The Mathematics of Evolution: The Lactase Persistent Gene

Mammalian babies drink milk. Almost all non-human adult mammals do not drink milk. Some human adult mammals drink milk (northern Europeans, East Africans), while many adult human mammals (East Asian, Afro-American, Basque) cannot drink milk without suffering lactose intolerance symptoms (lactose, a milk sugar, cannot be metabolized).

Here’s the story: mammalian infants have an enzyme, lactase that enables lactose to be metabolized. This enzyme is normally lost after the infants are weaned. However in certain groups where dairy farming has been carried out, a gene enabling lactase persistence enables the enzyme to continue to be present. This gene was not present in these groups (Northern Europeans/East Africans) 8000 to 10,000 years ago, but is now (77% or higher in Northern Europeans). Therefore it must have appeared as a mutation and by enhancing survivability, spread.

This latter was the story I heard in John Hawks audiobook, “The Rise of Humans”, (see also this Nature article), and it seemed plausible, but as physicist I wanted numbers. The best science according to Fr. Stanley Jaki is quantitative, so that predictions or retrodictions can be assessed quantitatively. And I have found such a mathematical test in an article by Todd Bersagiliari and many others, Genetic Signatures…

Dancing on a tightrope of very involved statistical and Markov chain calculations (I have to confess I don’t fully understand all the math, but accept it) the authors find that this mutated gene that allowed persistence of the lactase enzyme action enhanced survivability by between .09 and 0.19 for the Scandinavian population and between 0.014 and 0.15 for the East African. I take this “coefficient of selection” to mean that those Scandinavians carrying this dominant gene produced between 1.09 to 1.19 more children per generation than those who did not have the gene.

Critical comments solicited, if I have misunderstood the conclusions of the cited papers. Finally, let me say that I’m happy to join or at least not throw brickbats at the Neo-Darwinians who argue for survival of the fittest as a mechanism for evolution.



I am finding it difficult to follow the reasoning in your comment, as you state the enzyme exists is all infants. If this is so, you need to address the “loss after infants are weaned” matter - if for some reason the loss is related to factors that have not been identified, than we do not know and cannot discuss this. Just how would a gene that is present in all infants disappear in the same adults, and then reappear in these same adults as a result of mutation and survivability? I have read your comments a number of times and I cannot see what mutation has to do with what s discussed here. Perhaps you may have more information of what is meant by loss of the enzyme after or before the loss(?), followed by mutation of the same enzyme, and if so, I would be interested in reading it in your response. Cheers…

GJDS, it’s an early hour where I am (3am), I’m suffering from insomnia, so I put in that post. Sorry if it’s incoherent. I’m not enough of a geneticist to give you a complete answer other than to repeat what I’ve heard and read: in mammals the enzyme activity for lactase normally disappears after weaning. I guess the evolutionary point is why keep a non used enzyme around. How this is is accomplished on a molecular biology basis, I don’t know but it it is. Perhaps the linked articles will give you a more complete reference. The enzyme is not mutated: a gene enabling the enzyme to persist has been mutated. Again, exactly how this is accomplished I don’t know, but perhaps the linked articles will explain it better. Here’s the Wikipedia article on this . My main point was that I didn’t see how overcoming lactose intolerance enhanced survivability (number of children with lactase persistence mutation gene), but evidently these researchers have come up with such a number to fit present day genetics.


Thanks for the link - I am not a geneticist, but from your link, I see that two phenotype are discussed, and these are related to the lactose tolerance and non-tolerance. I gather that infants may inherit the genes for each of these, and this seems to be dealt with by mathematical treatments. I guess the comments with Nuno on another thread may apply, in that we are unable to give a clear mechanism linking the genotype and phenotype, and mutations can become a nebulous concept (which then causes me to question the inferred natural selection, or survivability). As a chemist, I tend to look for chemical mechanisms and biochemical pathways; mutations seem to cover a large number of notions - but I will leave this to geneticists.

Here is some new information on Lactase Persistence

GJDS, one point that isn’t explained by these articles: what is the frequency of mutation? What is calculated is an “excess probability” which translates eventually, after a lot of hair-raising statistical inferences, to a “selective advantage” coefficient. I don’t see anywhere in the paper a number representing the frequency of mutation, but perhaps it is there. If anyone more knowledgeable reads this paper, I would appreciate it if they pointed out what that number might be, and if it’s reasonable on the basis of generally known mutation rates.

Isn’t it “too soon” to determine if lactase persistence is a selective advantage? From the paper I sent it was only a few thousands years old. The record of its migration is available but I don’t think you can say if this gene was selected as it is too recent and humans would work around this gene as in the past few thousand years, civilization could provide other things to eat besides dairy products.


