708

Table 44. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
20	4	3	500	200	1269	1.002	TRUE

Rainbow Trout

Table 45. Model coefficients.

term	estimate	lower	upper	svalue
bEfficiency	-2.5231214	-2.6866753	-2.3622262	10.5517083
bEfficiencySampledLength	0.0130893	-0.1211983	0.1575440	0.2513557
bSurvival	-0.4203665	-0.6230200	-0.2022955	10.5517083
sSurvivalYear	0.3202229	0.1494315	0.5567204	10.5517083

Table 46. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
20	4	3	500	200	1245	1.004	TRUE

Walleye

Table 47. Model coefficients.

term	estimate	lower	upper	svalue
bEfficiency	-3.4823829	-3.6751832	-3.2836537	10.551708
bEfficiencySampledLength	0.1408444	-0.0096443	0.3072884	3.837463
bSurvival	0.1627794	-0.1159230	0.5335165	1.918713
sSurvivalYear	0.5072542	0.2027299	0.9284454	10.551708

Table 48. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
20	4	3	500	200	1250	1.003	TRUE

Capture Efficiency

Table 49. 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`	SD of `bEfficiencySessionAnnual`
`Session[i]`	Session of `i`^th visit
`Tagged[i]`	Number of marked fish tagged prior to `i`^th visit

Mountain Whitefish

Subadult

Table 50. Model coefficients.

term	estimate	lower	upper	svalue
bEfficiency	-4.3325555	-4.8716536	-3.972499	10.55171
sEfficiencySessionAnnual	0.5109049	0.0557932	1.199599	10.55171

Table 51. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
1544	2	3	500	100	348	1.007	TRUE

Table 52. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
1544	2	3	500	1.007	1.003	1.018	TRUE

Adult

Table 53. Model coefficients.

term	estimate	lower	upper	svalue
bEfficiency	-4.5105939	-4.8621361	-4.2430894	10.55171
sEfficiencySessionAnnual	0.2421517	0.0099348	0.6899536	10.55171

Table 54. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
1743	2	3	500	100	274	1.005	TRUE

Table 55. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
1743	2	3	500	1.005	1.009	1.006	TRUE

Rainbow Trout

Subadult

Table 56. Model coefficients.

term	estimate	lower	upper	svalue
bEfficiency	-3.0188375	-3.1536514	-2.9024322	10.55171
sEfficiencySessionAnnual	0.3913347	0.2806158	0.5274097	10.55171

Table 57. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
1778	2	3	500	100	1210	1.005	TRUE

Table 58. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
1778	2	3	500	1.005	1.006	1.003	TRUE

Adult

Table 59. Model coefficients.

term	estimate	lower	upper	svalue
bEfficiency	-3.4578577	-3.5950825	-3.3440267	10.55171
sEfficiencySessionAnnual	0.1819033	0.0083283	0.3835974	10.55171

Table 60. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
1848	2	3	500	100	413	1.009	TRUE

Table 61. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
1848	2	3	500	1.009	1.006	1.007	TRUE

Walleye

Table 62. Model coefficients.

term	estimate	lower	upper	svalue
bEfficiency	-3.8705161	-4.1191975	-3.6574368	10.55171
sEfficiencySessionAnnual	0.5746183	0.3691441	0.8283321	10.55171

Table 63. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
1898	2	3	500	100	984	1.004	TRUE

Table 64. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
1898	2	3	500	1.004	1.004	1.002	TRUE

Abundance

Table 65. 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 66. Model coefficients.

term	estimate	lower	upper	svalue
bDensity	4.7215469	4.3641478	5.0891416	10.5517083
bDensitySiteAnnual2	0.0002748	-0.0004346	0.0014950	1.0943274
bEfficiencyVisitType[2]	1.3323795	1.1979106	1.4666057	10.5517083
bEfficiencyVisitTypeDensity[1]	0.0000566	-0.0001016	0.0003560	0.8426244
sDensityAnnual	0.6292131	0.4586582	0.9050668	10.5517083
sDensitySite	0.7650127	0.6233089	0.9537284	10.5517083
sDensitySiteAnnual	0.4260734	0.3707332	0.4853979	10.5517083
sDispersion	-0.8013172	-0.8859588	-0.7206539	10.5517083
sDispersionVisitType[2]	0.6799922	0.5236369	0.8427045	10.5517083

