Old and New Deleterious Mutations

Here is another foray into simple quantitative analysis. My record with quick and dirty models like this is like my experience doing algebra on the blackboard in front of a class: miserable. I will proof this one and I certainly hope that Anonymous is still hanging around to put things right.

The number of deleterious dominant mutations depends on conditions (e.g. paternal age) in recent generations, more so the more deleterious the mutation is. If g is the mean age of fathers then, given the model we have been discussing, there are 2g–20 mutations from the father each generation. If the mutations are neutral or recessive or even mildly deleterious they just accumulate for a long time.

Now let us think about deleterious dominant mutations that confer a selective disadvantage s per generation. If u is the fraction of all mutations that have selective disadvantage s, then in the most recent generation the number of this class of mutations is (2g–20)(u), from the last generation it is (2g–20)(1-s)(u), from the one previous to that it is (2g–20)(1-s)^2(u), and so on. The ultimate equilibrium frequency is u(2g–20)/s.

For example consider mutations with selective disadvantage s=0.01. The equilibrium frequency of this is given by this formula, and only 4% derive from the most recent 4 generations.

Now consider more serious mutations, those with selective disadvantage of s=0.10. In this case the last 4 generations contribute 40% of the total number, i.e. about ten times as many. For the even more bad class in which s=0.20 the recent (4 generation) fraction is a whopping 60%.

This is, I believe, the basis of Greg’s remarks that for seriously bad mutations only the mating system, i.e. paternal age, in the last few hundred years matters while for neutral and recessive mutations the numbers depend on a much longer history.

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23 Responses to Old and New Deleterious Mutations

  1. typal says:

    Deleterious mutations would be removed more quickly than that model predicts by the consanguineous marriage that’s extensively practised in polgynous populations.
    Is it true Bushmen males marry at 14 ?

    • gcochran says:

      Inbreeding is high in at least some populations in the Middle East, but is not high in west Africa. I don’t know the age at which Bushmen marry, but the reported average paternal age of the !Kung is 35.8

      • typal says:

        ” The highest rates of consanguineous marriage occur in north and sub-Saharan Africa, the Middle East, and west, central, and south Asia. In these regions even couples who regard themselves as unrelated may exhibit high levels of homozygosity,” see Consanguinity, human evolution, and complex diseases

        “The Maternal Uncle, or nijaay in Wolof, often helps to settle family disputes. He may also be expected to help his sisters in times of need when the parents are no longer able. Among many groups in Senegal, a prefered marriage for a man is to his nijaay’s daughter” Here

        Hammer et al ‘ Sex-biased evolutionary forces shape genomic patterns of human diversity.’ found not much X chromosome variability in Senegal although
        ‘Polygynists and their wives in sub-Saharan Africa: an analysis of five Demographic and Health Surveys.’ says “Polygyny is very common in Senegal, high in Uganda and Ghana, and fairly common in Kenya and Zambia.”

        The Evolution of Human Sociality By Stephen K. Sanderson states
        “Of the 752 societies in the Ethnographic Atlas for which data are available , 188 practice cross – cousin marriage. Most of these (154 or 82%) practice bilateral cross-cousin marriage, 30 (16%) practice matrilateral cross cousin marriage, and only 4 (2%) practice patrilateral cross-cousin marriage”
        “In many societies the preferred marriage for a boy is with his mother’s brother’s daughter” (Homans and Schneider, 1955 ). …”

      • gcochran9 says:

        I looked at recent measurements of long runs of homozygosity (ROH): west Africans didn’t have high levels.

      • Greying Wanderer says:

        “I looked at recent measurements of long runs of homozygosity (ROH): west Africans didn’t have high levels.”

        I may be misunderstanding but isn’t there a possible distinction here between populations who consciously choose cousin marriage as part of their culture, keep track of who is related to who and repeat the process within the *same set of related familes* over many generations and a population that marries semi-randomly (or practise cousin-marriage but doesn’t keep track over generations) within a low total population pool who unconsciously marry cousins because everyone in their marriage pool is a cousin?

        I’d have thought the latter case might represent a different kind of inbreeding with its own distinct signature in the same way the former kind has long runs of long ROH?

