Table SF-02 Rank scores derived from ocean ecosystem indicators data found in Table SF-03 and color-coded to reflect ocean conditions for salmon growth and survival (green = good; yellow = intermediate; red = poor). Lower numbers indicate better ocean ecosystem conditions, or "green lights" for salmon growth and survival. To arrive at these rank scores for each ocean ecosystem indicator, all years of sampling data from Table SF-03 were compared (within each row).
Table SF-03. Data for rank scores of ocean ecosystem indicators.
Data for rank scores of ocean ecosystem indicators. Download data for rank scores of ocean ecosystem indicators as a *.csv.
Figure SF-01 shows correlations between adult Chinook salmon counts at the Bonneville Dam and coho salmon smolt to adult survival (%) (PFMC 2019a) versus a simple composite integrative indicator – the mean rank of all the ecosystem indicators (the second line from the bottom) in Table SF-02. This index explains about 50% of the variance in adult returns. A weakness of this simple non-parametric approach is that each indicator is given equal weight, an assumption that may not be true. Therefore, we are exploring a more quantitative analysis of the ocean indicators shown in Table 3, using principal component analysis (PCA).
Principal component analysis (PCA) was run on the indicator data. This procedure reduces the number of variables in the dataset as much as possible, while retaining the bulk of information contained in the data (a sort of weighted averaging of the indicators). Another important feature of PCA is that the principal components (PCs) are uncorrelated. This eliminates one of the original problems with the indicator data set (i.e., multi co-linearity). The first principal component (PC1) explains 54% of the ecosystem variability among years while the second principal component explains only 14%. Therefore, PC1 is used as a new predictor variable in a linear regression analysis of adult salmon returns (this process is termed principal component regression, or PCR) and those results are shown below in Figure SF-02.
In addition to correlating PC1 with salmon returns, we incorporated this metric into a more formal modeling structure. Specifically, we used sibling regression and dynamic linear modeling (DLM; Scheuerell & Williams 2005) to relate PC1 to returns. DLMs are similar to linear regression, but allow the regression coefficient(s) to vary over time, effectively allowing for a shift in the magnitude of response to ocean conditions. In all models, we allowed the coefficients for siblings and PC1 to vary, but kept a constant model intercept.
The best model for both spring and fall Chinook salmon showed support for a dynamic effect of jack counts, but not of PC1. For coho salmon, there was no support for any parameter to vary, resulting in a simple linear regression model (of logit-transformed SAR).
We are working towards stock-specific salmon return outlooks by using methods that can optimally weight the indicators for each response variable in which we are interested (Burke et al. 2013).