Table 67. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
3020	9	3	500	200	246	1.016	TRUE

Table 68. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	-0.2198328	-0.2722096	-0.3079951	-0.2389008	8.966746
variance	0.6983168	0.9911020	0.9445128	1.0348459	10.551708
skewness	0.0440552	0.2601992	0.1889356	0.3368542	10.551708
kurtosis	-0.4749788	-0.3401765	-0.4808510	-0.1664530	3.922352

Adult

Table 69. Model coefficients.

term	estimate	lower	upper	svalue
bDensity	5.7350361	5.4371950	6.0083993	10.55171
bDensitySiteAnnual2	-0.0012229	-0.0015595	-0.0008745	10.55171
bEfficiencyVisitType[2]	1.4221561	1.2281110	1.6012701	10.55171
bEfficiencyVisitTypeDensity[1]	0.0009679	0.0003505	0.0018524	8.22978
sDensityAnnual	0.5004073	0.3636975	0.7130026	10.55171
sDensitySite	0.7866482	0.6085898	1.0190803	10.55171
sDensitySiteAnnual	0.2695262	0.2103980	0.3398227	10.55171
sDispersion	-0.6724000	-0.7386631	-0.6080522	10.55171
sDispersionVisitType[2]	0.4993310	0.3593028	0.6240796	10.55171

Table 70. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
3020	9	3	500	200	183	1.028	TRUE

Table 71. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	-0.2181289	-0.2754738	-0.3104299	-0.2362249	6.8512685
variance	0.6784253	0.9995885	0.9542885	1.0455724	10.5517083
skewness	0.0646806	0.2045044	0.1265059	0.2794385	10.5517083
kurtosis	-0.2445684	-0.2919418	-0.4321163	-0.1223153	0.8426244

Rainbow Trout

Subadult

Table 72. Model coefficients.

term	estimate	lower	upper	svalue
bDensity	4.4844163	4.2533695	4.7025400	10.55171
bDensitySiteAnnual2	0.0034010	0.0000069	0.0107329	4.32289
bEfficiencyVisitType[2]	1.4391033	1.2917451	1.6112370	10.55171
bEfficiencyVisitTypeDensity[1]	-0.0012491	-0.0015710	-0.0009401	10.55171
sDensityAnnual	0.2812460	0.1762081	0.4366609	10.55171
sDensitySite	0.8103242	0.6619382	0.9841066	10.55171
sDensitySiteAnnual	0.4594808	0.4128931	0.5103665	10.55171
sDispersion	-0.9931035	-1.0693165	-0.9141010	10.55171
sDispersionVisitType[2]	0.7202672	0.5668938	0.8783220	10.55171

Table 73. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
3020	9	3	500	200	342	1.016	TRUE

Table 74. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	-0.1899087	-0.2429425	-0.2792487	-0.2052862	8.966746
variance	0.6332183	1.0252891	0.9782449	1.0750202	10.551708
skewness	-0.1000613	0.1249807	0.0486386	0.1983276	10.551708
kurtosis	-0.1348843	-0.2705761	-0.3988109	-0.0992383	3.202980

Adult

Table 75. Model coefficients.

term	estimate	lower	upper	svalue
bDensity	5.0776552	4.8701680	5.2779643	10.551708
bDensitySiteAnnual2	-0.0015156	-0.0025034	-0.0002746	5.266306
bEfficiencyVisitType[2]	1.2606920	1.1125814	1.4123855	10.551708
bEfficiencyVisitTypeDensity[1]	-0.0005207	-0.0009444	0.0005992	1.647826
sDensityAnnual	0.4264776	0.2976366	0.6184260	10.551708
sDensitySite	0.7409243	0.5698442	0.9549844	10.551708
sDensitySiteAnnual	0.2813581	0.2274583	0.3303467	10.551708
sDispersion	-1.0031767	-1.0876630	-0.9275556	10.551708
sDispersionVisitType[2]	0.5282350	0.3746196	0.6864147	10.551708

Table 76. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
3020	9	3	500	200	472	1.021	TRUE

