Further up the family tree.

So I've been researching my family tree, a subject that is utterly fascinating to everyone on the planet, with the exception of those people who aren't me. It's an intriguing insight into one's roots -- I can go back more than 14 generations to 17th century Sussex on one particular, well-researched line. Or I could if there wasn't a strong suspicion that one rude forefather not too far back along this branch was illegitimate, making his father's ancestry a moot point. (I guess it was his mother who was the rude one.)

But because I'm living in America, I'm almost entirely dependent on the internet and the online availability of English census data going back to 1841 and the official register of births, marriages, and deaths from 1837. Online parish records are patchier. That's what's so useful about the websites that try to link you with other researchers, by spotting common names in your published family tree.

And last weekend, I made contact with Vicky in Manchester, England, because of our shared ancestor, Jeremiah Chadwick (1807-1890), my great-great-great-great-grandfather. Now, I'm particularly interested in this twiglet of the tree, because it contains just about the only direct forebear I've found with any claim to fame: Jeremiah's son Richard Sheldon Chadwick (1829 - 1892), who was a traveling lecturer, spiritualist, phrenologist, and a published poet. Vicky is descended from his sister, Mary, and because she lives where Jeremiah spent his days -- he was a revivalist preacher at the Manchester Mission -- she may have some insights into his life from local research.

But what brings compound interest and heritage together is this whole business of consanguinity -- roughly how many of your genes can you expect to share with someone else in your family? And it's back to the power of those pesky exponentials, only in reverse.

You get exactly half your DNA from each parent.* So your consanguinity with your mother or father, son or daughter is 50%.**

Every step on the family tree halves it. Grandparents, grandchildren, aunts, uncles, nephews, nieces, and half-siblings: 25%. Cousins, great-grandparents, great-grandchildren: 12.5% or one-eighth. And so on.

Thus, while I'm more than delighted as a matter of family history to have obtained a signed first (i.e., only) edition of The Pleasures of Poetry, the Purgatory of Poets and other Poems by Richard Sheldon Chadwick, "The Teetotaler," from 1848, it's with the knowledge that we two literary men (and I use the term very, very loosely, in both cases) have only 3.125% of our genes in common. No bragging rights there. And I certainly didn't inherit his apparent aversion to alcohol.

So I attempted to calculate my relationship to Vicky. It's actually easier than you might think -- bear with me. First cousins share grandparents, second cousins share great-grandparents, etc. See the pattern? You count the number of "greats" and "grands" in the name of your "most recent common ancestor." The number is the degree of cousinhood. Simple.

But if you get different numbers, that's where "removal" comes in. In this case, the lower number is the degree of cousinhood, and the difference between the numbers is the removal. So Jeremiah, being my 4th-great-grandfather, gets me a score of 5 (4 greats + 1 grand). But Vicky has only 4; she's one generation closer to the esteemed Jeremiah. (She's younger than me, but clearly her branch wasn't in such a hurry to reproduce over the years.) Thus we are fourth cousins, once removed. Her new baby, born on Valentine's day this year, shares a birthday with 11-year-old Primus. They are therefore fifth cousins, once removed.

By contrast, the Queen of England is first cousin, 14 times removed from her namesake, Elizabeth I (1533-1603).

What does it mean? Well, in terms of consanguinity, you start with that first-cousin score of one eighth. Every additional degree of cousinhood is two more steps on the tree, which quarters the number. Every degree of removal is only one step, so that only halves it. It turns out that Vicky and I have less than one-thousandth*** of our genes in common. Or 0.09765625%.

If we ever meet, I'm not expecting any family resemblances.

That's the power of reverse compound interest. For the two Queen Elizabeths, it means -- mathematically -- that only one gene in 65,536 is the same due to inheritance along the most direct line. (Which wasn't the line of succession, incidentally.) Since the current thinking is we don't have more than about 30,000 genes, that means Q.E.II is much more likely to have the same genes as Q.E.I because of sheer random chance than because of descent. Primogeniture, my arse.

And that's when it struck me. In my meager research to date, I've been concentrating on my pathway back through my direct ancestors, branching with each generation and thus doubling the amount of research, despite the dwindling records. What about all those bits that go out to the side, like your great-grandfather's sister's family, the stuff that serious researchers bother about? Did my great-great-aunt -- just a first name in a box, gleaned from a census form -- marry a Beechey? Did she have a daughter or a granddaughter who married a Beechey?

In other words, could the line back to my adoptive family be shorter than I'd ever imagined? Could I unknowingly have a greater level of consanguinity with a living Beechey than I do with that far, distant ancestor who happened to plug my birthname, Russell, into the line?

And, by the same reasoning, could those elitist Mayflower madames be more closely related to their dry cleaners or their doormen than to any 1621 pilgrim to these shores? I do hope so. This is, after all, America.

Which is all just an excuse to send you to this mind-blowing Wikipedia page about cousins. Skip the stuff I just lifted and get down to what happens when a set of half-siblings marries another set of half-siblings. Somebody's actually worked this out!

*Doesn't mean you take after each one evenly. Each time a sperm or egg cell (a gamete) is formed, it grabs only half of the parent's chromosomes. It's a random process. You may have sprung from an egg that has a huge batch of dominant genes, easily overwhelming your dad's submissive ones, so you take after your mother more. Lucky you. But then there's all that jumbling and mutating to deal with in the process as well.

**It's 50% for siblings, too, but that's even more of an assumption. Because of the randomness issue (see previous footnote), any two gametes produced by the same person have, on average, about half of their genes in common. But in practice, two gametes from, say, a father could potentially have many more than half their genes in common, or hardly any. This means the actual consanguinity between siblings can vary enormously. For example, the Olsen twins aren't identical twins genetically, but they clearly share enough of the genes that govern their looks and sizes to get away with playing the same character on Full House.

*** One in 1,024 to be exact. Sound familiar?