I am currently a postdoc and will soon be applying for a faculty position in computer science. I am inclined to not ask my postdoc host for a reference letter when applying.
The reason I don't want to ask my postdoc host for a letter is because I have been a postdoc for less than a year and have mostly worked independently or with remote collaborators. So far I have only coauthored one paper with my host. (It's a good but not great paper.) Also, I am supported by a general fellowship -- i.e. I am not formally "tied" to my host, which means I don't think he feels strong "ownership" of me as a postdoc. It is not a true mentorship relationship.
I think my postdoc host would write a positive letter for me, but it would be weak for the aforementioned reasons -- he simply doesn't know me that well. I have other potential letter writers who would be able to write stronger letters.
What is worse? A weak letter from my postdoc host or no letter? Is this something I should try to explain on my application?
Any advice is greatly appreciated!