Table 77. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	-0.1727064	-0.2369004	-0.2723400	-0.1984671	10.55171
variance	0.6324302	1.0350861	0.9862599	1.0823075	10.55171
skewness	-0.1471385	0.0855498	0.0097631	0.1573428	10.55171
kurtosis	-0.0219842	-0.2468565	-0.3788988	-0.0956251	8.22978

Walleye

Table 78. Model coefficients.

term	estimate	lower	upper	svalue
bDensity	4.7446058	4.5223653	5.0079572	10.551708
bDensitySiteAnnual2	-0.0033426	-0.0047263	-0.0010526	6.303781
bEfficiencyVisitType[2]	0.9589834	0.7691844	1.1062192	10.551708
bEfficiencyVisitTypeDensity[1]	0.0014959	-0.0006350	0.0066874	1.970508
sDensityAnnual	0.5654281	0.3915802	0.8428269	10.551708
sDensitySite	0.2852635	0.1754512	0.4202860	10.551708
sDensitySiteAnnual	0.2189440	0.1362712	0.3107260	10.551708
sDispersion	-0.8431508	-0.9172370	-0.7710493	10.551708
sDispersionVisitType[2]	0.5412947	0.3641323	0.6940544	10.551708

Table 79. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
3020	9	3	500	200	232	1.014	TRUE

Table 80. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	-0.1873520	-0.2562592	-0.2952159	-0.2170104	10.551708
variance	0.6942008	1.0403979	0.9959675	1.0872702	10.551708
skewness	-0.1845375	0.1052695	0.0314730	0.1783667	10.551708
kurtosis	-0.2415461	-0.3446436	-0.4699096	-0.1921884	2.512789

Fecundity

Table 81. Parameter descriptions.

Parameter	Description
`bFecundity`	Intercept of `eFecundity`
`bFecundityWeight`	Effect of `log(Weight)` on `log(bFecundity)`
`eFecundity[i]`	Expected `Fecundity` of `i`^th fish
`Fecundity[i]`	Fecundity of `i`^th fish (eggs)
`sFecundity`	SD of residual variation in `log(Fecundity)`
`Weight[i]`	Weight of `i`^th fish (g)

Mountain Whitefish

Table 82. Model coefficients.

term	estimate	lower	upper	svalue
bFecundity	2.9434157	2.1499255	3.7243986	10.55171
bFecundityWeight	0.9941571	0.8747059	1.1132891	10.55171
sFecundity	0.1309413	0.1013519	0.1763504	10.55171

Table 83. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
28	3	3	500	500	890	1.001	TRUE

Table 84. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.0007544	0.0035540	-0.3718694	0.3767449	0.0096437
variance	0.9031600	0.9833955	0.5273010	1.6138927	0.4392688
skewness	-0.0053713	0.0009168	-0.7991967	0.8153463	0.0154610
kurtosis	-0.7054780	-0.3573449	-1.1378323	1.5474069	1.0419333

Table 85. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
28	3	3	500	1.001	1.007	1.004	TRUE

Stock-Recruitment

Table 86. Parameter descriptions.

Parameter	Description
`bAlpha`	`eRecruits` per `Stock` at low `Stock` density
`bBeta`	Expected density-dependence
`bEggLoss`	Effect of `EggLoss` on `log(eRecruits)`
`EggLoss`	Proportional egg loss
`Eggs`	Total egg deposition
`eRecruits`	Expected `Recruits`
`Recruits`	Number of Age-1 recruits
`sRecruits`	SD of residual variation in `log(Recruits)`

Mountain Whitefish

Table 87. Model coefficients.

term	estimate	lower	upper	svalue
bAlpha	0.0036417	0.0010400	0.0083519	10.5517083
bBeta	0.0000002	0.0000000	0.0000005	10.5517083
bEggLoss	-0.4536097	-2.4498831	1.9636046	0.5390837
sRecruits	0.5839171	0.4265604	0.8513871	10.5517083

Table 88. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
19	4	3	500	50	954	1.004	TRUE

Table 89. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	12.8398026	0.0044291	-0.4631205	0.4469220	10.5517083
variance	0.8847771	0.9608151	0.4451833	1.7566240	0.3097251
skewness	-0.0813545	-0.0107121	-0.9332061	0.9698862	0.2063030
kurtosis	-1.2203252	-0.4598808	-1.2562672	1.6686948	3.7572924

