Common ancestors

I’m quite pleased that the last “More or Less” question that’s been selected for me happens to be one of my pet topics (I’ve also written a cut-down reply for the magazine section of the BBC news website). The original email 1 was rather long (as is, inevitably, this post), but essentially, the question is this

A listener, Jonathan Triggell has been looking at the Bible. In particular he’s interested in Jesus’ lineage. The Bible says Jesus was in the line of King David – which is important because the Messiah was expected to be of royal descent.

But it also has this to say about David’s son, Solomon

King Solomon, however, loved many foreign women besides Pharaoh’s daughter—Moabites, Ammonites, Edomites, Sidonians and Hittites. They were from nations about which the Lord had told the Israelites, “You must not intermarry with them, because they will surely turn your hearts after their gods.” Nevertheless, Solomon held fast to them in love. He had seven hundred wives of royal birth and three hundred concubines, and his wives led him astray.

Jonathan’s question is this: if Solomon had about a thousand wives and mistresses, assuming he fathered children with many of them, wouldn’t it be the case that by the time of Jesus – many generations later – pretty much everyone in Israel could claim to be a descendant of King David?

It might sound like a question for a pub quiz, rather than a science journal. But the fundamental mathematics behind family trees forms the basis of evolution and genetics, and so cuts to the heart of modern biology. In fact, I reckon there’s a strong case for teaching genetics and evolution by first talking about family trees and genealogy – a subject which is of immediate personal relevance to people. Regardless of my personal opinion, genealogy and genetics has led to number of relevant research published in journals of statistics (Chang, 1999), biology (Matsen, Evans, 2008), and even physics (Derrida, Manrubia, Zanette, 2000).

