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).