This interesting research from Joslin research center on mice shows strong links between the two. What I like most abt this research direction is that they are already jumping from mice to men:
Diabetes researchers have long noticed that labs have different rates of success breeding mice to have the equivalent of Type 1 diabetes. At first, many scientists attributed this to poor management of genetic drift in some labs, but this theory didn’t hold up. If you transferred a group of mice from a lab with a lower rate of diabetes to a lab with a higher rate, the transferred group would soon exhibit the same rate of diabetes found in the new surroundings.
It is intriguing to compare this paper to another one on T2 diabetes that we quoted recently: