# Middle Columbia River Fish Indexing Analysis 2019

The suggested citation for this analytic report is:

Thorley, J.L. and Amies-Galonski E. (2020) Middle Columbia River Fish Indexing Analysis 2019. A Poisson Consulting Analysis Appendix. URL: https://www.poissonconsulting.ca/f/1050384286.

## Background

The key management questions to be addressed by the analyses are:

1. Is there a change in abundance of adult life stages of fish using the Middle Columbia River (MCR) that corresponds with the implementation of a year-round minimum flow?
2. Is there a change in growth rate of adult life stages of the most common fish species using the MCR that corresponds with the implementation of a year-round minimum flow?
3. Is there a change in body condition (measured as a function of relative weight to length) of adult life stages of fish using the MCR that corresponds with the implementation of a year-round minimum flow?
4. Is there a change in spatial distribution of adult life stages of fish using the MCR that corresponds with the implementation of a year-round minimum flow?

Other objectives include the estimation of species richness and diversity. The year-round minimum flow was implemented in the winter of 2010 at the same time that a fifth turbine was added.

## Methods

### Data Preparation

The data were collected by Okanagan Nation Alliance and Golder Associates.

#### Life-Stage

The four primary fish species were categorized as fry, juvenile or adult based on their lengths.

### Statistical Analysis

Model parameters were estimated using Bayesian methods. The Bayesian estimates were produced using JAGS and STAN . For additional information on Bayesian estimation the reader is referred to .

Unless indicated otherwise, the Bayesian analyses used uninformative normal prior distributions . The posterior distributions were estimated from 1500 Markov Chain Monte Carlo (MCMC) samples thinned from the second halves of 3 chains . Model convergence was confirmed by ensuring that the split $$\hat{R} \leq$$ getOption("mb.rhat") and $$\textrm{ESS} \geq 150$$ for each of the monitored parameters . Where $$\hat{R}$$ is the potential scale reduction factor and $$\textrm{ESS}$$ is the effective sample size.

The sensitivity of the estimates to the choice of priors was examined by multiplying the standard deviations of the normal (and log-normal) priors by 10 and using $$\hat{R}$$ to test whether the samples where drawn from the same posterior distribution .

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 . 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.

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) . 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 .

The analyses were implemented using R version 3.6.2 and the mbr family of packages.

#### Growth

Annual growth was estimated from the inter-annual recaptures using the Fabens method for estimating the von Bertalanffy (VB) growth curve . The VB curves is based on the premise that

$\frac{dl}{dt} = k (L_{\infty} - l)$

where $$l$$ is the length of the individual, $$k$$ is the growth coefficient and $$L_{\infty}$$ is the mean maximum length.

Integrating the above equation gives

$l_t = L_{\infty} (1 - e^{-k(t - t0)})$

where $$l_t$$ is the length at time $$t$$ and $$t0$$ is the time at which the individual would have had no 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 at large.

Key assumptions of the growth model include:

• $$k$$ can vary with discharge regime and randomly with year.
• The residual variation in growth is normally distributed.

Mountain Whitefish with a FL $$>$$ 250 mm at release were excluded from the growth analysis as they appeared to be undergoing biphasic growth.

#### Condition

Condition was estimated via an analysis of mass-length relations .

More specifically the model was based on the allometric relationship

$W = \alpha L^{\beta}$

where $$W$$ is the weight (mass), $$\alpha$$ is the coefficent, $$\beta$$ is the exponent and $$L$$ is the length.

To improve chain mixing the relation was log-transformed, i.e.,

$\log(W) = \log(\alpha) + \beta \log(L)$

and the logged lengths centered, i.e., $$\log(L) - \text{mean}({\log(L)})$$, prior to model fitting.

Key assumptions of the condition model include:

• $$\alpha$$ can vary with the regime and season and randomly with year.
• $$\beta$$ can vary with the regime and season and randomly with year.
• The residual variation in weight is log-normally distributed.

Fry were excluded from the condition analysis.

#### Occupancy

Occupancy, which is the probability that a particular species was present at a site, was estimated from the temporal replication of detection data , i.e., each site was surveyed multiple times within a season. A species was considered to have been detected if one or more individuals of the species were caught or counted. It is important to note that the model estimates the probability that the species was present at a given (or typical) site in a given (or typical) year as opposed to the probability that the species was present in the entire study area. We focused on Northern Pikeminnow, Burbot, Lake Whitefish, Rainbow Trout, Redside Shiner and Sculpins because they were low enough density to not to be present at all sites at all times yet were encounted sufficiently often to provide information on spatial and temporal changes.

Key assumptions of the occupancy model include:

• Occupancy varies with season.
• Occupancy varies randomly with site and site within year.
• The effect of year on occupancy is autoregressive with a lag of one year and varies with discharge regime.
• Sites are closed, i.e., the species is present or absent at a site for all the sessions in a particular season of a year.
• Observed presence is described by a bernoulli distribution, given occupancy.

#### Count

The count data were analysed using an overdispersed Poisson model (Kery 2010, pp 168-170; Kery and Schaub 2011, pp 55-56) to provide estimates of the lineal river count density (count/km). The model estimates the expected count which is the product of the abundance and observer efficiency. In order to interpret the estimates as relative densities it is necessary to assume that changes in observer efficiency are negligible.

Key assumptions of the count model include:

• The count density (count/km) varies as an exponential growth model with the rate of change varying with discharge regime.
• The count density varies with season.
• The count density varies randomly with site, year and site within year.
• The counts are gamma-Poisson distributed.

In the case of suckers the count model replaced the first assumption with

• The count density varies with discharge regime.

#### Movement

The extent to which sites are closed, i.e., fish remain at the same site between sessions, was evaluated from a logistic ANCOVA . The model estimated the probability that intra-annual recaptures were caught at the same site versus a different one.

Key assumptions of the site fidelity model include:

• Site fidelity varies with season, fish length and the interaction between season and fish length.
• Observed site fidelity is Bernoulli distributed.

Fry were excluded from the movement analysis.

#### 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 percent 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.

#### Abundance

The catch and geo-referenced count data were analysed using a capture-recapture-based overdispersed gamma-Poisson model to provide estimates of capture efficiency and absolute abundance. To maximize the number of recaptures the model grouped all the sites into a supersite for the purposes of estimating the number of marked fish but analysed the total captures at the site level.

Key assumptions of the full abundance model include:

• The density (fish/km) varies as an exponential growth model with the rate of change varying with discharge regime.
• The density varies with season.
• The density varies randomly with site, year and site within year.
• Efficiency (probability of capture) varies by season and method (capture versus count).
• Efficiency varies randomly by session within season within year.
• Marked and unmarked fish have the same probability of capture.
• There is no tag loss, migration (at the supersite level), mortality or misidentification of fish.
• The number of fish caught is gamma-Poisson distributed.
• The overdispersion varies by encounter type (count versus capture).

In the case of Adult Suckers the abundance model replaced the first assumption with

• The density varies with discharge regime.

#### Distribution

The site within year random effects from the count and abundance models were analysed using a linear mixed model to estimate the distribution.

Key assumptions of the linear mixed model include:

• The effect varies by river kilometer.
• The effect of river kilometer varies by discharge regime.
• The effect of river kilometer varies randomly by year.
• The effect is normally distributed.

The effects are the predicted site within year random effects after accounting for all other predictors including the site and year random effects. As such an increase in the distribution represents an increase in the relative density of fish closer to Revelstoke Dam. A positive distribution does not however necessarily indicate that the density of fish is higher closer to Revelstoke Dam.

#### Species Richness

The estimated probabilities of presence for the six species considered in the occupany analyses were summed to give the expected species richnesses by site and year.

#### Species Evenness

The site and year estimates of the lineal bank count densities from the count model for Rainbow Trout, Suckers, Burbot and Northern Pikeminnow were combined with the equivalent count estimates for Juvenile and Adult Bull Trout and Adult Mountain Whitefish from the abundance model to calculate the shannon index of evenness $$(E)$$. The index was calculated using the following formula where $$S$$ is the number of species and $$p_i$$ is the proportion of the total count belonging to the ith species.

