1 (A) Supplementary materials and methods 2 (B) Range modifications 3 The range modifications can be grouped into eight categories of decreasing certainty: 1) 4 range reductions for species with recent anthropogenic human-induced range expansions 5 (24 species; detailed description in can be found Supplementary Data 1; graphical 6 representation of results can be found in Supplementary Data 2), 2) range expansions 7 based on other sources for species with known range declines (162 species; detailed 8 description in can be found Supplementary Data 1; graphical representation of results can 9 be found in Supplementary Data 3), 3) merger of likely anthropogenic disjunct ranges by 10 filling intervening suitable habitats (272 species; detailed description in can be found 11 Supplementary Data 1; graphical representation of results can be found in Supplementary 12 Data 4), 4) expansion of ranges to entire islands (198 species; detailed description in can 13 be found Supplementary Data 1; graphical representation of results can be found in 14 Supplementary Data 5), 5) expansion of ranges for species with known, or at least highly 15 suspected, range declines to cover suitable areas contiguous with the current range (231 16 species; detailed description in can be found Supplementary Data 1; graphical 17 representation of results can be found in Supplementary Data 6), 6) estimation of ranges 18 based on the natural ranges of the extant species that the target species co-occurred with 19 at fossil sites (186 species; detailed description in can be found Supplementary Data 1; 20 graphical representation of results can be found in Supplementary Data 7), 7) estimation 21 of ranges based on the natural ranges of the extinct species that the target species co- 22 occurred with at fossil sites (3 species; detailed description in can be found 23 Supplementary Data 1; graphical representation of results can be found in Supplementary 24 Data 7), and 8) unique species-specific modifications in special cases (13 species; 25 detailed description in can be found Supplementary Data 1; graphical representation of 26 results can be found in Supplementary Data 8). For many species, the range 27 modifications involved several of the above processes and we listed them under the type 28 with the perceived lowest certainty. 29 1) Range restrictions 30 The distribution was restricted for a few species with recent large range expansions 31 linked to anthropogenic range restrictions of other species, which is likely the case for the 32 expansion of Canis latrans (coyote) following the range decreases in Canis lupus (grey 33 wolf) (Arjo & Pletscher, 1999). The distribution was also restricted for species for which 34 colonization of a large part of their current distribution appears to be strongly connected 35 to human migration and land use, e.g., Mus musculus (house mouse) (Cucchi et al., 36 2005). In addition, we interpreted the sudden appearance of commensal species on 37 isolated islands, contemporary with or after human arrival (Bover & Alcover, 2008) as 38 evidence of human-induced transport and removed these islands from the natural 39 distribution of such species. In total, we reduced the distribution of 24 species, from a 40 total of 36,421 occurrences to 24,628 occurrences in 110 × 110 km cells. Three species 41 (Canis latrans, Mus musculus, and Rattus norvegicus (brown rat)) had their ranges 42 restricted by more than 1000 occurrences. 43 2) Historical ranges 44 For historical ranges, some of the information, generally from areas with recent range 45 collapses, came from accurate sources such as Hall (1981), which covers North America, 46 but other sources, often those dealing with older range collapses, are more uncertain. 47 Despite the uncertainty of some of these sources, we are convinced that the estimated 48 ranges are closer to their natural ranges than the IUCN ranges. We changed the 49 distributions based on suggested historical distributions for 168 species, leading to an 50 increase from a total of 56,760 occurrences to 114,326 occurrences in 110 × 110 km 51 cells. A single species, Ceratotherium simum (white rhino), had its apparent range 52 restricted by 705 cells because the IUCN distribution simply maps entire countries 53 regardless of where in the country the animal occurs, whereas 13 species had their range 54 expanded by more than 1000 cells, Acinonyx jubatus (cheetah), Bison bison (American 55 bison), Bos primigenius (auroch), Caracal caracal (caracal), Camelus dromedarius 56 (dromedary), Felis silvestris (wild cat), Gulo gulo), Homo "Denisovans" (Denisovan 57 humans), Homo neanderthalensis (Neanderthal humans), Loxodonta africana (African 58 elephant), Lycaon pictus (African wild dog), Panthera leo (lion), Panthera onca (jaguar), 59 and Panthera tigris (tiger). 60 Modern humans (Homo sapiens), which are not mapped by IUCN and, therefore, 61 included in this list, also have an estimated historical range (Continental Africa) greater 62 than 1000 cells. Natural distributions can be defined for the other species in the genus 63 Homo, but the concept is less obviously applicable to our own species. However, the 64 hominin fossil record provides little indication of a stable co-occurrence of different 65 species in the genus Homo, even if hybridization between them has occurred to a limited 66 extent (Stringer, 2012). Continental Africa is the center of origin for Homo sapiens, and 67 no other species in the genus is known to have originated from the region during the Late 68 Pleistocene. Therefore, we assigned it as the natural range of Homo sapiens, as it can be 69 seen as the distribution of Homo sapiens that should have been maintained to avoid major 70 displacements of other Homo species during the Late Pleistocene. 71 3) Disjunct ranges 72 Disjunct ranges are occasionally a natural phenomenon, but many contemporary disjunct 73 distributions are anthropogenic in nature. This is evident for species for which 74 information is available regarding historic distribution, such as the historic range for the 75 larger African carnivores (Justina et al., 2005), but it is likely also the case for the many 76 species for which information on historic distributions is not available. If any of the 77 species we investigated had disjunct ranges, we looked for evidence or strong indications 78 of anthropogenic range decline (e.g., red-listing as endangered or critically endangered) 79 or evidence of poor knowledge of the true range (listed as “data deficient” or a note in the 80 IUCN description of poor knowledge of the species range). In cases in which such 81 evidence was found, but where we could not find information on the historic distribution, 82 we tried to connect the disjunct parts of the ranges unless we found evidence of 83 biological reasons for the disjunction. In particular, we did not expand ranges across 84 areas occupied by congeneric species that are currently not sympatric with the species in 85 question, as in the case of Hylobates lar (lar gibbon) in the Malay Peninsula north and 86 south of a thin band occupied by Hylobates agilis (agile gibbon). 87 For species for which the current distribution is fairly large (203 out of 272 species we 88 modified), we estimated the climatic convex hull using the climatic parameters yearly 89 temperature, winter temperature, and yearly precipitation (Hijmans et al., 2005) taken 90 from a rasterization of the range with grid cells of 0.1° × 0.1°. The convex hull was 91 estimated in R using the function inhull and the library geometry (Jewell, 2009; Barber et 92 al., 2013). After the convex hull was calculated, the disjunct ranges were joined if the 93 intermediate area was also within the climatically defined hull. This approach does not 94 guarantee that the intermediate area is suitable, but only that if the range is limited by our 95 chosen climatic predictors (or other factors with a sufficiently high correlation to the 96 chosen climatic parameters), the intermediate area should also be climatically suitable. 97 This approach implicitly assumes that the species is climatically limited; therefore, it 98 makes little sense for very narrowly distributed species. For narrowly distributed species, 99 we joined the IUCN ranges as lines or geographic convex hulls, when the intervening 100 areas are in the same habitat type as defined by the WWF ecoregions (Olson, 2001). 101 When the intervening areas consist of another habitat type (i.e. species occurring on both 102 sides of an alpine region) we joined the ranges as the shortest lines within habitat types 103 similar to the known occurences. In total, we joined disjunct populations in 272 species, 104 which led to an increase from a total of 18,113 occurrences to 23,882 occurrences in 110 105 × 110 km cells. The largest change was 558 cells for Felis margarita (sand cat), and in 70 106 species the changes were too small to be noticed on a 110 × 110 km grid. 107 4) Island species 108 Species historically endemic to islands smaller than 150,000 km2 (Java and all islands 109 smaller than this) for which a range decline was either known (including extinct species) 110 or at least very likely had their ranges expanded to the entire island(s). The current ranges 111 of many of the extant species in this category are ecologically narrow and often limited to 112 mountain forests. We acknowledge that it could mean true ecological specialization for 113 some of the species, but for most of these islands the mountains are the only areas with 114 natural habitat and, therefore, the only place where formerly generalist species survive, as 115 illustrated by the current distribution of many birds on Hawaii (Carter et al., 2009). 116 Despite the small potential exaggeration of the range by this expansion we think that the 117 estimated ranges are going to be closer to natural distributions than assuming that these 118 species are all mountain endemics. It should also be noted that all analyses were 119 performed on 110 × 110 km grid cells, so any exaggeration would only affect to the few 120 cells exclusively containing lowland areas. We changed the distribution this way for a 121 total of 198 species, leading to an increase from a total of 532 occurrences to 2,151 122 occurrences in 110 × 110 km cells. The largest change was 32 cells for four extinct 123 Caribbean species that expanded to all of Cuba and Isla de la Juventud: Boromys offella 124 (Oriente cave rat), Boromys torrei (Torres cave rat), Nesophontes major (greater Cuban 125 nesophontes), and Nesophontes micrus (western Cuban nesophontes). In 11 species the 126 changes were too small to be noticed on a 110 × 110 km grid. 127 5) Range expansions 128 A number of species have known, or at least likely, range declines, but with the historical 129 range either fully unknown or only known in parts of its range. Notable examples with 130 uncertainty in parts of the range include Ursus arctos (brown bear); Hall4 lists the 131 historical North American distribution, but the range decline in Eurasia is too ancient for 132 knowledge of the natural distribution to be known. A notable example of complete 133 uncertainty is Cervus nippon (sika deer), whose current range is very fragmented and 134 substantially smaller than the historical range, though the natural limits of the natural 135 range are uncertain. For such species, we