Middle Columbia River Fish Indexing Analysis 2014

The main intepretive report by ONA, Golder Associates and Poisson Consulting, which was prepared for BC Hydro, is available from ResearchGate.

The suggested citation for this online appendix is:

Thorley, J.L. and Beliveau, A. (2015) Middle Columbia River Fish Indexing Analysis 2014. URL: http://www.poissonconsulting.ca/f/1446318417.

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. 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.

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

Statistical Analysis

Hierarchical Bayesian models were fitted to the count data using R version 3.1.2 (Team 2013) and JAGS 3.4.0 (Plummer 2012) which interfaced with each other via jaggernaut 2.2.10 (Thorley 2013). For additional information on hierarchical Bayesian modelling in the BUGS language, of which JAGS uses a dialect, the reader is referred to Kery and Schaub (2011, 41–44).

Unless specified, the models assumed vague (low information) prior distributions (Kery and Schaub 2011, 36). The posterior distributions were estimated from a minimum of 1,000 Markov Chain Monte Carlo (MCMC) samples thinned from the second halves of three chains of at least 10,000 iterations in length (Kery and Schaub 2011, 38–40). Model convergence was confirmed by ensuring that Rhat (Kery and Schaub 2011, 40) was less than 1.1 for each of the parameters in the model (Kery and Schaub 2011, 61). Model adequacy was confirmed by examination of residual plots.

The posterior distributions of the fixed (Kery and Schaub 2011, 75) parameters are summarised in terms of a point estimate (mean), lower and upper 95% credible limits (2.5th and 97.5th percentiles), the standard deviation (SD), percent relative error (half the 95% credible interval as a percent of the point estimate) and significance (Kery and Schaub 2011, 37, 42).

Variable selection was achieved by dropping insignificant (Kery and Schaub 2011, 37, 42) fixed (Kery and Schaub 2011, 77–82) variables and uninformative random variables. A fixed variables was considered to be insignificant if its significance was \(\geq\) 0.05 while a random variable was considered to be uninformative if its percent relative error was \(\geq\) 80%.

The results are displayed graphically by plotting the modeled relationships between particular variables and the response with 95% credible intervals (CRIs) 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). Where informative the influence of particular variables is expressed in terms of the effect size (i.e., percent change in the response variable) with 95% CRIs (Bradford, Korman, and Higgins 2005).

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:

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., \(log(L) - \bar{log(L)}\), 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:

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:

Species Richness

The estimated probabilities of presence for the six species considered in the occupany analyses were summed to give the expected species richnesses at a given (or typical) site in a given (or typical) 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 abundance model include:

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:

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 observed fish lengths were corrected for the estimated length biases.

Abundance

The catch data were analysed using a capture-recapture-based overdispersed 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 abundance model include:

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.

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

The long-term congruence between the yearly fall fish metrics (Grw = Growth, Con = Condition, Blank = Abundance, Rkm = Distribution) by life stage (Juv = Juvenile, AD = Adult) and a range of environmental variables including the tri-monthly (JaMa = January - March, ApJn = April - June, JlSe = July - September, OcDe = October - December) discharge from Revelstoke Dam (Q10, QMu = Mean, Q90, QDlt = Mean absolute difference) and the elevation (Ele), the Pacific Decadal Oscillation (PDO), the chlorophyll-a (ChlA) and invertebrate production (Inv) and the kokanee abundance (KO) was examined using Dynamic Factor Analysis (Zuur, Tuck, and Bailey 2003). Due to the rotation problem the underlying trends were indeterminate (Abmann, Boysen-Hogrefe, and Pape 2014). The October to December discharge and elevation values were lead (opposite of lagged) by one year to account for the fact that they occurred after sampling.

Key assumptions of the Dynamic Factor Analysis (DFA) model include:

The similarities were represented visually by using non-metric multidimensional scaling (NMDS) to map the distances onto two-dimensional space. The more similar two time series are they closer they will tend to be in the resultant NMDS plot.

Short-Term Correlations

To assess the short-term congruence between the yearly fish metrics and the environmental variables, the pair-wise distances between the residuals from the DFA model were calculated as \(1 - abs(cor(x, y))\) where \(cor\) is the Pearson correlation, \(abs\) the absolute value and \(x\) and \(y\) are the two time series being compared.

The short-term similarities were represented visually by using NMDS to map the distances onto two-dimensional space.

Model Code

The JAGS model code, which uses a series of naming conventions, is presented below.

Growth

Variable/Parameter Description
bKIntercept Intercept for log(bK)
bKRegime[i] Effect of ith regime on bKIntercept
bKYear[i] Random effect of ith Year on bKIntercept
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 bKIntercept
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
Growth - Model1
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)
    log(bK[i]) <- 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]
} 

Condition

Variable/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
Condition - Model1
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] * Length[i]
    Weight[i] ~ dlnorm(log(eWeight[i]) , sWeight^-2)
  }
  tCondition1 <- bWeightRegimeIntercept[2]
  tCondition2 <- bWeightRegimeSlope[2]
}

Occupancy

Variable/Parameter Description
bOccupancy Intercept of logit(eOccupancy)
bOccupancyRegime[i] Effect of ith regime on logit(eOccupancy)
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)
eObserved[i] Probability of observing species on ith site visit
eOccupancy[i] Predicted occupancy (species presence versus absence) on ith site visit
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]
sOccupancyYear SD parameter for the distribution of bOccupancyYear[i]
Year[i] Year of ith site visit
Occupancy - Model1
model {

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

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

  sOccupancyYear ~ dunif(0, 5)
  for (yr in 1:nYear) {
    bOccupancyYear[yr] ~ dnorm(0, sOccupancyYear^-2)
  }

  sOccupancySite ~ dunif(0, 5)
  for (st in 1:nSite) {
    bOccupancySite[st] ~ dnorm(0, sOccupancySite^-2)
  }
  for (i in 1:length(Year)) {
    logit(eOccupancy[i]) <- bOccupancy
    + bOccupancyRegime[Regime[i]] + bOccupancySeason[Season[i]]
    + bOccupancySite[Site[i]] + bOccupancyYear[Year[i]]
    eObserved[i] <- eOccupancy[i]
    Observed[i] ~ dbern(eObserved[i])
  }
}

Count

Variable/Parameter Description
bDensity Intercept of log(eDensity)
bDensityRegime[i] Effect of ith regime on log(eDensity)
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] Effect of ith year on log(eDensity)
bDistribution Intercept of eDistribution
bDistributionRegime[i] Effect of ith regime on eDistribution
bDistributionSeason[i] Effect of ith season on eDistribution
bDistributionYear[i] Effect of ith year on eDistribution
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
eDistribution[i] Effect of centred river kilometre on ith site visit on log(eDensity)
ProportionSampled[i] Proportion of ith site that was sampled
sDispersion[i] SD of the overdispersion factor distribution
SiteLength[i] Length of ith site
Count - Model1
model {
  bDensity ~ dnorm(0, 5^-2)
  bDistribution ~ dnorm(0, 5^-2)
  bDensityRegime[1] <- 0