My answer can be summarised in 5 steps

1) Following both males and females through family trees results in numbers that explode exponentially as the generations tick by. 
As implied by Jonathan’s musings, there’s a massive mathematical difference between following an entire family tree, and following a single lineage (e.g. the male line, which is the normal sexist view as expounded in the bible). For example, imagine a constant-sized population, neither shrinking or expanding. If we look at all the descendants of a single parent, on average we’ll find two children, four grandchildren, eight great grandchildren, and so on: an exponential increase in descendants. In contrast, if we follow only the male line, we expect one son, one, grandson, one great grandson, and so on. Of course, that’s an average. A parent may not have any sons, or may have 2 or 3, so in specific instances, the numbers will fluctuate. Nevertheless, there is no expectation that number of male line descendants will increase or decrease in any particular case. So we don’t expect recent 2 male lineages to dominate a population: if they do, it may be because of unusually successful males, such as Ghengis Khan (Zerjal, Xue, Bertorelle, Wells, Bao, Zhu, Qamar, Ayub, Mohyuddin, Fu, others, 2003), or (presumably) King Solomon. This neither-increasing-or-decreasing argument applies equally to the female lineage, or in fact, for anything which has a probability of 1/2 or being transmitted, such as the overwhelming majority of your DNA 3. But if we follow all the descendants, not just the men, we might well find nearly everyone descended from Ghengis Khan or Solomon: exponential increases often produce surprising results. I’m assuming that, in these days of enlightened sexual equality, we’re are indeed interested in the descendants of King David through any route, not just his sons, his son’s sons, and so on.
2) A reasonable guess is that there are at least 35 generations separating King David and Jesus
As with any exponential growth, the number of generations is crucial. There are almost exactly 1000 years between Jesus and King David. Where we have good family records, for instance in rural Canadian (Tremblay, Vézina, 2000) and Iceland (Helgason, Hrafnkelsson, Gulcher, Ward, Stefánsson, 2003) populations, the average generation time is not twenty-five, but more like thirty years (although for females it is slightly less). Taking a massive leap of faith, and extrapolating that to iron-age palestine, gives around 33 generations. I suspect the actual generation time would be a bit lower than thirty years – as Jonathan pointed out in his full email, women reproduced pretty early (although high status men may have carried on reproducing into old age). 35 generations seems not unreasonable. An alternative leap of faith is to go with chronologies in the bible. Luke (3:23–38) lists 42 generations between King David and Jesus through the male line. Matthew lists 27 generations, but he definitely skips 4, and almost certainly more 4. Again, 35 seems a reasonable lower bound.
3) It is easier to do the maths backwards in time, looking at the number of ancestors of a set of people rather than the number of descendants of a single individual
The mathematical idea which has revolutionised the analysis of DNA sequences in the past 30 years is called “the coalescent”. It’s the idea that you can model genetic evolution by taking a sample of people and go backwards in time, working out the probabilities of where their ancestral DNA sequences might have come from 5. Similarly, you can do the same with actual ancestors, modelling what happens in theory if you consider parents, then grandparents, then great grandparents, etc. (Chang, 1999; Ohno, 1996). This produces an equivalent to our theoretical explosion in number of descendants. It’s been called the genealogical “paradox” (Pattison, 2007), and states that each of us must have 2 parents, 4 grandparents, 8 great grandparents, etc. Take (say) 35 generations back, and we must thus have 235, or 34 billion ancestors – more than the number of people alive in the world today. The resolution to this paradox is that many of these ancestors are duplicates – they represent the same person who is related through multiple overlapping paths though the family tree. This sort of inbreeding is famously seen in royal families, but actually exists, albeit between more distant relatives, for all humans. In response to one of Jonathan’s questions, we can indeed calculate how much duplication there is – sometimes known as “sibling overlap” (Ohno, 1996). Unsurprisingly, duplication is negligible for the first few generations, but then gets more and more important. Instead of giving the detail (which you can look up in the original papers) I’m going to take a different, and – I think – more intriguing route to answering his question.
4a) Theoretically, the most recent common ancestor of everyone in a randomly-mating population is amazingly recent (e.g. in a population the same size as in Jesus’ time, we find a common ancestor of everyone about 20 generations into the past)
This is something that I helped explain when co-authoring a chapter in “The Ancestor’s Tale” (Dawkins, 2004, 39-44). Because of the explosion in number of ancestors, you don’t have to go many generations back before you find common ancestors. You can model this by imagining a stable population of N humans. Take a handful of them, and randomly pick a father and a mother for each from among the N people in the previous generation. Now randomly pick 4 grandparents from the generation before that, and so on. Mathematically, it turns you need only go back on average log2N generations before every single person in the population holds at least one ancestor in common (Chang, 1999). The population of Israel in Jesus’ time was a few million at most (Broshi, Finkelstein, 1992). Log2(1 million) is 20 generations.
4b) An extension of this argument shows that only need go back a touch further (here, 35 rather than 20 generations) until every single person shares all their ancestors. Moreover, at this point, about 80% of the population turn out to be common ancestors.
There is a point in the past – the “identical ancestors” point – at which all ancestors are shared. Further back than this, if someone is your ancestor, they are also the ancestor of everyone else in your population. In the simplified theoretical model above, this only takes an average of 1.77 times longer (35 rather than 20 generations). If any person at that point is not an ancestor, it must be because they didn’t leave any children, or their children didn’t leave any children, etc etc. It turns out this is quite rare. Only 20% of people leave no descendants whatsoever. The other 80% eventually become ancestors of everybody (Chang, 1999). If we apply this simplistic model to Jesus and his one million contemporaries, almost exactly at the time you get back to King David, we expect every one of them to be able to trace their ancestry not only back to David, but also to about 80% of King David’s subjects, from merchants to swineherds. In summary, according to this simplified model, a random person in King David’s time (including King David himself), assuming they leave any descendants, will become an ancestor of everyone in Israel some time between 20 and 35 generations later down the line.
5) The details of the specific King David/Jesus case serve primarily to reduce the number of generations involved.
Of course, our imaginary population of a million randomly mating individuals is massively simplistic. We haven’t accounted for changes in population size, immigration, separate or isolated groups within the population, or indeed King Solomon’s impressive reproductive rate. Let’s take those in turn:
i) changes in population size
There were a couple of hundred thousand people in Israel round about Solomon’s time, which has increased to a few million in Jesus’ time (figure 2 from (Broshi, Finkelstein, 1992)). This would happen if every couple produced an average of 2.1 (rather than 2) reproductively successful children. Such a population expansion would spread family trees more widely and more rapidly than in our simple model (this is a standard result of coalescence theory). That means we don’t even need to go back to King David to get the required result. In fact, the population of Israel didn’t simply expand – there were population declines, then re-expansions, most drastically caused by the Assyrian invasions around 700 BCE (Broshi, Finkelstein, 1992). Population “bottlenecks” like this are even more effective in spreading ancestry wide and fast.
ii) immigration
Certainly many people would have immigrated into Israel during that time period. But this will only affect the calculations if the immigrants never interbred with the native population. That’s because there’s an 80% chance that a single interbreeding event will be enough to “contaminate” the family tree of any immigrant population, and since these populations are small, it should only take a few generations until all the immigrants have a native person in their ancestry. Nevertheless, it could be the case that in Jesus’ time there existed a small handful of people within very recent immigrant populations who were not descended from King David. Similarly, I think it’s reasonable to argue that the occasional interbreeding between Middle Eastern nationalities and Brits a few tens of generations ago is probably enough to ensure that basically all the population of the UK are also direct descended from King David.
iii) isolated subpopulations
The one thing that stands a chance of scuppering our calculations is if the population is split into isolated groups. However, as in the argument above, to be considered separate, these groups need to basically never interbreed with each other. To quote one of the paper on this subject, “substantial forms of population subdivision can still be compatible with very recent common ancestors.” (Rohde, Olson, Chang, 2004). In fact, even using current DNA studies, you can almost always detect distant shared relatives between distinct human populations (Henn, Hon, Macpherson, Eriksson, Saxonov, Pe'er, Mountain, 2012).
iv) massive reproductive success of one person
Solomon may have been an extreme case, but high-ranking men in the bible often mated with large numbers of people: maidservants, slaves, and so forth (Betzig, 2005), and this is often the case in early agricultural civilisations (Betzig, 2012). As with population bottlenecks, this produces very wide, rapidly expanding family trees, and reduces the time to common ancestry 6.To verify the numbers and to demonstrate the effect of a single large family, I knocked up a simple simulation, which you can run for yourself if you like 7. As expected, in a randomly-mating population of a million, if an individual leaves descendants, it takes about 34 generations before these descendants encapsulate the entire population. But if an individual leaves, say 100 children, not only are they basically assured of future representation, but the number of generations reduces from 34 to 18. I think this is clearly shows that, regardless of the exact details, we can confidently expect everyone in the population of Israel either in Jesus’ time (or even today 8) to be a direct descendant of David and also of Solomon.

