Extended Data Fig. 2: Method used to produce a composite estimate of the rate of change in abundance.

The survey data used here are for bateleur Terathopius ecaudatus, and were drawn from all four road transect studies. Average encounter rates within PAs and UPAs are shown for early (E) and recent (R) survey periods. For each period, we combined these to produce a weighted average for the study area in question, based on two scenarios, in which the average encounter rate within unsurveyed PAs was assumed either to be (1.) the same as in surveyed PAs, or (2.) the same as in UPAs. The land area to which the PA encounter rate was assumed to apply thus differed between these two scenarios, as indicated by the relative sizes of the green (PA) and red (UPA) boxes shown, exaggerated here for illustrative effect. These encounter rate values yielded four estimates of change for each study area between survey periods, corresponding to E1– > R1, E1– > R2, E2– > R1 and E2– > R2, as illustrated. We converted these estimates to annual rates of change for each study area, and multiplied them by the species’ range size within each area. We used the weighted values to calculate an average annual rate of change for each of the 256 permutations, derived from the four change estimates and four study areas. Finally, we calculated the median plus quartiles 1 and 3 from these permutations, and projected these over three generation lengths.