Fraser River sockeye salmon: data synthesis and cumulative impacts

o In some cases it may be the timing rather than the size of a variable that is drivingsockeye productivity. It would be a good idea to consider generating indices that reflectthis hypothesis or to evaluate timing through functional data analysis. For example,perhaps it is the timing of the plankton bloom rather than the magnitude of it that is mostimportant.Additional approaches / next stepsBayesian analytical approachParameter estimation, as described earlier, involves finding the parameter values for a givenmodel that best fit the observed data. Bayesian approaches allow the parameters to be describedwith a distribution rather than assuming they have a single true underlying value, which is theclassical or frequentist approach. These methods directly quantify uncertainty and are able tohandle very complex problems (Gelman et al. 2004) making them a natural next step to thetraditional regression analyses presented here. Hilborne and Walters (1992) specificallyrecommend Bayesian methods for fisheries data as a strategy for coping with heterogeneous data(i.e., data from different sources and potentially differing quality). While we have explicitlyconsidered model uncertainty (i.e., we have not assumed that one ‘true’ underlying model and setof parameter estimates exists) by looking at the relative weights of different candidate models,the Bayesian approach would extend that concept even further.Functional data analysisFunctional regression analysis differs from classical regression (used in this report) in that theregression coefficient is actually a function. In classical regression the covariates and theresponse variable have the same dimension. That is, if there is one productivity measure per year,then we need a corresponding data point for each covariate of interest. In reality many physicalcovariates such as: sea surface temperature or river discharge, are measured on a much finertemporal scale. Functional data analysis (FDA) enables the covariate to be incorporated at a finerscale by letting the parameter (i.e., regression coefficient) be a function rather than a fixed value.This approach may enable us to improve the ‘data reduction’ step described above as it will helpus to understand the behaviour of the covariate over time and hopefully better capture theunderlying behaviour that relates to the response variable. Ainsworth and Routledge (2011)describe how FDA may be applied for this specific purpose. However, they point out that expertbiological/system knowledge was still critical to the application.224