Table 90. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
19	4	3	500	1.004	1.009	1.627	FALSE

Rainbow Trout

Table 91. Model coefficients.

term	estimate	lower	upper	svalue
bAlpha	0.0038102	0.0011969	0.0082135	10.551708
bBeta	0.0000002	0.0000000	0.0000006	10.551708
bEggLoss	43.5317082	-7.1889609	92.8321575	3.474893
sRecruits	0.4326012	0.3204554	0.6366434	10.551708

Table 92. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
20	4	3	500	50	772	1.005	TRUE

Table 93. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	17.3373632	0.0036790	-0.4433163	0.4316881	10.5517083
variance	0.9608848	0.9743364	0.4874719	1.7549967	0.0608574
skewness	0.1625044	0.0132264	-0.9145807	0.9351975	0.4682289
kurtosis	0.3238386	-0.4688770	-1.2597471	1.6729996	1.8687137

Table 94. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
20	4	3	500	1.005	1.003	1.65	FALSE

Age-Ratios

Table 95. 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 96. Model coefficients.

term	estimate	lower	upper	svalue
bProbAge1	0.2377570	-0.0902671	0.5640274	2.8582213
bProbAge1Loss	-0.1449130	-0.5952169	0.3394578	0.8704698
sProbAge1	0.7717861	0.5772362	1.0755001	10.5517083

Table 97. Model summary.

n	K	nchains	niters	nthin	ess	rhat	converged
21	3	3	500	1	682	1.007	TRUE

Table 98. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.0010306	0.0059828	-0.4062282	0.4028671	0.0252090
variance	0.9088141	0.9562337	0.5005642	1.6728891	0.2331655
skewness	-0.4539816	-0.0101251	-0.9134044	0.9244399	1.6004235
kurtosis	-0.9846608	-0.4087201	-1.2445684	1.6615550	1.9856542

Table 99. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
21	3	3	500	1.007	1.002	1.005	TRUE

Adjusted Recruitment

Table 100. Parameter descriptions.

Parameter	Description
`b0`	Intercept for `eRb[i]`
`bEggLoss`	Effect of `EggLoss` on `eRb[i]`
`bMw`	Effect of `Mw` on `eRb[i]`
`Eggloss[i]`	Proportional RB egg loss for the `i`^th spawn year
`eRb[i]`	Expected value of `Rb[i]`
`Mw[i]`	Abundance of age-1 MW caught in the same year as age-1 RB from the `i`^th spawn year
`Rb[i]`	Abundance of age-1 RB for the `i`^th spawn year
`sRb`	SD of residual variation in `eRb[i]`

Table 101. Model coefficients.

term	estimate	lower	upper	svalue
b0	9.8273576	9.6874121	9.9726553	10.551708
bEggLoss	0.0863422	-0.0901280	0.2654751	1.588812
bMw	0.2991639	0.1229051	0.4786583	10.551708
sRb	0.3330808	0.2496527	0.4923357	10.551708

Table 102. Model convergence.

n	K	nchains	niters	nthin	ess	rhat	converged
21	4	3	500	50	1322	1.002	TRUE

Table 103. Model posterior predictive checks.

moment	observed	median	lower	upper	svalue
zeros	NA	NA	NA	NA	NA
mean	0.0073628	0.0095887	-0.4186765	0.4191436	0.0057785
variance	0.8271602	0.9832338	0.4648124	1.7211129	0.6553759
skewness	0.5683087	-0.0098563	-0.9260708	0.9488355	2.2525002
kurtosis	1.4564275	-0.4483787	-1.2644998	1.6850341	3.9223516

Table 104. Model sensitivity.

n	K	nchains	niters	rhat_1	rhat_2	rhat_all	converged
21	4	3	500	1.002	1.003	1.003	TRUE

Figures

Condition

Subadult

Mountain Whitefish

Rainbow Trout

Adult

Mountain Whitefish

Rainbow Trout

figures/condition/Adult/RB/year.png — Figure 5. Estimated change in condition relative to a typical year for a 500 mm Rainbow Trout by year (with 95% CRIs).

Walleye

figures/condition/Adult/WP/year.png — Figure 6. Estimated change in condition relative to a typical year for a 400 mm Walleye by year (with 95% CRIs).

