Specification of GAMMs of trip duration Tdur and model selection process.

Here f(.) denotes a non-parametric smooth and ‘|’ denotes an interaction between two terms (see equation (1) and text for key to the model terms). All models included a random effect on individual seals. Models where AR(1) autocorrelated errors were incorporated are marked ‘Y’. In the model selection process we followed the following steps: The most complex model M1 (equation 1) was fitted first. In M2, the “biological” variables length and sex were removed, and also the autocorrelation term. Model M3 considered if a complex smooth was necessary for DOY or could instead be replaced by a single Month term. Model M4 considered only non-biological factors but included AR(1). In M5 we further removed inter-trip duration to determine if only DOY interacting with Region were sufficient. Finally in M6 we considered a length effect nested within Sex without smoothing as a final test against M1. Using QAIC and significance tests on individual factors we selected M4 from the candidate set and we found that models that did not include both AR(1) errors or inter-trip duration were very lowly ranked (i.e. much larger QAIC values).