Lower Columbia River Rainbow Trout Spawning Analysis 2015

The suggested citation for this analytic report is:

Thorley, J.L. and Hogan, P.M. (2016) Lower Columbia River Rainbow Trout Spawning Analysis 2015. A Poisson Consulting Analysis Report. URL: http://www.poissonconsulting.ca/f/1611032936.


Each spring in the Lower Columbia River (LCR) below the Hugh L. Keenleyside Dam (HLK) and in the Lower Kootenay River (LKR) below the Brilliant Dam, thousands of Rainbow Trout spawn. Since 1992, BC Hydro has stabilized the spring discharge releases from HLK to protect Rainbow Trout redds from dewatering.

The primary goal of the current analysis to answer the following management questions:

Does the implementation of Rainbow Trout Spawning Protection Flows over the course of the monitoring period lead to an increase in the relative abundance of Rainbow Trout spawning in the LCR downstream of the HLK dam?

Does the implementation of RTSPF over the course of the monitoring period lead to an increase in the spatial distribution of locations (and associated habitat area) that Rainbow Trout use for spawning in the LCR downstream of HLK?

Does the implementation of RTSPF over the course of the monitoring period protect the majority of Rainbow Trout redds (as estimated from spawning timing) from being dewatered in the LCR downstream of HLK?


Data Preparation

The Rainbow Trout fish and redd aerial count data for the LCR and LKR were collected by Mountain Water Research and databased by Gary Pavan. The age-1 Rainbow Trout abundance data were provided by the Fish Population Indexing Program which is led by Golder Associates.

The study area was divided into three sections: the LCR above the LKR, the LKR and the LCR below the LKR. Redd and spawner counts upstream of Norns Creek Fan and downstream of Genelle were excluded from the section totals because they constitute less than 0.1% of the total count and were not surveyed in all years. The redd and spawner counts for the Right Upstream Bank above Robson Bridge were also excluded as they appear to be primarily driven by viewing conditions (and constitute less than 2.5% of the total). A decline in the redd count of more than one third of the previous maximum count for a particular section was inferred to be caused by poor viewing conditions (turbidity) and the affected spawner and redd section counts were excluded from any subsequent analyses.

Statistical Analysis

Hierarchical Bayesian models were fitted to the data using R version 3.2.3 (Team 2013) and JAGS 3.4.0 (Plummer 2012) which interfaced with each other via jaggernaut 2.3.1 (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 indicated otherwise, the models used prior distributions that were vague in the sense that they did not affect the posterior 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 (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).

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 Deviance Information Criterion (DIC) was not used because it is of questionable validity when applied to hierarchical models (Kery and Schaub 2011, 469).

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).

Model Descriptions

The following model descriptions observe several conventions.

Acoustic Detection

The spawner residence time in days at Norns Creek Fan was estimated from the acoustic detection data using a Generalised Linear Model. An acoustically tagged fish was considered to be resident on a particular day between March 7th and May 31st if it was detected by the Norns Creek receiver at location 1 for at least three hours (with at least three detections in each hour) between 8:00 and 12:00 (which corresponds to the general timing of the surveys).

Key assumptions of the residence time model include:

  • The residual variation in spawner residence time is log-normally distributed.


The spawner abundance and spawn timings were estimated from the aerial fish and redd counts for the three sections using an Area-Under-The-Curve (AUC) model.

Key assumptions of the AUC model include:

  • Spawner and redd arrival and departure times are normally distributed.
  • Spawner abundance varies by river section.
  • Spawner abundance varies randomly by year and section within year.
  • Spawner observer efficiency is between 0.9 and 1.1.
  • Peak spawn timing varies randomly by year.
  • Spawning duration varies by river section.
  • Mean spawner residence time is as determined by the Acoustic Detection model.
  • Redd observer efficiency is between 0.9 and 1.1.
  • The number of redds per spawner is a fixed constant.
  • The residual variations in the spawner and redd counts are described by separate overdispersed Poisson distributions.

The expected emergence timing was calculated from the estimated spawn timing and the surface water temperature under the assumption that Rainbow Trout embryos emerge after 480 accumulated thermal units (ATUs).

