The frigid Florida winter of a few years back really put the whammy on tropical aliens like the brown anole, but they are slowly rebounding.
As alien invaders go, these seem almost trivial now that exotic pythons are devastating the Everglades.
The python invasion is a whole 'nother
RANT post, and some of you won't like it.
These two species seem to be resource partitioning. They may both prey on insects, but they focus on different hunting grounds.
That's not to say they never interact, just that the predicted destruction of native anoles by this anole doesn't seem to have happened.