estimated the convex hull and expanded the 136 range to suitable areas of either selected parts of the range or the entire range. Generally, 137 we only expanded the range to areas continuous with current ranges, but for some species 138 we increased the range to all suitable ranges within defined areas, such as large islands 139 (e.g., Madagascar) or areas with a known Late Pleistocene presence for some Australian 140 species (Supplementary Data 1). The change in the distribution of the 231 species led to 141 an increase from a total of 57,438 occurrences to 100,273 occurrences in 110 × 110 km 142 cells. Thirteen species had their range expanded by more than 1000 cells: Bison bonasus 143 (European bison), Canis lupus, Castor fiber (Eurasian beaver), Cervus elaphus (red deer), 144 Crocuta crocuta (spotted hyena), Cuon alpinus (dhole), Equus hemionus (onager), 145 Hippopotamus amphibius (hippopotamus), Lynx lynx (Eurasian lynx), Martes zibellina 146 (sable), Panthera pardus (leopard), Rangifer tarandus (reindeer), and Ursus arctos). In 147 all, but three of the 15 cases (Castor fiber, Cuon alpinus, and Equus hemionus), the range 148 expansions for these species were based partly on expertly drawn maps of historic 149 distribution. In 14 species the changes were too small to be noticed on a 110 × 110 km 150 grid. 151 6 and 7) Estimation based on fossil co-occurrence 152 For a large number of species, most of them extinct and a few surviving in very small 153 areas (e.g., Hypogeomys antimena, Madagascar giant jumping rat), we estimated 154 potential distributions based on extant species they co-occurred with in fossil or subfossil 155 species assemblages. The approach is similar to the co-existence approach for inferring 156 paleoclimate based on co-occurring taxa (Mosbrugger & Utescher, 1997). The logic 157 behind this is that if all species are limited by similar ecological parameters, the current 158 distribution of extant species should be informative of the climatic suitability of the area 159 for the species whose distribution we try to infer. We assumed that the frequency of 160 species from the fossil sites occurring at a given locality today corresponds to the 161 probability that the extinct species occurred there, which logically must be true on 162 average for all extant species. We assigned all grid cells with at least 50% of the species 163 from the fossil site as the likely current range of the extinct species, i.e., as presence. 164 Whenever possible we only used fossil sites with at least 10 fossil species. For species 165 with a large number of fossil sites, we used the single fossil site where the species in 166 question has been found with the highest number of extant species in each Taxonomic 167 Databases Working Group (TDWG) level 3 regions, generally corresponding to 168 countries, but with some large countries (e.g., Canada or USA) broken into states 169 (Brummitt, 2001). For some of the more climatically variable TDWG regions, such as 170 Madagascar and California, we used several widely separated sites if possible. These 171 rules were relaxed for many species due to a lack of available fossil sites, and many 172 species had ranges estimated based on fossils from only some of the TDWG countries it 173 used to occur in and/or based on fossil sites with less than 10 co-occurring extant species. 174 Most of the fossil data were based on Graham & Lundelius (2010) for Canada and USA, 175 Ferrusquía-Villafranca et al. (2010) for Mexico, and the Paleobiology Database (2015) 176 for remaining areas, but were supplemented by primary literature for species with 177 insufficient records in these sources. When several fossil sites were used, we used the 178 geographically closest fossil site to estimate the probability of occurrence in each grid 179 cell. When the resulting ranges from this analysis were disjunct, we joined them based on 180 climatic convex hulls as explained earlier, and a few species had their ranges expanded 181 based on the climatic convex hull, such as when historic occurrence was known from a 182 region where we could not find any multispecies fossil site. For closely related species 183 not known to co-occur historically, we restricted the ranges so they did not co-occur in 184 our estimated potential ranges. For this analysis, we used the inferred potential ranges of 185 all species rather than the current IUCN ranges. For three species, we could not find 186 sufficient data on co-occurrence with extant species and estimated their potential range 187 based on the estimated ranges of other extinct species, though this led to additional 188 uncertainty. 189 Our motivation for choosing this approach is that it enables us to estimate the potential 190 distribution based on a few (or only one) specimens, which is important because a large 191 proportion of the species we wish to map are only known from a few fossil findings. This 192 is most obvious for Brachyprotoma obtusata (a giant skunk), for which FaunMaps’ 193 massive collection of fossil information only has three known Late Pleistocene fossil 194 occurrences from Pennsylvania, Utah, and Yukon (Graham & Lundelius, 2010). An 195 advantage of our approach is that an increase in the number of fossil sites for a species is 196 not guaranteed to increase its distribution, but may increase the precision of the 197 inferences. Thus, large and relatively easily identifiable species, such as Mammut 198 americanum (American mastodon), will not necessarily have larger inferred ranges than 199 species such as the aforementioned giant skunk that, for whatever reason, occurs rarely at 200 fossil sites despite apparently having a wide distribution. A problem with our approach is 201 that we assume that all fossils from a site are contemporary and, though we only use 202 fossils from a single fossil layer when such information is readily available from the 203 sources, the assumption of contemporaneity is unlikely to be entirely valid. Therefore, we 204 may potentially estimate distributions based on assemblages of species that have never 205 co-occurred, which could bias the estimated ranges. Still, the bias would normally lead to 206 a reduction in the size of the inferred range because species that did not overlap in time at 207 the fossil site would also be less likely to co-occur today. 