# Middle Columbia River Fish Indexing Analysis 2016

The suggested citation for this analytic report is:

Thorley, J.L. and Campos M. (2017) Middle Columbia River Fish Indexing Analysis 2016. A Poisson Consulting Analysis Report. URL: http://www.poissonconsulting.ca/f/577548349.

## 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, species diversity (evenness) and the modeling of environmental-fish metric relationships and scale age data. 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 provided by Golder Associates.

#### Life-Stage

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

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

### Statistical Analysis

Model parameters were estimated using Bayesian methods. The estimates were produced using JAGS (Plummer 2015). For additional information on Bayesian modelling in the BUGS language, of which JAGS uses a dialect, the reader is referred to Kery and Schaub (2011).

Unless indicated otherwise, the Bayesian analyses used uninformative normal prior distributions (Kery and Schaub 2011, 36). The posterior distributions were estimated from 2,000 Markov Chain Monte Carlo (MCMC) samples thinned from the second halves of four chains (Kery and Schaub 2011, 38–40). Model convergence was confirmed by ensuring that $$\hat{R} < 1.1$$ (Kery and Schaub 2011, 40) for each of the monitored parameters (Kery and Schaub 2011, 61).

The parameters are summarised in terms of the point estimate, standard deviation (sd), the z-score, lower and upper 95% confidence/credible limits (CLs) and the p-value (Kery and Schaub 2011, 37, 42). The estimate is the median (50th percentile) of the MCMC samples, the z-score is $$\mathrm{mean}/\mathrm{sd}$$ and the 95% CLs are the 2.5th and 97.5th percentiles. A p-value of 0.05 indicates that the lower or upper 95% CL is 0.

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

The results are displayed graphically by plotting the modeled relationships between particular variables and the response(s) with the remaining variables held constant. In general, continuous and discrete fixed variables are held constant at their mean and first level values, respectively, while random variables are held constant at their typical values (expected values of the underlying hyperdistributions) (Kery and Schaub 2011, 77–82). When informative the influence of particular variables is expressed in terms of the effect size (i.e., percent change in the response variable) with 95% confidence/credible intervals (CIs, Bradford, Korman, and Higgins 2005).

The analyses were implemented using R version 3.3.2 (R Core Team 2016) and the jmbr package.

#### Growth

Annual growth was estimated from the inter-annual recaptures using the Fabens method (Fabens 1965) for estimating the von Bertalanffy (VB) growth curve (von Bertalanffy 1938). 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:

• $$L_{\infty}$$ is constant.
• $$k$$ can vary with discharge regime.
• $$k$$ can vary randomly with year.
• The residual variation in growth is normally distributed.

#### Condition

Condition was estimated via an analysis of mass-length relations (He et al. 2008).

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., $$\log(L) - \overline{\log(L)}$$, prior to model fitting.

Preliminary analyses indicated that the variation in the exponent $$\beta$$ with respect to year was not informative.

Key assumptions of the final condition model include:

• The expected weight varies with length as an allometric relationship.
• The intercept of the log-transformed allometric relationship is described by a linear mixed model.
• The intercept of the log-transformed allometric relationship varies with discharge regime and season.
• The intercept of the log-transformed allometric relationship varies randomly with year, site and the interaction between year and site.
• The slope of the log-transformed allometric relationship is described by a linear mixed model.
• The slope of the log-transformed allometric relationship varies with discharge regime and season.
• The slope of the log-transformed allometric relationship varies randomly with year.
• The residual variation in weight for the log-transformed allometric relationship is independently and identically normally distributed.

#### Occupancy

Occupancy, which is the probability that a particular species was present at a site, was estimated from the temporal replication of detection data (Kery, 2010; Kery and Schaub, 2011, pp. 238-242 and 414-418), 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 (probability of presence) is described by a generalized linear mixed model with a logit link.
• Occupancy varies with season.
• Occupancy varies randomly with site.
• 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.

#### 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.

#### Count

The count data were analysed using an overdispersed Poisson model (Kery, 2010; Kery and Schaub, 2011, pp. 168-170,180 and 55-56) to provide estimates of the lineal river count density (count/km) by year and site. Unlike Kery (2010) and Kery and Schaub (2011), which used a log-normal distribution to account for the extra-Poisson variation, the current model used a gamma distribution with identical shape and scale parameters because it has a mean of 1 and therefore no overall effect on the expected count. The count data does not enable us to estimate abundance nor observer efficiency, but it enables us to estimate an expected count, which is the product of the two. As such it is necessary to assume that changes in observer efficiency are negligible in order to interpret the estimates as relative density.

Key assumptions of the count model include:

• Lineal density (fish/km) is described by an autoregressive generalized linear mixed model with a logarithm link.
• Lineal density (fish/km) varies with season.
• Lineal density (fish/km) varies randomly with year, site and the interaction between site and year.
• The effect of year on lineal density (fish/km) is autoregressive with a lag of one year and varies with discharge regime.
• The counts are gamma-Poisson distributed, given the mean count.

#### Movement

The extent to which sites are closed, i.e., fish remain at the same site between sessions, was evaluated from a logistic ANCOVA (Kery 2010). 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, length and the interaction between season and length.
• Observed site fidelity is Bernoulli distributed.

#### Observer Length Correction

The bias (accuracy) and error (precisions) in observer’s fish length estimates were quantified using a model with a categorical distribution that compared the proportions of fish in different length-classes for each observer to the equivalent proportions for the measured fish.

Key assumptions of the observer length correction model include:

• The expected length bias can vary by observer.
• The expected length error can vary by observer.
• The residual variation in length is independently and identically normally distributed.

The observed fish lengths were corrected for the estimated length biases.

#### 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:

• Lineal density (fish/km) varies by season.
• Lineal density varies randomly with site and the interaction between site and year.
• Lineal density varies by river km (distribution).
• The effect of river km on lineal density varies with discharge regime and season.
• The effect of river km on lineal density varies randomly with year.
• Lineal density varies by year as a first-order autoregressive term.
• The change in the annual lineal density varies by discharge regime.
• The change in the annual lineal density varies randomly by 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.
• Observed fish are encountered at a different rate to captured fish.
• 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).

Adult Large-Scale Suckers and Adult Rainbow Trout were analysed using a reduced model with 1) no effect of regime or river km on lineal density; 2) no difference in the error or efficiency between encounter types and 3) no autoregressive component, i.e., with the lineal density varying randomly by year as a straight random effect.

#### 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 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.

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

### Growth

model {

bKIntercept ~ dnorm (0, 5^-2)

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

sKYear ~ dunif (0, 5)
for (i in 1:nYear) {
bKYear[i] ~ dnorm(0, sKYear^-2)
bK[i] <- exp(bKIntercept + bKRegime[step(i - Threshold) + 1] + bKYear[i])
}

bLinf ~ dunif(100, 1000)
sGrowth ~ dunif(0, 100)

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

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

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

Template 1.