Jeong and Rienzo 2014 give a good overview of how different types of genetic traits of adaptation compare to each other - they contrast Lactase Persistence with skin pigmentation, high altitude adaptation and height. This article is actually in a whole issue on Genetics of human evolution so you may also want to check out the other papers in that issue. If you’re interested in human mutation rates then Scally and Durbin 2012 may be an interesting read.

Thank you Nuno for the links. They’re on my to-do list.

Dear Dr. Kurland

I find what you have to say to be very interesting. I have known that certain groups of peoples throughout the world cannot tolerate milk products. This is very interesting indeed. What are your thoughts in relation to the unity of the human species? Also, as a theologian, I have to ask about your thoughts of God and his relationship to creation. Did you know that Jewish people have more problems with diabetes than other groups? Do you have any thoughts on that?

Concerning Lactose tolerance: Here’s a good video by Howard Hughes Medical Institute: The Evolution of Lactose Tolerance.



The gist of these discussions centers on how the term “mutation” is used. It seems to me that any variation in humans (or any species for that matter) can be appropriated into the term, and from there we have the “hair-raising” arguments for all sorts of results. I find such an approach scientifically unsatisfying and have avoided such vast generalisations in my research efforts.

The mutation rate doesn’t really enter into it. They(*) estimated the selection coefficient from the present frequency of the allele and its estimated age, based on how strong selection would have had to be to increase the frequency to that level. The age of the allele was estimated from the length of the haplotype it was found on – that is, how far around the selected variant everyone shares the same set of variants. When a mutation is new, it is found on a single genetic background (the one on which it first occurs). Over time, and as the mutation becomes more frequent in the population, recombination and other mutations mean that the variant will be found on increasingly diverse backgrounds. Such age estimates have large uncertainties, but the extreme length of the unbroken haplotype around this variant means that it is only some thousands of years old – very young by genetic standards.

(*) We, actually – I was one of the authors of that paper, although I didn’t have anything to do with this calculation.


No, it’s not too soon. The fact that it reached such high frequency (something like 70%, depending on the population) in a large population in just a few thousand years means that it had to be driven by strong selection.


There is good (but not conclusive) evidence for the molecular mechanism of lactase persistence, at least for the European variant. The lactase-persistent allele creates a binding site for the transcription factor OCT-1, which enhances transcription of the lactase gene when bound to the site. If you have that variant, lactase is transcribed even in adulthood; otherwise, not.


That video was amazing. Thanks.

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Thanks, after watching the video I see how fast such high frequency selection can work. It is an amazing culture/evolution example.

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I cant add anything to comments by Steve and Nuno on the genetics of lactase persistence. But I would make a general comment related to GJDS comment concerning mutations and phenotype. The word mutation can be a bit nebulous, since it can refer to genotype mutations (actually changes in DNA sequence) or phenotype changes, meaning an observable change in a trait. Its the latter that is the target of natural selection, but the phenotypic changes are caused by the genotype changes. So for evolution to occur, there must be a very tight connection between genotype and phenotype. And there is.

What complicates things is that some genotype changes (as in the case of lactase) are not found in the gene that codes for the phenotype (the enzyme lactase) but in the regulatory regions (or the regulatory genes themselves) that control whether the structural gene (lactase gene in this case) is actually made by the cell. We are now learning that the gene regulatory networks that control gene expression (like on off switches or dimmers) are more important for biological life than we used to think. And this means that they are very important targets for evolutionary change as well, possibly even more important that changes in the sequence of the protein coding genes.


Thank you for your comment Henry. With respect to your inquiry about the unity of the human species, one criteria for members of a group to belong to the same species is that they can interbreed, with fertile offspring. So, that criterion certainly holds for all the ethnic and racial groups that populate this planet. And, as I understand it, there was some interbreeding with Neanderthals, and certain racial groups (European mainly) contain a significant proportion of genes common to Neanderthals (as i recall this is about 4%).

I didn’t know that Jews were more prone to diabetes (Type 2?) than other groups. Do you happen to have a reference for that–I’d like to explore the topic. I know my maternal grandmother had Type 2 diabetes, as does my wife (who is not ethnically Jewish). There are genetic problems common to Jews of Eastern European heritage–Tey-Sachs disease being the most notable.

Thanks for your answer Steve. To paraphrase that answer, what you’re saying is that one mutated gene, expressing itself as a dominant characteristic (phenotype?), is enough to set the wheels going if it conveys a significant survival advantage. (signifcant being of the order of 10%).

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