Lower Columbia River Rainbow Trout Spawning 2020

Area-Under-The-Curve

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

Key assumptions of the AUC model include:

• Spawner abundance varies by river section.
• Spawner abundance varies randomly by year and section within year.
• Spawner observer efficiency is between 0.8 and 1.0.
• Number of redds per spawner is between 1 and 2.
• Spawner residence time is between 14 and 21 days as determined in a previous year’s analysis.
• Redd residence time is between 30 and 40 days.
• Spawner arrival and departure times are normally distributed.
• Spawner arrival duration (SD of normal distribution) varies randomly by river segment.
• Peak spawner arrival timing varies randomly by year.
• The residual variations in the spawner and redd counts are described by separate Negative Binomial distributions.

Spawners

Key assumptions of the spawner stock-recruitment model include:

• The recruits per spawner at low density (\(\alpha\)) is normally distributed with a mean of 90 and a SD of 50.

The mean of 90 for \(\alpha\) 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.

Eggs

Key assumptions of the egg stock-recruitment model include:

• The recruits per spawner at low density (\(\alpha\)) is normally distributed with a mean of 0.0625 and a SD of 0.03.

The mean of 0.625 is based on a 50% egg survival, 50% post-emergence fall survival, 50% overwintering survival and 50% summer survival.

Stage

The spreadsheet Norn's Fan stage discharge curve.xls predicts the stage at CNN (in m) from the discharge (in cms) from HLK and BRDs dam based on the multiple regression equation

\[\text{CNN} = 417.133 + 0.001883826 \cdot \text{HLK} + 0.000559058 \cdot \text{BRD}\]

We predict the stage from the discharge using a multiple second-order polynomial regression with interactions. The main part model was of the following form:

\[\text{CNN} = \text{b0} + \text{bHLK} \cdot \text{HLK} + \text{bHLK2} \cdot \text{HLK}^2 + \text{bBRD} \cdot \text{BRD} + \text{bBRD2} \cdot \text{BRD}^2 + \text{bHLKBRD} \cdot \text{HLK} \cdot \text{BRD} + \text{bHLK2BRD} \cdot \text{HLK}^2 \cdot \text{BRD}\] To ensure model convergence \(\text{HLK}\) and \(\text{BRD}\) were the standardized discharges. The model also included a parameter to correct for an offset in \(\text{CNN}\) from May 1st 2017.

Area-Under-The-Curve

data {
  int<lower=0> nObs;
  int<lower=0> nSection;
  int<lower=0> nSegment;
  int<lower=0> nYear;

  int Year[nObs];
  int Section[nObs];
  int Segment[nObs];
  real Doy[nObs];
  int Fish[nObs];
  int Redds[nObs];
parameters {
  vector<lower=3,upper=9>[nSection] bFishAbundanceSection;

  real<lower=0> sFishAbundanceYear;
  vector[nYear] bFishAbundanceYear;
  real<lower=0> sFishAbundanceSectionYear;
  vector[nSection * nYear] bFishAbundanceSectionYear;

  real<lower=0.8,upper=1.0> bFishObserverEfficiency;
  real<lower=0.0,upper=2.0> bReddObserverEfficiency;

  real<lower=1, upper=2> bReddPerFish;

  real<lower=14, upper=21> bFishResidenceTime;
  real<lower=30, upper=40> bReddResidenceTime;

  real<lower=100, upper=150> bPeakFishArrivalTiming;

  real<lower=0,upper=21> sPeakFishArrivalTimingYear;
  vector[nYear] bPeakFishArrivalTimingYear;

  real<lower=log(10), upper=log(50)> bFishArrivalDuration;

  real<lower=0> sFishArrivalDurationSegmentYear;
  vector[nSegment * nYear] bFishArrivalDurationSegmentYear;

  real<lower=0, upper=2> bDispersionRedds;
  real<lower=0, upper=2> bDispersionFish;
model {
  vector[nObs] eFishAbundance;
  vector[nObs] ePeakFishArrivalTiming;
  vector[nObs] eFishArrivalDuration;

  vector[nObs] eRedds;
  vector[nObs] eFish;

  sFishAbundanceYear ~ normal(0, 1);
  bFishAbundanceYear ~ normal(0, sFishAbundanceYear);
  sFishAbundanceSectionYear ~ normal(0, 1);
  bFishAbundanceSectionYear ~ normal(0, sFishAbundanceSectionYear);

  bPeakFishArrivalTimingYear ~ normal(0, sPeakFishArrivalTimingYear);
  bFishArrivalDurationSegmentYear ~ normal(0, 1);
  bFishArrivalDurationSegmentYear ~ normal(0, sFishArrivalDurationSegmentYear);