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

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

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

  sDispersion ~ dunif(0, 5)
  for (i in 1:length(Year)) {
    eDistribution[i] <- bDistribution
      + bDistributionRegime[Regime[i]]
      + bDistributionSeason[Season[i]]
      + bDistributionYear[Year[i]]

    log(eDensity[i]) <- bDensity
      + eDistribution[i] * RiverKm[i]
      + bDensityRegime[Regime[i]]
      + bDensitySeason[Season[i]]
      + bDensitySite[Site[i]]
      + bDensityYear[Year[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])
  }
  tAbundance <- bDensityRegime[2]
  tDistribution <- bDistributionRegime[2]
}

Movement

Variable/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
Movement - Model1
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])
  }
}

Observer Length Correction

Variable/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
Observer Length Correction - Model1
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)
  }
}

Abundance

Variable/Parameter Description
bDensity Intercept for log(eDensity)
bDensityRegime[i] Effect of ith Regime on bDensity
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
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
Marked[i] Number of marked fish caught in ith river visit
Tagged[i] Number of fish tagged prior to ith river visit
Abundance - Model1
model {

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

  bDensityRegime[1] <- 0
  bDistributionRegime[1] <- 0
  for(i in 2:nRegime) {
    bDensityRegime[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)
  }

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

  bType[1] <- 1
  for (i in 2:nType) {
    bType[i] ~ dunif(0, 10)
  }

  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]])
  }

  sDispersion ~ dunif(0, 5)
  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]) <- bDensity
      + eDistribution[i] * RiverKm[i]
      + bDensityRegime[Regime[i]]
      + bDensitySeason[Season[i]]
      + bDensitySite[Site[i]]
      + bDensityYear[Year[i]]
      + bDensitySiteYear[Site[i], Year[i]]

    eCatch[i] <- eDensity[i] * SiteLength[i] * ProportionSampled[i] * eEfficiency[i] * bType[Type[i]]

    eDispersion[i] ~ dgamma(1 / sDispersion^2, 1 / sDispersion^2)

    Catch[i] ~ dpois(eCatch[i] * eDispersion[i])
  }
  tAbundance <- bDensityRegime[2]
  tDistribution <- bDistributionRegime[2]
}
Variable/Parameter Description
bDistance[i,j] Euclidean distance between ith and jth Variable
bTrendYear[t,y] Expected value for tth trend in yth Year
eValue[v,y,t] Expected standardised value for vth Variable in yth Year considering tth trends
sTrend SD in trend random walks
sValue SD for residual variation in Value
Value[i] Standardised value for ith data point
Variable[i] Variable for ith data point
Year[i] Year of ith data point
Z[v,y] Expected weighting for vth Variable in yth Year
model{

  sTrend ~ dunif(0, 1)
  for (t in 1:nTrend) {
    bTrendYear[t,1] ~ dunif(-1,1)
    for(y in 2:nYear){
      bTrendYear[t,y] ~ dnorm(bTrendYear[t,y-1], sTrend^-2)
    }
  }

  for(v in 1:nVariable){
    for(t in 1:nTrend) {
      Z[v,t] ~ dunif(-1,1)
    }
    for(y in 1:nYear){
      eValue[v,y,1] <- Z[v,1] * bTrendYear[1,y]
      for(t in 2:nTrend) {
        eValue[v,y,t] <- eValue[v,y,t-1] + Z[v,t] * bTrendYear[t,y]
      }
    }
  }

  sValue ~ dunif(0, 1)
  for(i in 1:length(Value)) {
    Value[i] ~ dnorm(eValue[Variable[i], Year[i], nTrend], sValue^-2)
  }

  for(i in 1:nVariable) {
    for(j in 1:nVariable) {
      bDistance[i,j] <- sqrt(sum((Z[i,]-Z[j,])^2))
    }
  }
}

Results

Model Parameters

The posterior distributions for the fixed (Kery and Schaub 2011 p. 75) parameters in each model are summarised below.

Growth - Bull Trout

Parameter Estimate Lower Upper SD Error Significance
bKIntercept -1.8218 -2.1170 -1.5128 0.1458 17 0.0010
bKRegime[2] 0.0184 -0.4323 0.3983 0.2027 2300 0.8903
bLinf 851.2000 799.7000 919.0000 30.6000 7 0.0010
sGrowth 31.6850 28.7520 35.1080 1.6090 10 0.0010
sKYear 0.3004 0.1492 0.5388 0.1048 65 0.0010
tGrowth 0.0184 -0.4323 0.3983 0.2027 2300 0.8903
Convergence Iterations
1.01 10000

Growth - Mountain Whitefish

Parameter Estimate Lower Upper SD Error Significance
bKIntercept -2.6984 -3.0438 -2.3537 0.1767 13 0.0010
bKRegime[2] 0.2167 -0.2672 0.6785 0.2326 220 0.3228
bLinf 360.8500 342.4600 381.4800 9.9300 5 0.0010
sGrowth 10.8910 10.4030 11.4250 0.2640 5 0.0010
sKYear 0.3738 0.2081 0.6564 0.1264 60 0.0010
tGrowth 0.2167 -0.2672 0.6785 0.2326 220 0.3228
Convergence Iterations
1.01 20000

Growth - Rainbow Trout

Parameter Estimate Lower Upper SD Error Significance
bKIntercept -1.655 -2.805 -0.487 0.586 70 0.0120
bKRegime[2] -0.304 -1.393 0.670 0.495 340 0.4492
bLinf 583.400 431.300 902.100 120.400 40 0.0010
sGrowth 26.260 17.230 41.080 6.260 45 0.0010
sKYear 0.392 0.010 1.475 0.398 190 0.0010
tGrowth -0.304 -1.393 0.670 0.495 340 0.4492
Convergence Iterations
1.04 10000

Condition - Bull Trout

Parameter Estimate Lower Upper SD Error Significance
bWeightIntercept 6.83125 6.78961 6.86973 0.02032 1 0.0010
bWeightRegimeIntercept[2] -0.09680 -0.16540 -0.02900 0.03560 70 0.0095
bWeightRegimeSlope[2] 0.04480 -0.09060 0.19340 0.07250 320 0.5161
bWeightSeasonIntercept[2] -0.00320 -0.02488 0.01874 0.01113 680 0.7910
bWeightSeasonSlope[2] 0.01740 -0.03570 0.07300 0.02730 310 0.5236
bWeightSlope 3.15920 3.06850 3.23770 0.04090 3 0.0010
sWeight 0.14103 0.13699 0.14508 0.00201 3 0.0010
sWeightSiteIntercept 0.01308 0.00199 0.02552 0.00589 90 0.0010
sWeightSiteYearIntercept 0.01841 0.00571 0.02868 0.00574 62 0.0010
sWeightYearIntercept 0.05594 0.03527 0.08938 0.01409 48 0.0010
sWeightYearSlope 0.11530 0.06900 0.19080 0.03430 53 0.0010
tCondition1 -0.09680 -0.16540 -0.02900 0.03560 70 0.0095
tCondition2 0.04480 -0.09060 0.19340 0.07250 320 0.5161
Convergence Iterations
1.02 80000