    • Interesting question. If you sit around the campfires in the evening and listen to the chatter much of it is about arranging marriages for one’s children. Years of talk and negotiation and such. Nancy Howell once told me that these arranged marriages last on average 3 days: in other words the whole adult talkathon has no effect at all on the formation of real pair bonds. Older people of course complain about “in the old days we obeyed our parents” but it turns out they did not.
      I have never known a real marriage of a 14 year old, male or female. Early twenties for males would by me guess: Nancy Howell’s book would have real data.

    • jb says:

      I have a description of a very traditional Bushman marriage, written by someone who actually lived among them in the 1950s and witnessed the ceremony. The bride was about 9 years old and the groom about 16, and this was quite typical. However the traditional Bushman idea of marriage was rather different than ours, and marriage did not imply sexual relations, which would not occur until the girl had passed menarche.

      Incidentally, traditional Bushmen frowned on adultery, which was rare, for reasons involving lack of privacy, a universal ability to read footprints in the sand, and poison arrows.

      • harpend says:

        Yes, Bushmen are indeed seriously monogamous. Their family organization would bring smiles to faces of Republicans.

        I presume the description you have is by Lorna Marshall or her daughter Elizabeth Marshall Thomas. They still do this very occasionally, but this is the “marriage” carefully arranged by the parents. Biologically it doesn’t mean a thing. The kids “separate” and grow up, marry mostly whom they want to.

      • jb says:

        The book was The Old Way: A Story of the First People, by Elizabeth Marshall Thomas. I’m sure you are familiar with it, but for those who aren’t I highly recommend it. Marshall’s parents studied the Bushmen in the 1950′s, and Elizabeth was there as part of the team. She first wrote about the experience shortly afterwards in The Harmless People, and then, after 50 years, revisited her first and subsequent experiences with the Bushmen in The Old Way.

        Aside from all the details about the lives of the Bushmen, the book advances an overall argument that I found quite interesting, and moderately convincing: Marshall argues that of all the traditional peoples we know about, the way of life of the Bushmen is the closest to the way our ancestors lived over the past 150,000 years as they were evolving into modern humans, and that we should think of it as a sort of baseline when it comes to understanding human nature. Hence the title of the book: the traditional way of life of the Bushmen is “The Old Way” for all of humanity.

  2. Paul Jaminet says:

    I think that’s correct. It also shows that the best age for fatherhood is 10.
    Now what about traits like IQ that depend on contributions from many genes. Odds are the current IQ of nations will be affected by practices at all time depths.

  3. gcochran says:

    The model is of course intended for g greater or equal to 20. Yes, probably all time depths matter, but I think they show up in characteristically different ways.

  4. D McAllister says:

    I think there is something wrong with your formula because the number of mutations with a selective disadvantage is increasing with time. I think what you said is n(i) = u(2g-20)(1-s)^i, where n(i) is the number of mutations with selective disadvantage s in generation i and i is the number of previous generations. If I have understood correctly, then the greater the selective disadvantage s, the faster the number of deleterious mutations increases

    • harpend says:

      That is right: the number of mutations that I carry all happened in the past. Some of them a long time ago, some recently. What increases with time (in the past) is the total number I have. Point of the post is that really bad deleterious dominants I carry are much more recent than the mildly deleterious dominants, which are older on average. In both cases the total number converges to mu/s, wich is a standard formula in population genetics.

  5. Anonymous says:

    If paternal age is the main factor for reducing average IQ modern high IQ humans are doing their best to downgrade the fitness of their progeny as complex education leads to late reproduction:
    academics have a very high average paternal and maternal age- this seems to have been true a long time at least in Europe, where marrying and reproducing was on the average postponed until the man had taken over the farm or trade from his father, usually in the mid-thirties.

    • harpend says:

      Right. The late age at motherhood, and thus fatherhood, of SWPLs is not good for long term fitness.

      Here is where a matrilineal structure might win. Among the Herero, about whom I am always writing, there are plenty of high achieving women. They do better in schools than males, and banks and offices and stores are full of women who have completed secondary school. The common pattern is that these women have a couple of babies while they are teenagers, then go off to school very seriously. The kids are left with mom, or a sister, or auntie, or other matrilineally related women.

      So they get the best design prize. Young male fathers (I presume) to father their children and the freedom to get educated.

