You already know about it, just in different terms. You have one father and mother, but two grandfathers, four great grandfathers, four great grandmothers, etc. Which of these is your "bloodline"? Either all of them or none. Each of them is likely (in the general case anyway) also a grandparent to many other children with other intermedaries. Which of these is their descendant bloodline? If you get rid of weird socially contingent criteria like "first son", the answer is obviously none of them. It's just a big web, going back thousands of years at minimum. Billions of years back to the first sexually reproducing eukaryote, if you want to think of it that way.