Pros and cons of not having PhD advisor's letter of recommendation after postdoc? I have finished my PhD and am currently a postdoc. Since receiving my PhD, I have not worked with my PhD advisor. I am planning to apply for jobs for after I finish my postdoc — mostly tenured-track positions.

I am considering not asking my PhD advisor for a letter of recommendation. I feel this might be appropriate because I plan to ask my postdoc advisor to write a letter, because my PhD advisor may not have kept up with my current research, because my coauthors know my work better, and for other reasons.

What are the pros and cons of not having my PhD advisor as a letter writer?
The only time that you shouldn't ask for a letter of recommendation from your PhD advisor is when you are not allowed to ask for one. This is not often the case, but it does arise in a few instances. The best-known one I can think of is that in Germany a Doktorvater (supervisor) is not allowed to write a letter of recommendation in support of an applicant whose PhD he supervised. 

Other than that, you should have your PhD advisor write a letter; it is expected by just about everyone that the supervisor will write a letter, and it will definitely raise questions for you if you do not submit such a letter. If there is a particularly compelling reason, then, you should have that well in hand at the time when you are writing your applications. Otherwise, you'll have a lot more explaining to do, and probably a lot of potential postdoc supervisors may not even bother giving your application a second look.