Recent posts got me thinking about genetic inheritance, and how people are often rather interested in tracing their lineage, especially if it leads back to some significant historical figure. I thought it might be fun to do some math, to try to work out how much of a person’s genome might be traceable to a particular person.

Common descent predicts that if we go back far enough, all humans will share some common ancestor. Interestingly this does not mean that this common ancestor was the "first" human, nor does it mean that all other humans living at the time had their lines extinguished.

In the case of male lineage we have the rather interesting situation that the Y-chromosome is carried only by men, and so is always passed directly from father to son, and we also have a history of female lineage in that mitochondrial DNA is passed directly from mother to child. So every male has the same Y-chromosome as his father (ignoring mutations) and every person has the same mitochondrial DNA as their mother (ignoring mutations).

What this means is that we can create two trees of descent for all humanity, one for the Y-chromosome and one for mitochondrial DNA, where the branching of these trees can be determined by the patterns of mutation in the respective genes. At the top of these trees, we find Y-chromosomal Adam and Mitochondrial Eve. What’s really interesting is that these two actual people (who really did exist) lived tens of thousands of years and thousands of miles apart.

In Dan Brown’s moviebook The DaVinci Code, the big secret that was being protected was [SPOILER ALERT] that Sophie, grand-daughter of renowned curator Jacques Saunière, was a direct descendent of Our Lord Jesus Himself, ie she carried the Holy Blood. I wondered recently, what are the odds that any of His Holy Chromosomes might have made it into her DNA?

A naive approach to this question involves looking at the likelihood that any one chromosome might be passed on to the next generation, and then multiplying that by the number of generations that have passed since. A safe bet for the number of generations seems like 100, with an average generational gap of 20 years (probably it would be shorter on average which is why I consider this a safe bet).

A parent passes 23 chromosomes to each offspring, so a given chromosome has a 1/2 chance of being passed on within any particular generation, which means it has a 1/4 chance of being passed down 2 generations, a 1/8 chance of being passed down 3, etc etc. In general:

probability that chromosome is passed to an x-generation descendant = 1/2^x

so the likelihood that Sophie would inherit any particular chromosome from Jesus through any particular line of descent would be 1/2¹⁰⁰, or less than 1 in a million-trillion-trillion. From this we can calculate that the chances that she inherits any of His DNA in this manner are 1-(1-1/2¹⁰⁰)²³, or less than 1 in ten-thousand-trillion-trillion… slightly better odds, but still not great.

As I mentioned above, this is a naive approach, and only valid as an answer if at least one of the following is true:

1. Each of her ascendants was the only child to reproduce. This would be true if for instance each generation had only a single child (which may perhaps be feasible if they were being kept secret and protected as the vessel for the Holy Blood down through the ages, but still it seems unlikely– given mortality rates the line would almost certainly have perished)
2. No direct decendent of Jesus ever reproduced with any other direct descendent of Jesus, so no kissing cousins, be they first, second or ninetieth. This also is exceedingly unlikely, because assuming natural birth rates the genes would have rapidly diffused to the point where in any given region everyone is at least a ninth or tenth cousin– at some point the descendants of Jesus would run out of people to breed with if they were so picky.

So assuming that Jesus and his descendants reproduced at the same rates as other people, his DNA would have spread far and wide (just like everyone else’s) and a significant portion of the current population would have inherited some part of his genome by direct descent. At this point, apart from the vanishingly small likelihood mentioned above Sophie would have the same likelihood of inheriting Jesus’ genes as anyone else who can trace some ancestry back to the region about two thousand years ago, which would include almost anyone of African, European or Middle Eastern descent. In short, I would have about the same chance of inheriting DNA from Jesus as Sophie would.

To calculate this likelihood (that I might have inherited some DNA from a particular person living in Jerusalem about 2000 years ago) is really really complex, but I can at least get the upper bound by estimating a minimum population size which could have contained all of my ancestry from 2000 years ago. Let’s assume that all my ancestry was at this time encompassed within the Roman Empire, and the Empire had a population of 4 million. Let’s now assume that only 2 million of those people went on to reproduce. Let’s further assume that only 1 million of those had enough fertile children and grandchildren to ensure likely survival of their lineage.

Now I can roughly estimate the odds that any given chromosome in my body might be passed down directly from any particular fertile individual living at that time. Since each of my chromosomes has to trace back to someone within that nominal population of a million, the chances for any given chromosome are roughly 1 in a million. Since I have 46 chromosomes in total, the chances that any of my chromosomes come via direct descent from any particular person are 1-(1-1/1,000,000)⁴⁶, or less than 1 in twenty thousand.

So, even if you could trace your line back to Jesus Himself, the chances that any of His genetic material would survive in you today is rather remote. We have an upper bound, assuming Jesus and His descendants were prolific and enjoyed mixing it up with distant relatives on occasion, of about 1 in twenty thousand, and a lower bound of virtually zero if the Holy Blood was passed down from one offspring to another in a single non-branching line of descent.

The only case that would guarantee His genes being passed all the way down the tree is in the case of an unbroken patrilineal line (via the Y-chromosome) through father to son all the way down– and it would truly be interesting if some such descendant could be found, because that Y-chromosome would have to have come originally from the father of Jesus, and I’m sure a lot of people would be rather keen to get a look at it.