FLorida HOA responsibilities regardling 'Rodents

The first place to look for the responsibilities of your HOA is in your governing docs (bylaws, CCRs, Deed restrictions, etc.). Beyond that I looked at Florida statute 720, which governs HOAs and did not find any reference to "rodent" or "pest". Unless your docs say otherwise, rodent control would probably be each homeowner's responsibility. I think generally that wildlife living in woods, fields, and other outdoor areas in Florida is to be expected, so I don't think the HOA would have any responsibility unless specifically identified in your docs.