I don't see Anderson being cut, but he is likely to be lower on the depth chart than many of us thought a few months ago. Barmore has come on strong very early and taken one of the higher spots. Maybe even a starter spot before long. While Davis was good last year, he has stepped it up to another level this year, and fits in really well with what the Patriots want to do. As does Godchaux, though he has been slightly disappointing, but is still a better fit.
It kind of leads one to ask, what does Anderson do? You want a 3rd down pass rushing specialist? Keep Chase. You want to stop the run? Put in Davis and Godchaux. You want an all rounder? Guy and Barmore are better options. You want a more traditional 4-3 option that can lean on run defense? Wise is the better answer most likely. Anderson would fit much better in a more traditional 4-3 as a smaller DT. But that isn't much of what the Pats do right now. I still think he makes the team, but the way things are looking and how other guys have stepped up, he just won't see the field much.