The proportions of spawners at each site were used to calculate the Shannon Index, an information-theoretic measure of the diversity in the abundance distribution of a resource (Krebs 1999). In the current context, the Shannon Index takes into account both the number of spawning sites and how the spawning activity is distributed among these, with a higher index indicating a greater spatial distribution of spawning.

The Shannon Index \(H\) is given by \[ H = - \sum{p_i log(p_i)}\] where \(p_i\) is the proportion of the spawning activity at the \(i\)th location.


The relationship between the number of spawners and the number of age-1 recruits in the fall of the following year was estimated using a Beverton-Holt stock-recruitment model.

Key assumptions of the stock-recruitment model include:

  • The prior probability distribution for the maximum number of recruits per spawner (R0) is normally distributed with a mean of 90 and a SD of 50.
  • The residual variation in the number of age-1 recruits is log-normally distributed.

The prior probability distribution mean of 90 for R0 was based on an average of 2,900 eggs per female spawner, a 50:50 sex ratio, 50% egg survival, 50% post-emergence fall survival, 50% overwintering survival and 50% summer survival.

Model Code

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

Acoustic Detections

Variable/Parameter Description
bResidenceTime Intercept of log(eResidenceTime)
eResidenceTime[i] Expected residence time of ith spawner
ResidenceTime[i] Observed residence time of ith spawner
sResidenceTime SD of residual variation about log(eResidenceTime)
Acoustic Detections - Model1
  bResidenceTime ~ dnorm(0, 5^-2)
  sResidenceTime ~ dunif(0, 5)

  for(i in 1:length(ResidenceTime)){
    log(eResidenceTime[i]) <- bResidenceTime
    ResidenceTime[i] ~ dlnorm(log(eResidenceTime[i]), sResidenceTime^-2)


Variable/Parameter Description
bRdObsEfficiency Redd observer efficiency
bRdResidence Redd residence time
bReddPerSpawner Number of redds per spawner
bSpAbundance Intercept of log(eSpAbundance)
bSpAbundanceSite[i] Effect of ith site on log(eSpAbundance)
bSpAbundanceSiteYear[i, j] Effect of ith site within jth year on log(eSpAbundance)
bSpAbundanceYear[i] Effect of ith year on log(eSpAbundance)
bSpArrivalPeak Intercept of eSpArrivalPeak
bSpArrivalPeakYear[i] Effect of ith year on eSpArrivalPeak
bSpArrivalWidthSite[i] Effect of ith site on log(eSpArrivalWidth)
bSpObsEfficiency Spawner observer efficiency
bSpResidence Spawner residence time
Dayte[i] Day of the year on ith count
eFishDispersion Overdispersion of Fish
eRdAbundance[i] Expected redd abundance on ith count
eReddDispersion Overdispersion of Redds
eSpAbundance[i] Expected spawner abundance on ith count
eSpArrivalPeak[i] Expected peak of spawner arrival timing on ith count
eSpArrivalWidth[i] Expected SD of spawner arrival timing on ith count
Fish[i] Observed number of fish on ith count
Redds[i] Observed number of redds on ith count
sFishDispersion SD of overdispersion for Fish
Site[i] Site of ith count
sReddDispersion SD of overdispersion for Redds
sSpAbundanceSiteYear SD of effect of site within year on log(eSpAbundance)
sSpAbundanceYear SD of effect of year on log(eSpAbundance)
sSpArrivalPeakYear SD of effect of year on eSpArrivalPeak
sSpArrivalWidth Intercept of log(eSpArrivalWidth)
Year[i] Year of ith count
Area-Under-The-Curve - Model1
  bSpAbundance ~ dnorm(5, 5^-2)

  bSpArrivalPeak ~ dnorm(0, 14^-2)
  sSpArrivalWidth ~ dunif(log(14), log(42))
  bSpResidence ~ dnorm(11, 3.07^-2) T(6.31, 18.16)

  bSpObsEfficiency ~ dunif(0.9, 1.1)

  bSpAbundanceSite[1] <- 0
  for (i in 2:nSite) {
    bSpAbundanceSite[i] ~ dnorm(0, 2^-2)

