## Two aunts and nephew sex

Why is your great-grandmother great? Keeping track of family relations can be difficult. Fortunately, a bit of mathematical logic can clarify who should be called what, and why — and even measure the degree of genetic similarity between different relatives. Ancestor Lineage To begin at the beginning well, your beginning, anyway , you surely had two parents, a mother and father: Continuing backwards, they each had two parents, giving you a total of four grandparents: For example, your maternal lineage is: Since each ancestor has two parents one mother and one father , you have a total of 2n ancestors at level n: In short, your ancestors form a perfect binary tree — simplicity itself.

Unlike with ancestors, there is no simple formula for your number of descendants. Rather, you have to count up all of your children, and all of their children, and so on. For example, even if you have five children, it is possible that none of them will have children of their own, in which case your number of grandchildren will be zero.

On the other hand, if they each have five children of their own, then you will have twenty-five grandchildren — a lot more. When people have more than one child, this fattens the family tree, creating new relationships like sister and niece and great-aunt and more.

For starters, if your parents have additional children besides you, then they are of course your siblings, that is your sisters and brothers: If you and your siblings each have children, then those children are first-cousins of each other.

Then, if the two first-cousins each have children, then those children are second-cousins of each other; and their children are third-cousins, and so on: Thus, first-cousins share two grandparents but no parents , and second-cousins share two great-grandparents but no grandparents , and so on. Thus, children of first-cousins are second-cousins, and children of second-cousins are third-cousins, and so on.

In fact, if we regard siblings as 0-level cousins, then this reasoning applies to siblings too: If your cousins have children, then what are they to you? To see where your second-cousins come from, we have to move one more level up. And their children are your second-cousins: The same pattern continues upwards for all earlier generations. Siblings of your nth-level ancestors are your great Furthermore, the nth cousins of your mth-level ancestors, and also the mth-level descendants of your nth cousins, are your nth cousins m times removed.

This attitude presumably has an evolutionary basis: Well, first of all, about Furthermore, some people may share other genes with us just by chance; for example, if I meet a stranger whose eyes are brown just like mine are, that does not necessarily establish that we are close relatives. In addition, there is lots of randomness in how genes are passed on each individual gets half of their genetic material from their mother and half from their father, but which bits come from which parent is chosen at random and cannot be predicted , so we cannot draw precise conclusions with certainty.

To deal with all of this, we assign to each pair of individuals a relatedness coefficient which represents the expected fraction ie, the fraction on average of their genes which are forced to be identical by virtue of their family relationship. This approach averages out all of the randomness, while focusing on genetic similarities specifically due to family connections.

According to this definition, strangers have a relatedness of zero the smallest possible value. By contrast, your relatedness with yourself is one the largest possible value. Other relatedness coefficients fall between these two extremes. So far so good: Next consider your maternal grandmother. She gave half of her genes to your mother, and then your mother gave half of her genes to you.

It is possible that the half you took is exactly the same as the half your grandmother gave. It is also possible that the half you took has no overlap at all with the half your grandmother gave. But on average, that is, in expectation, exactly half of the genetic material you took from your mother originated from your maternal grandmother. Continuing up the tree, your relatedness with your great-grandmother is one-half of one-half of one-half, that is: For siblings, the situation is a little bit more complex.

Consider first the case of two half-siblings half-sisters or half-brothers , that is, people who share just one parent. One special case is identical twins, who have identical genes and thus a relatedness coefficient of one.

What about first-cousins-once-removed, and all of that? We can summarise the relatedness coefficients of various relationships in a table: This table can be thought of as indicating your level of evolutionary imperative to protect and assist your various relatives.

That perspective was nicely summarised by the early evolutionary biologist J. Different life forms can lead to different mathematics: You can read more about the intricacies of bee relationships in the appendix! It seems that those Bedouins knew their inequalities well!

Families of all shapes and sizes Of course, the evolutionary imperative associated with relatedness coefficients does not tell the whole story. You would hopefully protect your spouse over your second-cousin even though, strictly speaking, your relatedness coefficient with your spouse is zero since you have no actual blood relationship. And, parents of adopted children should surely treat them just like biological children, despite the lack of true genetic connection.

Other family relationships can arise too. Meanwhile, a woman who marries your father after your mother becomes your step-mother or step-father, if the genders are reversed. Of course, your genetic relatedness coefficient with your in-laws and your step-relations is zero, since your relationship is through marriage rather than actual blood lines. Family relations can lead to unexpected surprises.

At a recent large family reunion, I met a young man whom I did not know. After some discussion, we determined that my great-grandfather was the brother of his great-grandmother — making us third cousins. Furthermore, my great-grandmother was the sister of his great-grandfather, too. That is, three generations earlier, a brother-and-sister pair had married off with a sister-and-brother pair.

I am honoured to share one sixty-fourth of your genes.