The beaver enjoys an extensive range as the below map shows. However, it is presently absent in most of penninsular Florida. The scientific literature offers no reason for this absence. I propose the beaver can not currently live in south Florida because the alligator population is too dense there.
Top: Current range map of the beaver. Bottom: Current range map of the alligator. The ranges of the 2 species overlapped in Florida during the Pleistocene.
Pleistocene-aged fossils of beavers are among those found from the Monkey Jungle Hammock site just outside of Miami, Florida, proving that beavers formerly did live in south Florida. Presently, beavers do co-exist with alligators in the southern parts of South Carolina, Georgia, Alabama, Mississippi, Texas, and all of Louisiana. I suspect 2 factors allow for this co-existence: the population of alligators in these states is not as dense as it is in penninsular Florida, and the existence of major rivers flowing from north to south allows beavers from the north to replace those killed by alligators. There is a population of beavers in north Florida near the mouth of the Suwannee River. The river provides a conduit for beaver colonization. There are no major rivers in south Florida that could facilitate the colonization of beavers from farther north.
Alligator fossils from Florida’s Pleistocene are common, so alligators were not rare in Ice Age Florida. Nevertheless, the presence of beavers then in south Florida suggests the alligator population was not as dense as it is today, especially during stadials. Though there were some wetlands, the region was much drier then. The environment was likely dominated by dry longleaf pine savannahs on sandy soils with some oak scrub and open semi-tropical woodlands. It was harder for alligators to come into contact and breed in large numbers like they do today. Instead, large male alligators defended their small springs from smaller males, driving them into unsuitable habitat where they were likely to perish. Moreover, alligators weren’t necessarily at the top of the food chain–jaguars and saber-tooths likely fed upon adults, and a large population of bears gorged on the eggs. Somewhat cooler summers may have slowed down their reproduction as well. With the alligator population held in check, beavers could live in a less stressful environment.
My hypothesis is worth studying. A simple way would be to determine how many alligators (large enough to prey on beavers) live per square mile in south Florida and compare that with alligator per square mile in areas where the 2 species overlap.