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

#### Species Diversity

The site and year estimates of the lineal bank count densities from the count model for Rainbow Trout, Suckers, Burbot and Northern Pikeminnow were combined with the equivalent count estimates for Adult Bull Trout and Adult Mountain Whitefish from the abundance model to calculate species diversity profiles . Species diversity profiles can take similarities among species into account, allow for a range of weightings of rare versus common species (via the $$q$$ sensitivity parameter), and estimate the effective number of species.

Like the species richness and evenness estimates, the species diversity profile estimates treated all species equally. The $$q$$ sensitivity parameter, which measures the insensitivity to rare species, ranged from $$0$$ (equivalent to richness) through $$1$$ (equivalent to evenness) to $$2$$ (equivalent to ).

### Model Templates

#### Growth

.model {

bKIntercept ~ dnorm(0, 5^-2)

bKRegime[1] <- 0
for(i in 2:nRegime) {
bKRegime[i] ~ dnorm(0, 5^-2)
}

sKAnnual ~ dnorm(0, 5^-2) T(0, )
for (i in 1:nAnnual) {
bKAnnual[i] ~ dnorm(0, sKAnnual^-2)
log(bK[i]) <- bKIntercept + bKRegime[step(i - Threshold) + 1] + bKAnnual[i]
}

bLinf ~ dnorm(600, 300^-2) T(100, 1000)
sGrowth ~ dnorm(0, 100^-2) T(0, )
for (i in 1:length(Growth)) {

eGrowth[i] <- (bLinf - LengthAtRelease[i]) * (1 - exp(-sum(bK[Annual[i]:(Annual[i] + Years[i] - 1)])))

Growth[i] ~ dnorm(eGrowth[i], sGrowth^-2)
}
tGrowth <- bKRegime[2]
..

Block 1. The model description.

#### Condition

.model {

bWeightIntercept ~ dnorm(5, 5^-2)
bWeightSlope ~ dnorm(3, 5^-2)

bWeightRegimeIntercept[1] <- 0
bWeightRegimeSlope[1] <- 0

for(i in 2:nRegime) {
bWeightRegimeIntercept[i] ~ dnorm(0, 5^-2)
bWeightRegimeSlope[i] ~ dnorm(0, 5^-2)
}

bWeightSeasonIntercept[1] <- 0
bWeightSeasonSlope[1] <- 0
for(i in 2:nSeason) {
bWeightSeasonIntercept[i] ~ dnorm(0, 5^-2)
bWeightSeasonSlope[i] ~ dnorm(0, 5^-2)
}

sWeightYearIntercept ~ dnorm(0, 1^-2) T(0,)
sWeightYearSlope ~ dnorm(0, 1^-2) T(0,)
for(yr in 1:nYear) {
bWeightYearIntercept[yr] ~ dnorm(0, sWeightYearIntercept^-2)
bWeightYearSlope[yr] ~ dnorm(0, sWeightYearSlope^-2)
}

sWeight ~ dnorm(0, 1^-2) T(0,)
for(i in 1:length(Year)) {

eWeightIntercept[i] <- bWeightIntercept + bWeightRegimeIntercept[Regime[i]] + bWeightSeasonIntercept[Season[i]] + bWeightYearIntercept[Year[i]]

eWeightSlope[i] <- bWeightSlope + bWeightRegimeSlope[Regime[i]] + bWeightSeasonSlope[Season[i]] + bWeightYearSlope[Year[i]]

log(eWeight[i]) <- eWeightIntercept[i] + eWeightSlope[i] * LogLength[i]
Weight[i] ~ dlnorm(log(eWeight[i]) , sWeight^-2)
}
tCondition1 <- bWeightRegimeIntercept[2]
tCondition2 <- bWeightRegimeSlope[2]
..

Block 2. The model description.

#### Occupancy

.model {

bRate ~ dnorm(0, 5^-2)

sRateYear ~ dnorm(0, 5^-2) T(0,)
for(i in 1:nYear) {
bRateYear[i] ~ dnorm(0, sRateYear^-2)
}

bRateRev5 ~ dnorm(0, 5^-2)

bOccupancyYear[1] ~ dnorm(0, 5^-2)
for (i in 2:nYear) {
eRateYear[i-1] <- bRate + bRateYear[i-1] + bRateRev5 * YearRev5[i-1]
bOccupancyYear[i] <- bOccupancyYear[i-1] + eRateYear[i-1]
}

bOccupancySpring ~ dnorm(0, 5^-2)

sOccupancySite ~ dnorm(0, 5^-2) T(0,)
sOccupancySiteYear ~ dnorm(0, 5^-2) T(0,)
for (i in 1:nSite) {
bOccupancySite[i] ~ dnorm(0, sOccupancySite^-2)
for (j in 1:nYear) {
bOccupancySiteYear[i,j] ~ dnorm(0, sOccupancySiteYear^-2)
}
}

for (i in 1:length(Observed)) {
logit(eObserved[i]) <- bOccupancyYear[Year[i]] + bOccupancySpring * Spring[i] + bOccupancySite[Site[i]] + bOccupancySiteYear[Site[i], Year[i]]
Observed[i] ~ dbern(eObserved[i])
}
..

Block 3. The model description.

#### Count

.model {
bDensity ~ dnorm(0, 5^-2)

bRate ~ dnorm(0, 5^-2)
bRateRev5 ~ dnorm(0, 5^-2)

bTrendYear[1] <- bDensity
for(i in 2:nYear) {
bTrendYear[i] <- bTrendYear[i-1] + bRate + bRateRev5 * YearRev5[i-1]
}

bDensitySeason[1] <- 0
for (i in 2:nSeason) {
bDensitySeason[i] ~ dnorm(0, 5^-2)
}

sDensityYear ~ dnorm(0, 5^-2) T(0,)
for (i in 1:nYear) {
bDensityYear[i] ~ dnorm(0, sDensityYear^-2)
}

sDensitySite ~ dnorm(0, 5^-2) T(0,)
sDensitySiteYear ~ dnorm(0, 2^-2) T(0,)
for (i in 1:nSite) {
bDensitySite[i] ~ dnorm(0, sDensitySite^-2)
for (j in 1:nYear) {
bDensitySiteYear[i, j] ~ dnorm(0, sDensitySiteYear^-2)
}
}

sDispersion ~ dnorm(0, 5^-2) T(0,)
for (i in 1:length(Year)) {

log(eDensity[i]) <- bTrendYear[Year[i]] + bDensitySeason[Season[i]] + bDensityYear[Year[i]] + bDensitySite[Site[i]] + bDensitySiteYear[Site[i],Year[i]]

eCount[i] <- eDensity[i] * SiteLength[i] * ProportionSampled[i]
eDispersion[i] ~ dgamma(1 / sDispersion^2, 1 / sDispersion^2)
Count[i] ~ dpois(eCount[i] * eDispersion[i])
}
tCount <- bRateRev5
..

Block 4. The model description.

#### Movement

.model {
bMoved ~ dnorm(0, 5^-2)
bLength ~ dnorm(0, 5^-2)

bMovedSpring ~ dnorm(0, 5^-5)
bLengthSpring ~ dnorm(0, 5^-5)

for (i in 1:length(Moved)) {
logit(eMoved[i]) <- bMoved + bMovedSpring * Spring[i] + (bLength + bLengthSpring * Spring[i]) * Length[i]
Moved[i] ~ dbern(eMoved[i])
}
..

Block 5.

