If not for the magic of recombinant DNA, about half the people reading this would be completely unrelated to one of their great-great-grandparents.
To understand why requires little more than simple arithmetic, but before getting to that it's worth looking at the other reason why we're less related to our ancestors than might be naively assumed, which is what's known in the technical literature as "extra-pair copulation", wherein a child is fathered by someone who isn’t the mother's socially pair-bonded partner. There's pretty good data suggesting that somewhere between 2 and 20 percent of children are conceived in this manner.
The range is broad because different societies have wildly different rates: in relatively egalitarian modern societies the number is at the low end. In societies with a high level of social stratification it tends to be higher. Somalia is apparently amongst the highest, despite adultery being punishable by death there.
Even a rate of 2 percent multiplies up over the generations, though: we all have sixteen great-great-grandparents and are the result of fifteen conceptions between their generation and ours. Our sixteen great-great-grandparents produced our 8 great-grandparents who produced our 4 grandparents who produced our 2 parents who produced 1 of us: 8+4+2+1=15.
If each of those conceptions had a 2% chance of being "extra-pair", what are the odds that someone has at least one male "social" ancestor that isn't a genetic ancestor?
The way we find the probability of something happening due to multiple different events--each of which has its own probability--is to take one minus the probability that it doesn't happen in any of those events. Otherwise we'd have to account carefully for the cases where the thing happened for multiple reasons: a great-great-grandmother's fling with the reddleman and a grandmother greeting the troops liberating Belgium a little more enthusiastically than she would admit to later on, say.
But while events that do happen can have multiple causes, events that don't happen don't happen in exactly one way, so the probabilities of them not happening compose by simple multiplication: if one child is conceived by its socially pair-bonded parents 98% of the time, then the probability for two children is 0.98*0.98, and so on.
For fifteen conceptions, the odds that all of them are what they seem to be—if there's a 2% chance of things being otherwise—comes out to 0.98 raised to the power of 15, which is equal to about 75%.
It follows from this that about a quarter of the people reading this are not related to one of their great-great-grandfathers. In contrast, almost everyone is at least somewhat related to all of their great-great-grandmothers. This is a fundamental inequality that could be addressed in the modern world by genetic analysis of every newborn and its parents, which will probably become routine eventually for purely medical reasons, although the social implications of redressing this fundamental inequality could be quite interesting as well.
There is, however, another reason why about half of us are less related to at least one of our great-great-grandparents than the others, and in this case the reason depends only on the simplest of simple arithmetic, although inevitably the complexities and nuances of biology make a mess of the pristine mathematical clarity when we dig deeper into the issue. But let's start with the simple arithmetic.
To see it at work, go back another couple of generations, to our great-to-the-sixth-power ancestors, of whom we have sixty-four. Humans have forty-six chromosomes in twenty-three pairs, with one of the each pair inherited from each parent.
So if we go back six generations we have sixty-four ancestors, but we only have forty-six chromosomes. Ergo, in the simplest case (which is not the real case, because biology gets complicated as I'll explain below) we aren't related at all to eighteen of our sixth-generation ancestors, because their chromosomes got lost in the shuffle. In fact it's worse than that, because some of our ancestors got lucky and we inherited more than one chromosome from them--we might have chromosome 2 and 13 from our great-great-grandmother on the line of purely maternal descent, say--which leaves a couple of others in the dust.
When applied across four generations, this means that about half of us are missing a chromosome from at least one of our sixteen great-great-grandparents.
If that was the whole story, though, people would be dropping out of evolutionary history all the time, which would be wasteful even by the standards of kindly old Mother Nature, who dooms the vast majority of every generation of every species to early and basically pointless death.
What comes to the rescue is recombination, which happens during meiosis, the process where cells with a full complement of chromosomes (46) divide to create eggs or sperm that have just twenty-three. Meiosis is still a poorly-understood process in which chromosomes are shunted around and paired up, so the paternal and maternal versions of chromosome 10, say, are physically lined up with each other. At this stage they can swap segments, exchanging maternal genes for paternal and vice-versa, which means the chromosomes that wind up in sperm and egg cells are not exact replicas of what we ourselves received from our parents.
They're pretty close, though.
Recombination is an important process in mixing up our genes so that the parasites and diseases that pursue every species through evolutionary time have a harder go of it. But it falls far short of randomizing our chromosomes, which would make us unrecognizably dissimilar to any of our grandparents, whose unique capabilities and vulnerabilities are a product of all their genes combined. While individual genes matter, and can be selected for under special circumstances, the dominant unit of selection is the organism, which has to work as a whole to succeed in its environment.
It follows from this that some of our ancestors lose out relative to others in the chromosomal lottery, which--looked at from another perspective--contributes to the diversity of our descendents.
Very interesting! I hadn’t really thought about it previously. Appreciating the diversity of topics here!