Condition - Mountain Whitefish

Parameter Estimate Lower Upper SD Error Significance
bWeightIntercept 4.78875 4.76928 4.80754 0.00997 0 0.0010
bWeightRegimeIntercept[2] -0.04307 -0.06920 -0.01494 0.01373 63 0.0078
bWeightRegimeSlope[2] -0.05090 -0.12800 0.02540 0.03890 150 0.1778
bWeightSeasonIntercept[2] -0.03843 -0.04735 -0.03053 0.00427 22 0.0010
bWeightSeasonSlope[2] -0.06508 -0.10478 -0.02382 0.02025 62 0.0010
bWeightSlope 3.20633 3.15996 3.24697 0.02262 1 0.0010
sWeight 0.09692 0.09521 0.09863 0.00086 2 0.0010
sWeightSiteIntercept 0.01036 0.00546 0.01758 0.00299 59 0.0010
sWeightSiteYearIntercept 0.01093 0.00687 0.01516 0.00209 38 0.0010
sWeightYearIntercept 0.02712 0.01655 0.04399 0.00713 51 0.0010
sWeightYearSlope 0.05628 0.02991 0.10296 0.01890 65 0.0010
tCondition1 -0.04307 -0.06920 -0.01494 0.01373 63 0.0078
tCondition2 -0.05090 -0.12800 0.02540 0.03890 150 0.1778
Convergence Iterations
1.02 20000

Condition - Rainbow Trout

Parameter Estimate Lower Upper SD Error Significance
bWeightIntercept 4.56534 4.52899 4.60259 0.01794 1 0.0010
bWeightRegimeIntercept[2] -0.00360 -0.05980 0.05100 0.02600 1600 0.9182
bWeightRegimeSlope[2] -0.05310 -0.17980 0.07500 0.06540 240 0.4092
bWeightSeasonIntercept[2] -0.07479 -0.10810 -0.04213 0.01679 44 0.0010
bWeightSeasonSlope[2] 0.01370 -0.07000 0.09940 0.04310 620 0.7346
bWeightSlope 3.09140 3.01810 3.17190 0.03840 2 0.0010
sWeight 0.11033 0.10350 0.11829 0.00381 7 0.0010
sWeightSiteIntercept 0.02911 0.00847 0.05630 0.01228 82 0.0010
sWeightSiteYearIntercept 0.01623 0.00071 0.03833 0.01054 120 0.0010
sWeightYearIntercept 0.02401 0.00105 0.06068 0.01533 120 0.0010
sWeightYearSlope 0.08460 0.03700 0.16050 0.03200 73 0.0010
tCondition1 -0.00360 -0.05980 0.05100 0.02600 1600 0.9182
tCondition2 -0.05310 -0.17980 0.07500 0.06540 240 0.4092
Convergence Iterations
1.08 10000

Occupancy - Rainbow Trout

Parameter Estimate Lower Upper SD Error Significance
bOccupancy -1.230 -2.606 0.243 0.692 120 0.0819
bOccupancyRegime[2] 0.951 -0.492 2.513 0.746 160 0.1637
bOccupancySeason[2] -0.111 -0.776 0.594 0.328 620 0.6947
sOccupancySite 2.173 1.430 3.252 0.483 42 0.0010
sOccupancyYear 1.139 0.627 1.925 0.353 57 0.0010
Convergence Iterations
1.02 10000

Occupancy - Burbot

Parameter Estimate Lower Upper SD Error Significance
bOccupancy -2.181 -3.185 -1.216 0.496 45 0.0010
bOccupancyRegime[2] 0.674 -0.904 2.416 0.806 250 0.3913
bOccupancySeason[2] -0.601 -1.249 0.050 0.334 110 0.0719
sOccupancySite 0.987 0.598 1.607 0.263 51 0.0010
sOccupancyYear 1.232 0.671 2.310 0.401 67 0.0010
Convergence Iterations
1.03 10000

Occupancy - Lake Whitefish

Parameter Estimate Lower Upper SD Error Significance
bOccupancy -1.2720 -2.156 -0.3870 0.4410 70 0.0100
bOccupancyRegime[2] 0.2570 -1.535 1.8170 0.8250 650 0.7166
bOccupancySeason[2] -3.9130 -5.879 -2.5030 0.8250 43 0.0010
sOccupancySite 0.5257 0.213 0.9202 0.1854 67 0.0010
sOccupancyYear 1.2540 0.722 2.1070 0.3490 55 0.0010
Convergence Iterations
1.04 10000

Occupancy - Northern Pikeminnow

Parameter Estimate Lower Upper SD Error Significance
bOccupancy -2.282 -3.587 -0.976 0.637 57 0.0010
bOccupancyRegime[2] 0.335 -1.286 2.171 0.883 520 0.6927
bOccupancySeason[2] -2.028 -3.074 -1.070 0.509 49 0.0010
sOccupancySite 1.641 0.976 2.741 0.448 54 0.0010
sOccupancyYear 1.237 0.630 2.327 0.451 69 0.0010
Convergence Iterations
1.01 10000

Occupancy - Redside Shiner

Parameter Estimate Lower Upper SD Error Significance
bOccupancy -2.314 -3.875 -0.427 0.859 75 0.0240
bOccupancyRegime[2] -0.056 -2.231 2.077 1.091 3900 0.9641
bOccupancySeason[2] -0.756 -1.524 0.014 0.394 100 0.0559
sOccupancySite 2.276 1.375 3.794 0.606 53 0.0010
sOccupancyYear 1.719 0.937 2.903 0.534 57 0.0010
Convergence Iterations
1.03 10000

Occupancy - Sculpins

Parameter Estimate Lower Upper SD Error Significance
bOccupancy -0.326 -1.850 1.063 0.723 450 0.6547
bOccupancyRegime[2] 1.509 -0.525 3.793 1.085 140 0.1637
bOccupancySeason[2] -0.379 -1.020 0.251 0.321 170 0.2496
sOccupancySite 1.412 0.914 2.168 0.327 44 0.0010
sOccupancyYear 2.018 1.258 3.248 0.532 49 0.0010
Convergence Iterations
1.02 10000

Count - Rainbow Trout

Parameter Estimate Lower Upper SD Error Significance
bDensity -1.6990 -2.6990 -0.7400 0.4960 58 0.0010
bDensityRegime[2] 0.8900 -0.3570 2.1380 0.6550 140 0.1682
bDensitySeason[2] -0.0603 -0.4302 0.3274 0.1982 630 0.7556
bDistribution -0.5130 -0.7795 -0.2516 0.1360 51 0.0010
bDistributionRegime[2] 0.2334 0.0079 0.4421 0.1106 93 0.0484
bDistributionSeason[2] 0.0176 -0.0871 0.1291 0.0567 610 0.7827
sDensitySite 1.2410 0.7710 2.0910 0.3230 53 0.0010
sDensitySiteYear 0.5237 0.3410 0.7221 0.0951 36 0.0010
sDensityYear 0.9490 0.4910 1.6010 0.2930 59 0.0010
sDispersion 0.8411 0.7329 0.9597 0.0597 13 0.0010
sDistributionYear 0.1349 0.0349 0.2778 0.0601 90 0.0010
tAbundance 0.8900 -0.3570 2.1380 0.6550 140 0.1682
tDistribution 0.2334 0.0079 0.4421 0.1106 93 0.0484
Convergence Iterations
1.07 20000