Growth

Mountain Whitefish

figures/growth/MW/year.png — Figure 8. Estimated change in von Bertalanffy growth coefficient (k) relative to a typical year by year (with 95% CIs).

figures/growth/MW/year_rate.png — Figure 9. Predicted maximum growth by year (with 95% CIs).

Rainbow Trout

figures/growth/RB/year.png — Figure 10. Estimated change in von Bertalanffy growth coefficient (k) relative to a typical year by year (with 95% CIs).

figures/growth/RB/year_rate.png — Figure 11. Predicted maximum growth by year (with 95% CIs).

Walleye

figures/growth/WP/year.png — Figure 12. Estimated change in von Bertalanffy growth coefficient (k) relative to a typical year by year (with 95% CIs).

figures/growth/WP/year_rate.png — Figure 13. Predicted maximum growth by year (with 95% CIs).

Movement

figures/fidelity/length_all_uncorrected.png — Figure 14. Probability of recapture at the same site versus a different site by fish length (with 95% CRIs).

figures/fidelity/length_all.png — Figure 15. Site fidelity by fish length (with 95% CRIs).

Length-At-Age

Mountain Whitefish

figures/lengthatage/MW/age0.png — Figure 17. Average length of an age-0 individual by year.

figures/lengthatage/MW/age1.png — Figure 18. Average length of an age-1 individual by year.

figures/lengthatage/MW/age2.png — Figure 19. Average length of an age-2 individual by year.

figures/lengthatage/MW/age3.png — Figure 20. Average length of an age-3+ individual by year.

Rainbow Trout

figures/lengthatage/RB/hist.png — Figure 21. Length-frequency histogram with length-at-age predictions.

figures/lengthatage/RB/age0.png — Figure 22. Average length of an age-0 individual by year.

figures/lengthatage/RB/age1.png — Figure 23. Average length of an age-1 individual by year.

figures/lengthatage/RB/age2.png — Figure 24. Average length of an age-2+ individual by year.

Survival

Adult

Mountain Whitefish

figures/survival/Adult/MW/efficiencybank.png — Figure 26. Predicted annual efficiency for an adult Mountain Whitefish.

Rainbow Trout

figures/survival/Adult/RB/year.png — Figure 27. Predicted annual survival for an adult Rainbow Trout.

figures/survival/Adult/RB/efficiencybank.png — Figure 28. Predicted annual efficiency for an adult Rainbow Trout.

Walleye

figures/survival/Adult/WP/year.png — Figure 29. Predicted annual survival for an adult Walleye.

figures/survival/Adult/WP/efficiencybank.png — Figure 30. Predicted annual efficiency for an adult Walleye.

Observer Length Correction

figures/observer/observer.png — Figure 31. Length inaccuracy and imprecision by observer, year and species.

figures/observer/uncorrected.png — Figure 32. Uncorrected length density plots by species, year and observer.

figures/observer/corrected.png — Figure 33. Corrected length density plots by species, year and observer.

Capture Efficiency

figures/efficiency/all.png — Figure 34. Predicted capture efficiency by species and life stage (with 95% CRIs).

Mountain Whitefish

Subadult

Adult

Rainbow Trout

Subadult

Adult

Walleye

figures/efficiency/WP/Adult/session-year.png — Figure 39. Predicted capture efficiency for an adult Walleye by session and year (with 95% CRIs).

Abundance

figures/abundance/relative.png — Figure 42. Effect of counting (versus capture) on encounter efficiency at typical density by species and stage (with 95% CIs).

figures/abundance/dispersion.png — Figure 43. Effect of counting (versus capture) on overdispersion by species and stage (with 95% CIs).

Mountain Whitefish

Subadult

Adult

figures/abundance/MW/Adult/evennes.png — Figure 50. Estimated evenness of adult Mountain Whitefish at index sites by year (with 95% CIs).

figures/abundance/MW/Adult/index.png — Figure 51. Estimated density of adult Mountain Whitefish at non-index relative to index sites by year.

Rainbow Trout

Subadult

Adult

figures/abundance/RB/Adult/evennes.png — Figure 58. Estimated evenness of adult Rainbow Trout at index sites by year (with 95% CIs).

figures/abundance/RB/Adult/index.png — Figure 59. Estimated density of adult Rainbow Trout at non-index relative to index sites by year.

