Lower Columbia River Sculpin and Dace Stranding Analysis 2013

The main intepretive report by AMEC Environment & Infrastructure is available from BC Hydro.

The suggested citation for this online appendix is:

Thorley, J.L. (2014) Lower Columbia River Sculpin and Dace Stranding Analysis 2013. A Poisson Consulting Ltd. Analysis Report. URL: http://www.poissonconsulting.ca/f/1090742912.

Background

Discharge reductions associated with the operation of HLK and Brilliant Dams on the Lower Columbia River, British Columbia, can cause fish stranding.

The management question the current analysis attempts to answer is:

Which operations, and at what season, pose the highest risk of stranding or interference with the normal life cycles of sculpins and dace?

Methods

Data Collection

Following reduction events, crews are dispatched to salvage stranded fish from areas of concern. At each site the crew record the number of pools, the number of pools surveyed and the number of fish counted by species, genus, family or all species in the surveyed pools. Since 2011, the crew have also lengthed a subsample of individuals.

Data Preparation

The fish stranding data were provided by Golder Associates in the form of an Access database. The discharge data were queried from a BC Hydro database maintained by Poisson Consulting.

The data were prepared for analysis using R version 3.1.0 (Team, 2013).

Pool Stranding

During the pool stranding data preparation it was assumed that:

Discharge

During the discharge data preparation it was assumed that:

Statistical Analysis

Hierarchical Bayesian models were fitted to the stranding data using R version 3.1.0 (Team, 2013) and JAGS 3.4.0 (Plummer, 2012) which interfaced with each other via jaggernaut 1.8.1 (Thorley, 2014). 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) pages 41-44.

Unless specified, the models assumed vague (low information) prior distributions (Kéry and Schaub, 2011, p. 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 (Kéry and Schaub, 2011, pp. 38-40). Model convergence was confirmed by ensuring that Rhat (Kéry and Schaub, 2011, p. 40) was less than 1.1 for each of the parameters in the model (Kéry and Schaub, 2011, p. 61). Model adequacy was confirmed by examination of residual plots.

The posterior distributions of the fixed (Kéry and Schaub, 2011, p. 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 (Kéry and Schaub, 2011, p. 37,42).

Variable selection was achieved by dropping uninformative explanatory variables where a variable was considered to be uninformative if its percent relative error was \(\geq\) 100%. In the case of fixed effects this is approximately equivalent to dropping insignificant variables, i.e., those with a significance \(\geq\) 0.05.

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) (Kéry and Schaub, 2011, pp. 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 et al. 2005). Plots were produced using the ggplot2 R package (Wickham, 2009).

Pool Stranding

The probability of stranding a threshold number of fish was analysed using a hierarchical Bayesian general linear mixed model (GLMM) (Kéry and Schaub, 2011, pp. 73-74).

Key assumptions of the GLMM include:

Preliminary analysis indicated that the data were not overdispersed. Preliminary analysis also indicated that the rate of reduction, the delay between the reduction and salvage and the diel period were not informative predictors of the probability of stranding.

Model Code

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

Pool Stranding

Variable/Parameter Description
bStranding Intercept for logit(eStranding)
bStrandingDayte Effect of Dayte on logit(eStranding)
bStrandingDayte2 Quadratic effect of Dayte on logit(eStranding)
bStrandingMagnitude Effect of Magnitude on logit(eStranding)
bStrandingRecontoured Effect of Recontoured on logit(eStranding)
bStrandingStage Effect of Stage on logit(eStranding)
Dayte[i] Standardised day of the year for the ith site visit
eStranding[i] Expected probability of a stranding event for the ith site visit
Magnitude[i] Standardised magnitude of the reduction for the ith site visit
Recontoured[i] Whether the site of the ith site had been recontoured
Site[i] Site of the ith site visit
sStrandingSite SD of effect of Site on logit(eStranding)
sStrandingYear SD of effect of Year on logit(eStranding)
Stage[i] Standardised stage of the reduction for the ith site visit
Stranding[i] Whether there was a stranding event for the ith site visit
Year[i] Year of the ith site visit
Pool Stranding - Model1
model{

