SUPPLEMENTAL INFORMATION Figure S1. Title: Correlation between physical variables. Legend: Kendall’s correlation coefficients (τ) at national and continental levels; colors represents strength and sign of the correlation (from negative red, to white, to positive blue). Acronyms: PPT Precipitation, TMP Temperature, ELE Elevation, SLO Terrain slope, SOI Soil fertility. Figure S2. Title: Alternative current representativeness. Legend: Alternative relationship between current protection extent (%) and equality (G') in South America. In contrast to Fig. 3, equality values (G') were calculated considering a variable number of bins following the Sturges binning method (1926). Equality is calculated on the basis of physical continuous variables. Continental and Uruguayan results (in blue) did not feed linear regressions. Figure S3. Title: Efficiency of increasing protection extent in the protection equality. Legend: Calculated as the relationship of the differences between decades in extent and equality. Figure S4. Title: Evolution of representativeness based on biogeographical units. Legend: Temporal evolution of the relationship between protection extent (%) and equality (G') in South America. Equality is calculated on the basis of biogeographical units. Each dot indicates the end point of a temporal period except for 1960 one, which indicates the data before 1960, inclusively. Uruguay has only one ecoregion (i.e. the Uruguayan savanna), and thus, no equality values could be quantified. Figure S5. Title: Conservation priorities. Legend: Detailed national conservation priorities (Pr) in South America according to the current spatial distribution of protection extent along physical gradients, classified into deciles (D). Red represents the highest priority, dark green the lowest. White lines represent subnational political divisions. In the detail of South America, the entire continent is considered as a single unit. Figure S5. cont. Figure S6. Title: Distribution of protected areas. Legend: Current spatial distribution of protection extent along physical gradients in South America. See graphic explanations in Fig. 2. Lower and upper j classes were grouped using the percentile values 0.025 and 0.975 of the i continuous variable. Figure S6. cont. Table S1. Title: Specific conservation priorities. Legend: Main priorities in conservation at country and continental levels in South America considering protection extent along five physical gradients. Uruguay is excluded due to the very small extent of its protected area network (0.09% distributed in 4 units since 2006, Table 1). Country Priorities Argentina Humid, fertile lowlands of the Pampas ecoregion. Subhumid, warm temperate flat plains of the northern Espinal ecoregion, between the flooded wetlands along the Paraná River and the Sierras de Córdoba mountain range. Semiarid, hot and fertile lowlands of the central and northern Dry Chaco ecoregion. Bolivia Arid to semiarid, cold plateaus of the Puna ecoregions. Humid lowlands plains of the southwestern Amazon basin (Beni savanna ecoregion). Brazil Semiarid, hot, inland areas of northeastern Brazil (Caatinga ecoregion). Inland areas from the Bahia coastal forests (Bahia interior forests ecoregion). Eastern, central and southern subhumid highlands of the Cerrado ecoregion. Middle-level plateaus to high slope mountain areas of southern Atlantic Brazil (Araucaria moist forests ecoregion). Tropical dry forests of eastern Brazil, between the Caatinga and the Cerrado ecoregions (Atlantic dry forest ecoregion). Fertile plains of the southern part of the Rio Grande do Sul state (Uruguayan savanna ecoregion). Colombia Northern hot, semiarid to subhumid plains (including dry and moist forests and xeric shrublands ecoregions). Northern strip of the Llanos ecoregion, characterized by hot, subhumid to humid conditions, and surrounding broadleaf forests. Western coast of the country, between the Pacific Ocean and the peaks of the northern Andes (Chocó- Darién moist forests and Northwestern Andean montane forests ecoregions). Fertile central valley of the upper Magdalena River, between the eastern and central ranges of the Andes (Magdalena Valley dry forests ecoregion), and higher lands on both sides of the valley (Magdalena Valley montane forests ecoregion). Dry to highly humid, fertile regions of the Cauca Valley, between the central and western ranges of the Andes (Cauca Valley montane and dry forests ecoregions). Chile North half of the country, characterized by temperate to warm, semiarid to arid conditions (particularly the Chilean matorral and Atacama desert ecoregions). Semiarid, cold to temperate, eastern foothills of the Southern Andes (Patagonian steppe ecoregion). Ecuador Warm and fertile central coasts (Ecuadorian dry forests ecoregion). Humid, western plains and foothills of the Andes (Western Ecuador moist forests ecoregion). Western strip of the Napo moist forest ecoregion. Guayanas Coastal areas of Surinam and Guyana, and the southern driest portion of Guyana (Guianan savanna ecoregion). Contrary to its neighbors, this last country has a very low protection extent (Table 1). Paraguay More humid and relatively colder central and eastern half of the country (Humid Chaco and Atlantic forest ecoregions). Peru Arid coastal plains of the Sechura desert ecoregion. Arid to semiarid, cold plateaus of the Puna ecoregions. Humid eastern slopes of the Peruvian Andes (Peruvian Yungas ecoregion). Venezuela Northern and northeastern Llanos ecoregion, characterized by hot, subhumid to humid conditions, and surrounding broadleaf forests and xeric shrublands (Apure- Villavicencio dry forests and La Costa xeric shrublands ecoregions). Fertile, hot plains of West Lake Maracaibo (Maracaibo dry forests ecoregion) and the hot plains of the northeastern states of Monagas and Delta Amacuro (Orinoco wetlands and Orinoco Delta swamp forests ecoregions). REFERENCES Sturges HA. 1926. The Choice of a Class Interval. Journal of the American Statistical Association 21:65- 66. 10.1080/01621459.1926.10502161 .