  sSpAbundanceYear ~ dunif(0, 2)
  for (i in 1:nYear) {
    bSpAbundanceYear[i] ~ dnorm(0, sSpAbundanceYear^-2)

  sSpAbundanceSiteYear ~ dunif(0, 2)
  for (i in 1:nSite) {
    for (j in 1:nYear) {
      bSpAbundanceSiteYear[i, j] ~ dnorm(0, sSpAbundanceSiteYear^-2)

  sSpArrivalPeakYear ~ dunif(0, 28)
  for (i in 1:nYear) {
    bSpArrivalPeakYear[i] ~ dnorm(0, sSpArrivalPeakYear^-2)

  bSpArrivalWidthSite[1] <- 0
  for(i in 2:nSite){
    bSpArrivalWidthSite[i] ~ dnorm(0, 1^-2)

  bReddPerSpawner ~ dunif(0, 4)

  bRdResidence ~ dnorm(100, 50^-2)

  bRdObsEfficiency ~ dunif(0.9, 1.1)

  sFishDispersion ~ dunif(0, 2)
  sReddDispersion ~ dunif(0, 2)

  for (i in 1:length(Fish)) {
    log(eSpAbundance[i]) <- bSpAbundance +
                            bSpAbundanceSite[Site[i]] +
                            bSpAbundanceYear[Year[i]] +
                            bSpAbundanceSiteYear[Site[i], Year[i]]

    eSpArrivalPeak[i] <- bSpArrivalPeak + bSpArrivalPeakYear[Year[i]]
    log(eSpArrivalWidth[i]) <- sSpArrivalWidth + bSpArrivalWidthSite[Site[i]]

    eSpFracArrived[i] <- pnorm(
                           (eSpArrivalPeak[i] - bSpResidence/2),
    eSpFracDeparted[i] <- pnorm(
                            (eSpArrivalPeak[i] + bSpResidence/2),
    eFish[i] <- (eSpFracArrived[i] - eSpFracDeparted[i])
                * eSpAbundance[i]
                * bSpObsEfficiency

    eFishDispersion[i] ~ dgamma(1/sFishDispersion^2, 1/sFishDispersion^2)
    Fish[i] ~ dpois(eFish[i] * eFishDispersion[i])

    eRdAbundance[i] <- eSpAbundance[i] * bReddPerSpawner

    eRdFracArrived[i] <- pnorm(
                           (eSpArrivalPeak[i] - bSpResidence/2),
    eRdFracDeparted[i] <- pnorm(
                            (eSpArrivalPeak[i] + bRdResidence/2),
    eRedds[i] <- (eRdFracArrived[i] - eRdFracDeparted[i])
                 * eRdAbundance[i]
                 * bRdObsEfficiency

    eReddDispersion[i] ~ dgamma(1/sReddDispersion^2, 1/sReddDispersion^2)
    Redds[i] ~ dpois(eRedds[i] * eReddDispersion[i])


Variable/Parameter Description
eRecruits[i] Expected number of recruits in ith year
k Maximum number of recruits
R0 Maximum number of recruits per spawner
Recruits[i] Observed number of age-1 fish in (i+1)th year
sRecruits SD of residual variation about log(eRecruits)
Stock[i] Observed number of spawners in ith year
Stock-Recruitment - Model1
  R0 ~ dnorm(90, 50^-2) T(0, )
  k ~  dnorm(2*10^4, (2*10^3)^-2) T(0, )
  sRecruits ~ dunif(0, 5)

  for(i in 1:length(Stock)){
    eRecruits[i] <- R0 * Stock[i] / (1 + Stock[i] * (R0 - 1) / k)
    Recruits[i] ~ dlnorm(log(eRecruits[i]), sRecruits^-2)


Model Parameters

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

Acoustic Detections

Parameter Estimate Lower Upper SD Error Significance
bResidenceTime 2.3470 1.7430 2.9140 0.294 25 7e-04
sResidenceTime 1.0443 0.7157 1.6373 0.236 44 7e-04
Convergence Iterations
1.01 1000


