Curtis and Qua Creeks Productivity Analysis 2018

Data Collection

The data were collected by the Salmo Streamkeepers and Poisson Consulting in 2015 and by the Salmo Streamkeepers from 2016 to 2018. The invertebrate data were processed by Westcott Environmental Services and the water chemistry and periphyton data by CARO Analytic. The data were provided to Poisson in the form of an Excel database.

Data Preparation

The data were manipulated using R version 3.5.2 (R Core Team 2015) and imported into an SQLite database.

Statistical Analysis

Model parameters were estimated using Bayesian methods. The Bayesian estimates were produced using JAGS (Plummer 2003). For additional information on Bayesian estimation the reader is referred to McElreath (2016).

Unless indicated otherwise, the Bayesian analyses used uninformative normal prior distributions (Kery and Schaub 2011, 36). The posterior distributions were estimated from 1500 Markov Chain Monte Carlo (MCMC) samples thinned from the second halves of 3 chains (Kery and Schaub 2011, 38–40). Model convergence was confirmed by ensuring that \(\hat{R} \leq 1.1\) (Kery and Schaub 2011, 40) and \(\textrm{ESS} \geq 150\) for each of the monitored parameters (Kery and Schaub 2011, 61). Where \(\hat{R}\) is the potential scale reduction factor and \(\textrm{ESS}\) is the effective sample size.

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 informative, 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 3.5.2 (R Core Team 2015) and the mbr family of packages.

Model Descriptions

Model Templates

Periphyton Growth

model{
  bA ~ dnorm(0, 5^-2) 
  bK ~ dnorm(-5, 5^-2)

  sAYearCreekLocationSeries ~ dunif(0, 1)
  sKYearCreekLocationSeries ~ dunif(0, 1)
  for(i in 1:nYear) {
    for(j in 1:nCreek) {
      for(k in 1:nLocation) {
        for(l in 1:nSeries) {
          bAYearCreekLocationSeries[i, j, k, l] ~ dnorm(0, sAYearCreekLocationSeries^-2)
          bKYearCreekLocationSeries[i, j, k, l] ~ dnorm(0, sKYearCreekLocationSeries^-2)
        }
      }
    }
  }

  sPeriphyton ~ dunif(0, 1)
  for (i in 1:length(Periphyton)) {
    log(eA[i]) <- bA +  bAYearCreekLocationSeries[Year[i],Creek[i],Location[i],Series[i]]
    log(eK[i]) <- bK +  bKYearCreekLocationSeries[Year[i],Creek[i],Location[i],Series[i]]
    ePeriphyton[i] <- eA[i] * (1 - exp(-eK[i] * Days[i]))
    Periphyton[i] ~ dlnorm(log(ePeriphyton[i]), sPeriphyton^-2)
  }
..

Template 1. The model description.

Rainbow Trout Density

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

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

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

  bEfficiency ~ dnorm(0, 2^-2)

  sEfficiencyYearSitePass ~ dunif(0, 2)
  for(i in 1:nYear) {
    for(j in 1:nSite) {
      for(k in 1:nPass) {
        bEfficiencyYearSitePass[i,j,k] ~ dnorm(0, sEfficiencyYearSitePass^-2)
      }
    }
  }

  for (i in 1:length(SiteLength)) {
    log(eDensity[i]) <- bDensity + bDensityCreek[Creek[i]] + bDensitySite[Site[i]]
    eAbundance[i] ~ dpois(eDensity[i] * SiteLength[i])
    eRemaining[i,1] <- eAbundance[i]

    for(j in 1:nPass) {
      logit(eEfficiency[i,j]) <- bEfficiency + bEfficiencyYearSitePass[Year[i], Site[i], j]
      Catch[i,j] ~ dbin(eEfficiency[i,j], eRemaining[i,j])
      eRemaining[i,j+1] <- eRemaining[i,j] - Catch[i,j]
    }
  }
..

Template 2. The model description.

Tables

Periphyton Growth

Table 1. Parameter descriptions.

Table 2. Model coefficients.

Table 3. Model summary.

Rainbow Trout Density

Table 4. Parameter descriptions.

Table 5. Model coefficients.

Table 6. Model summary.

Bull Trout

Table 7. Bull Trout captured during electrofishing surveys.

Figures

Water Temperature

Periphyton Growth

Benthic Invertebrates

Rainbow Trout Length-Weight

Rainbow Trout Density

Chemical