208 Some fossil sites, especially in Europe, were dominated by hyper-generalists, which are 209 not informative of the climate of the fossil site; therefore, we removed them from species 210 lists prior to analyses of co-occurrence. In order to define hyper-generalists, we separated 211 the world into 10 habitat types, eight of them identical to the biomes of Olson (2010): 1) 212 Tropical and Subtropical Moist Broadleaf Forests, 2) Boreal Forest/Taiga, 3) Tropical 213 and Subtropical Grasslands, Savannas, and Scrublands, 4) Temperate Grasslands, 214 Savannas, and Scrublands, 5) Tundra, 6) Montane Grasslands and Scrublands, 7) 215 Mediterranean Forests, Woodlands, and Scrublands, 8) Deserts and Xeric Scrublands. 216 The remaining habitats were made by merging biomes from Olson (2010). 9) Tropical 217 and Subtropical Dry Broadleaf Forests or Tropical and Subtropical Coniferous Forests, 218 10) Temperate Broadleaf and Mixed Forests or Temperate Coniferous Forests. We then 219 rasterized the distribution of these habitats and, for all species with a grid cell of 1°×1°, 220 removed all cells that had more than one type of habitat, counted the number of habitat 221 types found within the range of each species, and classified any species whose range 222 included at least nine of the 10 habitat types as a hyper-generalist. Following these 223 criteria, we removed the following 12 species from the analysis of the distribution by co- 224 occurrence: Sus scrofa (wild boar), Lasiurus cinereus (hoary bat), and 10 carnivores 225 (Canis lupus, Crocuta crocuta, Cuon alpinus, Felis silvestris, Lutra lutra (European 226 otter), Panthera pardus, Puma concolor (cougar), Ursus arctos, Ursus americanus 227 (American black bear) and Vulpes vulpes (red fox)). 228 The change in the distribution of the 185 species whose range was estimated based on co- 229 occurrences with extant species led to an increase from a total of 181 occurrences to 230 117,136 occurrences in 110 × 110 km cells, whereas the change in the distribution of the 231 three species whose range was estimated by co-occurrence with other extinct species led 232 to an increase from a total of 0 occurrences to 2,779 occurrences in 110 × 110 km cells. 233 Fifty species whose ranges were estimated by co-occurrences with extant species had 234 their range expanded by more than 1000 cells. For eight of the species, the expansion was 235 greater than 2000 cells: Arctodus simus (North American short-faced bear), Canis dirus 236 (dire wolf), Coelodonta antiquitatis (woolly rhinoceros), Eremotherium laurillardi (Pan- 237 American ground sloth), Mammuthus primigenius (woolly mammoth), Neochoerus 238 aesopi (a giant capybara), Panthera spelaea (cave lion), and Stephanorhinus 239 kirchbergensis (Merck’s rhinoceros). Two of the species whose ranges were based on co- 240 occurrences with extinct species had their range expanded by more than 1000 cells: 241 Holmesina paulacoutoi (a pampathere) and Tapirus rondoniensis (an extinct South 242 American tapir). 243 Notably, this method will overestimate the distribution of true relictual species that used 244 to co-occur with widespread species, but it may underestimate the distribution of 245 generalist species only known from non-analogous species communities. The combined 246 effect of these two things may potentially balance each other, but researchers using the 247 specific maps may need to be particularly cautious with the maps of Elasmotherium 248 sibiricum (a giant rhinoceros), Equus ovodovi (a horse), Homotherium latidens (European 249 Dirk-toothed cat), Kolpochoerus majus (an African pig), Metridiochoerus compactus (an 250 African pig), Neolicaphrium recens (a litoptern), Pliomys lenki (an European vole), 251 Rusingoryx atopocranion (an African antelope), Soergelia minor (an Eurasian musk-ox), 252 and Tapirus rondoniensis because the estimated ranges are substantially larger than the 253 area geographically encompassing their known late-Quaternary occurrences, and for 254 Doedicurus clavicaudatus (a South American glyptodont) and Tremarctos floridanus 255 (Florida spectacled bear) because their estimated ranges are substantially smaller than 256 similarly expected from their known late-Quaternary occurrences. 