It is clear from Equation 1 that the particular dataset investigated will influence the evidence for a given model. Therefore we will now investigate the effect of different isotopic contrasts within a dataset on the resulting evidence for each of the three models discussed in Campbell et al.. While in the main text only specific combinations of isotopic contrasts are discussed, the evidence for every possible combination was evaluated for each of the three models (384 combinations in total) and is available in Tables S1-6 of the electronic supplementary information.