  bStranding ~ dnorm(0, 5^-2)
  bStrandingMagnitude ~ dnorm(0, 2^-2)

  bStrandingStage ~ dnorm(0, 2^-2)

  bStrandingDayte ~ dnorm(0, 2^-2)
  bStrandingDayte2 ~ dnorm(0, 2^-2)

  bStrandingRecontoured[1] <- 0 
  for (i in 2:nRecontoured) {
    bStrandingRecontoured[i] ~ dnorm(0, 2^-2)
  }

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

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

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

    logit(eStranding[i]) <- bStranding + bStrandingMagnitude * Magnitude[i] + bStrandingStage * Stage[i] + bStrandingDayte * Dayte[i] + bStrandingDayte2 * Dayte[i]^2 + bStrandingRecontoured[Recontoured[i]] + bStrandingSite[Site[i]] + bStrandingYear[Year[i]]

    Stranding[i] ~ dbern(eStranding[i])
  }
}

Results

Model Parameters

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

Pool Stranding - Sculpin - One Or More

Parameter Estimate Lower Upper SD Error Significance
bStranding -3.16066 -4.1376 -2.3169 0.46753 29 0.0000
bStrandingDayte -0.27833 -0.4405 -0.1075 0.08280 60 0.0000
bStrandingDayte2 -0.01394 -0.2132 0.1756 0.09815 1395 0.9093
bStrandingMagnitude 0.25979 0.1164 0.3976 0.07254 54 0.0000
bStrandingRecontoured[2] -1.17882 -1.8244 -0.5874 0.31787 52 0.0000
bStrandingStage -0.62849 -0.8252 -0.4379 0.09768 31 0.0000
sStrandingSite 1.70997 1.0933 2.7044 0.40697 47 0.0000
sStrandingYear 0.61514 0.3688 1.0140 0.16176 52 0.0000
Rhat Iterations
1.04 4000

Pool Stranding - Sculpin - Ten Or More

Parameter Estimate Lower Upper SD Error Significance
bStranding -5.29866 -7.2943 -3.76398 0.8906 33 0.0000
bStrandingDayte -0.30239 -0.6545 0.04839 0.1797 116 0.0960
bStrandingDayte2 -0.55314 -1.0329 -0.12428 0.2310 82 0.0093
bStrandingMagnitude 0.03771 -0.2787 0.33702 0.1605 816 0.8040
bStrandingRecontoured[2] -1.42702 -2.5061 -0.34954 0.5471 76 0.0107
bStrandingStage -0.51754 -0.8722 -0.18193 0.1742 67 0.0013
sStrandingSite 2.68710 1.4082 4.42674 0.7799 56 0.0000
sStrandingYear 0.88486 0.4123 1.51799 0.2928 62 0.0000
Rhat Iterations
1.07 4000

Pool Stranding - Dace - One Or More

Parameter Estimate Lower Upper SD Error Significance
bStranding -3.2405 -4.64792 -2.2710 0.59887 37 0.0000
bStrandingDayte -0.7207 -1.00739 -0.4543 0.14410 38 0.0000
bStrandingDayte2 -1.1041 -1.46664 -0.7673 0.18265 32 0.0000
bStrandingMagnitude 0.2399 0.08096 0.4035 0.08229 67 0.0013
bStrandingRecontoured[2] -0.6503 -1.42697 0.1401 0.39908 120 0.1120
bStrandingStage -0.3800 -0.62671 -0.1641 0.11692 61 0.0000
sStrandingSite 1.8781 1.04138 3.1457 0.55011 56 0.0000
sStrandingYear 0.6460 0.29142 1.1217 0.20903 64 0.0000
Rhat Iterations
1.08 2000