257 In order to validate the fossil co-occurrence approach we tried estimating the range of 39 258 North American species within continental United States and Canada based on their fossil 259 occurrences in Faunmap (Graham & Lundelius, 2010). The 39 species were the 11 260 terrestrial species of Artidactyla (Alces americanus (American moose), Antilocapra 261 americana (Pronghorn), Bison bison, Cervus elaphus, Odocoileus hemionus (Mule deer), 262 Odocoileus virginianus (White-tailed deer), Oreamnos americanus (Rocky Mountain 263 goat), Ovibos moschatus, Ovis canadensis (Bighorn sheep), Ovis dalli (Thinhorn sheep) 264 and Rangifer tarandus) and the 28 terrestrial species of Carnivora (Alopex lagopus 265 (Arctic fox), Bassariscus astutus (Ringtail), Canis latrans, Canis lupus, Canis rufus (Red 266 wolf), Gulo gulo, Lontra canadensis (North American river otter), Lynx canadensis 267 (Canadian lynx), Lynx rufus (Bobcat), Martes americana (American marten), Martes 268 pennanti (Fisher), Procyon lotor (Racoon), Mephitis mephitis (Striped skunk), Mustela 269 erminea (Stoat), Mustela frenata (Long-tailed weasel), Mustela nigripes (Black-footed 270 ferret), Mustela nivalis (Least weasel), Neovison vison (American mink), Puma concolor 271 (Cougar), Spilogale gracilis (Western spotted skunk), Spilogale putorius (Eastern spotted 272 skunk), Taxidea taxus (American badger), Urocyon cinereoargenteus (Gray fox), Ursus 273 americanus (American black bear), Ursus arctos (Brown bear), Vulpes macrotis (Kit 274 fox), Vulpes velox (Swift fox) and Vulpes vulpes (Red fox)), which has a substantial part 275 of their current range within continental United States and Canada and fossil occurrences 276 in the Faunmap database. While doing this we used the same taxon specific modifications 277 we used for the extinct species (Supplementary Data 1). For our test case this meant that 278 we did not allow any range overlap between four sets of closely related species (Ovis 279 canadensis / Ovis dalli, Canis lupus / Canis rufus, Spilogale gracilis / Spilogale putorius 280 and Vulpes macrotis / Vulpes velox), that we restricted the occurrence of the members of 281 Caprinae (Oreamnos americanus, Ovis canadensis and Ovis dalli) to mountainous 282 regions, and that we expanded the range of six species (Alces americanus, Bison bison, 283 Canis lupus, Martes americana, Mustela erminea and Mustela nivalis) northwards to 284 include the Labrador peninsula because they have predicted ranges south and north of 285 Laurentide Ice Sheet and on both coasts and the entire peninsula was within their climatic 286 convex hull. A true natural lack from the Labrador peninsula therefore seemed highly 287 unlikely. 288 The diversity we predicted this way was highly correlated with the historic diversity for 289 these species (i.e., the diversity based on their known historical ranges, which we for 290 these species assume to be identical to their natural ranges) (ρ=0.856), and this 291 correlation was higher than the corresponding correlation between the current and 292 historic diversity (ρ=0.762). The average predicted diversity for this validation (total 293 mean 18.6; Artidactyla mean 5.1; carnivora mean 13.5) was also were similar to the 294 values based on their historic diversity (total mean 18.0; Artidactyla mean 4.0; carnivora 295 mean 14.0). Finally to look at the patterns geographically, we compared the overall shape 296 of the diversity gradient between the current, the historic and the predicted species 297 diversity (Figure S11) and found that the co-occurrence predicted diversity pattern 298 accurately represent the placement of the high diversity areas according to the known 299 historical ranges, while the current diversity pattern does not. 300 301 8) Species-specific modifications 302 For 13 species, we opted for unique species-specific solutions because none of the other 303 approaches were appropriate; the data needed to use them could not be found (e.g., 304 extinct species for which no suitable multi-species fossil site could be found) or we 305 judged that species-specific choices would better capture the natural ranges than the 306 standard method. The species covered here broadly comprise three types: 1) species with 307 very limited knowledge of their historic distribution, but decent knowledge of ecology 308 and general late-Quaternary geography, making it possible to estimate their natural range: 309 Equus ferus (horse) and Lynx pardinus (Iberian lynx); 2) relatively poorly known fossil 310 species with no records from any good multi-species fossil sites: Agalmaceros blicki (a 311 South American deer), Cuvieronius hyodon (a gompthothere), Cryptoprocta spelea (giant 312 fossa), Dactylopsila kambuayai (a New Guinean possum), Elephas iolensis (an extinct 313 African relative of the Asian elephant), and Petauroides ayamaruensis (a New Guinean 314 possum); and 3) poorly known species accepted by IUCN with large uncertainty of the 315 correct location of the type locality Eudorcas rufina (red gazelle), Gerbillus agag (a 316 gerbil), Gerbillus burtoni (a gerbil), Juscelinomys candango (Candango mouse), and 317 Makalata obscura (dusky spiny tree rat). This led to an increase from a total of 11 318 occurrences to 11,132 occurrences in 110 × 110 km cells, largely caused by an increase 319 in Equus ferus from 8 to 9,257 and from 0 to 1,243 for Elephas iolensis. 320 321 322 (B) Esimation of functional diversity 323 For the functional diversity analyses of all species and non-marine species, we focused 324 on the three dimensions of niche space, habitat, body size, and diet, whereas the analysis 325 of the three terrestrial subsets only focused on body size and diet. 326 For habitat, we coded all animals as flying (bats), aquatic (coded as freshwater or marine 327 by IUCN), or terrestrial (non-bats coded as terrestrial by IUCN), with several species 328 coded as both aquatic and terrestrial. Body sizes were initially based on Smith et al. 329 (2005), but supplemented with data from other sources for missing species. In total, we 330 ended with estimated sizes for 5675 species, and the sizes of the remaining 68 species 331 were set as the size of their closest relative with information on body size. All species 332 were categorized into classes of 0.5 log10 units (i.e., one class for species between 100 and 333 100.5 gram and one for species between 100.5 and 101 gram). For diet, we coded all 334 animals as carnivores or herbivores, with omnivores coded as both herbivores and 335 carnivores. Thus, our treatment of functional diversity can be seen as a multidimensional 336 version of the bin-filling approach of (Huang et al., 2012). 