When you try applying these ideas to the entire world population, you can get surprising figures (Rohde, Olson, Chang, 2004). Accounting for inbreeding, local populations, occasional migration, etc , it seems as if it only takes about 100 generations (i.e. less than 3000 years!) before you find someone in the world who is a direct ancestor of everyone alive today (Lachance, 2009), and less than twice this time before everyone alive to day has exactly the same ancestors (although, of course, through different paths). Think about this forwards in time. It means every as long as your children leave some children, you personally are assured of being a direct ancestor of all of humanity in a few thousand years’ time. What a legacy!

References

Betzig, L. (2012). Means, variances, and ranges in reproductive success: comparative evidence. Evolution and Human Behavior. doi:10.1016/j.evolhumbehav.2011.10.008
Betzig, L. (2005). Politics as Sex: The Old Testament Case. Evolutionary Psychology, 3, 326–346.
Broshi, M., & Finkelstein, I. (1992). The Population of Palestine in Iron Age II. Bulletin of the American Schools of Oriental Research, 287, 47–60. Retrieved from http://www.jstor.org/stable/1357138
Chang, J. T. (1999). Recent common ancestors of all present-day individuals. Advances in Applied Probability, 31(4), 1002–1026. doi:10.1239/aap/1029955256
Dawkins, R. (2004). The ancestor’s tale : a pilgrimage to the dawn of life. London: Weidenfeld & Nicolson.
Derrida, B., Manrubia, S. C., & Zanette, D. H. (2000). Distribution of repetitions of ancestors in genealogical trees. Physica A: Statistical Mechanics and its Applications, 281(1), 1–16. Retrieved from http://www.sciencedirect.com/science/article/pii/S0378437100000315
Helgason, A., Hrafnkelsson, B., Gulcher, J. R., Ward, R., & Stefánsson, K. (2003). A populationwide coalescent analysis of Icelandic matrilineal and patrilineal genealogies: evidence for a faster evolutionary rate of mtDNA lineages than Y chromosomes. American journal of human genetics, 72(6), 1370–1388. doi:10.1086/375453
Henn, B. M., Hon, L., Macpherson, J. M., Eriksson, N., Saxonov, S., Pe’er, I., & Mountain, J. L. (2012). Cryptic Distant Relatives Are Common in Both Isolated and Cosmopolitan Genetic Samples. PLoS ONE, 7(4), e34267. doi:10.1371/journal.pone.0034267
Lachance, J. (2009). Inbreeding, pedigree size, and the most recent common ancestor of humanity. Journal of Theoretical Biology, 261(2), 238–247. doi:10.1016/j.jtbi.2009.08.006
Matsen, F. A., & Evans, S. N. (2008). To what extent does genealogical ancestry imply genetic ancestry? Theoretical Population Biology, 74(2), 182–190. doi:10.1016/j.tpb.2008.06.003
Ohno, S. (1996). The Malthusian parameter of ascents: What prevents the exponential increase of one’s ancestors? Proceedings of the National Academy of Sciences, 93(26), 15276. Retrieved from http://www.pnas.org/content/93/26/15276.short
Pattison, J. E. (2007). Estimating inbreeding in large, semi-isolated populations: Effects of varying generation lengths and of migration. American Journal of Human Biology, 19(4), 495–510. doi:10.1002/ajhb.20610
Rohde, D. L. T., Olson, S., & Chang, J. T. (2004). Modelling the recent common ancestry of all living humans. Nature, 431(7008), 562–566. doi:10.1038/nature02842
Tremblay, M., & Vézina, H. (2000). New estimates of intergenerational time intervals for the calculation of age and origins of mutations. The American Journal of Human Genetics, 66(2), 651–658. Retrieved from http://www.sciencedirect.com/science/article/pii/S0002929707634375
Zerjal, T., Xue, Y., Bertorelle, G., Wells, R. S., Bao, W., Zhu, S., … others. (2003). The genetic legacy of the Mongols. The American Journal of Human Genetics, 72(3), 717–721. Retrieved from http://www.sciencedirect.com/science/article/pii/S0002929707605874

Notes:

  1. Here’s the relevant portion of Jonathan Trigell’s email

    You probably know that Jesus was said to be of the line of David, who was the greatest Jewish king. But I was thinking about this the other day and it occurred to me that David’s son and successor King Solomon was said to have had 700 wives and 300 concubines (or definitely had 700 wives and 300 concubines, for those who believe in the inerrancy of the Bible). So actually there were probably thousands upon thousands of people in first century Palestine who could quite correctly claim David as an ancestor (possibly almost everyone Jewish could).

    Scholars put Solomon’s reign from circa 970 to 931 BC, so if we take 950 years for simplicities sake. And assume a generation is 25 years (This is probably generous: virtually all Jewish men at that time were married before they were 21 and girls usually at around 15). And assume that each person has 3 children (again this is a rough but  cautious guess: families were typically large – having many children was seen as a sacred duty – but infant mortality was very high, so if you assume 3 children reaching adulthood then that is probably the conservative end of the spectrum, and may balance for those who died childless). Population was expanding in spite of disease and war, so 3 is the minimum whole number to consistently be doing so, but I’m hoping you can improve on my guesswork.

