If you are asking if the tendency towards being an empath flow with the bloodline as an inherited characteristic of our DNA, I am sure the answer is yes!
However, can it be cultivated (aka learned) in addition? Again, yes. Although it may be more accurate to say that it can also be unlearned; babies are natural empaths and we are socialized into identifying ourselves as separate from others. Our wider Western culture regards (or used to regard) everything we know about being empaths as being an active imagination (in children) or just B.S. (in adults).
I am sure it is a combination of the two and I believe that many of us on this site can look at our families and see traits of being an empath in our relatives. It is often said that it flows more through the female bloodline than the male although it may be more accurate to say that the women are more likely to a acknowledge and manifest the ability.
P.S. if, as RyuukoGo asked, you meant something different by "Discern" then my apologies!