Count - Burbot

Parameter Estimate Lower Upper SD Error Significance
bDensity -2.1160 -3.1210 -1.1920 0.4930 46 0.0010
bDensityRegime[2] 0.5580 -0.7300 2.0660 0.7230 250 0.4310
bDensitySeason[2] -0.8420 -1.4070 -0.2600 0.2910 68 0.0058
bDistribution -0.0930 -0.3294 0.1296 0.1217 250 0.4232
bDistributionRegime[2] 0.0741 -0.1960 0.3532 0.1400 370 0.5798
bDistributionSeason[2] 0.0520 -0.1489 0.2890 0.1112 420 0.6648
sDensitySite 0.8547 0.4812 1.4167 0.2371 55 0.0010
sDensitySiteYear 0.4091 0.0735 0.7864 0.1881 87 0.0010
sDensityYear 1.1740 0.6670 1.8430 0.3090 50 0.0010
sDispersion 1.2123 0.9288 1.4938 0.1413 23 0.0010
sDistributionYear 0.1545 0.0042 0.4699 0.1095 150 0.0010
tAbundance 0.5580 -0.7300 2.0660 0.7230 250 0.4310
tDistribution 0.0741 -0.1960 0.3532 0.1400 370 0.5798
Convergence Iterations
1.08 20000

Count - Northern Pikeminnow

Parameter Estimate Lower Upper SD Error Significance
bDensity -2.5760 -3.6690 -1.7400 0.4910 37 0.0010
bDensityRegime[2] 0.0570 -1.5000 1.8730 0.8390 3000 0.9961
bDensitySeason[2] -2.3860 -4.2830 -0.8380 0.8670 72 0.0020
bDistribution -0.5311 -0.8974 -0.2505 0.1698 61 0.0010
bDistributionRegime[2] 0.0109 -0.3993 0.5896 0.2367 4500 0.9082
bDistributionSeason[2] 0.0306 -0.4633 0.4880 0.2428 1600 0.8663
sDensitySite 0.4197 0.0441 0.9846 0.2494 110 0.0010
sDensitySiteYear 0.6942 0.2967 1.1578 0.2223 62 0.0010
sDensityYear 1.1830 0.5540 1.9070 0.3630 57 0.0010
sDispersion 1.3930 1.1430 1.6588 0.1357 19 0.0010
sDistributionYear 0.2710 0.0341 0.6450 0.1535 110 0.0010
tAbundance 0.0570 -1.5000 1.8730 0.8390 3000 0.9961
tDistribution 0.0109 -0.3993 0.5896 0.2367 4500 0.9082
Convergence Iterations
1.04 10000

Count - Suckers

Parameter Estimate Lower Upper SD Error Significance
bDensity 1.9919 1.6230 2.3801 0.1878 19 0.0010
bDensityRegime[2] 0.8786 0.4453 1.3550 0.2333 52 0.0010
bDensitySeason[2] -0.5730 -0.8155 -0.3187 0.1254 43 0.0010
bDistribution -0.1463 -0.2546 -0.0399 0.0572 73 0.0132
bDistributionRegime[2] 0.0984 -0.0166 0.2240 0.0592 120 0.0829
bDistributionSeason[2] -0.1547 -0.2366 -0.0748 0.0406 52 0.0010
sDensitySite 0.4630 0.2749 0.7650 0.1270 53 0.0010
sDensitySiteYear 0.4721 0.3624 0.5916 0.0594 24 0.0010
sDensityYear 0.3102 0.1454 0.5536 0.1073 66 0.0010
sDispersion 0.7922 0.7398 0.8459 0.0262 7 0.0010
sDistributionYear 0.0572 0.0046 0.1325 0.0361 110 0.0010
tAbundance 0.8786 0.4453 1.3550 0.2333 52 0.0010
tDistribution 0.0984 -0.0166 0.2240 0.0592 120 0.0829
Convergence Iterations
1.1 80000

Movement - Bull Trout

Parameter Estimate Lower Upper SD Error Significance
bLength 0.00455 0.00141 0.00782 0.00163 70 0.0040
bLengthSeason[2] 0.00155 -0.00872 0.01440 0.00576 740 0.7965
bMoved -1.81500 -3.29300 -0.41300 0.71800 79 0.0140
bMovedSeason[2] 0.24000 -5.23000 4.96000 2.54000 2100 0.8563
Convergence Iterations
1.01 10000

Movement - Mountain Whitefish

Parameter Estimate Lower Upper SD Error Significance
bLength -0.00006 -0.00642 0.00599 0.00317 11000 0.9961
bLengthSeason[2] -0.02774 -0.04229 -0.01615 0.00667 47 0.0010
bMoved -0.10900 -1.69000 1.50000 0.81700 1500 0.9022
bMovedSeason[2] 5.83000 2.94400 9.37000 1.59800 55 0.0010
Convergence Iterations
1.07 10000

Movement - Rainbow Trout

Parameter Estimate Lower Upper SD Error Significance
bLength 0.0076 -0.00618 0.02122 0.00697 180 0.2695
bLengthSeason[2] 0.2315 0.05600 0.50860 0.11170 98 0.0020
bMoved -2.6020 -6.23100 0.63800 1.75200 130 0.1258
bMovedSeason[2] -70.7000 -153.90000 -17.20000 33.70000 97 0.0020
Convergence Iterations
1.05 10000

Movement - Largescale Sucker

Parameter Estimate Lower Upper SD Error Significance
bLength -0.0127 -0.02673 -0.00042 0.00677 100 0.0406
bLengthSeason[2] -0.1508 -0.34480 -0.01020 0.08690 110 0.0136
bMoved 5.4100 -0.06000 11.58000 3.00000 110 0.0580
bMovedSeason[2] 65.2000 3.70000 149.00000 37.90000 110 0.0213
Convergence Iterations
1.03 20000

Observer Length Correction - Bull Trout

Parameter Estimate Lower Upper SD Error Significance
bLength[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
bLength[2] 0.78680 0.72240 0.85420 0.03430 8 0.001
bLength[3] 0.90578 0.89742 0.93318 0.00738 2 0.001
sLength[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
sLength[2] 4.51600 1.37100 9.65400 2.21800 92 0.001
sLength[3] 1.11810 1.00300 1.43850 0.14270 19 0.001
Convergence Iterations
1.09 20000

Observer Length Correction - Mountain Whitefish

Parameter Estimate Lower Upper SD Error Significance
bLength[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
bLength[2] 0.66805 0.65234 0.68480 0.00810 2 0.001
bLength[3] 0.96368 0.94432 0.98423 0.01034 2 0.001
sLength[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
sLength[2] 3.93900 3.38600 4.53600 0.29700 15 0.001
sLength[3] 4.60500 3.96700 5.34900 0.35000 15 0.001
Convergence Iterations
1.01 10000