    So after those 38 generations how many people would be able to claim the line of David based on Solomon’s 1000 wives and concubines?

    Using 3 this would be 3,000 and if they then had 3 children each reaching adulthood then this would become 9,000 with the next generation becoming 27,000.

    If the original 1,000 is multiplied by 3 for each succeeding generation, after 38 generations the number would I believe exceed the number of people in the world then.

    1000 x 3 raised to the power 38  (3 x3x3 …x3)

    This equals 1.35 x 10 to the power 21, which is many times more than the people in the world even today. Certainly far more than the Jewish population of first century Palestine.

    But obviously this figure isn’t going to be the true number, because an unknown (but increasing over time) percentage of those descendants would certainly have eventually married other descendants, so their children would be duplicates.

    So the key is obviously to figure out how many of those children in a closed system would be duplicates. Which may be impossible, I don’t know? Is there anyway of computing that at all?

    If there were only three million native people in the land of Israel in the first century (which is one estimate I have read) then would they all be related to David? In fact even if you assumed that Solomon ‘only’ had a couple of hundred children (and obviously this initial unknown is probably the biggest flaw in any computation) then after 38 generations, would virtually everyone still be related to him?

    I believe that 0.5% of the entire world’s population are currently descended from Genghis Khan (or at least they carry a specific marker on the Y chromosome traceable to a common ancestor from the Asian Steppe who history suggests could only have fathered that many children at that time if he was Genghis Khan) and that figure as a percentage naturally increases with each generation.

    Is there any way of establishing duplicates in this Israel puzzle, or by how many times the average person was related to King David, or at least improving on my probably flawed and shoddy assumptions?

  2. Just by random change, one lineage will eventually dominate any finite population, but that is expected to take a large number of generations.
  3. The idea that individual “genes” (or more precisely, DNA variants) neither spread inexorably through a population, nor are diluted out of existence (rather, they perform a “random walk”), is what lead to the general acceptance of Darwin’s theory of evolution in the early 20th century. The basic concept is often rather convolutedly introduced to biology students as “Hardy-Weinberg” equilibrium, a complex sounding word for an almost trivial concept.
  4. As with many biblical topics, the wikipedia page is pretty good on the debate, and through exactly which line (Mary or Joseph) the line is purported to have come. Unfortunately, it seems unclear if any of the other genealogical links in the bible are actually maternal rather than paternal
  5. Not only is it useful because we can collect detailed information (e.g. DNA sequences) from current-day individuals, and work backwards, but it also automatically excludes having to look at those ancestors who didn’t leave any descendants
  6. In fact, it is basically equivalent to a population bottleneck then expansion which only applies to males
  7. Simply download the R statistical software packageand run the forwards simulation of a randomly mating population below, which takes a good few minutes to run:


    replicates <- 200;
    N <- 1000000;
    num.children <- 1;
    max.gens <- 35;
    descendants <- replicate(replicates, {
    cat('.'); #keep an eye on how we are doing
    pop <- rep(1, N) #at the start, all individuals in pop have value = 1
    pop[1:num.children] <- 0 #flag up the focal ancestors with value = 0
    pop<-sample(pop) #randomize them
    dim(pop) <- c(N/2,2)
    colnames(pop) <- c("Males", "Females")
    n.descendants <- rep(NA, max.gens)
    for (i in 1:max.gens) {
    # flag up descendants by simple multiplication - any individual with father or mother == 0 gets flagged as 0
    pop[] <- sample(pop[,'Males'], N, replace=TRUE) * #pick N random fathers, a la Wright-Fisher model
    sample(pop[,'Females'], N, replace=TRUE) #pick N random mothers, a la Wright-Fisher model
    n.descendants[i] <- N-sum(pop)
    };
    return(n.descendants);})
    rownames(descendants) <- paste("Gen", 1:max.gens)
    print(descendants)

  8. That is, excluding those people who have moved to Israel recently from isolated oceanic islands, and who have not bred into the population

37 thoughts on “Common ancestors

  1. I was interested in the BBC article, but I have to go back one more step to ask this question: If Jesus is supposed to be God, according to Christianity, how does he have a human lineage? And even if he did, it couldn’t possibly be through Joseph. I’m confused…

    • Well, that’s apparently why some theologians say that at least one of the lineages was Mary’s. It’s not my area, I’m afraid,

  2. My Pa is in his 60s and has pregnated women 8 times (five of which in the last 6 years). I expect that he will have two or three more before he reaches 65 as his women find it more profitable than actually working for a living and he has no self-control.
    As a result he lives VERY poorly and his first lot of children are resentful as they will no longer receive any financial inherritance.

  3. I really enjoyed reading your blog about the common ancestor. I found it easy to understand, even though the numbers were difficult to internalise. Nanna 5

  4. Would you mind elaborating more eg on the Australian Aborigines, who appear to have had been isolated for rather more than 3,000 years before, say, 1606. Or maybe weren’t?

  5. So the Bible is correct in terms of Jesus’s lineage?

    In Luke he begins with Joseph and goes back to David, Abraham and Adam (Luke 3:31, 34, 38). He is giving evidence to show that Jesus “will be great and will be called the Son of the Most High; and the Lord God will give Him the throne of His father David; and He will reign over the house of Jacob forever, and His kingdom will have no end” (1:32-33).