  for (i in 1:nObs) {
    eFishAbundance[i] = exp(bFishAbundanceSection[Section[i]] + bFishAbundanceYear[Year[i]] + bFishAbundanceSectionYear[((Section[i] - 1) * Year[i]) + Year[i]]);

    ePeakFishArrivalTiming[i] = bPeakFishArrivalTiming + bPeakFishArrivalTimingYear[Year[i]];

    eFishArrivalDuration[i] = exp(bFishArrivalDuration + bFishArrivalDurationSegmentYear[((Segment[i] - 1) * Year[i]) + Year[i]]);

    eRedds[i] = eFishAbundance[i] * bReddPerFish * bReddObserverEfficiency * (normal_cdf(Doy[i], ePeakFishArrivalTiming[i], eFishArrivalDuration[i]) - normal_cdf(Doy[i], ePeakFishArrivalTiming[i] + bReddResidenceTime, eFishArrivalDuration[i]));

    eFish[i] = eFishAbundance[i] * bFishObserverEfficiency * (normal_cdf(Doy[i], ePeakFishArrivalTiming[i], eFishArrivalDuration[i]) - normal_cdf(Doy[i], ePeakFishArrivalTiming[i] + bFishResidenceTime, eFishArrivalDuration[i]));
  }
  Redds ~ neg_binomial_2(eRedds, 1/bDispersionRedds);
  Fish ~ neg_binomial_2(eFish, 1/bDispersionFish);

Block 1. Model description.

Stock-Recruitment

.model {

  bAlpha ~ dnorm(90, 50^-2) T(1,)
  bBeta ~ dnorm(0, 1/10^-2) T(0,)

  bDewatered ~ dnorm(0, 100^-2)

  sRecruits ~ dnorm(0, 2^-2) T(0, )
 for(i in 1:length(Stock)) {
    log(eRecruits[i]) <- log(bAlpha * Stock[i] / (1 + bBeta * Stock[i])) + bDewatered * Dewatered[i]
    Recruits[i] ~ dlnorm(log(eRecruits[i]), sRecruits^-2)
  }

.model {
  bAlpha ~ dnorm(0.0625, 0.03^-2) T(0,)
  bBeta ~ dnorm(0, 1/100000^-2) T(0, )

  bEggLoss ~ dnorm(0, 100^-2)

  sRecruits ~ dnorm(0, 2^-2) T(0,)
  for(i in 1:length(Recruits)){
    log(eRecruits[i]) <- log(bAlpha * Eggs[i] / (1 + bBeta * Eggs[i])) + bEggLoss * EggLoss[i]
    Recruits[i] ~ dlnorm(log(eRecruits[i]), sRecruits^-2)
  }

Stage

.model{
  bIntercept ~ dnorm(420, 2^-2)

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

  bHLK ~ dnorm(0, 1^-2)
  bHLK2 ~ dnorm(0, 1^-2)

  bLKR ~ dnorm(0, 1^-2)
  bLKR2 ~ dnorm(0, 1^-2)

  bHLKLKR ~ dnorm(0, 1^-2)
  bHLK2LKR ~ dnorm(0, 1^-2)

  bCor <- 0.4
  eCorStage[1] <- eStage[1]
  for(i in 2:length(Stage)){
    eCorStage[i] <- eStage[i] + bCor^(Days[i] - Days[i-1]) * (Stage[i-1] - eStage[i-1])
  }

  sStage ~ dnorm(0, 1^-2) T(0, )
  for(i in 1:length(Stage)){
    eStage[i] <- bIntercept + bOffset[Offset[i]] + bHLK * HLK[i] + bLKR * LKR[i] + bHLK2 * HLK[i]^2 + bLKR2 * LKR[i]^2 + bHLKLKR * HLK[i] * LKR[i] + bHLK2LKR * HLK[i]^2 * LKR[i]

    Stage[i] ~ dnorm(eCorStage[i], sStage^-2)
  }

Block 4. The model description.

Dewatering

Table 1.

Area-Under-The-Curve

Table 2. Parameter descriptions.

Table 3. Model coefficients.

Table 4. Model summary.

Stock-Recruitment

Stage

Table 11. Parameter descriptions.

Table 12. Model coefficients.

Table 13. Model summary.

Summary

Table 14. Dewatered redd counts.

Spawning

Stations

Sensor Data

Dewatering

Area-Under-The-Curve

White Sturgeon

Drone Counts

Stock-Recruitment

Egg Mortality

Stage