    • Greying Wanderer says:

      “this seems to have been true a long time at least in Europe, where marrying and reproducing was on the average postponed until the man had taken over the farm or trade from his father, usually in the mid-thirties.”

      http://en.wikipedia.org/wiki/Hajnal_line

      “West of this line, the average age of marriage for women was 23 or more,[3] men 26, spouses were relatively close in age,[4] a substantial number of women married for the first time in their thirties and forties, and 10% to 20% of adults never married.[5][6][7] East of the line, the mean age of both sexes at marriage was earlier, spousal age disparity was greater and marriage more nearly universal.”

      That’s Europe. My understanding of polygynous societies is the men tend to be wealthy and a lot older which i’d assume could have a dramtic effect if men provide the bulk of the mutations?

      I’d have thought the total effect of all these different factors must be the rate of adding deleterious mutations minus the rate of shedding them. I don’t know what effect the polygynous form of marriage culture might have on the rate of shedding? If it was bad for shedding too then you’d imagine that system must have a pretty powerful other benefit at least in the environments where it is rooted? Perhaps a consequence of higher average levels of genetic load is it tends to lead to a more winner takes all harem-esque marriage culture as a least-worst option?

  6. a very knowing American says:

    “The appropriate age for marriage is around eighteen for girls and thirty-seven for men.” (Aristotle, Politics VII.1335a27)

    Classical Greeks were pretty monogamous, but still faced a shortage of women, as a result of female infanticide (at least in some places, including Athens). This pushed up ages at marriage for men. Female infanticide is probably more common in Eurasian peasant societies, where daughters were an economic burden, than in Africa, where daughters brought in bridewealth when they grew up.

  7. a very knowing American says:

    Last month on westhunt, the theory was that Africans have higher rates of mutation because of higher temperatures. This month, the theory is that maybe higher mutation rates result from later average paternal ages, which might result from widespread polygyny. Any other possibilities?

    Here’s one: Human testis sizes follow Rushton’s Rule, Africans>Europeans>East Asians. Cross species comparisons show that testis size reflects mating system. When females mate with multiple males during one reproductive cycle, sperm competition is particularly intense and there’s strong selection on males to increase sperm production. This seems broadly consistent with the cultural anthropology of sub-Saharan Africa, where de jure polygyny often goes together with de facto polyandry (female adultery). It seems plausible that there is some quantity/quality tradeoff in sperm production, with increased spermatogenesis via more frequent spermatogonial division coming at the cost of elevated mutation rates. Is there any cross species evidence for this? Do species with higher sperm production (eg chimps vs gorillas) also have elevated mutation rates or genetic load?

    There may be other possibilities too. Maybe running genetic arms races with parasites (something particularly intense in sub-Saharan Africa) forces compromises in DNA repair.

  8. typal says:

    Mormons: “old men tottering on the brink of the grave have been united to little girls scarcely in their teens”. But for the fact they practised consanguineous marriage, the Mormons would have a heavy genetic load.

  9. jb says:

    Even if this effect is real, how does the negative impact of additional mutations in the sperm of older fathers compare to other possible dysgenic trends in our society; in particular the negative correlation between fertility and intelligence, and the relaxation of selection against negative traits in general?

    It’s kind of hard for me to believe that a few additional de novo mutations in the children of older fathers is all that significant, given that they are stacked on top of the de novo mutations of the grandfathers, and great grandfathers, and so on over many generations. Over time it would add up of course, but it seems to me that over the next few generations at least the greatest excess of negative mutations will not be de novo, but rather older mutations that previously would have been filtered out by selection, but which in the absence of selection persist in the population.

    • Greying Wanderer says:

      “Even if this effect is real, how does the negative impact of additional mutations in the sperm of older fathers compare to other possible dysgenic trends in our society”

      Maybe that’s the point of polygyny in hot climates? Maybe the average amount of genetic load is so high that older men who’ve proven – by virtue of their relative wealth – that they had less of that load to start with are still a better genetic bet even though their age may add some negatives into the balance? If so then as you headed away from the tropics that requirement would weaken and other factors might come into play which more favored monogamy?

  10. jdub says:

    If the mutations affect IQ then first born children should be smarter than second born children, etc. There is some small birth order correlation with IQ.

  11. Pingback: Ikung bushmen | Upriverranch

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