    Just trying to understand where this article is coming from, only it seems as though a question is raised and then confirmed but the confirmation is never really summarized? For example; ‘Yes Jesus did come from the line of King David as the bible states’. (and then I guess added to that a personal opinion that this is to be expected as almost everyone did so the statement is absurd but still remains true).

    • Regardless of whether either of the the exact male-line lineages listed in the bible are correct, it seems indisputable that Jesus (as well as the vast majority of the population of Israel at that time) were direct descendants of King David.

  6. Are you aware of the research by myself and Kit Sturges some twenty years ago. We claim that we were the first to measure the loss of English surnames through six centuries. We have prepared a Second Edition but we have not found an honest publisher.

  7. 3000 years? so its possible we all had a common ancestor 3000 years ago? Adam? or would it be Noah as everyone else drowned…

  8. *****[rubbish]!

    The baby that Solomon refused to divide was not related to Solomon or his dad. What about all his decendants?

    You might be good at biology, but statistics is a dangerous thing in the hands of the unwary.

    • I’m not sure what you are getting at. I’m not saying people in Solomon’s time were all descendants of David. I’m saying that everyone in Israel in Jesus’ time (1000 years later) we likely to be direct descendants of David (and Solomon, for that matter). In fact, they are also likely to be descendants of the majority of the population in Solomon’s time, including (if he reproduced), the undivided baby in the Solomon story.

      Oh, and I hope you don’t mind me editing out your swearing …

  9. it seems to me that you have under-stated the amount of isolation between human populations. i believe that the populations of australia and the americas have been totally separate from (and had no contact with) semitic, european and asian peoples; and that this total isolation means that we need to go MUCH further back to find a common ancestor. your model makes mathematical sense, of course, but seems to ignore the huge barriers to genetic intermingling.

    • You’re right that the prediction relies on a (very) small amount of interbreeding between populations in different parts of the world. Any groups that have been completely isolated for 3000 years can’t possibly have a most recent common ancestor (MRCA) more recently than that. I didn’t go into this in the original post as the question was specifically about Israel. But the fascinating thing is that, from what I’ve read, archaeological evidence indicates a small amount of interchange between people in all known cases. It’s apparently not true that there was literally no contact in these cases (and it’s important not to fall into the trap of relying on a single piece of DNA, such as mitochondria or the Y chromosome, to deduce whether there was interbreeding). I highly recommend reading the 2004 Rhode, Olson & Chang paper in Nature (try http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/NatureCommonAncestors-Article.pdf). To quote

      “No large group is known to have maintained complete reproductive isolation for extended periods. The populations on either side of the Bering Strait appear to have exchanged mates throughout the period documented in the archaeological record[14]. Religious isolates such as the Samaritans occasionally have absorbed migrants from outside the group[15]. Even populations on isolated Pacific islands have experienced occasional infusions of newcomers[16].”

      They use a computer simulation with groups not only isolated by distance across the world, but also with restricted, historically timed migration across specific regions, such as the Bering Straits, N/S America, and Australasia, and they find:

      “Even if rates of migration between some adjoining populations are very low, the time to the MRCA tends not to change substantially. For example, with a migration rate across the Bering Strait of just one person in each direction every ten generations, rather than the ten per generation in the more conservative simulation described earlier, Tn only increases from 3,415 years to 3,668 years.”

      They also point out:

      “Actual migration rates among populations are very poorly known and undoubtedly have varied considerably in different times and places. Studies of hunter-gatherer groups and subsistence agricultural communities have found that anywhere from 1% [19] to as much as 30% [20] of mates are from outside the group.”

      Of course, that doesn’t exclude the existence of a few, extremely isolated populations, such as was supposedly the case for Tasmania. The calculations for the MRCA of the whole of humanity are rather sensitive to this effect, so it may be that there is a tiny fraction of humanity who lie outside the recent genealogical tree. I’d be interested to know of any substantiated examples of this. Either way, it shouldn’t invalidate my statement about the Davidic ancestry of Jesus.

      [14]. Fitzhugh, W. W. & Chausonnet, V. (eds) Crossroads of Continents: Cultures of Siberia and Alaska (Smithsonian Institution Press, Washington DC, 1988).

      [15]. Bonne ́-Tamir, B. et al. Maternal and paternal lineages of the Samaritan isolate: Mutation rates and time to most recent common male ancestor. Ann. Hum. Genet. 67, 153–164 (2003).

      [16]. Morton, N. E., Harris, D. E., Yee, S. & Lew, R. Pingelap and Mokil atolls: Migration. Am. J. Hum. Genet.
      23, 339–349 (1971).

      [19] Weiss, K. M. & Maruyama, T. Archeology, population genetics and studies of human racial ancestry. Am. J. Phys. Anthropol. 44, 31–50 (1976).

      [20] Ward, R. H. & Neel, J. V. Gene frequencies and microdifferentiation among the Makiritare indians. IV. A comparison of a genetic network with ethnohistory and migration matrices; a new index of genetic isolation. Am. J. Hum. Genet. 22, 538–561 (1970).