### 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 ~ dunif(0, 5)
sWeightYearSlope ~ dunif(0, 5)
for(yr in 1:nYear) {
bWeightYearIntercept[yr] ~ dnorm(0, sWeightYearIntercept^-2)
bWeightYearSlope[yr] ~ dnorm(0, sWeightYearSlope^-2)
}

sWeightSiteIntercept ~ dunif(0, 5)
sWeightSiteYearIntercept ~ dunif(0, 5)
for(st in 1:nSite) {
bWeightSiteIntercept[st] ~ dnorm(0, sWeightSiteIntercept^-2)
for(yr in 1:nYear) {
bWeightSiteYearIntercept[st, yr] ~ dnorm(0, sWeightSiteYearIntercept^-2)
}
}

sWeight ~ dunif(0, 5)
for(i in 1:length(Year)) {

eWeightIntercept[i] <- bWeightIntercept + bWeightRegimeIntercept[Regime[i]] + bWeightSeasonIntercept[Season[i]] + bWeightYearIntercept[Year[i]] + bWeightSiteIntercept[Site[i]] + bWeightSiteYearIntercept[Site[i],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]
..

Template 2.

### Occupancy

model {

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

sOccupancySite ~ dunif(0, 5)
for (st in 1:nSite) {
bOccupancySite[st] ~ dnorm(0, sOccupancySite^-2)

bRate ~ dnorm(0, 5^-2)

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

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

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

for (i in 1:length(Year)) {
logit(eObserved[i]) <- bOccupancyYear[Year[i]] + bOccupancySeason[Season[i]] + bOccupancySite[Site[i]]
Observed[i] ~ dbern(eObserved[i])
}
..

Template 3.

### Count

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

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

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

bDensityYear[1] ~ dnorm(0, 5^-2)
for (i in 2:nYear) {
eRateYear[i-1] <- bRate + bRateYear[i-1] + bRateRegime[YearRegime[i-1]]
bDensityYear[i] <- bDensityYear[i-1] + eRateYear[i-1]
}

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

sDispersion ~ dunif(0, 5)
for (i in 1:length(Year)) {

log(eDensity[i]) <- bDensityYear[Year[i]] + bDensitySeason[Season[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 <- bRateRegime[2]
..

Template 4.

### Movement

model {
bMoved ~ dnorm(0, 5^-2)
bLength ~ dnorm(0, 5^-2)
bMovedSeason[1] <- 0
bLengthSeason[1] <- 0

for(i in 2:nSeason) {
bMovedSeason[i] ~ dnorm(0, 5^-5)
bLengthSeason[i] ~ dnorm(0, 5^-5)
}

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

Template 5.

### Observer Length Correction

model {
for(i in 1:nClass) {
dClass[i] <- 1
}
pClass[1:nClass] ~ ddirch(dClass[])

bLength[1] <- 1
sLength[1] <- 1

for(i in 2:nObserver) {
bLength[i] ~ dunif(0.5, 2)
sLength[i] ~ dunif(1, 50)
}
for(i in 1:length(Length))  {
eClass[i] ~ dcat(pClass[])
eLength[i] <- bLength[Observer[i]] * ClassLength[eClass[i]]
eSLength[i] <- sLength[Observer[i]] * ClassSD
Length[i] ~ dnorm(eLength[i], eSLength[i]^-2)
}
..

Template 6.

### Abundance

model {

bEfficiency ~ dnorm(0, 5^-2)
bDistribution ~ dnorm(0, 5^-2)

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

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

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

bDensityYear[1] ~ dnorm(0, 5^-2)
for (i in 2:nYear) {
eRateYear[i-1] <- bRate + bRateYear[i-1] + bRateRegime[YearRegime[i-1]]
bDensityYear[i] <- bDensityYear[i-1] + eRateYear[i-1]
}

sDistributionYear ~ dunif(0, 2)
for (i in 1:nYear) {
bDistributionYear[i] ~ dnorm(0, sDistributionYear^-2)
}

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

sEfficiencySessionSeasonYear ~ dunif(0, 5)
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]]

eDistribution[i] <- bDistribution + bDistributionRegime[Regime[i]] + bDistributionSeason[Season[i]] + bDistributionYear[Year[i]]

log(eDensity[i]) <- bDensityYear[Year[i]] + eDistribution[i] * RiverKm[i]
+ bDensitySeason[Season[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 <- bRateRegime[2]
tDistribution <- bDistributionRegime[2]
..

Template 7.

## Results

### Growth

Table 2. Parameter descriptions.

Parameter Description
bK[i] Expected growth coefficient in the ith year
bKIntercept Intercept for log(bK)
bKRegime[i] Effect of ith regime on log(bK)
bKYear[i] Random effect of ith Year on log(bK)
bLinf Mean maximum length
eGrowth[i] Expected Growth of the ith recapture
Growth[i] Change in length of the ith fish between release and recapture
LengthAtRelease[i] Length of the ith recapture when released
nRegime[i] Number of regimes
sGrowth SD of residual variation in Growth
sKYear[i] SD of effect of Year on log(bK)
Threshold Last year of the first regime
Year[i] Year the ith recapture was released
Years[i] Number of years between release and recapture for the ith recapture

#### Bull Trout

Table 3. Model coefficients.

term estimate sd zscore lower upper pvalue
bKIntercept -1.8641739 0.1054579 -17.7080475 -2.0727196 -1.661006 0.0005
bKRegime$2$ 0.1068986 4.9147096 0.0093809 -9.2812376 9.516509 0.9860
bLinf 857.8394479 28.6424411 30.0296806 808.8380004 920.834623 0.0005
sGrowth 31.1828861 1.4089127 22.1873377 28.5533490 34.191604 0.0005
sKYear 0.2493117 0.0752564 3.4608626 0.1432783 0.437170 0.0005
tGrowth 0.1068986 4.9147096 0.0093809 -9.2812376 9.516509 0.9860

Table 4. Model summary.

n K nsamples nchains nsims duration rhat converged
260 6 2000 4 40000 7.916979 1 TRUE

#### Mountain Whitefish

Table 5. Model coefficients.

term estimate sd zscore lower upper pvalue
bKIntercept -2.6127914 0.1352452 -19.3441983 -2.8905518 -2.3589141 0.0005
bKRegime$2$ -0.1442619 4.9119432 -0.0419278 -9.6515815 9.5267152 0.9730
bLinf 355.1710280 8.1490568 43.6293579 340.7860764 372.5956513 0.0005
sGrowth 10.6877991 0.2428641 44.0263825 10.2439891 11.1882805 0.0005
sKYear 0.3505649 0.1112995 3.3281477 0.2104646 0.6355877 0.0005
tGrowth -0.1442619 4.9119432 -0.0419278 -9.6515815 9.5267152 0.9730

Table 6. Model summary.

n K nsamples nchains nsims duration rhat converged
1000 6 2000 4 40000 29.70091 1.01 TRUE

#### Rainbow Trout

Table 7. Model coefficients.