337 Diet data were based on Jones et al. (2009), but extrapolated to the entire genus, tribe, 338 subfamily, or family, and occasionally to closely related families if all members with 339 information had the same diet or to members of the same subgenus or species group if the 340 diet appeared constant within this smaller clade but variable in the genus. For genera 341 without information in the database for families without constant diet and for families not 342 listed in the database, we searched for information from elsewhere and included it if 343 possible. Thus, 4552 species could be classified as carnivores (including species eating 344 invertebrates and vertebrates), omnivores, or herbivores. The remaining 1195 species, 345 belonging to genera either without available diet information or with variable diet 346 between species, were given a probability of being in each of the three categories. These 347 probabilities were estimated based on a mean of the means approach, in which each 348 taxonomic group was weighted equally no matter how many species the group contained 349 (which is equivalent to maximum parsimony estimation on a purely taxonomic tree). This 350 is illustrated by a hypothetical subfamily with three genera. Genus A has 10 species, half 351 herbivores and half omnivores. Genus B has one species, an herbivore. The diet of genus 352 C is unknown, but we would assign it a probability of 0.75 for being an herbivore 353 (0.5×prob herbivore (Genus A) + 0.5×prob herbivore (Genus B)). 354 Next, we counted how many classes the species occurring in a given grid cell belonged to 355 based on diet and size (and habitat for all species and non-marine species); one such class 356 could be carnivorous flying mammals (bats) between 100.5 and 101 gram, another could 357 be terrestrial herbivores between 103 and 103.5 gram. The analyses were performed 100 358 times with reassignment of the probability of each diet each time for the 1195 uncertain 359 species and the median value of the analyses assigned to the cell. 360 361 References 362 Arjo, W.M. & Pletscher, D.H. (1999) Behavioral responses of coyotes to wolf 363 recolonization in northwestern Montana. Canadian Journal of Zoology, 77, 1919–1927. 364 Barber, C.B., Habel, K., Grasman, R., Gramacy, R.B., Stahel, A. & Sterratt, D.C. 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Nature, 485, 33-35. 409 Supplementary figures 410 Figure S1 411 Estimated current and present natural diversities for all mammals. 412 413 Figure S2 414 Estimated current and present natural diversities for all non-marine mammals. 415 416 Figure S3 417 Estimated current and present natural diversities for all terrestrial mammals. 418 419 Figure S4 420 421 Estimated current and present natural diversities for all large terrestrial mammals (>10 kg). 422 423 Figure S5 424 Estimated current and present natural diversities for all terrestrial megafauna (>44.5 kg). 425 426 Figure S6 427 Estimated total, historic and prehistoric loss for all mammals. 428 429 Figure S7 430 Estimated total, historic and prehistoric loss for all non-marine mammals. 431 432 Figure S8 433 Estimated total, historic and prehistoric loss for all terrestrial mammals. 434 435 Figure S9 436 Estimated total, historic and prehistoric loss for all large terrestrial mammals (>10 kg). 437 438 Figure S10 439 Estimated total, historic and prehistoric loss for all terrestrial megafauna (>44.5 kg). 440 441 Figure S11 442 443 The current diversity, the historic diversity and the predicted diversity based on the fossil co-occurrence approach for 39 North American mammals. 444 445 Figure S12 446 The relationship between species diversity and NDVI. 447 448 Figure S13 449 The relationship between phylogenetic diversity and NDVI. 450 451 Figure S14 452 The relationship between functional diversity and NDVI. 453 454 Figure S15 455 The relationship between species diversity and elevational range. 456 457 Figure S16 458 The relationship between phylogenetic diversity and elevational range. 459 460 Figure S17 461 The relationship between functional diversity and elevational range. Table S1. The relationship between diversity and environmental drivers for species diversity for the five different species sets. Standardized parameter estimates for a full SAR model are given along with standard errors of the estimate in parentheses. All P-values are based on Wald’s tests Terrestrial megafauna Total natural diversity Natural IUCN diversity Current diversity Intercept -0.031 (0.080)NS -0.061 (0.083)NS -0.062 (0.095)NS NS *** Elevational range 0.019 (0.016) 0.067 (0.017) 0.102 (0.018)*** Temperature 0.056 (0.069)NS 0.107 (0.073)NS -0.041 (0.079)NS log(precipitation) 0.002 (0.044)NS 0.070 (0.046)NS 0.039 (0.049)NS Precipitation seasonality -0.014 (0.022)NS 0.047 (0.023)* 0.021 (0.025)NS Temperature seasonality 0.097 (0.062)NS 0.071 (0.066)NS -0.066 (0.071)NS NDVI 0.509 (0.013)*** 0.427 (0.014)*** 0.327 (0.015)*** Open areas 0.076 (0.028)* 0.157 (0.030)*** 0.114 (0.032)*** log(precipitation): Open Areas 0.130 (0.041)** 0.104 (0.044)** 0.122 (0.047)** Temperature: Open Areas 0.027 (0.030)NS 0.086 (0.032)** 0.103 (0.035)** Pseudo R2 0.570 0.425 0.402 Large terrestrial species Total natural diversity Natural IUCN diversity Current diversity Intercept -0.023 (0.068)NS -0.047 (0.076)NS -0.058 (0.084)NS Elevational range 0.028 (0.015)NS 0.062 (0.015)*** 0.087 (0.017)*** Temperature 0.102 (0.065)NS 0.133 (0.068)* 0.027 (0.073)NS log(precipitation) 0.012 (0.042)NS 0.065 (0.043)NS 0.063 (0.047)NS Precipitation seasonality -0.018 (0.021)NS 0.017 (0.022)NS -0.000 (0.024)NS Temperature seasonality 0.069 (0.059)NS 0.059 (0.061)NS -0.041 (0.066)NS NDVI 0.547 (0.013)*** 0.451 (0.013)*** 0.383 (0.014)*** Open areas 0.098 (0.028)*** 0.153 (0.028)*** 0.128 (0.030)*** log(precipitation): Open Areas 0.166 (0.040)*** 0.134 (0.041)** 0.112 (0.044)* Temperature: Open Areas 0.040 (0.030)NS 0.084 (0.030)** 0.108 (0.033)*** Pseudo R2 0.666 0.483 0.466 All terrestrial species Total natural diversity Natural IUCN diversity Current diversity Intercept -0.014 (0.053)NS -0.024 (0.055)NS -0.019 (0.058)NS Elevational range 0.082 (0.014)*** 0.104 (0.014)*** 0.114 (0.015)*** Temperature 0.108 (0.058)NS 0.122 (0.061)* 0.074 (0.064)NS log(precipitation) 0.104 (0.040)** 0.136 (0.041)*** 0.150 (0.043)*** Precipitation seasonality -0.025 (0.020)NS -0.010 (0.020)NS -0.018 (0.021)NS Temperature seasonality -0.019 (0.052)NS -0.032 (0.054)NS -0.068 (0.056)NS NDVI 0.666 (0.013)*** 0.659 (0.013)*** 0.616 (0.014)*** Open areas 0.040 (0.026)NS 0.052 (0.027)NS 0.041 (0.028)NS log(precipitation): Open Areas 0.048 (0.038)NS 0.018 (0.039)NS 0.003 (0.041)NS Temperature: Open Areas 0.009 (0.028)NS 0.021 (0.029)NS 0.038 (0.030)NS Pseudo R2 0.775 0.740 0.734 Non-marine species Total natural diversity Natural IUCN diversity Current diversity Intercept 0.003 (0.050)NS 0.001 (0.051)NS 0.004 (0.054)NS Elevational range 0.064 (0.013)*** 0.076 (0.013)*** 0.082 (0.014)*** Temperature 0.102 (0.056)NS 0.112 (0.057)NS 0.086 (0.059)NS log(precipitation) 0.081 (0.036)* 0.095 (0.038)* 0.096 (0.039)* Precipitation seasonality -0.039 (0.019)* -0.031 (0.020)NS -0.036 (0.020)NS Temperature seasonality -0.182 (0.051)*** -0.214 (0.052)*** -0.235 (0.054)*** NDVI 0.658 (0.013)*** 0.654 (0.013)*** 0.621 (0.014)*** Open areas -0.009 (0.025)NS -0.007 (0.026)NS -0.016 (0.027)NS log(precipitation): Open Areas 0.057 (0.036)NS 0.044 (0.037)NS 0.039 (0.038)NS Temperature: Open Areas -0.026 (0.027)NS -0.026 (0.028)NS -0.018 (0.029)NS Pseudo R2 0.763 0.750 0.749 All species Total natural diversity Natural IUCN diversity Current diversity Intercept 0.008 (0.052)NS 0.007 (0.052)NS 0.010 (0.055)NS *** *** Elevational range 0.088 (0.013) 0.102 (0.014) 0.108 (0.014)*** Temperature 0.150 (0.057)** 0.161 (0.059)** 0.136 (0.061)* log(precipitation) 0.110 (0.034)** 0.129 (0.036)*** 0.129 (0.037)*** Precipitation seasonality -0.018 (0.020)NS -0.009 (0.021)NS -0.014 (0.022)NS Temperature seasonality -0.228 (0.052)*** -0.268 (0.054)*** -0.289 (0.056)*** NDVI 0.593 (0.015)*** 0.575 (0.016)*** 0.532 (0.016)*** Open areas -0.027 (0.026)NS -0.028 (0.028)NS -0.037 (0.028)NS log(precipitation): Open Areas 0.039 (0.035)NS 0.025 (0.037)NS 0.019 (0.037NS Temperature: Open Areas -0.029 (0.028)NS -0.029 (0.030)NS -0.018 (0.030)NS Pseudo R2 0.717 0.704 0.699 NS P > 0.05; * 0.05 > P>0.01; **0.01 > P > 0.001; *** P<0.001 Table S2. The relationship between diversity and environmental drivers for phylogenetic diversity for the five different species sets. Standardized parameter estimates for a full SAR model are given along with standard errors of the estimate in parentheses. All P-values are based on Wald’s tests Terrestrial megafauna Total natural diversity Natural IUCN diversity Current diversity Intercept -0.099 (0.077)NS -0.096 (0.097)NS 0.027 (0.108)NS NS NS Elevational range 0.014 (0.016) 0.025 (0.018) 0.095 (0.019)*** Temperature 0.168 (0.065)** 0.223 (0.073)** 0.063 (0.078)NS log(precipitation) -0.028 (0.044)NS 0.066 (0.048)NS 0.033 (0.051)NS Precipitation seasonality -0.019 (0.021)NS 0.009 (0.023)NS -0.030 (0.025)NS Temperature seasonality 0.130 (0.058)* 0.054 (0.064)NS -0.068 (0.069)NS NDVI 0.632 (0.013)*** 0.506 (0.014)*** 0.417 (0.015)*** Open areas 0.052 (0.030)NS 0.136 (0.033)*** 0.009 (0.035)NS log(precipitation): Open Areas 0.144 (0.043)*** 0.131 (0.047)** 0.178 (0.050)*** Temperature: Open Areas -0.033 (0.031)NS 0.035 (0.034)NS 0.044 (0.036)NS Pseudo R2 0.692 0.487 0.483 Large terrestrial species Total natural diversity Natural IUCN diversity Current diversity Intercept -0.019 (0.058)NS -0.041 (0.070)NS -0.038 (0.075)NS Elevational range 0.031 (0.015)* 0.060 (0.016)*** 0.086 (0.016)*** Temperature 0.135 (0.062)* 0.216 (0.068)** 0.140 (0.069)* log(precipitation) 0.024 (0.042)NS 0.068 (0.045)NS 0.089 (0.045)* Precipitation seasonality -0.031 (0.021)NS -0.009 (0.022)NS -0.017 (0.023)NS Temperature seasonality 0.103 (0.057)NS 0.105 (0.062)NS 0.007 (0.064)NS NDVI 0.645 (0.012)*** 0.558 (0.013)*** 0.476 (0.013)*** Open areas 0.072 (0.028)** 0.127 (0.029)*** 0.093 (0.029)** log(precipitation): Open Areas 0.103 (0.040)** 0.099 (0.042)* 0.087 (0.043)* Temperature: Open Areas 0.007 (0.029)NS 0.054 (0.031)NS 0.075 (0.031)* Pseudo R2 0.697 0.533 0.511 All terrestrial species Total natural diversity Natural IUCN diversity Current diversity Intercept -0.064 (0.056)NS -0.064 (0.060)NS -0.044 (0.064)NS Elevational range 0.061 (0.012)*** 0.077 (0.013)*** 0.086 (0.013)*** Temperature 0.247 (0.052)*** 0.290 (0.054)*** 0.251 (0.056)*** log(precipitation) 0.048 (0.035)NS 0.068 (0.036)NS 0.076 (0.037)* Precipitation seasonality -0.022 (0.017)NS -0.016 (0.017)NS -0.018 (0.018)NS Temperature seasonality 0.105 (0.045)* 0.068 (0.047)NS 0.039 (0.049)NS NDVI 0.740 (0.011)*** 0.742 (0.012)*** 0.712 (0.012)*** Open areas 0.056 (0.024)* 0.079 (0.025)** 0.053 (0.025)* log(precipitation): Open Areas 0.088 (0.034)* 0.084 (0.036)* 0.078 (0.037)* Temperature: Open Areas -0.021 (0.026)NS -0.014 (0.027)NS -0.001 (0.027)NS Pseudo R2 0.828 0.812 0.789 Non-marine species Total natural diversity Natural IUCN diversity Current diversity Intercept -0.041 (0.052)NS -0.039 (0.054)NS -0.025 (0.057)NS Elevational range 0.059 (0.012)*** 0.068 (0.012)*** 0.074 (0.012)*** Temperature 0.273 (0.051)*** 0.301 (0.053)*** 0.278 (0.054)*** log(precipitation) 0.032 (0.034)NS 0.044 (0.035)NS 0.046 (0.036)NS Precipitation seasonality -0.024 (0.016)NS -0.018 (0.017)NS -0.021 (0.017)NS Temperature seasonality -0.031 (0.045)NS -0.076 (0.046)NS -0.099 (0.048)* NDVI 0.747 (0.012)*** 0.742 (0.012)*** 0.716 (0.012)*** Open areas 0.033 (0.023)NS 0.045 (0.024)NS 0.026 (0.025)NS log(precipitation): Open Areas 0.095 (0.033)** 0.092 (0.034)** 0.091 (0.035)* Temperature: Open Areas -0.046 (0.025)NS -0.044 (0.026)NS -0.036 (0.026)NS Pseudo R2 0.827 0.816 0.794 All species Total natural diversity Natural IUCN diversity Current diversity Intercept -0.014 (0.046)NS -0.009 (0.048)NS 0.012 (0.052)NS *** *** Elevational range 0.055 (0.012) 0.067 (0.012) 0.072 (0.013)*** Temperature 0.190 (0.048)*** 0.220 (0.051)*** 0.204 (0.052)*** log(precipitation) 0.092 (0.029)** 0.109 (0.031)*** 0.110 (0.032)*** Precipitation seasonality 0.002 (0.017)NS 0.013 (0.017)NS 0.009 (0.018)NS Temperature seasonality -0.084 (0.043)NS -0.136 (0.046)** -0.156 (0.047)** NDVI 0.757 (0.013)*** 0.750 (0.014)*** 0.727 (0.014)*** Open areas 0.027 (0.023)NS 0.038 (0.024)NS 0.022 (0.025)NS log(precipitation): Open Areas 0.060 (0.030)NS 0.056 (0.032)NS 0.051 (0.033)NS Temperature: Open Areas -0.026 (0.024)NS -0.026 (0.026)NS -0.019 (0.026)NS Pseudo R2 0.819 0.801 0.780 NS P > 0.05; * 0.05 > P>0.01; **0.01 > P > 0.001; *** P<0.001 Table S3. The relationship between diversity and environmental drivers for functional diversity for the five different species sets. Standardized parameter estimates for a full SAR model are given along with standard errors of the estimate in parentheses. All P-values are based on Wald’s tests Terrestrial megafauna Total natural diversity Natural IUCN diversity Current diversity Intercept 0.004 (0.049)NS -0.019 (0.062)NS 0.020 (0.069)NS NS NS Elevational range 0.021 (0.015) 0.033 (0.017) 0.102 (0.019)*** Temperature 0.091 (0.061)NS 0.208 (0.071)** 0.096 (0.080)NS log(precipitation) 0.017 (0.043)NS 0.032 (0.048)NS 0.073 (0.055)NS Precipitation seasonality 0.007 (0.021)NS 0.031 (0.024)NS 0.018 (0.027)NS Temperature seasonality 0.276 (0.054)*** 0.108 (0.063)NS -0.031 (0.071)NS NDVI 0.688 (0.013)*** 0.547 (0.014)*** 0.442 (0.017)*** Open areas 0.051 (0.028)NS 0.078 (0.032)* 0.039 (0.036)NS log(precipitation): Open Areas 0.104 (0.041)* 0.121 (0.046)** 0.106 (0.052)* Temperature: Open Areas 0.022 (0.030)NS 0.009 (0.033)NS -0.002 (0.038)NS Pseudo R2 0.681 0.480 0.462 Large terrestrial species Total natural diversity Natural IUCN diversity Current diversity Intercept 0.002 (0.045)NS -0.018 (0.054)NS 0.031 (0.057)NS Elevational range 0.018 (0.014)NS 0.028 (0.015)NS 0.062 (0.017)*** Temperature 0.123 (0.058)* 0.203 (0.064)** 0.091 (0.070)NS log(precipitation) -0.005 (0.042)NS 0.006 (0.044)NS 0.079 (0.048)NS Precipitation seasonality 0.004 (0.020)NS 0.043 (0.022)* 0.036 (0.024)NS Temperature seasonality 0.301 (0.052)*** 0.275 (0.057)*** 0.287 (0.062)*** NDVI 0.713 (0.013)*** 0.615 (0.014)*** 0.538 (0.015)*** Open areas 0.030 (0.028)NS 0.050 (0.029)NS 0.043 (0.032)NS log(precipitation): Open Areas 0.110 (0.040)** 0.108 (0.042)* 0.095 (0.047)* Temperature: Open Areas -0.006 (0.029)NS -0.004 (0.031)NS 0.026 (0.034)NS Pseudo R2 0.722 0.575 0.558 All terrestrial species Total natural diversity Natural IUCN diversity Current diversity Intercept -0.019 (0.036)NS -0.022 (0.033)NS -0.015 (0.034)NS Elevational range 0.070 (0.012)*** 0.080 (0.013)*** 0.089 (0.012)*** Temperature 0.227 (0.049)*** 0.267 (0.049)*** 0.211 (0.050)*** log(precipitation) 0.036 (0.037)NS 0.036 (0.037)NS 0.072 (0.037)* Precipitation seasonality 0.022 (0.018)NS 0.035 (0.017)* 0.031 (0.017)NS Temperature seasonality 0.390 (0.044)*** 0.396 (0.043)*** 0.399 (0.043)*** NDVI 0.812 (0.012)*** 0.794 (0.012)*** 0.768 (0.012)*** Open areas 0.059 (0.025)* 0.068 (0.025)** 0.050 (0.025)* log(precipitation): Open Areas 0.059 (0.036)NS 0.081 (0.036)* 0.051 (0.036)NS Temperature: Open Areas 0.013 (0.027)NS 0.007 (0.027)NS 0.033 (0.027)NS Pseudo R2 0.849 0.829 0.820 Non-marine species Total natural diversity Natural IUCN diversity Current diversity Intercept 0.031 (0.042)NS 0.011 (0.030)NS 0.016 (0.032)NS Elevational range 0.034 (0.011)** 0.037 (0.011)*** 0.046 (0.011)*** Temperature 0.169 (0.046)*** 0.179 (0.045)*** 0.146 (0.048)** log(precipitation) 0.040 (0.030)NS 0.047 (0.031)NS 0.066 (0.032)* Precipitation seasonality -0.003 (0.015)NS -0.002 (0.016)NS -0.007 (0.016)NS Temperature seasonality 0.166 (0.041)*** 0.134 (0.040)*** 0.138 (0.041)*** NDVI 0.811 (0.011)*** 0.807 (0.011)*** 0.787 (0.012)*** Open areas 0.020 (0.022)NS 0.031 (0.022)NS 0.014 (0.023)NS log(precipitation): Open Areas 0.100 (0.031)** 0.116 (0.032)*** 0.093 (0.032)** Temperature: Open Areas 0.007 (0.023)NS -0.003 (0.024)NS 0.013 (0.024)NS Pseudo R2 0.861 0.854 0.839 All species Total natural diversity Natural IUCN diversity Current diversity Intercept 0.019 (0.054)NS -0.011 (0.039)NS -0.009 (0.041)NS ** ** Elevational range 0.049 (0.015) 0.047 (0.016) 0.060 (0.016)*** Temperature 0.050 (0.061)NS -0.047 (0.061)NS -0.087 (0.063)NS log(precipitation) 0.117 (0.038)** 0.133 (0.041)** 0.157 (0.042)*** Precipitation seasonality 0.019 (0.021)NS 0.024 (0.023)NS 0.012 (0.023)NS Temperature seasonality 0.011 (0.054)NS -0.042 (0.054)NS -0.042 (0.056)NS NDVI 0.750 (0.017)*** 0.748 (0.018)*** 0.720 (0.018)*** Open areas 0.022 (0.030)NS 0.050 (0.032)NS 0.035 (0.033)NS log(precipitation): Open Areas 0.059 (0.039)NS 0.084 (0.043)NS 0.054 (0.044)NS Temperature: Open Areas 0.022 (0.032)NS 0.023 (0.034)NS 0.040 (0.035)NS Pseudo R2 0.724 0.708 0.682 NS P > 0.05; * 0.05 > P>0.01; **0.01 > P > 0.001; *** P<0.001 462