  10. But surely, as Jesus was “the son of God”, the descriptions in the bible of the male line back to David are wrong?

    Perhaps he was related to David via Mary – but not Joseph as the latter supposedly had nothing to do with the conception!

    • Of course, it depends on whether you believe in the virgin birth of Jesus. The Mary point is well documented in the Wikipedia page I linked to in the blog article.

  11. Hi,

    I think your assumptions are all wrong.

    1) Firstly, there are 2 lineages of Jesus mentioned in the Bible. Luke’s gospel is through Joseph, Matthew gospel’s is through Mary. In jewish tradition, which tribe you are in is via the female family line.

    2) You assume random matings. Humans aren’t like this. Certain groups do not interbreed, as there are cultural barriers, so your mathematics treating human breeding like random events cannot apply. This in particular applies to royal bloodlines, class etc. not saying it doesnt happen, but it changes the mathematics considerably, and your aguement breaks down.

    3) Surviving children who in turn have children cannot be statisically normalised in the way you have done. Mortaility rates in children at the time in question was very high, which has been ignored in your calculations. Some families have high survival rates, others low. Family trees are not normally distributed as a result.

    3) your “inbreeding events” will be a lot higher than you have postulated. this is because in smaller communities, everyone will have a common ancestor within a certain time – and the further back in time you go, these common ancestors will be continuously repeated. But outside those communities interbreeding is very low, or nearly non existent. Its the SIZE of the community that therefore becomes the deciding factor. In the modern world, we have a global village, but this is a modern phenomena. Prior to the modern world, communities were small.

    4) taking this further, you have also neglected the fact that there were 12 tribes of Israel – and these tribes did not commonly interbreed.

    Your problem here is you have treated the entire Israel population as a single community. That is where your assumptions fall down, and your calculations become invalid.

    Also, the idea that 80% of us living will eventually be an ancestor to the whole planet is also flawed. this is because as the population increases more and more people choose not to have children. This would mean that 4 out of 5 people will have at least one child in their lifetime. This is a broad sweeping statement, and depends on where you live, affluence, culture, religion, etc… ie, One person in India may have 10 children for example, while more than half the population of Britain choose to have none – yet the numbers, when averaged, come out the same.

    one more thing – In Solomon’s case, just because on paper he had 300 wives, and 700 concubines, does not mean he .. er .. serviced them all. Or indeed they all had children. Wives at the time were seen as a symbol of wealth and success. The point being that Solomon was extremely wealthy. He was supposed to be very wise too – the number of wives he had seems to counters that argument…

    • Thanks for the well thought out (and polite!) comments. I’ve replied to a number of them above. Your point 1) is well taken, and I think covered in the wikipedia article on the genealogy of Jesus. Point 2) is what geneticists call “population substructure”. Even if you take this into account, it doesn’t much change the result (e.g. see the Lachance paper from 2009). For point 3, the assumption in these models is not that every family has 2 children, but that family size is basically poisson distributed – some people have 0, some 1, some 2, some 3, etc. This would be seem even with astronomically high infant mortality, as long as children die at random. If, however, different families have different mortalities, or some are more reproductively successful than others, that will cause a much large variation in reproductive family size. That should only serve to decrease the time to the most recent common ancestor (MRCA). You have a good point (later in your comment) that it will, however, decrease the figure of 80% of the population becoming a universal common ancestor. I’m not aware of any papers that specifically investigate this, but it’s certainly worthwhile, and an easy calculation to make. Your other point 3) I’ve tried to tackle in my reply to Miko Sloper above – essentially, archeology suggests that all known historical populations showed some degree of interbreeding with neighbours (this is also substantiated by genetic data), and this is enough to generate a very recent MRCA. If it’s true for groups that are extremely religiously distinct, I’d be confident that was also true of the 12 tribes of Israel (your point 4).

      As for reproductive success of Solomon and the like, then try looking at

      Betzig, L. (2005) Politics as Sex: The Old Testament Case. Evolutionary Psychology. 3: 326-346

      She also has a less anecdotal paper plotting variance in reproductive success versus the mean (where under poisson assumptions, the variance should equal the mean) for a number of different tribal groups:

      Betzig, L. (2012) Means, variances, and ranges in reproductive success. Evolution and Human Behavior 33. 309–317

      I don’t have any particular opinion on those papers. I don’t think they invalidate the general point

  12. Um, have you considered the fact that 3000 years ago there had been no geneflow between the new world and the old world populations of humans for thousands of years? Simple facts like this one utterly invalidate the ramblings of a purely theoretical model. Viz.: No one living in South America 3000 years ago was any old worlder’s ancestor. The idea just sounds kind of dumb when you say it out loud. Sorry, man. Intellectual *******[posturing] not welcome on my BBC.

    • It’s not my area, but according to what I’ve read, that’s not actually true. The computer simulation in the Rohde, Olsen & Chang paper specifically took account of highly restricted (but nevertheless present) mating across the Bering Straits and also into South America, in line with (they claim) the archeological evidence. See my comment to Miko Sloper above.

      You’ve also got to be careful not to equate gene flow with mating. After some time into the past, there will be many matings which do not leave signals in any of the gene trees. In my opinion, that’s why relying on just mtDNA or Y chromosomes to tell the story of humanity can be extremely misleading, as has been somewhat shown by the recent evidence of breeding between Neanderthals and modern humans.