term estimate sd zscore lower upper pvalue
bKIntercept -1.8943749 0.4945770 -3.9365546 -2.9571878 -1.116554 0.0005
bKRegime$2$ 0.0560165 4.9793517 0.0015026 -9.8213993 10.068428 0.9880
bLinf 571.8868548 132.6802529 4.5985788 438.8368763 945.168842 0.0005
sGrowth 25.3967997 6.2181659 4.2508564 17.1872513 41.000639 0.0005
sKYear 0.3052896 0.3990389 1.0444827 0.0297265 1.494123 0.0005
tGrowth 0.0560165 4.9793517 0.0015026 -9.8213993 10.068428 0.9880

Table 8. Model summary.

n K nsamples nchains nsims duration rhat converged
16 6 2000 4 40000 0.7223349 1.03 TRUE

### Condition

Table 9. 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
bWeightSiteIntercept[i] Random effect of ith site on bWeightIntercept
bWeightSiteYearIntercept[i,j] Random effect of ith site in jth year on bWeightIntercept
bWeightSlope Intercept for eWeightSlope
bWeightYearIntercept[i] Random 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] Slope for log(eWeight[i])
Length[i] Length of ith fish
sWeight Residual SD of Weight
sWeightSiteIntercept SD for the effect of site on bWeightIntercept
sWeightSiteYearIntercept SD for the effect of the combination of site and year on eWeightIntercept
sWeightYearIntercept SD of the effect of year on bWeightIntercept
sWeightYearSlope SD for the random effect of year on eWeightSlope
Weight[i] Weight of ith fish

#### Bull Trout

Table 10. Model coefficients.

term estimate sd zscore lower upper pvalue
bWeightIntercept 6.8224727 0.0184439 369.8938491 6.7839311 6.8584054 0.0005
bWeightRegimeIntercept$2$ -0.1061049 0.0286127 -3.6768983 -0.1595558 -0.0450472 0.0005
bWeightRegimeSlope$2$ 0.0457349 0.0571055 0.8369983 -0.0623809 0.1626876 0.3690
bWeightSeasonIntercept$2$ 0.0014480 0.0092923 0.1386271 -0.0167606 0.0197889 0.8630
bWeightSeasonSlope$2$ 0.0116925 0.0236088 0.4968422 -0.0335823 0.0584057 0.6110
bWeightSlope 3.1612666 0.0374257 84.4896154 3.0857082 3.2373123 0.0005
sWeight 0.1372626 0.0018490 74.2445946 0.1337674 0.1408549 0.0005
sWeightSiteIntercept 0.0110831 0.0057811 1.9514451 0.0011294 0.0240219 0.0005
sWeightSiteYearIntercept 0.0173022 0.0054113 3.1187082 0.0039206 0.0264252 0.0005
sWeightYearIntercept 0.0498527 0.0123718 4.1864850 0.0331467 0.0821260 0.0005
sWeightYearSlope 0.0974516 0.0256138 3.9272937 0.0614732 0.1602472 0.0005
tCondition1 -0.1061049 0.0286127 -3.6768983 -0.1595558 -0.0450472 0.0005
tCondition2 0.0457349 0.0571055 0.8369983 -0.0623809 0.1626876 0.3690

Table 11. Model summary.

n K nsamples nchains nsims duration rhat converged
3013 13 2000 4 640000 7361.41509962082s (~2.04 hours) 1.02 TRUE

#### Mountain Whitefish

Table 12. Model coefficients.

term estimate sd zscore lower upper pvalue
bWeightIntercept 4.7881401 0.0082425 580.9473113 4.7730303 4.8056091 0.0005
bWeightRegimeIntercept$2$ -0.0382501 0.0123472 -3.1213338 -0.0634617 -0.0153703 0.0050
bWeightRegimeSlope$2$ -0.0257996 0.0270373 -0.9529919 -0.0810421 0.0268842 0.3110
bWeightSeasonIntercept$2$ -0.0444107 0.0039602 -11.2071809 -0.0523081 -0.0365914 0.0005
bWeightSeasonSlope$2$ -0.1015766 0.0175103 -5.7976748 -0.1353067 -0.0666228 0.0005
bWeightSlope 3.2101925 0.0177418 180.9159728 3.1742461 3.2445277 0.0005
sWeight 0.0985979 0.0008188 120.4330214 0.0969835 0.1001991 0.0005
sWeightSiteIntercept 0.0062915 0.0027945 2.3246821 0.0013797 0.0126423 0.0005
sWeightSiteYearIntercept 0.0135861 0.0018326 7.4197902 0.0101365 0.0172210 0.0005
sWeightYearIntercept 0.0228453 0.0059260 4.0204448 0.0152810 0.0382084 0.0005
sWeightYearSlope 0.0423574 0.0139876 3.1614422 0.0226610 0.0759205 0.0005
tCondition1 -0.0382501 0.0123472 -3.1213338 -0.0634617 -0.0153703 0.0050
tCondition2 -0.0257996 0.0270373 -0.9529919 -0.0810421 0.0268842 0.3110

Table 13. Model summary.

n K nsamples nchains nsims duration rhat converged
7458 13 2000 4 40000 1338.432 1.02 TRUE

#### Rainbow Trout

Table 14. Model coefficients.

term estimate sd zscore lower upper pvalue
bWeightIntercept 4.6176353 0.0153242 301.3392645 4.5888573 4.6487672 0.0005
bWeightRegimeIntercept$2$ -0.0105954 0.0212952 -0.5219893 -0.0560419 0.0289769 0.5840
bWeightRegimeSlope$2$ -0.0342521 0.0572297 -0.6200595 -0.1476211 0.0723243 0.5300
bWeightSeasonIntercept$2$ -0.0682439 0.0146064 -4.6786801 -0.0963354 -0.0401625 0.0005
bWeightSeasonSlope$2$ 0.0042373 0.0408189 0.1270415 -0.0713895 0.0888590 0.9080
bWeightSlope 3.0907217 0.0373988 82.7121557 3.0239487 3.1700691 0.0005
sWeight 0.1080384 0.0035052 30.8339165 0.1011158 0.1151982 0.0005
sWeightSiteIntercept 0.0171618 0.0114959 1.6089359 0.0007372 0.0454984 0.0005
sWeightSiteYearIntercept 0.0195131 0.0108562 1.8618730 0.0029640 0.0416312 0.0005
sWeightYearIntercept 0.0217561 0.0134809 1.7602155 0.0029458 0.0545759 0.0005
sWeightYearSlope 0.0733275 0.0263202 2.9585403 0.0385498 0.1391262 0.0005
tCondition1 -0.0105954 0.0212952 -0.5219893 -0.0560419 0.0289769 0.5840
tCondition2 -0.0342521 0.0572297 -0.6200595 -0.1476211 0.0723243 0.5300

Table 15. Model summary.

n K nsamples nchains nsims duration rhat converged
546 13 2000 4 80000 86.5664749145508s (~1.44 minutes) 1.07 TRUE

#### Largescale Sucker

Table 16. Model coefficients.