#### Abundance

.model {
bDensity ~ dnorm(0, 5^-2)

bRate ~ dnorm(0, 5^-2)
bRateRev5 ~ dnorm(0, 5^-2)

bTrendYear[1] <- bDensity
for(i in 2:nYear) {
bTrendYear[i] <- bTrendYear[i-1] + bRate + bRateRev5 * YearRev5[i-1]
}

bDensitySeason[1] <- 0
for (i in 2:nSeason) {
bDensitySeason[i] ~ dnorm(0, 5^-2)
}

sDensityYear ~ dnorm(0, 5^-2) T(0,)
for (i in 1:nYear) {
bDensityYear[i] ~ dnorm(0, sDensityYear^-2)
}

sDensitySite ~ dnorm(0, 5^-2) T(0,)
sDensitySiteYear ~ dnorm(0, 2^-2) T(0,)
for (i in 1:nSite) {
bDensitySite[i] ~ dnorm(0, sDensitySite^-2)
for (j in 1:nYear) {
bDensitySiteYear[i, j] ~ dnorm(0, sDensitySiteYear^-2)
}
}

bEfficiency ~ dnorm(0, 5^-2)

bEfficiencySeason[1] <- 0
for(i in 2:nSeason) {
bEfficiencySeason[i] ~ dnorm(0, 5^-2)
}

sEfficiencySessionSeasonYear ~ dnorm(0, 5^-2) T(0,)
for (i in 1:nSession) {
for (j in 1:nSeason) {
for (k in 1:nYear) {
bEfficiencySessionSeasonYear[i, j, k] ~ dnorm(0, sEfficiencySessionSeasonYear^-2)
}
}
}

bMultiplier <- 0
sDispersion ~ dnorm(0, 2^-2)
bMultiplierType[1] <- 0
sDispersionType[1] <- 0
for (i in 2:nType) {
bMultiplierType[i] ~ dnorm(0, 2^-2)
sDispersionType[i] ~ dnorm(0, 2^-2)
}

for(i in 1:length(EffIndex)) {

logit(eEff[i]) <- bEfficiency + bEfficiencySeason[Season[EffIndex[i]]] + bEfficiencySessionSeasonYear[Session[EffIndex[i]],Season[EffIndex[i]],Year[EffIndex[i]]]

Marked[EffIndex[i]] ~ dbin(eEff[i], Tagged[EffIndex[i]])
}

for (i in 1:length(Year)) {

logit(eEfficiency[i]) <- bEfficiency + bEfficiencySeason[Season[i]] + bEfficiencySessionSeasonYear[Session[i], Season[i], Year[i]]

log(eDensity[i]) <- bTrendYear[Year[i]] + bDensitySeason[Season[i]] + bDensityYear[Year[i]] + bDensitySite[Site[i]] + bDensitySiteYear[Site[i],Year[i]]

log(eMultiplier[i]) <- bMultiplier + bMultiplierType[Type[i]]

eCatch[i] <- eDensity[i] * SiteLength[i] * ProportionSampled[i] * eEfficiency[i] * eMultiplier[i]

log(esDispersion[i]) <- sDispersion + sDispersionType[Type[i]]

eDispersion[i] ~ dgamma(esDispersion[i]^-2 + 0.1, esDispersion[i]^-2 + 0.1)

Catch[i] ~ dpois(eCatch[i] * eDispersion[i])
}
tAbundance <- bRateRev5
..

Block 6. The model description.

#### Distribution

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

bRkm ~ dnorm(0, 1^-2)
bRkmRev5 ~ dnorm(0, 1^-2)

sRkmYear ~ dnorm(0, 1^-2) T(0,)
for(i in 1:nYear) {
bRkmYear[i] ~ dnorm(0, sRkmYear^-2)
}
sEffect ~ dnorm(0, 1^-2) T(0,)
for(i in 1:length(Effect)) {
eEffect[i] <- bEffect + (bRkm + bRkmRev5 * Rev5[i] + bRkmYear[Year[i]]) * Rkm[i]
Effect[i] ~ dnorm(eEffect[i], sEffect^-2)
}
tDistribution <- bRkmRev5

Block 7. The model description.

## Results

### Tables

#### Stage

Table 1. Length cutoffs by species and stage.

Species Fry Juvenile
Bull Trout < 120 < 400
Mountain Whitefish < 120 < 175
Rainbow Trout < 120 < 250
Largescale Sucker < 120 < 350

#### Growth

Table 2. Parameter descriptions.

Parameter Description
Annual[i] Year
bK[i] Expected growth coefficient in the ith Annual
bKAnnual[i] Effect of ith Annual on bKIntercept
bKIntercept Intercept for log(bK)
bKRegime[i] Effect of ith Regime on bKIntercept
bLinf Mean maximum length
eGrowth[i] Expected Growth of the ith fish
Growth[i] Change in length of the ith fish between release and recapture (mm)
LengthAtRelease[i] Length of the ith fish when released (mm)
sGrowth SD of residual variation about eGrowth
sKAnnual SD of bKAnnual
Threshold Last Annual of the first regime
Years[i] Number of years between release and recapture for the ith fish
##### Bull Trout

Table 3. Model coefficients.

term estimate sd zscore lower upper pvalue
bKIntercept -1.7507336 0.1199146 -14.6232718 -1.9888049 -1.5167030 0.0006662
bKRegime[2] -0.0600006 0.1428115 -0.4356453 -0.3661568 0.2211612 0.6482345
bLinf 844.0686142 24.6485065 34.3096957 802.3650682 897.4461141 0.0006662
sGrowth 32.0269299 1.2930389 24.8580730 29.9001309 34.8539006 0.0006662
sKAnnual 0.2659911 0.0693731 3.9725837 0.1687522 0.4461194 0.0006662
tGrowth -0.0600006 0.1428115 -0.4356453 -0.3661568 0.2211612 0.6482345

Table 4. Model summary.

n K nchains niters nthin ess rhat converged
344 6 3 500 500 1128 1.002 TRUE

Table 5. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
344 6 3 500 1.002 1.004 1.002 TRUE
##### Mountain Whitefish

Table 6. Model coefficients.

term estimate sd zscore lower upper pvalue
bKIntercept -1.7606502 0.1656696 -10.621613 -2.0833212 -1.4416248 0.0006662
bKRegime[2] 0.0828494 0.2171573 0.394426 -0.3511366 0.4929744 0.6495670
bLinf 287.1680765 2.3396592 122.772254 282.7681925 292.0508562 0.0006662
sGrowth 9.6000819 0.2015170 47.630110 9.2045096 9.9965840 0.0006662
sKAnnual 0.4095895 0.1020587 4.167034 0.2777268 0.6707852 0.0006662
tGrowth 0.0828494 0.2171573 0.394426 -0.3511366 0.4929744 0.6495670

Table 7. Model summary.

n K nchains niters nthin ess rhat converged
1142 6 3 500 500 1136 1.003 TRUE

Table 8. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
1142 6 3 500 1.003 1.013 1.006 TRUE
##### Largescale Sucker

Table 9. Model coefficients.

term estimate sd zscore lower upper pvalue
bKIntercept -2.352517 3.470345 -0.7511485 -10.0123652 3.977219 0.4337109
bKRegime[2] -2.898824 3.450703 -0.7691769 -9.1704883 4.534619 0.4603598
bLinf 635.111272 99.015320 6.6794026 536.8266817 928.031775 0.0006662
sGrowth 8.981498 0.366308 24.5662641 8.3355939 9.754696 0.0006662
sKAnnual 2.116388 1.292681 1.8975718 0.9771194 6.022412 0.0006662
tGrowth -2.898824 3.450703 -0.7691769 -9.1704883 4.534619 0.4603598

Table 10. Model summary.

n K nchains niters nthin ess rhat converged
303 6 3 500 500 82 1.064 FALSE

Table 11. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
303 6 3 500 1.064 1.757 2.912 FALSE

#### Condition

Table 12. Parameter descriptions.

