I have encountered "pers. commun." in some academic papers when referring to a source or reference . Like in :
Authors also made sure that they covered the range of self-focused and symptom-focused constructs (Nolen-Hoeksema, 2001, pers. commun.).
Attempts at using nutrient-solution culture for screening have been unsuccessful ( M.E. McDaniel, 1989, Texas A and M University, pers commun.).
What does it stand for?
I looked it up in some dictionaries but couldn't find anything.
As said by Thomas in a comment, it means personal communication.
Under this phrase, there can be any kind of communication: a discussion (in the university corridors, at a conference, before a couple of beers etc.), an email or whatever.
The communicated piece of information might be something already published, something that is going to be published, or something that will be never published but it is related to the communicator's experience.
For instance, while doing a certain research, I might stumble across some curious phenomenon of which I don't know the origin: the phenomenon might be totally secondary with respect to my research, but I'm curious and I ask someone else, maybe an expert in another field, the origin of this phenomenon. Then, while writing up a paper I might say: you see that bump over there in Figure 2? Well, it has nothing to do with what I'm saying here, but it's due to this and that, Jack told me (tacitly: I'm writing this in the paper because then you, reviewer, will not ask me: hey, what's that bump in Figure 2?)
In your examples, instead, the personal communications are really more related to the research described in the papers.