term estimate sd zscore lower upper pvalue
bWeightIntercept 6.8090532 0.0315213 216.065780 6.7533875 6.8741236 5e-04
bWeightSeasonIntercept$2$ 0.0214070 0.0054512 3.914817 0.0111581 0.0319266 5e-04
bWeightSeasonSlope$2$ 0.1753231 0.0477888 3.647121 0.0782321 0.2657080 5e-04
bWeightSlope 2.8715268 0.1148855 24.992947 2.6488541 3.0997607 5e-04
sWeight 0.0824593 0.0012222 67.514292 0.0801789 0.0850479 5e-04
sWeightSiteIntercept 0.0058696 0.0035599 1.721824 0.0003922 0.0137578 5e-04
sWeightSiteYearIntercept 0.0099943 0.0033401 2.914380 0.0023342 0.0156410 5e-04
sWeightYearIntercept 0.0687345 0.0304800 2.490380 0.0409592 0.1434882 5e-04
sWeightYearSlope 0.2447352 0.1190849 2.303969 0.1406327 0.5794410 5e-04

Table 17. Model summary.

n K nsamples nchains nsims duration rhat converged
2303 9 2000 4 2560000 13246.787014246s (~3.68 hours) 1.01 TRUE

### Occupancy

Table 18. Parameter descriptions.

Parameter Description
bOccupancySeason[i] Effect of ith season on logit(eOccupancy)
bOccupancySite[i] Effect of ith site on logit(eOccupancy)
bOccupancyYear[i] Effect of ith year on logit(eOccupancy)
bRate Intercept of eRateYear
bRateRegime[i] Effect of ith regime on eRateYear
bRateYear[i] Effect of ith year on eRateYear
eObserved[i] Probability of observing species on ith site visit
eOccupancy[i] Predicted occupancy (species presence versus absence) on ith site visit
eRateYear[i] Change in bOccupancyYear between year i-1 and year i
nRegime Number of regimes in the dataset (2)
nSeason Number of seasons in the dataset (2)
nSite Number of sites in the dataset
nYear Number of years of data
Observed[i] Whether the species was observed on ith site visit (0 or 1)
Regime[i] Regime ofith site visit
Season[i] Season of ith site visit
Site[i] Site of ith site visit
sOccupancySite SD parameter for the distribution of bOccupancySite[i]
sRateYear SD parameter for the distribution of bRateYear
Year[i] Year of ith site visit

#### Rainbow Trout

Table 19. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySeason$2$ -0.0441430 0.2915208 -0.1708046 -0.6390309 0.4998309 0.8820
bRate 0.1674582 0.4529931 0.2846738 -0.9314858 0.9347612 0.6640
bRateRegime$2$ -0.2266203 0.7641868 -0.2506344 -1.6226028 1.4674321 0.7290
sOccupancySite 2.0798967 0.5124052 4.2201985 1.3927839 3.4513820 0.0005
sRateYear 1.1922660 0.4346520 2.9070743 0.6336904 2.3222262 0.0005

Table 20. Model summary.

n K nsamples nchains nsims duration rhat converged
969 5 2000 4 320000 268.80225276947s (~4.48 minutes) 1.01 TRUE

#### Burbot

Table 21. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySeason$2$ -0.4620141 0.3136597 -1.496502 -1.0958380 0.1373124 0.1340
bRate 0.4578239 0.4878937 1.092664 -0.3184839 1.7031044 0.2080
bRateRegime$2$ -1.1638224 0.7380314 -1.604433 -2.8300107 0.3062082 0.0960
sOccupancySite 0.9581696 0.2568683 3.863209 0.5895874 1.6206694 0.0005
sRateYear 1.0661645 0.4140664 2.745384 0.5268541 2.1326053 0.0005

Table 22. Model summary.

n K nsamples nchains nsims duration rhat converged
969 5 2000 4 160000 136.861769199371s (~2.28 minutes) 1.1 TRUE

#### Lake Whitefish

Table 23. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySeason$2$ -4.8610298 0.8170743 -6.0436608 -6.729908 -3.5350161 0.0005
bRate 0.2263339 0.5772797 0.3193839 -1.000189 1.2968137 0.6760
bRateRegime$2$ -0.3982608 0.9016562 -0.4806933 -2.144271 1.3748100 0.6400
sOccupancySite 0.4687208 0.1709773 2.8065144 0.176911 0.8683258 0.0005
sRateYear 1.7872412 0.4652836 3.9738154 1.141766 2.9399117 0.0005

Table 24. Model summary.

n K nsamples nchains nsims duration rhat converged
969 5 2000 4 160000 133.611914157867s (~2.23 minutes) 1.07 TRUE

#### Northern Pikeminnow

Table 25. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySeason$2$ -2.0446042 0.4132843 -4.964727 -2.8447114 -1.2730866 0.0005
bRate 0.3893736 0.2700138 1.481535 -0.1127161 0.9666526 0.1160
bRateRegime$2$ -0.4623232 0.4427830 -1.063541 -1.3694467 0.4010425 0.2560
sOccupancySite 1.2954298 0.3630245 3.712130 0.7974610 2.1987692 0.0005
sRateYear 0.7211602 0.2760132 2.767365 0.3524526 1.3854180 0.0005

Table 26. Model summary.

n K nsamples nchains nsims duration rhat converged
969 5 2000 4 160000 132.825829982758s (~2.21 minutes) 1.03 TRUE

#### Redside Shiner

Table 27. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySeason$2$ -0.9425609 0.3646064 -2.6128776 -1.7072231 -0.2768414 0.0080
bRate 0.4374469 0.4668138 0.9401063 -0.4845830 1.4254734 0.3160
bRateRegime$2$ -0.5191104 0.8430247 -0.6537988 -2.3532710 1.1045241 0.4790
sOccupancySite 2.1613548 0.5989423 3.7590343 1.3514431 3.7588346 0.0005
sRateYear 1.4990505 0.4964205 3.1823567 0.8319064 2.7345524 0.0005

Table 28. Model summary.

n K nsamples nchains nsims duration rhat converged
969 5 2000 4 320000 258.049988031387s (~4.3 minutes) 1.04 TRUE

#### Sculpins

Table 29. Model coefficients.

term estimate sd zscore lower upper pvalue
bOccupancySeason$2$ -0.3573008 0.2716340 -1.318421 -0.8740651 0.1831799 0.1790
bRate 0.4900018 0.3408342 1.373709 -0.2558886 1.0852118 0.1890
bRateRegime$2$ -0.8687456 0.7312247 -1.172275 -2.2202616 0.6533350 0.2220
sOccupancySite 1.2830207 0.3115779 4.266274 0.8582813 2.0429250 0.0005
sRateYear 1.3498246 0.3537100 3.959291 0.8564961 2.2655003 0.0005

Table 30. Model summary.

n K nsamples nchains nsims duration rhat converged
969 5 2000 4 160000 141.722540855408s (~2.36 minutes) 1.07 TRUE

### Count

Table 31. Parameter descriptions.

