Maine’s largest biomedical research institution is planning its first out-of-state research branch if it can secure public funding in Florida. Bar Harbor-based Jackson Laboratory, which specializes in mouse genetics, has been in talks about building a 145,000-square-foot research center in southwest Florida. The goal is to create a new research laboratory where scientists would apply genetic research toward human health problems. Jackson Lab trustees could decide by the end of summer whether to proceed if the Florida Legislature and the county government agree to spend more than $200 million. Some people are asking why the facility can’t be located inMaine. But Gov. John Baldacci’s office says Maine can’t compete with Florida when it comes to incentives.