The climatic risk of Amazonian protected areas is driven by climate velocity until 2050

average values recorded from a reference climatic period of 1970–2000 [36]. To represent future climate data, we used an ensemble of 5 GCMs (S1 Table) selected from the World Cli- mate Research Program Coupled Model Intercomparison Project phase 6 (CMIP6) for the period 2041–2060 under a greenhouse gas concentration scenario SSP245. This scenario pre- dicts an average trajectory within the range of future paths where trends continue their histori- cal patterns without substantial deviations. This condition has the potential to reflect a minimum-gain trajectory of climate governance, where societies rapidly reduce emissions but not enough to limit warming to below 2˚C. In practice, some countries may reach and increase in temperature of 3˚C by the end of the 21st century–, which is above the objective established in the Paris Agreement of 2015 [41, 42]. Forward and backward velocities We used an algorithm based on analogous climates to calculate the forward and backward cli- matic velocities [43, 44]. The algorithm determined the trajectories with the least climatic dis- similarity between current (annual averages) and future projections, using the least-cost path configuration. To define the specific analogous climate for each cell, we examined the set of values covered by the standard deviation of monthly historical variability of average tempera- ture and total annual precipitation of each cell between 1970 and 2000. We measured distances between similar climates using two climatic variables Bio1 and Bio12 by first measuring the

distances for each variable and then averaging them. Thus, for each pixel in the study area we calculated the lowest cost path to a cell with similar climatic conditions. A greater distance indicated a greater hazard for the cell in terms of spatial redistribution of climatic conditions. To calculate the forward velocity, we determined the future analog that corresponded to the present values of the climatic variables. Similarly, we calculated the path with the lowest cost between a cell with a climate projected for the future and another with similar conditions in the present to calculate the backward velocity. Cells for which no correspondence could be found in future projections represented “disappearing climates” or “novel climates” when the new climate fell outside the historical annual variability of any other region of the Amazon [3]. Climate risk assessment We calculated forward and backward climate velocities for all pixels within PAs and ILs using baseline (1970–2000) and mid-21st century climate (2041–2060) data. We then classified each protected area based on a joint characterization of forward and backward velocities, dividing the range of velocity values into low, moderate, and high using three equal area quantiles. This resulted in a nine-quadrant bivariate plot (S3 Fig). PAs without analogs were those that lacked analogs in any cell. We compared the median velocity of the entire network of PAs and ILs to the median speed in UAs to evaluate the effectiveness of the spatial arrangement of the PAs

and ILs system in reducing climatic velocity. Similarly, we compared how median climatic velocities differed between PA and IL categories. We also performed cell-level analyses to com- pare value variability across different scales of analysis. To quantify the spatial extent of no- analog cells, we counted the number of no-analog cells in each of the PAs and ILs and com- pared the extensions of no-analogs between UAs, ILs and PAs. Finally, we compared the geo- graphic distribution of the region identified as no-analogous with the distributions of climate deltas (i.e., the difference between present and future mean temperature (2050–1990) classified as low, medium and high) and the historical annual variability (i.e., 1 standard deviation) of precipitation and temperature (from 1970–2000) across cells (S2 Fig). This allowed us to dem- onstrate the spatial overlap between areas with higher climate deltas and lower historical cli- mate variability and future no-analog cells. PLOS ONE Amazonian protected areas and climate velocity PLOS ONE | https://doi.org/10.1371/journal.pone.0286457 June 22, 2023 5 / 14