Observer Length Correction - Suckers

Parameter Estimate Lower Upper SD Error Significance
bLength[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
bLength[2] 0.70585 0.69649 0.71564 0.00492 1 0.001
bLength[3] 0.90656 0.88490 0.92860 0.01133 2 0.001
sLength[1] 1.00000 1.00000 1.00000 0.00000 0 0.001
sLength[2] 2.47600 1.84200 3.29000 0.35700 29 0.001
sLength[3] 6.57400 5.28100 8.11200 0.75600 22 0.001
Convergence Iterations
1 10000

Abundance - Bull Trout - Adult

Parameter Estimate Lower Upper SD Error Significance
bDensity 4.2687 3.90600 4.62950 0.18250 8 0.0010
bDensityRegime[2] -0.1643 -0.52200 0.20230 0.18260 220 0.3274
bDensitySeason[2] -0.2960 -0.88400 0.31100 0.30500 200 0.3274
bDistribution 0.0441 -0.05310 0.13620 0.04770 210 0.3354
bDistributionRegime[2] 0.0179 -0.07110 0.10990 0.04610 510 0.6747
bDistributionSeason[2] 0.1611 0.09460 0.23410 0.03640 43 0.0010
bEfficiency -3.4853 -3.69240 -3.26470 0.10920 6 0.0010
bEfficiencySeason[2] 0.0170 -0.59500 0.60400 0.30100 3500 0.9422
bType[1] 1.0000 1.00000 1.00000 0.00000 0 0.0010
bType[2] 2.1460 1.09400 3.79900 0.71700 63 0.0010
sDensitySite 0.4391 0.26470 0.71190 0.11480 51 0.0010
sDensitySiteYear 0.4457 0.35560 0.54100 0.04850 21 0.0010
sDensityYear 0.1700 0.01310 0.38750 0.10130 110 0.0010
sDispersion 0.4171 0.33830 0.49460 0.03980 19 0.0010
sDistributionYear 0.0333 0.00119 0.08638 0.02348 130 0.0010
sEfficiencySessionSeasonYear 0.2488 0.15630 0.34780 0.04730 39 0.0010
tAbundance -0.1643 -0.52200 0.20230 0.18260 220 0.3274
tDistribution 0.0179 -0.07110 0.10990 0.04610 510 0.6747
Convergence Iterations
1.02 1e+05

Abundance - Bull Trout - Juvenile

Parameter Estimate Lower Upper SD Error Significance
bDensity 2.6560 1.9860 3.2710 0.3380 24 0.0010
bDensityRegime[2] 0.4230 -0.4520 1.4470 0.4780 220 0.3134
bDensitySeason[2] 0.4260 -0.1780 1.0940 0.3250 150 0.1797
bDistribution -0.0214 -0.1586 0.1235 0.0723 660 0.7346
bDistributionRegime[2] -0.0014 -0.1376 0.1372 0.0645 9800 0.9881
bDistributionSeason[2] 0.0110 -0.0623 0.0925 0.0380 700 0.7825
bEfficiency -3.0141 -3.2602 -2.7443 0.1338 9 0.0010
bEfficiencySeason[2] -0.3880 -1.0420 0.2340 0.3230 160 0.2216
bType[1] 1.0000 1.0000 1.0000 0.0000 0 0.0010
bType[2] 0.6140 0.1960 1.3680 0.3170 95 0.0010
sDensitySite 0.6765 0.4235 1.0614 0.1704 47 0.0010
sDensitySiteYear 0.1613 0.0195 0.3048 0.0770 88 0.0010
sDensityYear 0.7138 0.4196 1.2311 0.2127 57 0.0010
sDispersion 0.3809 0.2562 0.4934 0.0608 31 0.0010
sDistributionYear 0.0695 0.0041 0.1929 0.0496 140 0.0010
sEfficiencySessionSeasonYear 0.2636 0.1574 0.3864 0.0577 43 0.0010
tAbundance 0.4230 -0.4520 1.4470 0.4780 220 0.3134
tDistribution -0.0014 -0.1376 0.1372 0.0645 9800 0.9881
Convergence Iterations
1.07 1e+05

Abundance - Mountain Whitefish - Adult

Parameter Estimate Lower Upper SD Error Significance
bDensity 6.65010 6.33150 6.92360 0.15360 4 0.0010
bDensityRegime[2] -0.08270 -0.32640 0.18070 0.12740 310 0.4931
bDensitySeason[2] -0.53220 -0.76530 -0.29620 0.12010 44 0.0010
bDistribution 0.09300 -0.00700 0.19240 0.05180 110 0.0819
bDistributionRegime[2] 0.01580 -0.08280 0.12640 0.05280 660 0.7705
bDistributionSeason[2] -0.05378 -0.09752 -0.00928 0.02314 82 0.0220
bEfficiency -3.91190 -4.02290 -3.79080 0.06040 3 0.0010
bEfficiencySeason[2] 0.89140 0.67840 1.11290 0.10920 24 0.0010
bType[1] 1.00000 1.00000 1.00000 0.00000 0 0.0010
bType[2] 2.82900 1.61000 4.75600 0.81000 56 0.0010
sDensitySite 0.51760 0.33120 0.77480 0.11800 43 0.0010
sDensitySiteYear 0.35290 0.29030 0.41610 0.03260 18 0.0010
sDensityYear 0.10200 0.00420 0.24690 0.06590 120 0.0010
sDispersion 0.45295 0.41916 0.48820 0.01764 8 0.0010
sDistributionYear 0.06320 0.01800 0.12400 0.02690 84 0.0010
sEfficiencySessionSeasonYear 0.21520 0.15660 0.28380 0.03250 30 0.0010
tAbundance -0.08270 -0.32640 0.18070 0.12740 310 0.4931
tDistribution 0.01580 -0.08280 0.12640 0.05280 660 0.7705
Convergence Iterations
1.05 1e+05

Abundance - Mountain Whitefish - Juvenile

Parameter Estimate Lower Upper SD Error Significance
bDensity 5.9020 4.6740 7.2190 0.6500 22 0.0010
bDensityRegime[2] -0.3590 -1.5100 0.9210 0.5970 340 0.4192
bDensitySeason[2] 0.3830 -0.9140 1.6290 0.6280 330 0.5110
bDistribution 0.0952 -0.0975 0.3167 0.1048 220 0.3474
bDistributionRegime[2] 0.0302 -0.1417 0.2128 0.0863 590 0.6967
bDistributionSeason[2] -0.0984 -0.1725 -0.0254 0.0386 75 0.0100
bEfficiency -5.7830 -6.8390 -5.0540 0.4520 15 0.0010
bEfficiencySeason[2] 0.5540 -0.6780 1.8200 0.6240 220 0.3693
bType[1] 1.0000 1.0000 1.0000 0.0000 0 0.0010
bType[2] 1.4990 0.6660 3.2350 0.6760 86 0.0010
sDensitySite 0.9191 0.5861 1.4381 0.2158 46 0.0010
sDensitySiteYear 0.4743 0.3299 0.6275 0.0766 31 0.0010
sDensityYear 0.7310 0.3500 1.4820 0.2840 77 0.0010
sDispersion 0.5012 0.3968 0.5977 0.0516 20 0.0010
sDistributionYear 0.0844 0.0076 0.2214 0.0537 130 0.0010
sEfficiencySessionSeasonYear 0.2400 0.1041 0.3780 0.0695 57 0.0010
tAbundance -0.3590 -1.5100 0.9210 0.5970 340 0.4192
tDistribution 0.0302 -0.1417 0.2128 0.0863 590 0.6967
Convergence Iterations
1.06 1e+05

