I've got a question for the linguists.
Irish does not have s possessive case as in English eg. you don't `have' something it is `with you', `at you' or `on you'...
I am not a linguist but my understanding is that situation is similar to DNA in one respect. You can look at one individual type of something, in your question the possessive case, and come up with all kinds of theories. This would be, in my mind, akin to looking at one single STR, say DYS391, and developing theories that everyone who is DYS391=10 is Scottish, which probably isn't true. I think you have to look at all of the data possible in context of all of the types and cases. I think linguists try to do this when determining the language tree and ages.
I was wondering if these farmers could have disappeared without a trace yet some hunter gatherers survived ...
Does genetics tell us anything definite on this.
Anything is possible, but I think a clue from genetics is the lactase persistence genes that many in Northern Europe, in particular, have inherited. http://en.wikipedia.org/wiki/Lactose_intolerance
This would probably be associated with animal husbandry and dairy cattle... something that some elements of people associated with agriculture would be engaged in. I think that's what the archeology has shown.
Hunters on the other hand, were killing animals for meat and accessories. There was no advantage to this gene for them therefore that's probably not where Northern Europeans got it.