Walleye

figures/abundance/WP/Adult/year.png — Figure 60. Estimated abundance of adult Walleye by year (with 95% CIs).

figures/abundance/WP/Adult/site.png — Figure 61. Estimated lineal river count density of adult Walleye by site in a typical year (with 95% CIs).

figures/abundance/WP/Adult/evennes.png — Figure 62. Estimated evenness of adult Walleye at index sites by year (with 95% CIs).

figures/abundance/WP/Adult/index.png — Figure 63. Estimated density of adult Walleye at non-index relative to index sites by year.

Survival (Abundance-based)

Mountain Whitefish

figures/survival2/MW/year.png — Figure 64. Predicted annual survival for adult and subadult Mountain Whitefish.

Rainbow Trout

figures/survival2/RB/year.png — Figure 65. Predicted annual survival for adult and subadult Rainbow Trout.

Weight

Mountain Whitefish

Rainbow Trout

figures/weight/RB/year.png — Figure 67. Predicted weight of an adult Rainbow Trout by year (with 95% CIs).

Fecundity

Mountain Whitefish

figures/fecundity/MW/year.png — Figure 69. Predicted fecundity of an adult female Mountain Whitefish by year (with 95% CIs).

Rainbow Trout

figures/fecundity/RB/year.png — Figure 70. Predicted fecundity of an adult female Rainbow Trout by year (with 95% CIs).

Egg Deposition

Mountain Whitefish

figures/eggs/MW/year.png — Figure 71. Predicted total egg deposition by Mountain Whitefish by year (with 95% CIs).

Rainbow Trout

figures/eggs/RB/year.png — Figure 72. Predicted total egg deposition by Rainbow Trout by year (with 95% CIs).

Stock-Recruitment

Mountain Whitefish

figures/sr/MW/sr.png — Figure 73. Predicted stock-recruitment relationship by spawn year (with 95% CRIs).

figures/sr/MW/eggsurvival.png — Figure 74. Predicted egg to age-1 survival by total egg deposition (with 95% CRIs).

figures/sr/MW/loss.png — Figure 75. Predicted effect of egg loss on the number of age-1 recruits (with 95% CRIs).

Rainbow Trout

figures/sr/RB/sr.png — Figure 76. Predicted stock-recruitment relationship by spawn year (with 95% CRIs).

figures/sr/RB/eggsurvival.png — Figure 77. Predicted egg to age-1 survival by total egg deposition (with 95% CRIs).

figures/sr/RB/loss.png — Figure 78. Predicted effect of egg loss on the number of age-1 recruits (with 95% CRIs).

Age-Ratios

figures/ageratio/year-prop.png — Figure 79. Proportion of Age-1 Mountain Whitefish by spawn year.

figures/ageratio/year-loss.png — Figure 80. Percentage Mountain Whitefish egg loss by spawn year.

figures/ageratio/ratio-prop.png — Figure 81. Proportion of Age-1 Mountain Whitefish by percentage egg loss ratio, labelled by spawn year. The predicted relationship is indicated by the solid black line (with 95% CRIs).

figures/ageratio/loss-effect.png — Figure 82. Predicted effect of egg loss on the number of age-1 Mountain Whitefish recruits by egg loss relative to 10% egg loss (with 95% CRIs).

Adjusted Recruitment

figures/rbmw/rb_mw.png — Figure 83. Relationship between age-1 Rainbow Trout and age-1 Mountain Whitefish in the same year of capture by Rainbow Trout spawn year (with 95% CIs).

figures/rbmw/loss-effect.png — Figure 84. Predicted effect of egg loss on the number of age-1 Rainbow Trout recruits by egg loss relative to 10% egg loss (with 95% CRIs).

Recommendations

Develop fecundity vs weight relationship for Mountain Whitefish and Rainbow Trout on the Lower Columbia River.

Acknowledgements

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

BC Hydro
- Matt Casselman
- Guy Martel
- Teri Neighbour
- Margo Sadler
- Gillian Kong
Okanagan Nation Alliance
- Evan Smith
Golder Associates
- David Roscoe
- Dustin Ford
- Sima Usvyatsov
- Dana Schmidt
- Demitria Burgoon
- Chris King

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