I updated the map so it's clear that this is the world situation just before the Americas are settled (so now there's gonna be 'dogs in the U.S. and Australia). The five major werebeasts: jaguar (yellow), wolf (brown), hyena (greenly-brown), leopard (dun), and tiger (orange). There's also selkies in the Norwegian Sea. I gathered recorded events and legends and matched them to their megafauna's range and a little to human migrations. East Asia and Melanesia have a multiplicity of smaller populations or epigenes for freeform transformation, without any prevailing groups that consolidated into large populations of a single therianthrope (like how the present-day language families overtook smaller populations): you'd get crocs, boars, sharks, buffalo, dolphins, lions. Given their animal's characteristics, African were-hyenas ("spots" as opposed to Mideastern "stripes") would be either very masculine/feminine, or hermaphroditic when human. Whether ravening or protective, their role in the magical underground would definitely be militaristic.
Western Europe seems to have had 'wolves in Friesland, Schleswig, Normandy, north Dover, south France, the Jura, Picardie, Lorraine, Wallonia, the Pyrénées, Scythia, and the Welsh and Scotch forests. I guess there'd be a gradient from Slavs, Ugrians, and Germans down to Celts and then Latins; true wolves were also blocked from Spain and Italy. I guess in the 16th century they'd've reached a density high enough to pick up some curses, producing insane Renegades and quarter-bloods that sparked a lot of secular witch- and wolf-hunts IRL. The map is divided to show the pre-invasion situation in the Americas; Ian Woodward surmised that the ravaging wendigo came over with the Vikings, so I gave a little epigenes to the Cree and Dogrib lands. The nahuales would also become pumas and coyotes outside the indicated range.
Map prepared by the Invernotte-Klinik, Küsnacht; Ostafrikanische Magische Hochakademie, Dar es Salaam; Senior Zadith Hospital, Cairo; Centro Balam, Guatemala City; Bāgh Divan Library, Singapore and Hyderabad; Center for Land Use and Hexing and St. John Bosco College, Sedona, Ariz. [Sorry it took so long. Again, any suggestions for range changes welcome!]