Abundance - Rainbow Trout - Adult

Parameter Estimate Lower Upper SD Error Significance
bDensity 0.4830 -0.5060 1.5060 0.5160 210 0.3453
bDensityRegime[2] 0.5840 -0.1510 1.3070 0.3820 120 0.1211
bDensitySeason[2] -0.1260 -1.4350 1.4070 0.7230 1100 0.8135
bDistribution -0.3486 -0.6618 -0.0678 0.1513 85 0.0298
bDistributionRegime[2] 0.2662 -0.0281 0.5557 0.1488 110 0.0655
bDistributionSeason[2] -0.0335 -0.2166 0.1640 0.0963 570 0.6945
bEfficiency -2.8650 -3.5730 -2.2690 0.3390 23 0.0010
bEfficiencySeason[2] -0.2650 -1.8020 1.0260 0.7290 530 0.7600
bType[1] 1.0000 1.0000 1.0000 0.0000 0 0.0010
bType[2] 4.9460 0.2050 9.6860 2.9040 96 0.0010
sDensitySite 1.0340 0.5780 1.8000 0.3170 59 0.0010
sDensitySiteYear 0.4359 0.0552 0.8008 0.1900 86 0.0010
sDensityYear 0.2910 0.0140 0.8750 0.2352 150 0.0010
sDispersion 0.5192 0.0502 0.9077 0.2156 83 0.0010
sDistributionYear 0.1242 0.0053 0.3510 0.0973 140 0.0010
sEfficiencySessionSeasonYear 0.2475 0.0126 0.5690 0.1500 110 0.0010
tAbundance 0.5840 -0.1510 1.3070 0.3820 120 0.1211
tDistribution 0.2662 -0.0281 0.5557 0.1488 110 0.0655
Convergence Iterations
1.05 4e+05

Abundance - Largescale Sucker - Adult

Parameter Estimate Lower Upper SD Error Significance
bDensity 4.7830 3.6150 5.7510 0.5450 22 0.0010
bDensityRegime[2] 0.9140 -0.2680 2.4900 0.6560 150 0.1175
bDensitySeason[2] -0.9230 -1.8540 0.1420 0.5100 110 0.0956
bDistribution -0.1175 -0.3519 0.0884 0.1071 190 0.2209
bDistributionRegime[2] 0.0871 -0.1656 0.3376 0.1205 290 0.4180
bDistributionSeason[2] -0.1860 -0.2736 -0.1036 0.0429 46 0.0010
bEfficiency -3.7569 -4.0609 -3.4712 0.1500 8 0.0010
bEfficiencySeason[2] -0.9210 -1.9540 -0.0460 0.5010 100 0.0379
bType[1] 1.0000 1.0000 1.0000 0.0000 0 0.0010
bType[2] 2.4430 1.1000 4.9160 1.0690 78 0.0010
sDensitySite 0.4052 0.2018 0.7014 0.1272 62 0.0010
sDensitySiteYear 0.4326 0.2913 0.6044 0.0776 36 0.0010
sDensityYear 0.6470 0.1950 1.5500 0.3460 100 0.0010
sDispersion 0.5141 0.4324 0.6038 0.0426 17 0.0010
sDistributionYear 0.1076 0.0086 0.3355 0.0818 150 0.0010
sEfficiencySessionSeasonYear 0.3206 0.1967 0.4790 0.0714 44 0.0010
tAbundance 0.9140 -0.2680 2.4900 0.6560 150 0.1175
tDistribution 0.0871 -0.1656 0.3376 0.1205 290 0.4180
Convergence Iterations
1.03 2e+05
Parameter Estimate Lower Upper SD Error Significance
sTrend 0.4722 0.3318 0.6403 0.0787 33 0.001
sValue 0.7557 0.7026 0.8112 0.0277 7 0.001
Convergence Iterations
1.06 1e+05

Figures

Growth

figures/growth/growth.png
Figure 1. Predicted growth curve by species.

Growth - Bull Trout

figures/growth/BT/year.png
Figure 2. Predicted growth for a 500 mm Bull Trout by year (with 95% CRIs).

Growth - Mountain Whitefish

figures/growth/MW/year.png
Figure 3. Predicted growth for a 250 mm Mountain Whitefish by year (with 95% CRIs).

Growth - Rainbow Trout

figures/growth/RB/year.png
Figure 4. Predicted growth for a 300 mm Rainbow Trout by year (with 95% CRIs).

Condition

figures/condition/length.png
Figure 5. Predicted length-mass relationship by species.

Condition - Bull Trout - Juvenile

figures/condition/BT/juvenile/year.png
Figure 6. Body condition effect size estimates (with 95% CRIs) by year for a 300 mm juvenile Bull Trout.
figures/condition/BT/juvenile/site.png
Figure 7. Body condition effect size estimates (with 95% CRIs) by site for a 300 mm juvenile Bull Trout.

Condition - Bull Trout - Adult

figures/condition/BT/adult/year.png
Figure 8. Body condition effect size estimates (with 95% CRIs) by year for a 500 mm adult Bull Trout.
figures/condition/BT/adult/site.png
Figure 9. Body condition effect size estimates (with 95% CRIs) by site for a 500 mm adult Bull Trout.

Condition - Mountain Whitefish - Juvenile

figures/condition/MW/juvenile/year.png
Figure 10. Body condition effect size estimates (with 95% CRIs) by year for a 100 mm juvenile Mountain Whitefish.
figures/condition/MW/juvenile/site.png
Figure 11. Body condition effect size estimates (with 95% CRIs) by site for a 100 mm juvenile Mountain Whitefish.

Condition - Mountain Whitefish - Adult

figures/condition/MW/adult/year.png
Figure 12. Body condition effect size estimates (with 95% CRIs) by year for a 250 mm adult Mountain Whitefish.
figures/condition/MW/adult/site.png
Figure 13. Body condition effect size estimates (with 95% CRIs) by site for a 250 mm adult Mountain Whitefish.

Condition - Rainbow Trout - Juvenile

figures/condition/RB/juvenile/year.png
Figure 14. Body condition effect size estimates (with 95% CRIs) by year for a 150 mm juvenile Rainbow Trout.
figures/condition/RB/juvenile/site.png
Figure 15. Body condition effect size estimates (with 95% CRIs) by site for a 150 mm juvenile Rainbow Trout.