Parameter Description
bDensitySeason[i] Effect of ith season on log(eDensity)
bDensitySite[i] Effect of ith site on log(eDensity)
bDensitySiteYear[i, j] Effect of ith site in jth year on log(eDensity)
bDensityYear[i] Random effect of ith year on log(eDensity)
bRate Baseline rate of change (relative to the previous year) in eDensity due to year effect
bRateRegime[i] Deviate from bRate due to regime effect in the ith year
bRateYear[i] Random deviate from bRate due to year effect in the ith year
Count[i] Count on ith site visit
eCount[i] Expected count on ith site visit
eDensity[i] Lineal density on ith site visit
eDispersion[i] Overdispersion factor on ith site visit
eRateYear[i] Rate of change in year effect between the (i-1)th and ith year
ProportionSampled[i] Proportion of ith site that was sampled
sDispersion[i] SD of the overdispersion factor distribution
SiteLength[i] Length of ith site
sRateYear SD of the distribution of bRateYear

#### Rainbow Trout

Table 32. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensitySeason$2$ -0.0558554 0.1581371 -0.3617073 -0.3643737 0.2662402 0.7210
bRate 0.3097245 0.2203194 1.4084916 -0.1392948 0.7741460 0.1700
bRateRegime$2$ -0.5228539 0.4377085 -1.2193071 -1.3973239 0.3197493 0.2060
sDensitySite 1.6865947 0.4212903 4.1656691 1.1318535 2.7494199 0.0005
sDensitySiteYear 0.7651275 0.0933484 8.2263266 0.5961492 0.9668685 0.0005
sDispersion 0.8443905 0.0574568 14.7304306 0.7382854 0.9631970 0.0005
sRateYear 0.7548222 0.2675483 2.9365686 0.3623827 1.3600096 0.0005
tCount -0.5228539 0.4377085 -1.2193071 -1.3973239 0.3197493 0.2060

Table 33. Model summary.

n K nsamples nchains nsims duration rhat converged
969 8 2000 4 8e+05 4211.07110714912s (~1.17 hours) 1.04 TRUE

#### Burbot

Table 34. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensitySeason$2$ -0.7008740 0.2829301 -2.4583869 -1.2222639 -0.1576417 0.0150
bRate 0.3457599 0.4179139 0.8351192 -0.5379906 1.1403800 0.3660
bRateRegime$2$ -1.0494175 0.7563619 -1.3667513 -2.5285938 0.6490754 0.1530
sDensitySite 0.7770214 0.2460972 3.3195278 0.4582638 1.4287828 0.0005
sDensitySiteYear 0.4302179 0.1930011 2.1941856 0.0573630 0.7871522 0.0005
sDispersion 1.2101743 0.1418903 8.5651207 0.9409837 1.5045709 0.0005
sRateYear 1.2128722 0.4244377 3.0165039 0.6137706 2.3191154 0.0005
tCount -1.0494175 0.7563619 -1.3667513 -2.5285938 0.6490754 0.1530

Table 35. Model summary.

n K nsamples nchains nsims duration rhat converged
969 8 2000 4 8e+05 4453.63915920258s (~1.24 hours) 1.04 TRUE

#### Northern Pikeminnow

Table 36. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensitySeason$2$ -2.1944847 0.4198386 -5.258263 -3.0621880 -1.3987577 0.0005
bRate 0.3782332 0.2290669 1.665998 -0.0723541 0.8551925 0.0940
bRateRegime$2$ -0.4745792 0.4315332 -1.104948 -1.4151222 0.3749522 0.2260
sDensitySite 1.2618458 0.3686478 3.558548 0.7418742 2.1712440 0.0005
sDensitySiteYear 0.7494810 0.1873177 3.979125 0.3547730 1.1086029 0.0005
sDispersion 1.3409528 0.1319098 10.200577 1.1030656 1.6164564 0.0005
sRateYear 0.6680811 0.2510400 2.828973 0.3459029 1.3331360 0.0005
tCount -0.4745792 0.4315332 -1.104948 -1.4151222 0.3749522 0.2260

Table 37. Model summary.

n K nsamples nchains nsims duration rhat converged
969 8 2000 4 4e+05 1737.69567394257s (~28.96 minutes) 1.06 TRUE

#### Suckers

Table 38. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensitySeason$2$ -0.1043625 0.1084576 -0.9767647 -0.3150610 0.0997476 0.3410
bRate 0.0272163 0.2049856 0.2073784 -0.3128084 0.4364884 0.8670
bRateRegime$2$ -0.1173087 0.3499090 -0.3202261 -0.7991742 0.5485687 0.7600
sDensitySite 0.5379528 0.1409113 3.9748213 0.3531519 0.8806989 0.0005
sDensitySiteYear 0.5355914 0.0559827 9.6034547 0.4333479 0.6506571 0.0005
sDispersion 0.8414728 0.0258002 32.6535746 0.7936624 0.8939800 0.0005
sRateYear 0.6234944 0.1739960 3.7148641 0.3832156 1.0642525 0.0005
tCount -0.1173087 0.3499090 -0.3202261 -0.7991742 0.5485687 0.7600

Table 39. Model summary.

n K nsamples nchains nsims duration rhat converged
969 8 2000 4 3200000 12144.5328521729s (~3.37 hours) 1.03 TRUE

### Movement

Table 40. Parameter descriptions.

Parameter Description
bLength Coefficient for the effect of Length on logit(eMoved)
bLengthSeason[i] Coefficient for the effect of the interaction between Length and Season on logit(eMoved)
bMoved Intercept for logit(eMoved)
bMovedSeason[i] Effect of ith season on logit(eMoved)
eMoved[i] Probability of different site from previous encounter for ith recapture
Length[i] Length of ith recaptured fish
Moved[i] Indicates whether ith recapture is recorded at a different site from previous encounter
nSeason Number of seasons in the study (2)
Season[i] Season of ith recapture

#### Bull Trout

Table 41. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength 0.0047745 0.0015523 3.0964570 0.0018221 0.0078775 0.0005
bLengthSeason$2$ 0.0025145 0.0057703 0.5070124 -0.0072400 0.0158471 0.6450
bMoved -1.9223766 0.6872842 -2.7916148 -3.3285555 -0.6264036 0.0005
bMovedSeason$2$ -0.2097086 2.4943308 -0.1151158 -5.5714534 4.3615303 0.9350

Table 42. Model summary.

n K nsamples nchains nsims duration rhat converged
139 4 2000 4 40000 3.592058 1.01 TRUE

#### Mountain Whitefish

Table 43. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength -0.0000585 0.0031176 -0.0188312 -0.0058705 0.0060392 0.9780
bLengthSeason$2$ -0.0287949 0.0071939 -4.0197767 -0.0431402 -0.0147266 0.0005
bMoved -0.0752615 0.7955858 -0.0869078 -1.6451885 1.4199044 0.9290
bMovedSeason$2$ 6.0035221 1.7007025 3.5579101 2.7051475 9.2529943 0.0005

Table 44. Model summary.

n K nsamples nchains nsims duration rhat converged
455 4 2000 4 40000 11.02264 1.06 TRUE