      Apologies for editing your post to be more “family friendly”.

  13. The original question is very interesting but incorrect in it’s assumption that Jesus was descended from David through Solomon. The genealogy of Jesus detailed in Luke’s Gospel Chapter 3 clearly shows in verse 31 that Jesus was descended, not from Solomon but, from Nathan the son of David, the son of Jesse. In verse 23 it says that Joseph was the son of Heli, which he was ‘in-law’, as Heli was the father of Mary the mother of Jesus. The genealogy in Matthew Chapter 1 is that of Jesus through Joseph (not his natural father) who was descended from Solomon (verse 6). Verse 16 shows that Joseph’s father was Jacob.
    Having corrected the question this may make the answer a little easier to arrive at as Nathan did not have as many wives as his more famous brother.
    The throne of David continued through Solomon right up to the daughters of Zedekiah (Jeremiah Ch 43). These princesses were not killed but escaped with the prophet to continue the royal line. This royal line will continue for ever ( 2 Samuel 7:12-13) and when Jesus returns again He will take the throne which is rightfully his (Genesis Ch 49:10).
    It’s exciting to think that this throne continues to the present day and somebody is sitting on it. Much evidence suggests that our own Queen Elizabeth II is the latest monarch in this illustrious line. I recommend that you investigate this properly before discounting it out of hand.

    • My point is that, as long as you are even-handed about it, and follow both the male and the female descendants of King David (assuming someone of this name really existed), then pretty much everyone in Europe and the middle east will be descended from him (and, in fact, most of the other people, illustrious or otherwise, who existed at that time). Royal ancestry is nothing special really.

      • It’s a bit late to join this interesting discussion – but one of the odd things is that it does seem that royal ancestries can be a bit different – at least for a finite period and viewed in a particular fashion, notably via the Y-chromosome.

        If you take many of the current royal or recently royal families (Windsor, Mountbatten/Greece/Denmark/Romanov, Spain/Luxembourg/France, Belgium/Portugal, Italy/Savoy, Hohenzollern etc) and equally some well established British aristocratic families (Beaufort/Somerset/Plantagenet, Spencer, Stanley, Stuart/Scott/Montagu etc) you have family lines that can theoretically be traced back to 1100 and sometimes well beyond in a continuous male line.

        It remains to be proven (and some cases no doubt will be) whether these male lines are genetically sound all the way back or whether there was an unreported break here or there but it is striking how influential male lines seemingly survived right through to the modern period. OK so you can say that current/recent royals are by definition survivors and titles have often been passed from one failed patrilineal branch to a parallel one even so for some many ruling families (with a few exceptions – Sweden, Monaco etc) to have influential male lines going SO FAR back points to a striking male inheritance of power which has played out in the genes, specifically on the Y-chromosome. In contrast many of the female lines (such as the Queen’s) fade into obscurity within just a few generations.

        What is the mechanism for male inheritance like this? One factor might be that inheritance rules and power politics led to a much greater emphasis on producing sons and in many cases on giving land and titles to younger sons as well. What else? Who has studied this? [Of course pending rule changes in the UK, already in place in most other European monarchies, will end this dominant male-line pattern quite quickly]

        It would be interesting to know whether these male lines are typically commoner in the wider population than other male lines (and to gauge their relative success on this measure over a given period). The success of Genghis Khan and the the Uí Néill in spreading their Y-Chromosomes in their home range is presumably based heavily on a comparable mechanism of inheritance of power but then greatly augmented by tribal/social structures that allowed leaders to father many sons and placed a great emphasis on descent from a famous progenitor.

  14. As a biologist, I may suggest you should really consider the restriction factors.
    1. sharing grandfathers and grandmothers, we may define this as re-mix. e.g., marriage between COUSINS
    2. geographic restriction.

    then you will find your calculation is totally wrong. it is not 2^n, it is much much lower.

    • Yes, cousin marriage is an alternative way of specifying the same thing. Alternatively, Ohno (1996) calls it “sibling interference”. That’s why the 2^n figure starts becoming (obviously) ridiculous for large n.

      Nevertheless, the other papers I’ve cited (in particular, the Rohde and Lachance papers) show that geographical restricting and inbreeding make surprisingly little difference to the calculation of genealogical MRCAs. Have a look at them and see what you think.

  15. I find the racism implied in the religious slant of this story at odds with the word “scientific”. There seems to be a heavy political overlay to this story.

    The genetics are right but the basis is mythological – not scientific. The archaeological data on Roman Palestine (the name given to the country by the Greeks around 2600 years ago) makes it clear that at most only 25% of the population were Jewish. The rest were a mix of foreign elements – lots of Persians and Greeks, who had occupied the area through various wars, with the majority of the people the native Palestinians – descended from the Canaanites and Philistines. All peoples true histories should be respected. The influence of Persian and Greek culture on the history of the area and the religions that arose there was profound, and their influence is with us today.

    This genetist’s article has rewritten history by making the assumption that it was only Jewish people who lived there. Academic archaeologists or historians, especially the Israeli ones who lead the field – (and certainly not the gobbledgook of the “biblical” school), should be used by anyone calling themselves a scientist. It is also an insult to ignore the existence of the majority population in historic Palestine. It is racist to ignore the true population of a country – especially when used to forward an unsubstantiated historical or religious view.