Parameter Description
bWeightIntercept Intercept for eWeightIntercept
bWeightRegimeIntercept[i] Effect of ith Regime on bWeightIntercept
bWeightRegimeSlope[i] Effect of ith Regime on bWeightSlope
bWeightSeasonIntercept[i] Effect of ith Season on bWeightIntercept
bWeightSeasonSlope[i] Effect of ith Season on bWeightSlope
bWeightSlope Intercept for eWeightSlope
bWeightYearIntercept[i] Effect of ith Year on bWeightIntercept
bWeightYearSlope[i] Random effect of ith Year on bWeightSlope
eWeight[i] Expected Weight of the ith fish
eWeightIntercept[i] Intercept for log(eWeight[i])
eWeightSlope[i] Effect of LogLength on eWeightIntercept
LogLength[i] The centered log(Length) of the ith fish
sWeight SD of residual variation about eWeight
sWeightYearIntercept SD of bWeightYearIntercept
sWeightYearSlope SD of bWeightYearSlope
Weight[i] The Weight of the ith fish
##### Bull Trout

Table 13. Model coefficients.

term estimate sd zscore lower upper pvalue
bWeightIntercept 6.8166826 0.0242804 280.7480460 6.7704401 6.8659191 0.0006662
bWeightRegimeIntercept[2] -0.0838463 0.0336963 -2.4701919 -0.1495648 -0.0182574 0.0139907
bWeightRegimeSlope[2] 0.0402081 0.0460121 0.8920033 -0.0476286 0.1348475 0.3484344
bWeightSeasonIntercept[2] 0.0009707 0.0086753 0.0922100 -0.0159284 0.0174969 0.9253831
bWeightSeasonSlope[2] 0.0085434 0.0220951 0.3811584 -0.0356207 0.0515235 0.6828781
bWeightSlope 3.1675132 0.0331265 95.5808860 3.0986533 3.2312403 0.0006662
sWeight 0.1362534 0.0015990 85.1977311 0.1330747 0.1394445 0.0006662
sWeightYearIntercept 0.0675277 0.0140357 4.9424494 0.0483610 0.1030031 0.0006662
sWeightYearSlope 0.0867526 0.0211165 4.2331160 0.0562734 0.1389527 0.0006662
tCondition1 -0.0838463 0.0336963 -2.4701919 -0.1495648 -0.0182574 0.0139907
tCondition2 0.0402081 0.0460121 0.8920033 -0.0476286 0.1348475 0.3484344

Table 14. Model summary.

n K nchains niters nthin ess rhat converged
3630 11 3 500 200 675 1.003 TRUE

Table 15. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
3630 11 3 500 1.003 1.003 1.002 TRUE
##### Mountain Whitefish

Table 16. Model coefficients.

term estimate sd zscore lower upper pvalue
bWeightIntercept 4.8029945 0.0141002 340.6197156 4.7748676 4.8312753 0.0006662
bWeightRegimeIntercept[2] -0.0151951 0.0202780 -0.7538523 -0.0568943 0.0240782 0.4390406
bWeightRegimeSlope[2] -0.0061139 0.0247906 -0.2576246 -0.0552766 0.0416127 0.8121252
bWeightSeasonIntercept[2] -0.0446255 0.0038943 -11.4842247 -0.0525053 -0.0371512 0.0006662
bWeightSeasonSlope[2] -0.1053670 0.0178666 -5.8999711 -0.1408853 -0.0705854 0.0006662
bWeightSlope 3.2078663 0.0175648 182.6059766 3.1724569 3.2416189 0.0006662
sWeight 0.1001294 0.0007745 129.2741614 0.0985946 0.1016629 0.0006662
sWeightYearIntercept 0.0396337 0.0084986 4.8152238 0.0282522 0.0612275 0.0006662
sWeightYearSlope 0.0414961 0.0119166 3.5775354 0.0234636 0.0695947 0.0006662
tCondition1 -0.0151951 0.0202780 -0.7538523 -0.0568943 0.0240782 0.4390406
tCondition2 -0.0061139 0.0247906 -0.2576246 -0.0552766 0.0416127 0.8121252

Table 17. Model summary.

n K nchains niters nthin ess rhat converged
8530 11 3 500 500 1004 1.006 TRUE

Table 18. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
8530 11 3 500 1.006 1.006 1.15 FALSE
##### Rainbow Trout

Table 19. Model coefficients.

term estimate sd zscore lower upper pvalue
bWeightIntercept 4.7264442 0.0178071 265.4560365 4.6920934 4.7632632 0.0006662
bWeightRegimeIntercept[2] -0.0150140 0.0249748 -0.6173774 -0.0650983 0.0335656 0.4856762
bWeightRegimeSlope[2] -0.0519394 0.0448721 -1.1628595 -0.1383590 0.0350962 0.2191872
bWeightSeasonIntercept[2] -0.0705237 0.0153196 -4.6156100 -0.1000832 -0.0408214 0.0006662
bWeightSeasonSlope[2] 0.0222651 0.0364029 0.5943697 -0.0485086 0.0933276 0.5536309
bWeightSlope 3.0875166 0.0332232 92.9310496 3.0201936 3.1579685 0.0006662
sWeight 0.1099768 0.0031358 35.1242239 0.1043694 0.1165475 0.0006662
sWeightYearIntercept 0.0398596 0.0120961 3.4381871 0.0232159 0.0696368 0.0006662
sWeightYearSlope 0.0667392 0.0223293 3.1109495 0.0353323 0.1193577 0.0006662
tCondition1 -0.0150140 0.0249748 -0.6173774 -0.0650983 0.0335656 0.4856762
tCondition2 -0.0519394 0.0448721 -1.1628595 -0.1383590 0.0350962 0.2191872

Table 20. Model summary.

n K nchains niters nthin ess rhat converged
663 11 3 500 500 1203 1.003 TRUE

Table 21. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
663 11 3 500 1.003 1.004 1.001 TRUE
##### Largescale Sucker

Table 22. Model coefficients.

term estimate sd zscore lower upper pvalue
bWeightIntercept 6.8232546 0.0232227 293.810078 6.7778992 6.8667944 0.0006662
bWeightSeasonIntercept[2] 0.0216273 0.0053627 4.054425 0.0117158 0.0328505 0.0006662
bWeightSeasonSlope[2] 0.1629237 0.0465700 3.493556 0.0718370 0.2535204 0.0006662
bWeightSlope 2.9127933 0.0734495 39.626157 2.7561414 3.0586804 0.0006662
sWeight 0.0833673 0.0010978 75.946096 0.0812544 0.0856207 0.0006662
sWeightYearIntercept 0.0611456 0.0199913 3.262224 0.0390647 0.1148657 0.0006662
sWeightYearSlope 0.2076533 0.0674905 3.266476 0.1291200 0.3831665 0.0006662

Table 23. Model summary.

n K nchains niters nthin ess rhat converged
2769 7 3 500 500 843 1.002 TRUE

Table 24. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
2765 6 3 500 1.002 1.007 2.633 FALSE

#### Occupancy

Table 25. Parameter descriptions.

Parameter Description
bOccupancySite[i] Effect of ith site on bOccupancyYear
bOccupancySiteYear[i,j] Effect of ith site in jth year on bOccupancyYear
bOccupancySpring Effect of spring on bOccupancyYear
bOccupancyYear[i] Expected Occupancy in ith year
bRate Intercept of eRateYear
bRateRev5[i] Effect of Revelstoke 5 regime on bRate
bRateYear[i] Effect of ith year on biRate
eObserved[i] Probability of observing a species on ith site visit
eRateYear[i] Change in bOccupancyYear between year i-1 and year i
Observed[i] Whether the species was observed on ith site visit
sOccupancySite SD of bOccupancySite
sOccupancySiteYear SD of bOccupancySiteYear
sRateYear SD of bRateYear
##### Rainbow Trout

Table 26. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySpring -0.0211189 0.2933838 -0.0979971 -0.5964877 0.5512443 0.9427049
bRate 0.2537841 0.3430187 0.6925871 -0.5085145 0.8544788 0.4350433
bRateRev5 -0.2047145 0.5098728 -0.4001313 -1.2226440 0.8787705 0.6628914
sOccupancySite 2.0806027 0.4730078 4.5454854 1.4274104 3.3042769 0.0006662
sOccupancySiteYear 0.5931010 0.2000258 2.8809056 0.0950440 0.9331820 0.0006662
sRateYear 0.9728467 0.3069866 3.3034821 0.5344169 1.7067354 0.0006662

Table 27. Model summary.

n K nchains niters nthin ess rhat converged
1096 6 3 500 1000 366 1.005 TRUE
##### Burbot

Table 28. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySpring -0.5055025 0.3039636 -1.646470 -1.0616464 0.0981813 0.1112592
bRate 0.4443332 0.3858177 1.195467 -0.3066406 1.2791748 0.2005330
bRateRev5 -0.6188830 0.5591564 -1.128256 -1.7831547 0.4850129 0.2391739
sOccupancySite 1.0662578 0.3017792 3.686698 0.6769883 1.8392708 0.0006662
sOccupancySiteYear 0.4876430 0.2273156 2.091691 0.0259983 0.8943945 0.0006662
sRateYear 1.1010054 0.3185481 3.575430 0.6365314 1.8663881 0.0006662

Table 29. Model summary.

n K nchains niters nthin ess rhat converged
1096 6 3 500 1000 423 1.005 TRUE
##### Lake Whitefish

Table 30. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySpring -4.8888136 0.7989035 -6.2296245 -6.7578043 -3.6131507 0.0006662
bRate 0.2390948 0.4966443 0.4704596 -0.7520939 1.1535805 0.6322452
bRateRev5 -0.3323371 0.7794873 -0.4032121 -1.8436480 1.2587995 0.6815456
sOccupancySite 0.5073103 0.1717557 3.1062233 0.2565075 0.9383171 0.0006662
sOccupancySiteYear 0.2061891 0.1606613 1.4294934 0.0075733 0.5900137 0.0006662
sRateYear 1.5804621 0.3645380 4.4716618 1.0709421 2.4733664 0.0006662

Table 31. Model summary.

n K nchains niters nthin ess rhat converged
1096 6 3 500 1000 194 1.024 TRUE
##### Northern Pikeminnow

Table 32. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySpring -2.1552771 0.4337606 -4.973836 -3.0033473 -1.3202058 0.0006662
bRate 0.3351248 0.2862747 1.212567 -0.1742807 0.9804073 0.1832112
bRateRev5 -0.4626214 0.4161821 -1.144838 -1.3393860 0.3194777 0.2151899
sOccupancySite 1.3647952 0.3589283 3.945096 0.8552119 2.2392677 0.0006662
sOccupancySiteYear 0.5537642 0.2568455 2.104395 0.0483798 1.0224085 0.0006662
sRateYear 0.7056723 0.2677340 2.781286 0.3180342 1.3635894 0.0006662

Table 33. Model summary.

n K nchains niters nthin ess rhat converged
1096 6 3 500 1000 513 1.006 TRUE
##### Redside Shiner

Table 34. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySpring -0.9379891 0.3706036 -2.5505426 -1.6802086 -0.2304014 0.0099933
bRate 0.3703824 0.5136177 0.7603619 -0.5354205 1.5738008 0.4230513
bRateRev5 -0.5140931 0.7206089 -0.7622041 -2.0820541 0.8429950 0.4083944
sOccupancySite 2.2327082 0.6040548 3.8822362 1.4683617 3.7530884 0.0006662
sOccupancySiteYear 0.2818792 0.2056617 1.5032140 0.0196938 0.7611805 0.0006662
sRateYear 1.3237075 0.4201057 3.3006207 0.7483029 2.3454497 0.0006662

Table 35. Model summary.

n K nchains niters nthin ess rhat converged
1096 6 3 500 1000 249 1.007 TRUE
##### Sculpins

Table 36. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySpring -0.4346491 0.2748119 -1.6123220 -0.9821016 0.0799755 0.0992672
bRate 0.5347873 0.4357812 1.2439978 -0.2644184 1.4457847 0.2138574
bRateRev5 -0.6518429 0.6551080 -0.9900303 -1.9479542 0.6253316 0.2898068
sOccupancySite 1.3207870 0.3031855 4.4996817 0.9151275 2.1170614 0.0006662
sOccupancySiteYear 0.4126556 0.2059560 1.9538603 0.0180123 0.7767846 0.0006662
sRateYear 1.2839029 0.3284961 4.0313897 0.8045447 2.0550941 0.0006662

Table 37. Model summary.

n K nchains niters nthin ess rhat converged
1096 6 3 500 1000 224 1.008 TRUE

#### Count

Table 38. Parameter descriptions.

Parameter Description
bDensity bTrendYear in the first year
bDensitySeason Effect of season on bTrendYear
bDensitySite[i] Effect of ith site on bTrendYear
bDensitySiteYear[i,j] Effect of ith site in jth year on bDensityTrend
bDensityYear[i] Effect of ith year on bTrendYear
bRate Exponential population growth rate
bRateRev5 Effect of Rev5 on bRate
bTrendYear[i] The intercept for the log(eDensity) in the ith year
Count[i] Count on ith site visit
eCount[i] Expected count on ith site visit
eDensity[i] Expected lineal count density on ith site visit
eDispersion[i] Overdispersion on ith site visit
ProportionSampled[i] Proportion of site sampled on ith site visit
sDensitySite SD of bDensitySite
sDensitySiteYear SD of bDensitySiteYear
sDensityYear SD of bDensityYear
sDispersion[i] SD of eDispersion
SiteLength[i] Length of site on ith site visit
YearRev5[i] Whether the rate of change between the ith and i+1th year is effectd by Rev5
##### Rainbow Trout

Table 39. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity -2.7051949 0.6772050 -4.036072 -4.1463532 -1.4863898 0.0006662
bDensitySeason[2] -0.1193521 0.1536112 -0.736468 -0.4120815 0.1798996 0.4710193
bRate 0.2416045 0.0711581 3.452179 0.1123462 0.3984610 0.0019987
bRateRev5 -0.3484113 0.1304420 -2.696805 -0.6201202 -0.1138323 0.0099933
sDensitySite 1.5618622 0.3627564 4.435372 1.0473463 2.4749919 0.0006662
sDensitySiteYear 0.7064079 0.0775009 9.141961 0.5628694 0.8682872 0.0006662
sDensityYear 0.6272727 0.1787453 3.625837 0.3693837 1.0906850 0.0006662
sDispersion 0.7981945 0.0526826 15.192758 0.7014973 0.9106660 0.0006662
tCount -0.3484113 0.1304420 -2.696805 -0.6201202 -0.1138323 0.0099933

Table 40. Model summary.

n K nchains niters nthin ess rhat converged
1096 9 3 500 2000 980 1.006 TRUE
##### Burbot

Table 41. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity -2.9860636 0.7961686 -3.765667 -4.5799083 -1.4077311 0.0006662
bDensitySeason[2] -0.7763300 0.2796950 -2.789257 -1.3585135 -0.2739136 0.0046636
bRate 0.1790349 0.1107058 1.603171 -0.0346883 0.3979308 0.0966023
bRateRev5 -0.4014537 0.2131198 -1.882632 -0.8440015 0.0286095 0.0606262
sDensitySite 0.8635717 0.2456301 3.687171 0.5418852 1.4862107 0.0006662
sDensitySiteYear 0.4372803 0.1828296 2.336221 0.0597502 0.7758318 0.0006662
sDensityYear 1.0901883 0.2991498 3.762872 0.6480600 1.8221336 0.0006662
sDispersion 1.2125365 0.1340482 9.033011 0.9569587 1.4710729 0.0006662
tCount -0.4014537 0.2131198 -1.882632 -0.8440015 0.0286095 0.0606262

Table 42. Model summary.

n K nchains niters nthin ess rhat converged
1096 9 3 500 2000 1190 1.006 TRUE
##### Northern Pikeminnow

Table 43. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity -4.1309573 0.7767589 -5.405655 -5.8609401 -2.7906326 0.0006662
bDensitySeason[2] -2.3853256 0.4331203 -5.561123 -3.2941309 -1.6211892 0.0006662
bRate 0.3302540 0.0946643 3.565492 0.1626128 0.5379072 0.0006662
bRateRev5 -0.6243164 0.1678747 -3.782043 -0.9864425 -0.3262295 0.0019987
sDensitySite 1.2642294 0.3432588 3.849017 0.8051259 2.1237908 0.0006662
sDensitySiteYear 0.6673665 0.1909880 3.411952 0.2062757 0.9854695 0.0006662
sDensityYear 0.6337221 0.2138734 3.105955 0.3330658 1.1557920 0.0006662
sDispersion 1.3366890 0.1301647 10.310899 1.1002730 1.6054051 0.0006662
tCount -0.6243164 0.1678747 -3.782043 -0.9864425 -0.3262295 0.0019987

Table 44. Model summary.

n K nchains niters nthin ess rhat converged
1096 9 3 500 2000 1070 1.007 TRUE
##### Suckers

Table 45. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity 1.9723382 0.2166413 9.093113 1.5432369 2.4011244 0.0006662
bDensityRev5 0.5783026 0.2597159 2.226959 0.0656159 1.0905701 0.0246502
bDensitySeason[2] -0.3095755 0.0928386 -3.348808 -0.4865168 -0.1348317 0.0006662
sDensitySite 0.4500476 0.0989077 4.656642 0.3053964 0.6891601 0.0006662
sDensitySiteYear 0.5076887 0.0456408 11.125705 0.4214611 0.6024636 0.0006662
sDensityYear 0.5463992 0.0992974 5.587980 0.4008861 0.7852651 0.0006662
sDispersion 0.7383009 0.0221660 33.311984 0.6957616 0.7845337 0.0006662
tCount 0.5783026 0.2597159 2.226959 0.0656159 1.0905701 0.0246502

Table 46. Model summary.

n K nchains niters nthin ess rhat converged
1096 8 3 500 200 142 1.038 FALSE

#### Movement

Table 47. Parameter descriptions.

