Fraser River sockeye salmon: data synthesis and cumulative impacts

ocean during a particular month). Where our knowledge of the biological relationships could notreduce the number of variables we used a combination of correlation analysis and principalcomponents analysis to try to reduce the number of variables. We generated correlation matricesand scatterplots for the longest time series of data sets where we expected correlation (e.g.,multiple months of data for the same metric). Data reduction and interpretability are the primarygoals of a PCA. The idea is to try to determine which components explain the majority of thetotal system variability. Although you may need many variables to describe all of the variability,it is often the case that only a few are needed to account for most of the variability in the system(Johnson and Wichern 2002). The outcome of PCA is an ordered set of components (usually asmall number explain most of the variability). Each component is a linear combination of all ofthe variables. In most cases the loadings were spread pretty evenly among all months of data andwe simply chose to average across the plausible months. In a few cases, one or two months ofdata were included separately.Chlorophyll aThere were insufficient years of data to interpret correlations among chlorophyll monthly datasets. Instead we decided to simply use both the April and May monthly means and ignored theJune-Sept values based on our understanding of the hypothesized relationship betweenchlorophyll and ocean productivity during the period when smolts are leaving the Fraser river.For Strait of Georgia we were provided with two different locations of data (Central and North)but upon closer evaluation found that the Northern data set was far more variable (Figure A3.5-3) and so selected the Northern data set anticipating that it would be a more useful predictor. Werecognize that this was an arbitrary decision but given the severe data restrictions and lack ofsolid scientific basis for selecting one particular region or averaging the two regions, we decidedto use this approach for now.211