Fraser River sockeye salmon: data synthesis and cumulative impacts

ecruits for this analysis as we wanted to remove the harvest effect. First we plotted the mostrecent complete data set for recruits (i.e., 2006) to see the current concentration profile (i.e., theproportion of the total number of recruits by stock). Second we grouped the stocks into 5 timeperiods (12 years / 3 brood cycles each) to see if the stock composition had shifted over time.Stocks were averaged across the time period and then a cumulative sum of recruits by stock wasplotted for each time period. Two figures were generated: one with the y axis scaled to 1 and thesecond with the y axis on the raw recruit scale. This approach clearly illustrates the number ofstocks that account for the majority of the recruits, but it does not inform us about which stocksdominate or whether they have changed over time. Based on the knowledge that at least some ofthe stocks (i.e., Lower Shuswap) have cohorts with very different sizes, we split the data set bycohort to assess how the stock portfolios differed by cohort. We selected the eight most dominantstocks across all cohorts and plotted these annually in a stacked bar graph, while the remainingstocks were aggregated.Multiple regressionRegression analysis was the primary focus of our quantitative analyses and the most complexapproach applied. This section begins with a high level summary of regression intended toinform all readers (regardless of background) about the general approach and the limitations ofthe analysis. We then provide detailed descriptions of our approach to: data reduction, creationof model sets, candidate models, model structure, and model selection.General approachMultiple regression can be used to determine the relative importance of each covariate forexplaining the variability in sockeye productivity. Non-linear relationships between covariatesand sockeye productivity can be explored. Covariates that are hypothesized to have an additivecumulative impact on sockeye productivity (i.e., each factor on its own may have an insignificantbiological impact but when encountered together the sum of the effects may be biologicallyimportant) can be analyzed in groups rather than one at a time. Regression can also be used totest hypothesized interactions between covariates (i.e., multiplicative cumulative impacts).Multiple regression is valuable tool for addressing the primary objective of this analysis (i.e.,understanding the cumulative and relative impact of all of the stressors).Regression analysis is used to understand how different variables relate to one another. Typicallythere is one response variable (i.e., dependent variable) of interest and one or more predictorvariables (i.e., independent variables or covariates). In this case the dependent variable is anannual stock specific index of productivity. The independent variables are all factors identified208