# 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:

• Fish species code LND refers to long nose dace (LNC).
• The proportion of unidentified fish that were dace was the same as the proportion of identified fish (2.1%).
• The Genelle (Mainland) (LUB) site was recontoured in February 2003.

#### Discharge

During the discharge data preparation it was assumed that:

• The magnitude of a reduction event was the difference between the peak discharge in the previous 24 hours and the discharge at the time of the survey.
• The rate of a reduction event was the weighted mean hourly drop between the peak and the time of survey. Drops that were subsequently inundated prior to the survey were assigned zero weight while partially inundated drops were discounted accordingly.
• The time of a reduction event was the mean time between the peak and the survey weighted by the discounted drops.
• The delay was the number of hours between the time of the reduction event and the time of the survey.
• The stage was the discharge at the time of the reduction as the percent mean annual discharge (% MAD) of the section of river to take into account differences in river size.
• The diel period was whether or not the time of reduction occurred in daylight.

### 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:

• The probability of stranding varies with the magnitude of the reduction, the stage, whether a site has been recontoured and the day of the year as a second order polynomial.
• The probability of stranding can vary randomly with the site and year.
• Stranding events are Bernoulli distributed

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

## Acknowledgements

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