Shift in NRB
To estimate shifts in NRB, we calculated the average latitude of the ten northernmost grid cells and the prevalence (proportion of occupied 10x10 km cells for each species out of all cells with observations of any of the species) in both in T1 and T2(following Thomas & Lennon 1999). We calculated shifts in NRB (kilometers) by subtracting the NRB in T2 from that in T1, and similarly the change in prevalence by subtracting the prevalence in T2 from that in T1. The statistical significance of an average shift in NRB across all species can be estimated by modeling the change in kilometers between the periods as a function of change in prevalence. This approach was first presented by Thomas and Lennon (1999) and has been used in similar analyses (e.g. Brommer 2004; Pöyry et al.2009; Mason et al. 2015). If the intercept is positive and significantly different from zero, the inference is that the species group has, overall, shifted their NRBs more towards the north than expected purely from their change in prevalence. We used this approach to obtain a linear effect estimate of shift in km as a function of change in prevalence (Fig. S4a). We extracted the residuals of the model, per species, to obtain a corrected measure of NRB shifts. This estimate thus describes the residual shift in NRB that is not explained by the linear effect of prevalence across the studied species. These residuals correlate strongly with the raw shift in kilometers (Fig. S4b), but are a more conservative metric as the linear effect of prevalence change across species has been removed. To ensure that the results and conclusions were not biased by underlying differences in sampling patterns between the two periods, we conducted the same analysis with systematically collected data to confirm that the observational data does not overestimate the direction of shift in NRB (Text S3).