Parameter Estimate Lower Upper SD Error Significance
bRdObsEfficiency 0.99260 0.90380 1.09400 0.05670 10 0.0010
bRdResidence 71.01000 43.24000 110.14000 17.20000 47 0.0010
bReddPerSpawner 0.64620 0.46950 0.81150 0.08750 26 0.0010
bSpAbundance 7.41400 6.89100 7.98600 0.28100 7 0.0010
bSpAbundanceSite[2] -0.67200 -0.84640 -0.50110 0.08870 26 0.0010
bSpAbundanceSite[3] 0.53040 0.36200 0.70570 0.08810 32 0.0010
bSpArrivalPeak 33.99000 28.41000 40.10000 3.09000 17 0.0010
bSpArrivalWidthSite[2] -0.04748 -0.08543 -0.01241 0.01930 77 0.0119
bSpArrivalWidthSite[3] -0.02968 -0.06604 0.00506 0.01867 120 0.1089
bSpObsEfficiency 1.00210 0.90600 1.09520 0.05760 9 0.0010
bSpResidence 13.93500 9.09600 17.87100 2.34800 31 0.0010
sFishDispersion 0.75820 0.70570 0.81970 0.02870 8 0.0010
sReddDispersion 0.29901 0.26981 0.32930 0.01520 10 0.0010
sSpAbundanceSiteYear 0.21160 0.14940 0.29320 0.03560 34 0.0010
sSpAbundanceYear 0.67090 0.45030 0.98870 0.14160 40 0.0010
sSpArrivalPeakYear 7.30400 4.60500 10.85600 1.66300 43 0.0010
sSpArrivalWidth 3.32390 3.26020 3.38670 0.03170 2 0.0010
Convergence Iterations
1.16 8e+05


Parameter Estimate Lower Upper SD Error Significance
k 21239.0000 18616.0000 24129.0000 1426.0000 13 0.001
R0 113.1000 42.6000 199.7000 42.0000 69 0.001
sRecruits 0.3406 0.2304 0.5183 0.0763 42 0.001
Convergence Iterations
1.04 10000



Figure 1. Mean, minimum and maximum hourly discharge by date, location and pre- (1999-2006) versus post- (2007-2014) period.


Figure 2. Mean, minimum and maximum daily water temperature by date, location and pre (1999-2006) versus post (2007-2014) period. The time series were incomplete.

Acoustic Detections

Figure 3. Rainbow Trout detections at Norns Creek Fan by date, year and fish ID.
Figure 4. Rainbow Trout detections at Norns Creek Fan by date.
Figure 5. Rainbow Trout residence times at Norns Creek Fan.


Figure 6. Predicted and actual aerial fish and redd counts in the LCR above the LKR by date and year.
Figure 7. Predicted and actual aerial fish and redd counts in the LKR by date and year.
Figure 8. Predicted and actual aerial fish and redd counts in the LCR below the LKR by date and year.
Figure 9. Estimated total spawner abundance by year (with 95% CRIs).
Figure 10. Estimated start, peak and end emergence timing by year (with 95% CRIs).
Figure 11. Percent of peak spawner counts by river kilometre and year.
Figure 12. Shannon Index for the spatial distribution of spawners by year.
Figure 13. Estimated start, peak and end spawn timing by year (with 95% CRIs).
Figure 14.
Figure 15. Estimated percentage of redds dewatered by year (with 95% CRIs). The numbers indicate the number of visits.


Figure 16. Estimated age-1 recruits by year (with 95% CRIs) from LCR Fish Population Indexing.
Figure 17. Estimated stock-recruitment curve (with 95% CRIs).
Figure 18. Scatterplot of age-1 recruits versus percent redd dewatering.


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

  • BC Hydro
    • Margo Dennis
    • Guy Martel
    • Philip Bradshaw
    • James Baxter
  • Mountain Water Research
    • Jeremy Baxter
  • Poisson Consulting
    • Robyn Irvine
  • Highland Helicopters
    • Phil Hocking
    • Mark Homis
  • Golder Associates
    • Dustin Ford
    • Demitria Burgoon
    • David Roscoe
  • Additional Support
    • Clint Tarala
    • Gerry Nellestijn
    • Gary Pavan
    • Jay Bowers


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.

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

Krebs, Charles J. 1999. Ecological Methodology. 2nd ed. Menlo Park, Calif: Benjamin/Cummings.

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.


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