CSAS Teslin Reconstruction

Background

• DFO is undertaking status assessments of Yukon Chinook Conservation Units (CUs) as part of the CSAS process “Estimating Precautionary Approach Reference Points and Assessing Consequences of Harvest Control Rules for Canadian Origin Yukon Chinook salmon”.

• The general approach to estimating spawner abundance and relative abundance benchmarks for Yukon Chinook CUs relies on reconstructing spawners and recruitment using (1) border counts at the Eagle sonar and (2) identification of the proportion of fish at Eagle that belong to different genetic stock aggregates, which correspond roughly to CUs.

• For some CUs, including Teslin Chinook, the reconstructed spawner abundance seems to overestimate observed spawner abundance in tributary (aerial) surveys and is inconsistent with local knowledge of returns.

• Here, we explore options for estimating an index of CU-level spawner abundance for the Teslin Chinook CU based on two spawner surveys: Nisutlin River aerial survey and Wolf River aerial survey.

Proposed approach

Data

• Wolf River and Nisutlin River aerial surveys have been conducted since 1969, but there are some gaps in the time series. Notably, both surveys have a gap from 2012-2018 when monitoring was transitioning from DFO to the Teslin Tlingit First Nation (Gillian Rourke, pers. comm.)

library(dplyr)

# Read in long-form data of spawner surveys of tributaries
surveys_long <- read.csv('data/trib-spwn.csv') %>%
    filter(system %in% c("nisutlin", "wolf"))

# Extract range of years for surveys
yrs <- c(min(surveys_long$year):max(surveys_long$year))

# Construct data frame with survey counts for each year
surveys <- data.frame(
    nisutlin = surveys_long$estimate[surveys_long$system == "nisutlin"][match(yrs, surveys_long$year[surveys_long$system == "nisutlin"])],
    wolf = surveys_long$estimate[surveys_long$system == "wolf"][match(yrs, surveys_long$year[surveys_long$system == "wolf"])]
)
rownames(surveys) <- yrs

• There are other spawning streams and surveys within the Teslin Chinook CU, most notably:
  • Morley River, south of Teslin, which had spawner counts between 500 and 1000 fish in the 1980s. More recent surveys (2019 to 2021) saw much lower counts (9 to 71 fish).
  • Swift River, a tributary towards the southern end of Teslin Lake in BC, also had counts over 1,000 fish but data are not available since 1982.
• For this reason, the index of spawner abundance calculated from the Nisutlin and Wolf River surveys cannot be considered absolute abundance for this CU.
  • Other spawner surveys are likely too patchy to attempt expanding from these two “indicator” surveys to estimate a total spawner abundance to the CU.

Generating CU-level index

• To generate an index of spawner abundance for the CU by summing the counts from these aerial surveys, counts need to be imputed when they are missing for one survey of the other.

• When both surveys were not conducted, then it is not possible to estimate the index of spawner abundance for CU in that year.

• When just one survey is missing, we can impute that value based on the average proportional contribution of the missing survey to the index in other years.

# Calculate average spawners for each survey
avgSpawners <- apply(surveys, 2, sum, na.rm = TRUE) / apply(is.na(surveys) == FALSE, 2, sum)

# Calculate proportional contribution of each survey to the sum     
P <- matrix(avgSpawners / sum(avgSpawners, na.rm = TRUE), nrow = 1, dimnames = list(NULL, c("nisutlin", "wolf")))

• In this case, the average proportional contribution of Nisutlin to the index is \(P_1 =\) 0.66 and the average proportional contribution of Wolf is \(P_2 =\) 0.34.

• We can then impute the missing data by applying an expansion factor to the sum based on which survey is missing. The expansion factor for year \(y\) is calculated as: \[ E_y = \frac{1}{\sum_i(P_i \times w_{iy})} \] where \(w_{iy}\) is an indicator taking the value ‘1’ if an survey count is available for survey \(i\) in year \(y\) and ‘0’ if an survey count is not available.

# Create matrix to indicate when a survey is missing
w <- is.na(surveys) == FALSE
    
# Calculate expansion factor as 1 over the proportional contribution of the missing stream
E <- apply(matrix(rep(P, dim(w)[1]), nrow = dim(w)[1], ncol=dim(w)[2], byrow = TRUE) * w, 1, sum, na.rm=TRUE) ^ (-1)

# Expansions cannot be done when both surveys are missing
E[which(apply(w, 1, sum) == 0)] <- NA

# Calculate simple sum of observed counts
surveys$sum <- apply(surveys[, c("nisutlin", "wolf")], 1, sum, na.rm = TRUE)
surveys$sum[which(apply(w, 1, sum) == 0)] <- NA

# Calculate expanded sum of observed counts
surveys$expanded_index <- round(surveys$sum * E)

Results

• Current geometric mean abundance over the most recent generation (2019-2024) based on the expanded index of spawner abundance is 82 spawners.

• Percentile benchmarks based on the expanded index (if you went this route) would be \(S_{25}=\) 231 and \(S_{75}=\) 828, putting this CU in the Red status zone.

Figure 1. Time series of aerial survey counts for the Nisutlin River and Wolf River, along with a CU-level index of spawner abundance calculated as the expanded sum of these two surveys. See table below for data.

Figure 2. Comparison of run-reconstruction estimates of spawner abundance for the Yukon River Headwaters/Teslin Chinook CU compared to the index constructed from two aerial surveys (Fig. 1).

Table 1. Time series of aerial survey counts for the Nisutlin River and Wolf River, along with a CU-level index of spawner abundance calculated as the expanded sum of these two surveys.

Download as CSV