#### Rainbow Trout

Table 45. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength 0.0066614 0.0066712 1.040321 -0.0055244 0.0207671 0.300
bLengthSeason$2$ 0.2206368 0.1230785 1.866868 0.0255527 0.4914047 0.005
bMoved -2.5320647 1.7059594 -1.526541 -6.1421186 0.5783143 0.105
bMovedSeason$2$ -67.9724496 37.2760096 -1.878494 -149.6658038 -8.7183550 0.004

Table 46. Model summary.

n K nsamples nchains nsims duration rhat converged
23 4 2000 4 40000 0.8048799 1.05 TRUE

#### Largescale Sucker

Table 47. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength -0.0109916 0.0058396 -1.881884 -0.0228363 0.0008265 0.076
bLengthSeason$2$ -0.2056773 0.0932733 -2.182091 -0.3865780 -0.0231405 0.021
bMoved 4.5674208 2.5235068 1.810952 -0.5522363 9.7472728 0.080
bMovedSeason$2$ 90.1037990 41.0239003 2.178425 9.3551793 170.5578463 0.023

Table 48. Model summary.

n K nsamples nchains nsims duration rhat converged
70 4 2000 4 160000 5.18621802330017s 1.06 TRUE

### Observer Length Correction

Table 49. Parameter descriptions.

Parameter Description
bLength[i] Relative inaccuracy of theith Observer
ClassLength Mean Length of fish belonging to the ith class
dClass[i] Prior value for the relative proportion of fish in the ith class
eClass[i] Expected class of the ith fish
eLength[i] Expected Length of the ith fish
eSLength[i] Expected SD of the residual variation in Length for the ith
Length[i] Observed fork length of the ith fish
Observer[i] Observer of the ith fish where the first observer used a length board
pClass[i] Proportion of fish in the ith class
sLength[i] Relative imprecision of the ith Observer

#### Bull Trout

Table 50. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength$2$ 0.8295510 0.0587294 14.767478 0.8250688 0.9812908 5e-04
bLength$3$ 1.0905234 0.0751906 14.511789 0.9446459 1.2353038 5e-04
bLength$4$ 0.9982138 0.0392980 25.985577 0.9532832 1.0926534 5e-04
bLength$5$ 0.8487111 0.0367764 23.255621 0.7921152 0.9433502 5e-04
bLength$6$ 0.9921179 0.0493985 19.583259 0.8439292 0.9969706 5e-04
bLength$7$ 0.9605280 0.0759563 13.000224 0.9103218 1.0903138 5e-04
bLength$8$ 1.0169095 0.0537331 18.958199 0.9108885 1.1173630 5e-04
sLength$2$ 1.0413350 1.2949400 1.160473 1.0013062 5.2950826 5e-04
sLength$3$ 6.3852291 4.9522513 1.507112 1.3925108 20.0853509 5e-04
sLength$4$ 1.3653024 2.2831090 1.104397 1.0024408 8.7580734 5e-04
sLength$5$ 3.0746659 2.8720854 1.389820 1.0322016 11.2835228 5e-04
sLength$6$ 1.0300262 1.3582406 1.177558 1.0009804 6.1623492 5e-04
sLength$7$ 1.1668169 1.1535121 1.268215 1.0072669 5.1107757 5e-04
sLength$8$ 7.0935713 4.7057892 1.667923 1.3398539 18.7089936 5e-04

Table 51. Model summary.

n K nsamples nchains nsims duration rhat converged
1058 14 2000 4 5120000 21891.7364845276s (~6.08 hours) 1.41 FALSE

#### Mountain Whitefish

Table 52. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength$2$ 0.9239473 0.0075053 123.112458 0.9094790 0.9367955 5e-04
bLength$3$ 0.9137584 0.0156839 58.256684 0.8823468 0.9442200 5e-04
bLength$4$ 1.0083762 0.0091092 110.700216 0.9903784 1.0265663 5e-04
bLength$5$ 0.9307453 0.0049084 189.551196 0.9200066 0.9388649 5e-04
bLength$6$ 0.7627435 0.0051445 148.271709 0.7526195 0.7728329 5e-04
bLength$7$ 0.9784577 0.0101676 96.252021 0.9584882 0.9978365 5e-04
bLength$8$ 0.8497020 0.0157436 53.981561 0.8188708 0.8812846 5e-04
sLength$2$ 2.6767563 0.6596459 3.751118 1.1847571 3.3681802 5e-04
sLength$3$ 4.5891462 0.8363494 5.472418 2.9277363 6.2051080 5e-04
sLength$4$ 4.0824229 0.4050702 10.099657 3.3107849 4.9000491 5e-04
sLength$5$ 1.2634793 0.1900469 6.849920 1.0532771 1.8038236 5e-04
sLength$6$ 3.2271668 0.1891921 17.059692 2.8691190 3.6185026 5e-04
sLength$7$ 4.1329454 0.3829660 10.791872 3.3782864 4.8733304 5e-04
sLength$8$ 6.6058955 0.6543448 10.092474 5.3297159 7.8958873 5e-04

Table 53. Model summary.

n K nsamples nchains nsims duration rhat converged
7463 14 2000 4 160000 2951.50112128258s (~49.19 minutes) 1.06 TRUE

#### Suckers

Table 54. Model coefficients.

term estimate sd zscore lower upper pvalue
bLength$2$ 0.8200547 0.0122134 67.116151 0.7950339 0.8428677 5e-04
bLength$3$ 1.1119342 0.0325977 34.105340 1.0449897 1.1773771 5e-04
bLength$4$ 0.9507303 0.0057486 165.448619 0.9410518 0.9622337 5e-04
bLength$5$ 0.9018186 0.0017900 503.802139 0.8982251 0.9052863 5e-04
bLength$6$ 0.7499056 0.0058935 127.245130 0.7382510 0.7614752 5e-04
bLength$7$ 0.9224197 0.0113655 81.178089 0.9000950 0.9452503 5e-04
bLength$8$ 0.7085999 0.0188290 37.631013 0.6721234 0.7456156 5e-04
sLength$2$ 5.0507029 1.0358079 4.899389 3.0787038 7.1386204 5e-04
sLength$3$ 9.0276187 2.3308736 3.970438 5.3509156 14.3878126 5e-04
sLength$4$ 2.9661280 1.0638723 2.607776 1.0468088 4.5527721 5e-04
sLength$5$ 1.0212649 0.0299129 34.440664 1.0008292 1.1084714 5e-04
sLength$6$ 5.4572978 0.4315599 12.648395 4.6128940 6.2992004 5e-04
sLength$7$ 6.4705785 0.7831361 8.259786 4.9504104 8.0090055 5e-04
sLength$8$ 12.3621281 0.9936523 12.474686 10.5690973 14.4383197 5e-04

Table 55. Model summary.

n K nsamples nchains nsims duration rhat converged
3467 14 2000 4 40000 324.3198 1.02 TRUE

### Abundance

Table 56. Parameter descriptions.

