MIAMI—When Hurricane Irma sprinted toward Miami-Dade County, Jeff Ransom couldn’t sleep. He wasn’t just worried about gusts shattering windows, or sheets of rain drowning the highway—that’s far from unusual near his home in Broward County, where extreme weather verges on routine, and patches of U.S. 1 are regularly submerged.

Ransom, the county archaeologist, was preoccupied with an oak tree and its 350-year-old roots. If the tree capsized with enough intensity, he worried, the flailing roots cou…