Pool Stranding - Dace - Ten Or More

Parameter Estimate Lower Upper SD Error Significance
bStranding -3.9103 -5.01281 -2.9947 0.5237 26 0.0000
bStrandingDayte -0.6542 -1.11642 -0.2394 0.2242 67 0.0027
bStrandingDayte2 -1.2960 -1.87767 -0.7912 0.2808 42 0.0000
bStrandingMagnitude 0.3353 0.09034 0.5685 0.1202 71 0.0080
bStrandingRecontoured[2] -0.3395 -1.44092 0.7534 0.5785 323 0.5600
bStrandingStage -0.7419 -1.17223 -0.3517 0.2076 55 0.0000
sStrandingSite 1.4861 0.64940 2.6581 0.5195 68 0.0000
sStrandingYear 0.6774 0.15446 1.3534 0.2991 88 0.0000
Rhat Iterations
1.04 2000

Figures

Fork Length

figures/lengths/length-frequency.png
Figure 1. Length-frequency histogram by species group.

Pool Stranding - Sculpin - One Or More

figures/reduction/CC/1/magnitude.png
Figure 2. Expected probability of stranding one or more sculpin by magnitude of reduction.
figures/reduction/CC/1/stage.png
Figure 3. Expected probability of stranding one or more sculpin by river stage.
figures/reduction/CC/1/dayte.png
Figure 4. Expected probability of stranding one or more sculpin by day of the year.
figures/reduction/CC/1/recontoured.png
Figure 5. Expected probability of stranding one or more sculpin by before or after recontouring.
figures/reduction/CC/1/site.png
Figure 6. Expected probability of stranding one or more sculpin by site.
figures/reduction/CC/1/year.png
Figure 7. Expected probability of stranding one or more sculpin by year.

Pool Stranding - Sculpin - Ten Or More

figures/reduction/CC/10/magnitude.png
Figure 8. Expected probability of stranding ten or more sculpin by magnitude of reduction.
figures/reduction/CC/10/stage.png
Figure 9. Expected probability of stranding ten or more sculpin by river stage.
figures/reduction/CC/10/dayte.png
Figure 10. Expected probability of stranding ten or more sculpin by day of the year.
figures/reduction/CC/10/recontoured.png
Figure 11. Expected probability of stranding ten or more sculpin by before or after recontouring.
figures/reduction/CC/10/site.png
Figure 12. Expected probability of stranding ten or more sculpin by site.
figures/reduction/CC/10/year.png
Figure 13. Expected probability of stranding ten or more sculpin by year.

Pool Stranding - Dace - One Or More

figures/reduction/DC/1/magnitude.png
Figure 14. Expected probability of stranding one or more dace by magnitude of reduction.
figures/reduction/DC/1/stage.png
Figure 15. Expected probability of stranding one or more dace by river stage.
figures/reduction/DC/1/dayte.png
Figure 16. Expected probability of stranding one or more dace by day of the year.
figures/reduction/DC/1/recontoured.png
Figure 17. Expected probability of stranding one or more dace by before or after recontouring.
figures/reduction/DC/1/site.png
Figure 18. Expected probability of stranding one or more dace by site.
figures/reduction/DC/1/year.png
Figure 19. Expected probability of stranding one or more dace by year.

Pool Stranding - Dace - Ten Or More

figures/reduction/DC/10/magnitude.png
Figure 20. Expected probability of stranding ten or more dace by magnitude of reduction.
figures/reduction/DC/10/stage.png
Figure 21. Expected probability of stranding ten or more dace by river stage.
figures/reduction/DC/10/dayte.png
Figure 22. Expected probability of stranding ten or more dace by day of the year.
figures/reduction/DC/10/recontoured.png
Figure 23. Expected probability of stranding ten or more dace by before or after recontouring.
figures/reduction/DC/10/site.png
Figure 24. Expected probability of stranding ten or more dace by site.
figures/reduction/DC/10/year.png
Figure 25. Expected probability of stranding ten or more dace by year.

Acknowledgements

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

References