Just had a look at your saves... That's not Krynn - that's Iridium influence!
It seems like there's ONE planet that's giving the influence. Notice how (in the unexplored space) It's all straight lines.
They have one planet (Henrik III) with 2018 Influence, growing at 1.1 per turn.
I don't have much time atm, but in a few hours I'll take another look, if it's not already solved.
I expect it's an ideology thing.
Whoa, then Henrik III got taken over by the Krynn, and suddenly has 5016.5! Nice...
Edit: I had a bit of fun!
http://steamcommunity.com/sharedfiles/filedetails/?id=434094174
Something seems to happen when the planet gets conquered. (Tested multiple planets with all races)
When a planet is conquered, its influence seems to double (and then +% modifiers from tech, etc, on top of that)
I'll submit a ticket for this, referencing yours.
#GVX-928-59153