Condition - Rainbow Trout - Adult

figures/condition/RB/adult/year.png
Figure 16. Body condition effect size estimates (with 95% CRIs) by year for a 300 mm adult Rainbow Trout.
figures/condition/RB/adult/site.png
Figure 17. Body condition effect size estimates (with 95% CRIs) by site for a 300 mm adult Rainbow Trout.

Occupancy - Rainbow Trout

figures/occupancy/RB/year.png
Figure 18. Estimated occupancy of Rainbow Trout at a typical site by year (with 95% CRIs).
figures/occupancy/RB/site.png
Figure 19. Estimated occupancy of Rainbow Trout at a site in a typical year (with 95% CRIs).

Occupancy - Burbot

figures/occupancy/BB/year.png
Figure 20. Estimated occupancy of Burbot at a typical site by year (with 95% CRIs).
figures/occupancy/BB/site.png
Figure 21. Estimated occupancy of Burbot at a site in a typical year (with 95% CRIs).

Occupancy - Lake Whitefish

figures/occupancy/LW/year.png
Figure 22. Estimated occupancy of Lake Whitefish at a typical site by year (with 95% CRIs).
figures/occupancy/LW/site.png
Figure 23. Estimated occupancy of Lake Whitefish at a site in a typical year (with 95% CRIs).

Occupancy - Northern Pikeminnow

figures/occupancy/NPC/year.png
Figure 24. Estimated occupancy of Northern Pikeminnow at a typical site by year (with 95% CRIs).
figures/occupancy/NPC/site.png
Figure 25. Estimated occupancy of Northern Pikeminnow at a site in a typical year (with 95% CRIs).

Occupancy - Redside Shiner

figures/occupancy/RSC/year.png
Figure 26. Estimated occupancy of Redside Shiner at a typical site by year (with 95% CRIs).
figures/occupancy/RSC/site.png
Figure 27. Estimated occupancy of Redside Shiner at a site in a typical year (with 95% CRIs).

Occupancy - Sculpins

figures/occupancy/CC/year.png
Figure 28. Estimated occupancy of Sculpins at a typical site by year (with 95% CRIs).
figures/occupancy/CC/site.png
Figure 29. Estimated occupancy of Sculpins at a site in a typical year (with 95% CRIs).

Species Richness

figures/richness/year.png
Figure 30. Estimated species richness at a typical site by year (with 95% CRIs).
figures/richness/site.png
Figure 31. Estimated species richness at a site in a typical year (with 95% CRIs).

Count - Rainbow Trout

figures/count/RB/year.png
Figure 32. Estimated lineal river count density of Rainbow Trout by year (with 95% CRIs).
figures/count/RB/site.png
Figure 33. Estimated lineal river count density of Rainbow Trout by site (with 95% CRIs).
figures/count/RB/distribution.png
Figure 34. Estimated effect of centred river kilometre on log(Density) for Rainbow Trout by year (with 95% CRIs).

Count - Burbot

figures/count/BB/year.png
Figure 35. Estimated lineal river count density of Burbot by year (with 95% CRIs).
figures/count/BB/site.png
Figure 36. Estimated lineal river count density of Burbot by site (with 95% CRIs).
figures/count/BB/distribution.png
Figure 37. Estimated effect of centred river kilometre on log(Density) for Burbot by year (with 95% CRIs).

Count - Northern Pikeminnow

figures/count/NPC/year.png
Figure 38. Estimated lineal river count density of Northern Pikeminnow by year (with 95% CRIs).
figures/count/NPC/site.png
Figure 39. Estimated lineal river count density of Northern Pikeminnow by site (with 95% CRIs).
figures/count/NPC/distribution.png
Figure 40. Estimated effect of centred river kilometre on log(Density) for Northern Pikeminnow by year (with 95% CRIs).

Count - Suckers

figures/count/SU/year.png
Figure 41. Estimated lineal river count density of Sucker by year (with 95% CRIs).
figures/count/SU/site.png
Figure 42. Estimated lineal river count density of Sucker by site (with 95% CRIs).
figures/count/SU/distribution.png
Figure 43. Estimated effect of centred river kilometre on log(Density) for Sucker by year (with 95% CRIs).

Movement - Bull Trout

figures/movement/BT/length.png
Figure 44. Probability of recapture at the same site versus a different site by fish length and season (with 95% CRIs).

Movement - Mountain Whitefish

figures/movement/MW/length.png
Figure 45. Probability of recapture at the same site versus a different site by fish length and season (with 95% CRIs).

Movement - Rainbow Trout

figures/movement/RB/length.png
Figure 46. Probability of recapture at the same site versus a different site by fish length and season (with 95% CRIs).

Movement - Largescale Sucker

figures/movement/CSU/length.png
Figure 47. Probability of recapture at the same site versus a different site by fish length and season (with 95% CRIs).

Observer Length Correction

figures/observer/density.png
Figure 48. Observed and corrected length density plots for measured versus counted fish by observer and species.
figures/observer/bias.png
Figure 49. Predicted length inaccuracy relative to measures by observer and species (with 95% CRIs).
figures/observer/error.png
Figure 50. Predicted imprecision relative to measured by observer and species (with 95% CRIs).

Abundance

figures/abundance/multiplier.png
Figure 51. Recorded count versus expected catch by site, species and stage.

Abundance - Bull Trout - Adult

figures/abundance/BT/Adult/abundance.png
Figure 52. Abundance of Adult Bull Trout by year (with 95% CRIs).
figures/abundance/BT/Adult/site.png
Figure 53. Lineal river density of Adult Bull Trout by site (with 95% CRIs).
figures/abundance/BT/Adult/distribution.png
Figure 54. Estimated effect of centred river kilometre on log(Density) for Bull Trout by year (with 95% CRIs).
figures/abundance/BT/Adult/efficiency.png
Figure 55. Capture efficiency for Adult Bull Trout by session and year (with 95% CRIs).

Abundance - Bull Trout - Juvenile

figures/abundance/BT/Juvenile/abundance.png
Figure 56. Abundance of Juvenile Bull Trout by year (with 95% CRIs).
figures/abundance/BT/Juvenile/site.png
Figure 57. Lineal river density of Juvenile Bull Trout by site (with 95% CRIs).
figures/abundance/BT/Juvenile/distribution.png
Figure 58. Estimated effect of centred river kilometre on log(Density) for Bull Trout by year (with 95% CRIs).
figures/abundance/BT/Juvenile/efficiency.png
Figure 59. Capture efficiency for Juvenile Bull Trout by session and year (with 95% CRIs).

Abundance - Mountain Whitefish - Adult

figures/abundance/MW/Adult/abundance.png
Figure 60. Abundance of Adult Mountain Whitefish by year (with 95% CRIs).
figures/abundance/MW/Adult/site.png
Figure 61. Lineal river density of Adult Mountain Whitefish by site (with 95% CRIs).
figures/abundance/MW/Adult/distribution.png
Figure 62. Estimated effect of centred river kilometre on log(Density) for Mountain Whitefish by year (with 95% CRIs).
figures/abundance/MW/Adult/efficiency.png
Figure 63. Capture efficiency for Adult Mountain Whitefish by session and year (with 95% CRIs).

Abundance - Mountain Whitefish - Juvenile

figures/abundance/MW/Juvenile/abundance.png
Figure 64. Abundance of Juvenile Mountain Whitefish by year (with 95% CRIs).
figures/abundance/MW/Juvenile/site.png
Figure 65. Lineal river density of Juvenile Mountain Whitefish by site (with 95% CRIs).
figures/abundance/MW/Juvenile/distribution.png
Figure 66. Estimated effect of centred river kilometre on log(Density) for Mountain Whitefish by year (with 95% CRIs).
figures/abundance/MW/Juvenile/efficiency.png
Figure 67. Capture efficiency for Juvenile Mountain Whitefish by session and year (with 95% CRIs).

Abundance - Rainbow Trout - Adult

figures/abundance/RB/Adult/abundance.png
Figure 68. Abundance of Adult Rainbow Trout by year (with 95% CRIs).
figures/abundance/RB/Adult/site.png
Figure 69. Lineal river density of Adult Rainbow Trout by site (with 95% CRIs).
figures/abundance/RB/Adult/distribution.png
Figure 70. Estimated effect of centred river kilometre on log(Density) for Rainbow Trout by year (with 95% CRIs).
figures/abundance/RB/Adult/efficiency.png
Figure 71. Capture efficiency for Adult Rainbow Trout by session and year (with 95% CRIs).

Abundance - Largescale Sucker - Adult

figures/abundance/CSU/Adult/abundance.png
Figure 72. Abundance of Adult Largescale Sucker by year (with 95% CRIs).
figures/abundance/CSU/Adult/site.png
Figure 73. Lineal river density of Adult Largescale Sucker by site (with 95% CRIs).
figures/abundance/CSU/Adult/distribution.png
Figure 74. Estimated effect of centred river kilometre on log(Density) for Largescale Sucker by year (with 95% CRIs).
figures/abundance/CSU/Adult/efficiency.png
Figure 75. Capture efficiency for Adult Largescale Sucker by session and year (with 95% CRIs).

Species Diversity (Evenness)

figures/evenness/year.png
Figure 76.
figures/evenness/site.png
Figure 77.

Long-Term Trends

figures/dfa/fit.png
Figure 78. Standardised variables by year with the predicted values as black lines.
figures/dfa/mds.png
Figure 79. Non-metric multidimensional plot showing clustering of standardised variables by trend weightings.

Short-Term Correlations

figures/cor/data.png
Figure 80. Variable residuals by year.
figures/cor/mds.png
Figure 81. Non-metric multidimensional scaling (NMDS) plot showing clustering of variables by absolute correlations of short-term variation.

Significance

The following table summarises 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 on big relative to small fish. The Direction column indicates whether significant changes were positive or negative where a positive change for Distribution indicates a shift towards the dam.

Test Species Stage Significance Direction
Growth Mountain Whitefish 0.3228
Growth Rainbow Trout 0.4492
Growth Bull Trout 0.8903
Condition1 Mountain Whitefish 0.0078 -
Condition1 Rainbow Trout 0.9182
Condition1 Bull Trout 0.0095 -
Condition2 Mountain Whitefish 0.1778
Condition2 Rainbow Trout 0.4092
Condition2 Bull Trout 0.5161
Abundance Mountain Whitefish Juvenile 0.4192
Abundance Mountain Whitefish Adult 0.4931
Abundance Rainbow Trout 0.1682
Abundance Rainbow Trout Adult 0.1211
Abundance Bull Trout Juvenile 0.3134
Abundance Bull Trout Adult 0.3274
Abundance Largescale Sucker Adult 0.1175
Abundance Sucker 0.0010 +
Abundance Burbot 0.4310
Abundance Northern Pikeminnow 0.9961
Distribution Mountain Whitefish Juvenile 0.6967
Distribution Mountain Whitefish Adult 0.7705
Distribution Rainbow Trout 0.0484 +
Distribution Rainbow Trout Adult 0.0655
Distribution Bull Trout Juvenile 0.9881
Distribution Bull Trout Adult 0.6747
Distribution Largescale Sucker Adult 0.4180
Distribution Sucker 0.0829
Distribution Burbot 0.5798
Distribution Northern Pikeminnow 0.9082

Acknowledgements

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

References

Abmann, C., J. Boysen-Hogrefe, and M. Pape. 2014. “Bayesian Analysis of Dynamic Factor Models: An Ex-Post Approach Towards the Rotation Problem.” Kiel Working Paper No. 1902. Kiel, Germany: Kiel Institute for the World Economy.

Bradford, Michael J, Josh Korman, and Paul S Higgins. 2005. “Using Confidence Intervals to Estimate the Response of Salmon Populations (Oncorhynchus Spp.) to Experimental Habitat Alterations.” Canadian Journal of Fisheries and Aquatic Sciences 62 (12): 2716–26. https://doi.org/10.1139/f05-179.

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

He, Ji X., James R. Bence, James E. Johnson, David F. Clapp, and Mark P. Ebener. 2008. “Modeling Variation in Mass-Length Relations and Condition Indices of Lake Trout and Chinook Salmon in Lake Huron: A Hierarchical Bayesian Approach.” Transactions of the American Fisheries Society 137 (3): 801–17. https://doi.org/10.1577/T07-012.1.

Kery, Marc. 2010. Introduction to WinBUGS for Ecologists: A Bayesian Approach to Regression, ANOVA, Mixed Models and Related Analyses. Amsterdam; Boston: Elsevier. http://public.eblib.com/EBLPublic/PublicView.do?ptiID=629953.

Kery, Marc, and Michael Schaub. 2011. Bayesian Population Analysis Using WinBUGS : A Hierarchical Perspective. Boston: Academic Press. http://www.vogelwarte.ch/bpa.html.

Plummer, Martyn. 2012. “JAGS Version 3.3.0 User Manual.” http://sourceforge.net/projects/mcmc-jags/files/Manuals/3.x/.

Team, R Core. 2013. “R: A Language and Environment for Statistical Computing.” Vienna, Austria: R Foundation for Statistical Computing. http://www.R-project.org.

Thorley, J. L. 2013. “Jaggernaut: An R Package to Facilitate Bayesian Analyses Using JAGS (Just Another Gibbs Sampler).” Nelson, B.C.: Poisson Consulting Ltd. https://github.com/poissonconsulting/jaggernaut.

von Bertalanffy, L. 1938. “A Quantitative Theory of Organic Growth (Inquiries on Growth Laws Ii).” Human Biology 10: 181–213.

Zuur, A F, I D Tuck, and N Bailey. 2003. “Dynamic Factor Analysis to Estimate Common Trends in Fisheries Time Series.” Canadian Journal of Fisheries and Aquatic Sciences 60 (5): 542–52. https://doi.org/10.1139/f03-030.


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