During the Golden Age of Exploration, maps conveyed as much personality of a place as it did the detail about its physical layout. The continents were usually personified in art, (think Rubens in the early 17th century, among others)
Rubens has the four continents embraced by their four respected rivers, Africa-The Nile, Europe-The Danube, Asia-The Ganges, and America in the back with The Rio de la Plata. Which for those unfamiliar with South American geography is the “Silver River” that empties into the Atlantic at Buenos Aires. As there was more colonial success in South America at the time, and Rubens was a diplomat in service of the Spanish crown (among others) it is natural that he is more familiar with South America than El Norte, the symbolism remains the same though.
Europeanized or not, the personification of America began as a Minerva figure, but quickly took on the guise of an Indian Princess usually seen with, often times riding, some dangerous reptile. As in this frieze on a German building.
My favorite really is Adrien Colleart II’s mid-18th-century version where she, armed with bow and ax is riding a giant armadillo.
As for the subtle warnings to explorers, Henry Popple included some hard to miss “here be dragons” moments. The ever present alligator is near the princess, as well as a monkey, and and armed warrior. In case that wasn’t explicit enough (apparently Popple, knew his audience), she has her foot on a (ver European-looking) severed head that has been pierced with an arrow. To be fair, this map is the west coast of British Honduras and not specifically the North American continent, but the allusion is the same.
As relationships deteriorated (read as the Europeans lost control), the Princess grew ever more threatening, until she was at least replaced by a male indian warrior. This wasn’t just artistic license and/or personal choice as a religious edict called for the replacement of the female figures with that of a male.