Independence as a postdoc working with former PhD supervisor Having recently finished my PhD, I have now secured funding to act as PI on a project.

I continue to work alongside my former PhD supervisor, with the old supervisor listed as a collaborator on the new project.

The former supervisor frequently refers to me as their 'postdoctoral fellow'. Question 1: Is this appropriate, given that I am the PI on the new project? The former supervisor is certainly in a higher position than I (Professor, whereas I am indeed a postdoc), but I feel that I should not be considered 'their' worker.

The current project requires me to use equipment owned by the former supervisor, and we closely collaborate on a lot of work. I value the impact my former supervisor has had on my career so far, and would hope to continue to work with them in the future. Question 2: How can I best make clear (respectfully) that they are now a colleague?

(UK based)
The former supervisor frequently refers to me as their 'postdoctoral fellow'. Question 1: Is this appropriate, given that I am the PI on the new project? 


I have never encountered a "postdoctoral fellow" that does not have a supervisor.  But my experience is far from global.  As this article on postdoctoral research says, "Depending on the type of appointment, postdoctoral researchers may work independently or under the supervision of a principal investigator."  Later it says "In the US, a postdoctoral scholar is an individual holding a doctoral degree who is engaged in mentored research and/or scholarly training for the purpose of acquiring the professional skills needed to pursue a career path of his or her choosing."  

If you are the PI on your project then yes, I suppose that must mean that you do not have a formal supervisor.  However you can still have a mentor...and you should.  Your former PhD advisor's description of you as "theirs" need not imply that they view themselves as your boss; it may only mean that they are affiliated with you and are taking a role of mentoring you, as seems to be the case here.  

Let me also say that in that this person who is formally associated with the grant is your former PhD advisor and in that he owns (you say) the equipment that you are using both give him more oversight than some other independent researcher would expect.  If I borrow my friend's car that does not make her my boss, but it does give her some supervisory role over my use of the car.  A senior academic who owns equipment you are using should have some supervisory role in your work.


  Question 2: How can I best make clear (respectfully) that they are now a colleague?


I don't see what behavior of the supervisor indicates that he does not view you as a colleague.  I have a postdoc, and I view her as a colleague: a junior one, in which I have some supervisory role, but still a colleague: I have some projects she is not involved in, she has some projects I am not involved in except to hear her talk about them, and there are some projects we do together.  If she decided tomorrow that she only wanted to work on her own projects alone, that would in my view be suboptimal for both of us, but it would be her right. 

In some fields postdocs are treated rather differently: they are the highest level of workers for the PI professor.  But since you are a PI, that is not your situation.  

Having a senior colleague who can mentor you is extremely valuable.  I continue to mentor my PhD students after they get the PhD -- well, so far I have one, but soon two more -- but this mentorship is limited by my time and energy.  Any mentor should be guiding his/her mentees towards greater mastery, independence and autonomy.  Gradually the influence of mentors wanes: when I was an untenured assistant professor I had a research mentor and a teaching mentor; as a tenured associate professor I have no formal mentors anymore....which is a shame, since to paraphrase Yoda, much to learn, I still have.  But my work is still evaluated by more senior people -- that is a ubiquitous phenomenon in academia -- so it is still important for me to maintain good relationships with senior colleagues.  Unless people are literally telling me what to do, I tend to let it slide when people treat me with less "seniority" than I think I have.  

I am a little worried that you may have your eye on the wrong problem.  You have a one year position: what happens next year?  That's the key question, and your future relationship with your advisor is a key part of the answer.  You don't need to kowtow or be subservient to him: on the contrary, you're the PI, so when it comes to the work itself you get to call the shots (and you should).  But you are still looking for a lot of help from your supervisor -- help landing the best possible future job, if nothing else.  So trying to insist "You're not my mentor; I am fully independent from you" in a one-year position seems really to be a strategic mistake to me.  Instead you should apply yourself and show your former PhD supervisor how much stronger and more capable you have become, and then they can write you an excellent recommendation because all of your post-PhD growth and maturation took place before his eyes.