Fraser River sockeye salmon: data synthesis and cumulative impacts

as likely to be important by each of the other Cohen Commission Technical Reports (e.g., seasurface temperature). Regression analysis entails specifying a mathematical model that describesthe functional form of the relationship between the covariates and the response variable andusing the observed data to estimate the parameters in the model.Many different models are possible. For example, models may include different covariates,linear and non-linear covariates, and/or interactions among different covariates. As long as thereare sufficient data, parameters for any model can be estimated but just because parameters can beestimated does not mean the model is sensible. Not surprisingly there is a vast amount ofliterature dedicated to the subject of model selection and comparison. We use the Burnham andAnderson (1998) hypothesis-driven approach to model selection and inference. In hypothesisdrivenanalyses, the only factors that would be allowed to enter the analyses would be those thatare connected to a logical, and in this case, biologically justified hypothesis. This reduces thepotential that some variables will emerge as significant simply by chance and not as a result ofany underlying mechanism, which is quite likely to happen in a project where there are largenumbers of covariates and hence potential models. Standard practice is to select multiplefeasible candidate models, fit each model (i.e., estimate the parameters), and then compare theperformance of each model. There are many approaches for comparing among models; we usedthe small sample size corrected Akaike’s information criterion (AIC c ) (Burnham and Anderson,1998).This project is unusual in its scope. While the response variable, ln(R/S) is available for 19stocks across B.C. and approximately 50 years of data are available for each stock, the number ofpotential covariates is very large. A total of 126 quantitative and 5 qualitative data sets wereprovided to us from the other technical reports (Table A3.4-9). We then calculated an additional32 data sets from the originals. It is possible for a single data set to be linked to (i.e.,hypothesized to impact) multiple life stages of Fraser River sockeye. In addition, there are up to4 different age types (i.e., 4sub2, 5sub2, 4sub1, and 3sub1). These links are described in TableA3.4-5 through Table A3.4-9 and result in a total of 1058 possible covariates to include in theanalysis. However, not all covariates are available for all years and stocks. Models can only becompared using AICs when the models are fit using the same data. The implication of this isthat we cannot compare all models of interest on the full data set but instead must identify timeperiods with complete data for different subsets of the covariates. For example, there is a smallsubset of the covariates (e.g., sea surface salinity for the Strait of Georgia) that have dataextending back to 1950, but there are other covariates that only have data starting in 1996 (e.g.,chlorophyll a). If we wish to compare models with these two covariates (i.e. salinity andchlorophyll), we would have to either reduce the data set to those years with data for bothcovariates (i.e. limit the model to 1996-present and sacrifice the earlier data for salinity), or209