Parameter Description
bDensitySeason[i] Effect of ith Season on bDensity
bDensitySite[i] Random effect of ith Site on bDensity
bDensitySiteYear[i, j] Effect of ith Site in jth year on bDensity
bDensityYear[i] Random effect of ith Year on bDensity
bDistribution Intercept for eDistribution
bDistributionRegime[i] Effect of ith Regime on bDistribution
bDistributionSeason[i] Effect of ith Season on bDistribution
bDistributionYear[i] Random effect of ith Year on bDistribution
bEfficiency Intercept for logit(eEfficiency)
bEfficiencySessionSeasonYear[i, j, k] Effect of ith Session in jth Season of kth Year on bEfficiency
bRate Baseline rate of change (relative to the previous year) in eDensity due to year effect
bRateRegime[i] Deviate from bRate due to regime effect in the ith year
bRateYear[i] Random deviate from bRate due to year effect 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
eDistribution[i] Predicted relationship between centred river kilometre and ith site visit on bDensity
eEfficiency[i] Predicted efficiency during ith site visit
eRateYear[i] Rate of change in year effect between the (i-1)th and ith year
Marked[i] Number of marked fish caught in ith river visit
sRateYear SD of the distribution of bRateYear
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
bDensitySeason$2$ 0.2533460 0.3526480 0.7075806 -0.4234096 0.9637902 0.4750
bDistribution -0.0233601 0.0693394 -0.3429197 -0.1703516 0.1155390 0.7310
bDistributionRegime$2$ 0.0178055 0.0495882 0.3369297 -0.0878477 0.1129369 0.6890
bDistributionSeason$2$ -0.0053668 0.0330636 -0.1497046 -0.0673432 0.0603336 0.8880
bEfficiency -3.1456925 0.1503743 -20.9322654 -3.4414052 -2.8628312 0.0005
bEfficiencySeason$2$ -0.3680849 0.3521946 -1.0626181 -1.0710439 0.3097583 0.2830
bMultiplierType$2$ 0.0061974 0.2486555 0.0647286 -0.4353917 0.5237342 0.9850
bRate 0.2398310 0.1246984 1.9257873 -0.0254257 0.4808559 0.0750
bRateRegime$2$ -0.2953578 0.2231386 -1.3395355 -0.7454213 0.1305092 0.1640
sDensitySite 0.6256241 0.1618852 4.0192569 0.4141142 1.0325745 0.0005
sDensitySiteYear 0.1821771 0.0685620 2.5884171 0.0437079 0.3051739 0.0005
sDispersion -0.9557252 0.1600824 -6.0504939 -1.3264700 -0.6976038 0.0005
sDispersionType$2$ 1.1719990 0.2645835 4.4419450 0.6591284 1.7018247 0.0005
sDistributionYear 0.0588833 0.0377955 1.6893004 0.0066366 0.1534442 0.0005
sEfficiencySessionSeasonYear 0.2616722 0.0546470 4.8175419 0.1614897 0.3780271 0.0005
sRateYear 0.3999705 0.1237228 3.3837426 0.2380854 0.7120449 0.0005
tAbundance -0.2953578 0.2231386 -1.3395355 -0.7454213 0.1305092 0.1640
tDistribution 0.0178055 0.0495882 0.3369297 -0.0878477 0.1129369 0.6890

Table 58. Model summary.

n K nsamples nchains nsims duration rhat converged
1044 18 2000 4 320000 2270.38351392746s (~37.84 minutes) 1.09 TRUE

Table 59. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensitySeason$2$ -0.2882166 0.3631732 -0.6931211 -0.8930392 0.5449565 0.4590
bDistribution 0.0582116 0.0477049 1.2135668 -0.0404665 0.1443064 0.2350
bDistributionRegime$2$ 0.0426375 0.0378211 1.1245778 -0.0355627 0.1151198 0.2390
bDistributionSeason$2$ 0.1345567 0.0300632 4.4722849 0.0744979 0.1923452 0.0005
bEfficiency -3.6436894 0.1175444 -30.9586278 -3.8615137 -3.4078391 0.0005
bEfficiencySeason$2$ -0.0278121 0.3601965 -0.1923717 -0.8859242 0.5592198 0.9160
bMultiplierType$2$ 0.6207753 0.1884473 3.2836396 0.2474707 0.9902832 0.0020
bRate 0.0392847 0.0362042 1.1615108 -0.0235794 0.1210203 0.1890
bRateRegime$2$ -0.0852672 0.0874156 -1.0154568 -0.2865160 0.0750505 0.2730
sDensitySite 0.4525169 0.1191209 3.9748294 0.2944337 0.7601694 0.0005
sDensitySiteYear 0.4107809 0.0443360 9.2956743 0.3260812 0.5028637 0.0005
sDispersion -0.9387993 0.1042657 -9.0556224 -1.1721705 -0.7530630 0.0005
sDispersionType$2$ 0.7603995 0.1914199 3.9530481 0.3746911 1.1162625 0.0005
sDistributionYear 0.0287660 0.0208965 1.5181003 0.0021586 0.0780286 0.0005
sEfficiencySessionSeasonYear 0.2291219 0.0415293 5.5300904 0.1532975 0.3167081 0.0005
sRateYear 0.1318066 0.0768006 1.8128623 0.0181214 0.3089119 0.0005
tAbundance -0.0852672 0.0874156 -1.0154568 -0.2865160 0.0750505 0.2730
tDistribution 0.0426375 0.0378211 1.1245778 -0.0355627 0.1151198 0.2390

Table 60. Model summary.

n K nsamples nchains nsims duration rhat converged
1044 18 2000 4 40000 466.533728837967s (~7.78 minutes) 1.1 TRUE

#### Mountain Whitefish

##### Juvenile

Table 61. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensitySeason$2$ 0.4862685 0.6922579 0.7001886 -0.8450878 1.8823028 0.4790
bDistribution 0.0925140 0.1035882 0.8815221 -0.1046683 0.2989867 0.3840
bDistributionRegime$2$ 0.0592829 0.0767315 0.7893818 -0.0827539 0.2188564 0.3820
bDistributionSeason$2$ -0.0927744 0.0346993 -2.6870507 -0.1619466 -0.0267106 0.0080
bEfficiency -5.6909935 0.4475851 -12.7940782 -6.6846042 -4.9461266 0.0005
bEfficiencySeason$2$ 0.0854189 0.6929100 0.1075346 -1.3297729 1.4144776 0.9040
bMultiplierType$2$ 0.3644342 0.2513478 1.4489947 -0.1430174 0.8561175 0.1580
bRate 0.1757425 0.3396964 0.6057143 -0.3796173 0.9408574 0.5570
bRateRegime$2$ -0.2949386 0.5903909 -0.5254461 -1.5057016 0.8348206 0.5500
sDensitySite 0.8849467 0.2266866 4.0854721 0.5899266 1.4592510 0.0005
sDensitySiteYear 0.4996290 0.0693170 7.2209988 0.3684122 0.6423932 0.0005
sDispersion -0.6196515 0.0922471 -6.7298350 -0.8058056 -0.4495254 0.0005
sDispersionType$2$ 0.9069275 0.1816135 5.0131306 0.5538005 1.2843566 0.0005
sDistributionYear 0.0804613 0.0441286 1.9433969 0.0110435 0.1903641 0.0005
sEfficiencySessionSeasonYear 0.2879750 0.0658752 4.4281369 0.1658714 0.4345835 0.0005
sRateYear 0.6751302 0.3704022 2.0605684 0.3271509 1.8223557 0.0005
tAbundance -0.2949386 0.5903909 -0.5254461 -1.5057016 0.8348206 0.5500
tDistribution 0.0592829 0.0767315 0.7893818 -0.0827539 0.2188564 0.3820

