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Appendix S2: Supplementary information on how Generalized Additive Models (GAM) were fit to published model predictions to estimate effective degrees of freedom
Fig. S1. An example of how we fit Generalized Additive Models (GAM) to published model predictions to estimate effective degrees of freedom (EDF), the measure of degree of non-linearity used in this study. In this example, we fit GAM to the predicted effect of salinity on herring condition in the Central Baltic Sea published by Casini et al. 2010 (see authors’ Figure 3C). We digitized model predictions from a PDF of the manuscript using ImageJ software. We then sequentially fit GAM with a decreasing number of knots (k) to the digitized data until we identified the model that had the lowest number of knots and still maintained the shape of the published relationship (A-C). By reducing the number of knots we constrained the degrees of freedom and therefore the ‘wiggliness’ of the curve. Figures A (k=5) and B (k=4) show a similar shape to the published relationship, whereas Figure C (k=3) does not. Under this scenario, the EDF of the model presented in Figure B (3.00) is selected and recorded because this model has a relationship similar to the shape of the published relationship and the most conservative number of knots. Notably, the EDF of the model results shown in Figure B (3.00) is similar to the EDF published by Casini et al. 2010 (2.76; see authors’ Figure 3C), which supports the validity of this approach.
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