There is definitely some general relation between the two subjects within complexity theory, and as likely one of the few people who know what both fields entail, I've not come across anything specific or even general linking the two fields in a direct manner. I've seen some research that ties the two fields separately to other areas in an indirect manner, but I doubt this is of any interest to you.
One of the few papers I'm directly aware of in the space is "Analaysis and improvement of genetic algorithms using concepts from information theory" by John Edward Milton, though it's been quite some time since I read it, and I recall it being a thesis.
The closest thing I can think to refer you to is some of Melanie Mitchell's work. She's written a book entitled "Complexity: A Guided Tour" (Oxford University Press, 2011) which touches on both subjects underneath the umbrella of complexity studies though in separate chapters. This book is best described as popular science and doesn't have many (any) equations at all, so it'll give you only an idea of their relationship. If you contact her directly (I know she's on Twitter), perhaps she can give you more specifics.
I also maintain an open Mendeley group ITBio: Information Theory, Microbiology, Evolution, and Complexity which may be of some tangential help for your search. Unfortunately there are only a few dozen researchers who can function in the worlds of information theory and evolution/biology at the same time.
You might also delve into the work of Stuart Kauffman ("The Origins of Order" (Oxford University Press, 1993), though many serious information theorists refute the direction he takes mathematically as his grounding isn't in information theory itself) or Gregory Chaitin who have some interesting material tangential to the subject. The Santa Fe Institute may also have one or more interesting tangential researchers.
I'm quite interested to see/hear what your or others may come up with in this interesting space.