Table 62. Model summary.

n K nsamples nchains nsims duration rhat converged
815 18 2000 4 1280000 6681.29352998734s (~1.86 hours) 1.06 TRUE

Table 63. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensitySeason$2$ -0.6868749 0.1226750 -5.5925381 -0.9343428 -0.4451391 0.0005
bDistribution 0.0886822 0.0526896 1.7049560 -0.0126144 0.1913519 0.0920
bDistributionRegime$2$ 0.0420695 0.0409475 1.0423150 -0.0381254 0.1265885 0.2620
bDistributionSeason$2$ -0.0634293 0.0196418 -3.2163562 -0.1015703 -0.0241077 0.0010
bEfficiency -4.0053718 0.0658635 -60.7929739 -4.1304451 -3.8727384 0.0005
bEfficiencySeason$2$ 0.8860861 0.1256474 7.0727832 0.6472767 1.1345090 0.0005
bMultiplierType$2$ 0.4903411 0.1899299 2.5879390 0.1368843 0.8875594 0.0090
bRate 0.0063572 0.0489622 0.2945439 -0.0605749 0.1407975 0.8480
bRateRegime$2$ -0.0217268 0.0831710 -0.3367701 -0.2258688 0.1238516 0.7370
sDensitySite 0.4817200 0.1199897 4.2086238 0.3275907 0.8043769 0.0005
sDensitySiteYear 0.3702445 0.0305688 12.1085225 0.3107628 0.4295677 0.0005
sDispersion -0.8187999 0.0387121 -21.1373592 -0.8964936 -0.7413720 0.0005
sDispersionType$2$ 0.9273884 0.1211654 7.6386926 0.6788134 1.1644392 0.0005
sDistributionYear 0.0517590 0.0228657 2.3285342 0.0115348 0.1005678 0.0005
sEfficiencySessionSeasonYear 0.2546918 0.0347120 7.3610053 0.1916124 0.3307661 0.0005
sRateYear 0.0894262 0.0724479 1.4062163 0.0040934 0.2791827 0.0005
tAbundance -0.0217268 0.0831710 -0.3367701 -0.2258688 0.1238516 0.7370
tDistribution 0.0420695 0.0409475 1.0423150 -0.0381254 0.1265885 0.2620

Table 64. Model summary.

n K nsamples nchains nsims duration rhat converged
1044 18 2000 4 1280000 7749.5605905056s (~2.15 hours) 1.1 TRUE

#### Rainbow Trout

Table 65. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity 0.6533293 0.4609334 1.3877529 -0.3073958 1.5434404 0.1640
bDensitySeason$2$ 0.1720165 0.6778927 0.3018074 -1.0095224 1.6585467 0.7950
bEfficiency -2.6346217 0.2949553 -8.9435060 -3.2258291 -2.0674508 0.0005
bEfficiencySeason$2$ -0.3641696 0.6892913 -0.6109407 -1.8874158 0.8291461 0.5550
sDensitySite 1.1591075 0.3454002 3.5174602 0.7154463 2.0348782 0.0005
sDensitySiteYear 0.4936966 0.1503454 3.2774872 0.1919907 0.7889074 0.0005
sDensityYear 0.2497891 0.1971106 1.4120786 0.0174696 0.7465993 0.0005
sDispersion -1.2339171 0.9378023 -1.5792869 -4.1051578 -0.3330295 0.0005
sEfficiencySessionSeasonYear 0.3143309 0.1553879 1.9702533 0.0124534 0.6138537 0.0005

Table 66. Model summary.

n K nsamples nchains nsims duration rhat converged
740 9 2000 4 320000 467.732274055481s (~7.8 minutes) 1.04 TRUE

#### Largescale Sucker

Table 67. Model coefficients.

term estimate sd zscore lower upper pvalue
bDensity 5.2807106 0.2670364 19.7358861 4.7371381 5.7875626 0.0005
bDensitySeason$2$ 0.0043752 0.5339726 0.0447323 -0.9464182 1.1476755 0.9910
bEfficiency -3.3755875 0.1625481 -20.7593640 -3.6988653 -3.0548126 0.0005
bEfficiencySeason$2$ -1.2491326 0.5488653 -2.2899028 -2.3936702 -0.2555397 0.0110
sDensitySite 0.4422012 0.1264301 3.6323013 0.2578177 0.7503333 0.0005
sDensitySiteYear 0.4872211 0.0648153 7.5507728 0.3678700 0.6237233 0.0005
sDensityYear 0.4375645 0.2431456 2.0125583 0.1675406 1.0840311 0.0005
sDispersion -0.5288058 0.0618686 -8.5826487 -0.6594010 -0.4103021 0.0005
sEfficiencySessionSeasonYear 0.5601213 0.0860905 6.6103831 0.4176117 0.7566112 0.0005

Table 68. Model summary.

n K nsamples nchains nsims duration rhat converged
600 9 2000 4 320000 398.652538061142s (~6.64 minutes) 1.03 TRUE

### Significance

Table 69. The significance levels for the management hypotheses tested in the analyses where Condition1 is the effect of the regime change on weight for big and small fish and Condition2 is the effect of the regime change on big relative to small fish. The Direction column indicates whether significant changes were positive or negative.

Test Species Stage Significance Direction
Abundance Mountain Whitefish Adult 0.7370
Abundance Mountain Whitefish Juvenile 0.5500
Abundance Bull Trout Adult 0.2730
Abundance Bull Trout Juvenile 0.1640
Condition1 Mountain Whitefish 0.0050 -
Condition1 Rainbow Trout 0.5840
Condition1 Bull Trout 0.0005 -
Condition2 Mountain Whitefish 0.3110
Condition2 Rainbow Trout 0.5300
Condition2 Bull Trout 0.3690
Count Rainbow Trout 0.2060
Count Sucker 0.7600
Count Burbot 0.1530
Count Northern Pikeminnow 0.2260
Distribution Mountain Whitefish Adult 0.2620
Distribution Mountain Whitefish Juvenile 0.3820
Distribution Bull Trout Adult 0.2390
Distribution Bull Trout Juvenile 0.6890
Growth Mountain Whitefish 0.9730
Growth Rainbow Trout 0.9880
Growth Bull Trout 0.9860

## Acknowledgements

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

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