Some of the most familiar plants in older Southwest Florida yards are listed as invasive by the Florida Invasive Species Council. They escape into natural areas and crowd out native plants. Several can no longer be sold in Florida.
Remove these
Brazilian pepper: a shrubby tree with clusters of red berries, among Florida's most damaging invasives. Melaleuca: a papery-barked tree that overran parts of the Everglades. Australian pine: shallow-rooted and prone to toppling in storms. Foxtail or asparagus fern, common in older beds. Common lantana, which also hybridizes with the native species. Fountain grass, including the purple form.
Don't add more
Queen palm is listed as Category II in Central and South Florida. Existing trees can stay, but plant something else when they decline.
Good replacements
Muhly grass for fountain grass; native pineland lantana for common lantana; coontie or liriope for foxtail fern; cocoplum, Simpson's stopper or silver buttonwood for a Brazilian pepper screen.
Removing them well
Many of these resprout from stumps or roots, so removal should take out the root system or tubers, and stumps need follow-up. Bag berries and seed heads so birds and wind don't spread them.