Lower Duncan River Kokanee AUC Analysis 2017

Data Preparation

The 2017 survey data were provided by LGL Limited in the form of Excel tables. They were imported into the existing SQLite database. The data were clean and tidied (Wickham 2014) using R version 3.4.3 (R Core Team 2016). When there were repeated counts for a channel the higher of the two values was choosen. The mean daily discharge and water temperature values at Duncan River below Lardeau (DRL) were extracted from BC Hydro’s environmental database for the Kootenays, which is maintained by Poisson Consulting. The annual abundances of Kokanee spawning in Meadow Creek and the Lardeau River were provided by the Ministry of Forests, Lands and Natural Resource Operations.

Statistical Analysis

Model parameters were estimated using Bayesian methods. The estimates were produced using JAGS (Plummer 2015). 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 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 3.4.3 (R Core Team 2015) and the mbr family of packages.

Model Descriptions

Model Templates

Observer Efficiency

model{

  bEfficiency ~ dunif(0, 3)
  sDispersion ~ dunif(0, 5)

  for (i in 1:nObs){
    eAerial[i] <- Ground[i] * bEfficiency
    eDispersion[i] ~ dgamma(sDispersion^-2, sDispersion^-2)
    Aerial[i] ~ dpois(eAerial[i] * eDispersion[i])
  }
..

Template 1. Model definition.

Area-Under-The-Curve

model{
  bAbundance ~ dnorm(10, 5^-2)
  bPeakTiming ~ dunif(-14, 14)
  bDuration ~ dnorm(2, 1^-2)

  bEfficiency ~ dnorm(1.40, 0.38^-2) T(0.89, 2.40)
  bResidenceTime ~ dunif(7, 14)

  sAbundanceYear ~ dunif(0, 5)
  sPeakTiming ~ dunif(0, 14)
  for(i in 1:nYear){
    bAbundanceYear[i] ~ dnorm(0, sAbundanceYear^-2)
    bPeakTimingYear[i] ~ dnorm(0, sPeakTiming^-2)
  }

  bSD ~ dnorm(0, 10^-2)
  bSDAbundance ~ dnorm(0, 5^-2)
  for(i in 1:length(Count)){

    log(eAbundance[i]) <- bAbundance + bAbundanceYear[Year[i]]
    ePeakTiming[i] <- bPeakTiming + bPeakTimingYear[Year[i]]
    log(eDuration[i]) <- bDuration

    eArrived[i] <- pnorm(Dayte[i], (ePeakTiming[i] - bResidenceTime/2), eDuration[i]^-2)
    eDeparted[i] <- pnorm(Dayte[i], (ePeakTiming[i] + bResidenceTime/2), eDuration[i]^-2)
    eSpawners[i] <- (eArrived[i] - eDeparted[i]) * eAbundance[i]

    eEfficiency[i] <- bEfficiency

    log(eSD[i]) <- bSD + bSDAbundance * eAbundance[i]

    Count[i] ~ dnorm(eSpawners[i] * eEfficiency[i], eSD[i]^-2)
  }
..

Template 2. Model definition.

Tables

Observer Efficiency

Table 1. Parameter descriptions.

Table 2. Model coefficients.

Table 3. Model summary.

Table 4.

Channel Count

Table 5. Number of observed Kokanee distributed in the LDR main stem and side channels for 2017.

Area-Under-The-Curve

Table 6. Parameter descriptions.

Table 7. Model coefficients.

Table 8. Model summary.

Figures

Environmental

Observer Efficiency

Area-Under-The-Curve

Abundance

Window