Transplantation from one region of a person to another region of that same person is an autograft and has the best chance of succeeding. When a transplant is done between monozygotic twins, it is an isograft and has a complete MHC compatibility and a good chance of success. Allografts are between members of the same species, and xenografts are between members of different species. Both of these transplants have a high rate of rejection unless immunosuppression accompanies the transplant.