Parameter Description
bLength Effect of Length on bMoved
bLengthSpring Effect of Spring on bLength
bMoved Intercept for logit(eMoved)
bMovedSpring Effect of Spring on bMoved
eMoved[i] Probability of different site from previous encounter for ith recaptured fish
Length[i] Length of ith recaptured fish (mm)
Moved[i] Indicates whether ith recaptured fish is recorded at a different site from previous encounter
Spring[i] Whether the ith recaptured is from the spring
##### Bull Trout

Table 48. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength 0.0050559 0.0015796 3.2237394 0.0020402 0.0083934 0.0006662
bLengthSpring 0.0012484 0.0058311 0.3211759 -0.0076176 0.0152995 0.8187875
bMoved -2.0021253 0.6898047 -2.9212149 -3.4733841 -0.7255709 0.0019987
bMovedSpring 0.3117504 2.5278178 0.0604711 -5.3193628 4.4640225 0.8907395

Table 49. Model summary.

n K nchains niters nthin ess rhat converged
157 4 3 500 500 1437 1.001 TRUE
##### Mountain Whitefish

Table 50. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength -0.0019543 0.0028975 -0.6847212 -0.0074879 0.0035420 0.4803464
bLengthSpring -0.0263823 0.0066429 -3.9881570 -0.0401646 -0.0138978 0.0006662
bMoved 0.4406461 0.7379263 0.6124895 -0.9888788 1.8485747 0.5416389
bMovedSpring 5.4182611 1.5846881 3.4179195 2.3832482 8.5514241 0.0006662

Table 51. Model summary.

n K nchains niters nthin ess rhat converged
489 4 3 500 500 1268 1 TRUE
##### Rainbow Trout

Table 52. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength 0.0114662 0.0059343 1.986689 0.0006735 0.0250390 0.0366422
bLengthSpring 0.2159914 0.1212505 1.869137 0.0275220 0.4828487 0.0126582
bMoved -3.5209461 1.6116435 -2.280991 -7.0724454 -0.6771077 0.0139907
bMovedSpring -65.7943350 36.6070156 -1.892888 -147.2647827 -9.1633549 0.0099933

Table 53. Model summary.

n K nchains niters nthin ess rhat converged
27 4 3 500 500 1167 1.002 TRUE
##### Largescale Sucker

Table 54. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength -0.0106151 0.0054874 -1.979825 -0.0224177 -0.0006919 0.0379747
bLengthSpring -0.1762254 0.0847866 -2.142366 -0.3610148 -0.0343018 0.0086609
bMoved 4.4296540 2.3704001 1.925367 0.1732403 9.4337950 0.0419720
bMovedSpring 77.3757147 37.3347441 2.135704 14.6155554 158.8981791 0.0086609

Table 55. Model summary.

n K nchains niters nthin ess rhat converged
81 4 3 500 500 427 1.008 TRUE

#### Abundance

Table 56. Parameter descriptions.

Parameter Description
bDensity Intercept for log(eDensity) in the 1st year
bDensitySeason[i] Effect of ith season on bTrendYear
bDensitySite[i] Effect of ith site on bDensity
bDensitySiteYear[i,j] Effect of ith site in jth year on bDensity
bDensityYear[i] Effect of ith year on bDensity
bEfficiency Intercept for logit(eEfficiency)
bEfficiencySeason[i] Effect of ith season on bEfficiency
bEfficiencySessionSeasonYear[i, j, k] Effect of ith Session in jth Season of kth Year on bEfficiency
bRate Exponential annual population growth rate
bRateRev5[i] Effect of Rev5 on bRate
bTrendYear[i] Intercept for log(eDensity) in the ith year
Catch[i] Number of fish caught on ith site visit
eAbundance[i] Predicted abundance on ith site visit
eDensity[i] Predicted lineal density on ith site visit
eEfficiency[i] Predicted efficiency during ith site visit
Marked[i] Number of marked fish caught in ith river visit
sDensitySite SD of bDensitySite
sDensitySiteYear SD of bDensitySiteYear
sDensityYear SD of bDensityYear
sEfficiencySessionSeasonYear SD of bEfficiencySessionSeasonYear
Tagged[i] Number of fish tagged prior to ith river visit
##### Bull Trout
###### Juvenile

Table 57. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity 2.0529633 0.3643553 5.6419537 1.2940096 2.7447415 0.0006662
bDensitySeason[2] 0.2339380 0.3533404 0.6687714 -0.4216598 0.9338769 0.4990007
bEfficiency -3.1511169 0.1390130 -22.6589741 -3.4221171 -2.8809197 0.0006662
bEfficiencySeason[2] -0.3669385 0.3539413 -1.0534084 -1.0944416 0.3094929 0.2818121
bMultiplierType[2] 0.4924246 0.1440083 3.4447712 0.2230068 0.7787287 0.0019987
bRate 0.1428264 0.0434402 3.2989324 0.0601781 0.2313121 0.0033311
bRateRev5 -0.1486458 0.0835254 -1.7997614 -0.3177113 0.0086817 0.0566289
sDensitySite 0.6293581 0.1521014 4.2631644 0.4161771 1.0120476 0.0006662
sDensitySiteYear 0.2826389 0.0532901 5.2830055 0.1718522 0.3807650 0.0006662
sDensityYear 0.4003514 0.1084853 3.7611028 0.2304797 0.6409416 0.0006662
sDispersion -0.8975232 0.1265749 -7.1636252 -1.1868920 -0.6844391 0.0006662
sDispersionType[2] 0.4042719 0.2373376 1.6527969 -0.1067815 0.8328237 0.1205863
sEfficiencySessionSeasonYear 0.2522319 0.0468564 5.3671331 0.1631056 0.3467806 0.0006662
tAbundance -0.1486458 0.0835254 -1.7997614 -0.3177113 0.0086817 0.0566289

Table 58. Model summary.

n K nchains niters nthin ess rhat converged
1211 14 3 500 500 544 1.006 TRUE

Table 59. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity 4.1859710 0.2580021 16.1719566 3.6486484 4.6571261 0.0006662
bDensitySeason[2] -0.2033853 0.3449450 -0.5794384 -0.8363666 0.5130081 0.5389740
bEfficiency -3.6192948 0.1184504 -30.5606299 -3.8540114 -3.3957365 0.0006662
bEfficiencySeason[2] -0.0893283 0.3493405 -0.2860700 -0.8024300 0.5389374 0.7828115
bMultiplierType[2] 0.6087917 0.1190852 5.1062637 0.3835729 0.8434613 0.0006662
bRate 0.0182260 0.0256005 0.7258335 -0.0352378 0.0703218 0.4523651
bRateRev5 -0.0050941 0.0500328 -0.1205790 -0.1048534 0.0929095 0.9280480
sDensitySite 0.5212359 0.1262549 4.3101459 0.3634835 0.8390878 0.0006662
sDensitySiteYear 0.4018795 0.0392624 10.2805731 0.3295881 0.4796723 0.0006662
sDensityYear 0.2002960 0.0824979 2.4730273 0.0379251 0.3794340 0.0006662
sDispersion -0.9085711 0.0861245 -10.5559208 -1.0893487 -0.7475905 0.0006662
sDispersionType[2] 0.4059878 0.1669858 2.4245293 0.0692949 0.7318899 0.0179880
sEfficiencySessionSeasonYear 0.1999823 0.0414635 4.8791176 0.1242672 0.2851098 0.0006662
tAbundance -0.0050941 0.0500328 -0.1205790 -0.1048534 0.0929095 0.9280480