    There is no scientific proof of a King David or King Solomon, and very little of the bible has withstood the finds of modern scientific archaeology. The use of biblical characters gives some interesting colour to the genetics, but should have been prefaced with the facts – “there is no scientific proof these kings existed.” Stop mixing science and religion. I am surprised the BBC approve such racist and burbly stuff under the heading science.

    • Gosh, I’m sorry you think I have some sort of agenda here. I’m aware that there was a huge mix of people living in the area, and I don’t think I said that only Jewish people lived in the middle east at that time, did I? I certainly focussed on Jewish people, since that’s what the question was about. But my point is that anyone alive in the middle east at the time of Jesus could probably trace their ancestry back to 80% or so of the people living in that region 1000 years previously, including, presumably, the Persians, the Greeks, and whoever else happened to be around at that time, including Kings David and Solomon, if they existed (I didn’t realise this was a matter of dispute, but then, I’m not a historian). Indeed, if we are specifically talking about someone like a ruler, who is likely to have had more children than the average, then that’s even more likely.

      That seems to me to be a point that is politically and religiously neutral.

  16. Hi Yan, I don’t know about Christian rules, but in Jewish law to be a descendant of King David and qualify for the Royal line means patrilineal descent (we use patrilineal for tribe and matrilineal for “Jewishness”). IE it has to be father to son all the way down. I would bet that the number of people 2000 years ago who were descended from King David father to son was a much much smaller subset. Also, the children of Solomon with the 700 non-Jewish concubines don’t qualify for the Kingship. Only someone who is descended from a Jewish mother and is in the patrilineal line of King David can be King.

    • Yes, sorry if I didn’t make that clear. It’s the point of the whole article really. If you only restrict “descent” to mean only through the male line (i.e. patrilineal), then you don’t get the exponential effect, and (all other things being equal) the number of offspring follows a random walk, with a much smaller number predicted number of descendants in Jesus’ time. Indeed, there’s a good chance of complete extinction of the lineage. It should parallel the evolution of western surnames.

      If we relax the patrilineal restriction, as seems reasonable in these days of enlightened sexual equality, then you get the astonishing rapid spread and recent common ancestor times that I’ve been talking about.

      It’s unclear if the lineages quoted for Jesus (if even accurate) are strictly patrilineal. If you believe in the virgin birth, then Jesus can’t have been biologically in the patrilineal line from David anyway – although he could have been legally, I guess. It just shows the philosophical contortions you have to introduce if you believe any of this stuff.

  17. Hi Yan!

    I too am struggling with the assumptions here, although the model works fine given your assumption of randomly mating populations – but artificial life simulations are much more sophisticated than that now. Why have you chosen this model for your answer?

    On the question of assumptions but I have three questions :

    1) Even if we assume that there was mixing between the 12 tribes. Given the level of technology, and the wide dispersal of communities across a desert is it not reasonable to expect not just isolated groups, but chains of isolated groups.
    For example, if a village only interbreeds with the next village every 3 generations (say) and that village only interbreeds with the next village every 3 generations and so on, wouldn’t there be an exponentially growing laps in the transmission of genes geographically – this begs the question, how many generations does it take for genes from jerusalam to reach the furthest flung village? And puts big gaping holes in the “tree of ancestors” described, I think. These are just out of the air numbers and obviously traveling circuses etc provided genetic corridors so I’m just illustrating the principle.

    2) This research http://hbdchick.wordpress.com/2011/03/06/jewish-inbreeding/
    Plus research and current experience from india suggests that inbreeding from recent ancestors is actually very common across wide swathes of generations. Specifically certain marriages between first cousins, repeatedly over generations. Would this not also create channels of genetic similarity through the “tree of ancestry” even in large cities.

    3) You go out of your way to include the barber and the manservant – at what points in history do social limitations on genetic diversity have an effect (It is clear, for example in the cast systems of india).

    Could these three effects, working together have an impact on the model?

    Clearly – the dispersal of a particular gene set through a large number of offspring by a powerful man is a strong argument, what assumptions do we need to make about the subsequent success of those genes, what evidence is there?

    Lastly the Wikipedia (veracity questions noted) has much more distant figures for genetic adam and eve than the model presents. Why is this?

    I’m sorry that some people have been rude of flippant in their replies I eagerly await your further thoughts on this – perhaps I am missing something?

    All the best
    Shankar

    • Hi Shankar,

      Apologies I haven’t replied to this yet (I’m currently on holiday in the wilds of Scotland, away from internet most of the time). Thanks for your question. It’s made me go back and re-read some of the literature, and honed my thoughts on the matter, for which I’m extremely grateful. For that reason, I’m currently writing a thoughtful (i.e. pretty long) reply – I’ll try to post it in a few days, when I get back into internet contact.

  18. Hi Yan

    thanks for your excellent response to my question. I’ve been watching it develop with great interest.

    There’s no need to post this comment up but: there’s only one G in Trigell; it is mispelled both times in your article here.

    thanks

    Jonathan

    • Oh – so sorry about the misspelling. I’ve now corrected it.

      Glad I answered the question to your satisfaction. It’s certainly worth reading the Rohde, Olsen & Chang paper, if you have time. I’ve given a url to the full paper in one of the comment replies.

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