Table 60. Model summary.

n K nchains niters nthin ess rhat converged
1211 14 3 500 500 585 1.008 TRUE
##### Mountain Whitefish
###### Juvenile

Table 61. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity 5.6816464 0.6604471 8.6035822 4.3319739 7.0293233 0.0006662
bDensitySeason[2] 0.3877354 0.6940322 0.5775852 -0.9862879 1.8043141 0.5483011
bEfficiency -5.7826757 0.4486936 -12.9350860 -6.8125697 -4.9968378 0.0006662
bEfficiencySeason[2] 0.0998247 0.6950220 0.1240544 -1.3376216 1.4191500 0.8840773
bMultiplierType[2] 0.8969023 0.1924674 4.6497038 0.5359927 1.2755229 0.0006662
bRate 0.0935275 0.1469269 0.6613852 -0.1639698 0.4075821 0.5043304
bRateRev5 -0.1572920 0.1949248 -0.8265433 -0.5740876 0.1896977 0.4083944
sDensitySite 0.8950822 0.2138415 4.3546389 0.6112824 1.4368639 0.0006662
sDensitySiteYear 0.5395837 0.0618339 8.7534063 0.4259818 0.6700358 0.0006662
sDensityYear 0.4593405 0.1746362 2.7930515 0.2306607 0.8854366 0.0006662
sDispersion -0.5406260 0.0869359 -6.2824077 -0.7285570 -0.3865931 0.0006662
sDispersionType[2] 0.6002065 0.1506491 4.0109040 0.3235035 0.9039499 0.0006662
sEfficiencySessionSeasonYear 0.3201542 0.0608110 5.2990462 0.2154955 0.4435075 0.0006662
tAbundance -0.1572920 0.1949248 -0.8265433 -0.5740876 0.1896977 0.4083944

Table 62. Model summary.

n K nchains niters nthin ess rhat converged
995 14 3 500 500 116 1.037 FALSE

Table 63. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity 6.6330829 0.2123302 31.2507257 6.2198812 7.0452007 0.0006662
bDensitySeason[2] -0.6156399 0.1132639 -5.4645941 -0.8461007 -0.4002648 0.0006662
bEfficiency -3.9832943 0.0592741 -67.1998023 -4.1011046 -3.8668193 0.0006662
bEfficiencySeason[2] 0.8643610 0.1134215 7.5850353 0.6440628 1.0801909 0.0006662
bMultiplierType[2] 0.8309869 0.1170480 7.0989377 0.6029264 1.0579082 0.0006662
bRate -0.0033987 0.0180606 -0.1833426 -0.0378838 0.0331600 0.8574284
bRateRev5 0.0245543 0.0346176 0.7059429 -0.0464292 0.0904741 0.4963358
sDensitySite 0.5992936 0.1419010 4.3580822 0.4055336 0.9794851 0.0006662
sDensitySiteYear 0.4050866 0.0278353 14.5868181 0.3530109 0.4613234 0.0006662
sDensityYear 0.1187903 0.0625967 1.9073700 0.0099283 0.2524529 0.0006662
sDispersion -0.8099160 0.0364119 -22.2428965 -0.8809641 -0.7406524 0.0006662
sDispersionType[2] 0.4337653 0.0943264 4.6141835 0.2467712 0.6173565 0.0006662
sEfficiencySessionSeasonYear 0.2215050 0.0281099 7.9075601 0.1715526 0.2807482 0.0006662
tAbundance 0.0245543 0.0346176 0.7059429 -0.0464292 0.0904741 0.4963358

Table 64. Model summary.

n K nchains niters nthin ess rhat converged
1211 14 3 500 500 196 1.017 TRUE
##### Rainbow Trout

Table 65. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity 0.5035328 0.5535634 0.8991013 -0.6415210 1.6055876 0.3550966
bDensitySeason[2] 0.1665738 0.6970374 0.3021429 -1.0665170 1.6045870 0.8001332
bEfficiency -2.5466367 0.2585561 -9.9087863 -3.1236454 -2.0773126 0.0006662
bEfficiencySeason[2] -0.4533962 0.6920429 -0.6990281 -1.8533202 0.8223461 0.4990007
bMultiplierType[2] -0.0299201 1.9889840 0.0117350 -3.8220236 4.0732843 0.9906729
bRate 0.0023524 0.1369591 -0.0186858 -0.2877056 0.2683257 0.9853431
bRateRev5 0.0825676 0.1830594 0.4605125 -0.2820071 0.4425316 0.6215856
sDensitySite 1.1631629 0.3093726 3.9208599 0.7671309 1.9162633 0.0006662
sDensitySiteYear 0.5284092 0.1320284 3.9844240 0.2392489 0.7817148 0.0006662
sDensityYear 0.3544851 0.1994533 1.8540220 0.0270004 0.8289877 0.0006662
sDispersion -1.4727050 1.0531446 -1.6568585 -4.3706970 -0.4486307 0.0006662
sDispersionType[2] -0.0967444 2.0336782 -0.0198595 -3.9784430 4.0945658 0.9653564
sEfficiencySessionSeasonYear 0.3314460 0.1346054 2.4330432 0.0448715 0.5855767 0.0006662
tAbundance 0.0825676 0.1830594 0.4605125 -0.2820071 0.4425316 0.6215856

Table 66. Model summary.

n K nchains niters nthin ess rhat converged
875 14 3 500 500 132 1.016 FALSE
##### Largescale Sucker

Table 67. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity 5.1056970 0.2403126 21.2628672 4.6068258 5.5729691 0.0006662
bDensitySeason[2] -0.0089223 0.5552050 0.0502835 -0.9173956 1.2070935 0.9880080
bEfficiency -3.5133030 0.1438967 -24.4181839 -3.8002228 -3.2455222 0.0006662
bEfficiencySeason[2] -1.1053125 0.5598503 -2.0242550 -2.3361830 -0.1496616 0.0193205
bMultiplierType[2] 0.6392151 0.2209639 2.8979748 0.2108205 1.0853563 0.0059960
sDensitySite 0.4814094 0.1196857 4.1794057 0.3224456 0.7779551 0.0006662
sDensitySiteYear 0.4190435 0.0501355 8.3693694 0.3249745 0.5221869 0.0006662
sDensityYear 0.5051093 0.1780942 2.9973844 0.2689088 0.9405951 0.0006662
sDispersion -0.6902780 0.0677848 -10.1966320 -0.8308407 -0.5620322 0.0006662
sDispersionType[2] 0.4027684 0.1289317 3.0948560 0.1457699 0.6401236 0.0033311
sEfficiencySessionSeasonYear 0.4853366 0.0702473 6.9731355 0.3678391 0.6408407 0.0006662

Table 68. Model summary.

n K nchains niters nthin ess rhat converged
780 11 3 500 500 436 1.006 TRUE

#### Distribution

Table 69. Parameter descriptions.

Parameter Description
bEffect Intercept for eEffect
bRkm Effect of Rkm on bEffect
bRkmRev5 Effect of Rev5 on bRkm
bRkmYear[i] Effect of ith year on bRkm
eEffect Expected Effect
Effect Estimated site and year effect from the count or abundance model
Rkm Standardised river kilometre
sEffect SD of residual variation in Effect
sRkmYear SD of bRkmYear
##### Bull Trout
###### Juvenile

Table 70. Model coefficients.

term estimate sd zscore lower upper pvalue
bEffect 0.0005560 0.0070110 0.0624877 -0.0130753 0.0140627 0.9280480
bRkm -0.0024619 0.0037364 -0.6466934 -0.0093860 0.0050706 0.4963358
bRkmRev5 0.0046702 0.0053132 0.8619732 -0.0057774 0.0147606 0.3777482
sEffect 0.1175736 0.0050325 23.3820282 0.1083647 0.1278787 0.0006662
sRkmYear 0.0036914 0.0034803 1.2626905 0.0001472 0.0126233 0.0006662
tDistribution 0.0046702 0.0053132 0.8619732 -0.0057774 0.0147606 0.3777482

Table 71. Model summary.

n K nchains niters nthin ess rhat converged
285 6 3 500 10 180 1.008 TRUE

Table 72. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
285 6 3 500 1.008 1.007 1.014 TRUE

Table 73. Model coefficients.

term estimate sd zscore lower upper pvalue
bEffect 0.0000161 0.0146368 0.0397544 -0.0268423 0.0296271 0.9986676
bRkm -0.0068287 0.0091752 -0.7582207 -0.0251290 0.0114135 0.4203864
bRkmRev5 0.0209920 0.0135455 1.5354268 -0.0047073 0.0468544 0.1285809
sEffect 0.2532118 0.0112255 22.6257503 0.2333017 0.2753542 0.0006662
sRkmYear 0.0170700 0.0085107 2.0303378 0.0016103 0.0351675 0.0006662
tDistribution 0.0209920 0.0135455 1.5354268 -0.0047073 0.0468544 0.1285809

Table 74. Model summary.

n K nchains niters nthin ess rhat converged
285 6 3 500 10 270 1.01 TRUE

Table 75. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
285 6 3 500 1.01 1.017 1.012 TRUE
##### Mountain Whitefish

Table 76. Model coefficients.

term estimate sd zscore lower upper pvalue
bEffect -0.0007872 0.0167896 -0.0522631 -0.0335893 0.0329969 0.9560293
bRkm -0.0063828 0.0148024 -0.4466699 -0.0356024 0.0228475 0.6335776
bRkmRev5 0.0202507 0.0213924 0.9540819 -0.0226802 0.0609906 0.3257828
sEffect 0.2873738 0.0129032 22.3162554 0.2647355 0.3141468 0.0006662
sRkmYear 0.0354937 0.0104231 3.5071894 0.0184673 0.0601103 0.0006662
tDistribution 0.0202507 0.0213924 0.9540819 -0.0226802 0.0609906 0.3257828

Table 77. Model summary.

n K nchains niters nthin ess rhat converged
285 6 3 500 10 918 1.003 TRUE

Table 78. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
285 6 3 500 1.003 1.008 1.004 TRUE
##### Rainbow Trout

Table 79. Model coefficients.

term estimate sd zscore lower upper pvalue
bEffect 0.0014539 0.0205235 0.0629021 -0.0381008 0.0423060 0.9626915
bRkm -0.0275127 0.0168693 -1.6326304 -0.0609019 0.0055611 0.1019320
bRkmRev5 0.0506114 0.0251752 2.0188935 0.0034055 0.1011712 0.0353098
sEffect 0.3498825 0.0153002 22.9142667 0.3228388 0.3825013 0.0006662
sRkmYear 0.0401194 0.0127838 3.2422669 0.0195411 0.0692078 0.0006662
tDistribution 0.0506114 0.0251752 2.0188935 0.0034055 0.1011712 0.0353098

Table 80. Model summary.

n K nchains niters nthin ess rhat converged
285 6 3 500 10 956 1.004 TRUE

Table 81. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
285 6 3 500 1.004 1.003 1.002 TRUE
##### Burbot

Table 82. Model coefficients.

term estimate sd zscore lower upper pvalue
bEffect 0.0050579 0.0054731 0.9266906 -0.0056143 0.0159120 0.3604264
bRkm -0.0001730 0.0038312 -0.0712277 -0.0077430 0.0074115 0.9653564
bRkmRev5 0.0000940 0.0058511 -0.0095035 -0.0113190 0.0115683 0.9893404
sEffect 0.0926473 0.0039330 23.5786832 0.0852809 0.1005426 0.0006662
sRkmYear 0.0087613 0.0030949 2.9069827 0.0036781 0.0154934 0.0006662
tDistribution 0.0000940 0.0058511 -0.0095035 -0.0113190 0.0115683 0.9893404

Table 83. Model summary.

n K nchains niters nthin ess rhat converged
285 6 3 500 10 1007 1.004 TRUE

Table 84. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
285 6 3 500 1.004 1.004 1.002 TRUE
##### Northern Pikeminnow

Table 85. Model coefficients.

term estimate sd zscore lower upper pvalue
bEffect 0.0075408 0.0122483 0.5866496 -0.0179544 0.0309517 0.5549634
bRkm -0.0060325 0.0070691 -0.8410001 -0.0201001 0.0074931 0.4057295
bRkmRev5 0.0036046 0.0105771 0.3636478 -0.0168000 0.0253749 0.7295137
sEffect 0.2073002 0.0090617 22.9017328 0.1904712 0.2255666 0.0006662
sRkmYear 0.0117230 0.0065332 1.8561004 0.0011888 0.0259696 0.0006662
tDistribution 0.0036046 0.0105771 0.3636478 -0.0168000 0.0253749 0.7295137

Table 86. Model summary.

n K nchains niters nthin ess rhat converged
285 6 3 500 10 372 1.004 TRUE

Table 87. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
285 6 3 500 1.004 1.033 1.02 TRUE
##### Suckers

Table 88. Model coefficients.

term estimate sd zscore lower upper pvalue
bEffect -0.0033554 0.0193178 -0.141963 -0.0396495 0.0346014 0.8614257
bRkm -0.0176746 0.0159376 -1.100899 -0.0493184 0.0141814 0.2618254
bRkmRev5 0.0248050 0.0232503 1.075789 -0.0197124 0.0718914 0.2724850
sEffect 0.3216352 0.0142079 22.668846 0.2954979 0.3504725 0.0006662
sRkmYear 0.0388333 0.0117806 3.392725 0.0202747 0.0676331 0.0006662
tDistribution 0.0248050 0.0232503 1.075789 -0.0197124 0.0718914 0.2724850

Table 89. Model summary.

n K nchains niters nthin ess rhat converged
285 6 3 500 10 1056 1.003 TRUE

Table 90. Sensitivity of posteriors to choice of priors.

n K nchains niters rhat_1 rhat_2 rhat_all converged
285 6 3 500 1.003 1.004 1.003 TRUE

#### Effect Size

Table 91. The significance levels for the management hypotheses tested in the analyses. The Direction column indicates whether significant changes were positive or negative. The estimates and 95% lower and upper credible intervals are the effect sizes.

Analysis Species Stage Significance Direction Estimate Lower Upper
Abundance/Count - Density Sucker All 0.0246502 + 78 % 7 % 198 %
Abundance/Count - Rate Bull Trout Juvenile 0.0566289 -14 % -27 % 1 %
Abundance/Count - Rate Bull Trout Adult 0.9280480 -1 % -10 % 10 %
Abundance/Count - Rate Mountain Whitefish Juvenile 0.4083944 -15 % -44 % 21 %
Abundance/Count - Rate Mountain Whitefish Adult 0.4963358 2 % -5 % 9 %
Abundance/Count - Rate Rainbow Trout All 0.0099933 - -29 % -46 % -11 %
Abundance/Count - Rate Rainbow Trout Adult 0.6215856 9 % -25 % 56 %
Abundance/Count - Rate Burbot All 0.0606262 -33 % -57 % 3 %
Abundance/Count - Rate Northern Pikeminnow All 0.0019987 - -46 % -63 % -28 %
Condition Bull Trout Juvenile 0.0166556 - -9 % -16 % -3 %
Condition Bull Trout Adult 0.0273151 - -7 % -13 % -1 %
Condition Mountain Whitefish Juvenile 0.7441706 -1 % -7 % 5 %
Condition Mountain Whitefish Adult 0.4177215 -2 % -6 % 2 %
Condition Rainbow Trout Juvenile 0.8707528 0 % -6 % 7 %
Condition Rainbow Trout Adult 0.2485010 -3 % -9 % 2 %
Distribution Bull Trout Juvenile 0.3777482 0 % -1 % 1 %
Distribution Bull Trout Adult 0.1285809 2 % 0 % 5 %
Distribution Mountain Whitefish Adult 0.3257828 2 % -2 % 6 %
Distribution Rainbow Trout All 0.0353098 + 5 % 0 % 11 %
Distribution Sucker All 0.2724850 3 % -2 % 7 %
Distribution Burbot All 0.9893404 0 % -1 % 1 %
Distribution Northern Pikeminnow All 0.7295137 0 % -2 % 3 %
Growth Bull Trout All 0.6548967 -7 % -31 % 24 %
Growth Mountain Whitefish All 0.7268488 8 % -30 % 64 %

## Acknowledgements

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

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