The Mathematics of Evolution: The Lactase Persistent Gene

[glipsnort (Steve Schaffner)]

@Bob_Kurland

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.

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.

[glipsnort (Steve Schaffner)]

@Patrick

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.

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.

[glipsnort (Steve Schaffner)]

@GJDS

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

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.

[Patrick]

That video was amazing. Thanks.

[Patrick]

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

[Sy_Garte]

@GJDS

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).

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.

[Bob_Kurland (Robert J. Kurland, Ph.D.)]

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.

[Bob_Kurland (Robert J. Kurland, Ph.D.)]

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%).

[Bob_Kurland (Robert J. Kurland, Ph.D.)]

Thank you for the video reference Beagle Lady.

[glipsnort (Steve Schaffner)]

@Bob_Kurland

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%).

Right. Even with that large an advantage, there’s still a good chance (more than 50%) that the beneficial allele will disappear by chance while it’s still rare. (It doesn’t really matter if you can digest milk if you get hit by a truck before you pass on your mutation, for example.) But once there are more than a few copies present, the extra survival or reproductive advantage of the allele means that it will start shooting up in frequency – compound interest, basically.

[Bob_Kurland (Robert J. Kurland, Ph.D.)]

“There’s still a good chance (more than 50%) that the beneficial allele will disappear by chance while it’s still rare”. That’s what sticks in my craw as not intuitively appealing–just one mutation causing an effect–is there any sort of mathematical treatment that considers the possibility of multiple mutation events within some delta time interval, and how that affects the spread of the beneficial phenotype?

To put it another way: considered as a boundary value problem, the initial conditions are not really well defined.

[Henry (Henry Stoddard)]

Dear Dr. Kurland,

It is truly an honor to hear from you. I wish I could say that I have actual documentation for the Jewish situation. I heard this from my physician at the time. This was about forty years ago. He said it was Diabetes 2. Why did he tell my father and me? I am mostly a Gentile Christian of British, Dutch, Irish, Belgian and German origin; however, my ancestors were members of old American plantation families in Virginia and Northeastern North Carolina. Many plantation families that were Jewish married into Christian families. That happened in my case; therefore, our doctor checked us often for diabetes. Almost everyone in my father’s family has it who were born in America. I know about Tey-Sachs; however, no one in my family has that. I wish I had documentation on that. Perhaps I can search for some. I am a Southern Baptist who loves bacon, i.e. pork. I do have a friend who is a Reform Jewish Rabbi,but we have never discussed diabetes. I wish to thank you for the interest.

[Henry (Henry Stoddard)]

Dear Dr. Kurland,

I have found some articles by the Jewish Diabetes Association that could have you. I could not find a link; however, I typed in Jewish Diabetes Association and found many articles, especially about diabetes 2. I hope that will be of interest. I do wish there were a cure for this. I am hurting at this moment. My sugar levels must be going up.

[glipsnort (Steve Schaffner)]

@Bob_Kurland

That’s what sticks in my craw as not intuitively appealing–just one mutation causing an effect

If a single mutation has an important effect, as the mutation near lactase does, then it does. What do you find surprising – that a single mutation in the genome could have a large phenotypic effect, or that a single mutation in the population could spread to everyone?

@Bob_Kurland

is there any sort of mathematical treatment that considers the possibility of multiple mutation events within some delta time interval, and how that affects the spread of the beneficial phenotype?

Sure, there’s extensive theoretical modeling of all of these processes; that’s the subject of the field of population genetics.

There are several possibilities. There can be a single mutation that is successfully selected for; that’s what happened in lactase persistence in northern Europeans. If the beneficial variant isn’t already present in the population when a selective pressure arises, this is probably the most likely way that selection will work, since selected alleles typically reach high frequency quickly compared to the rate of new mutations. A second mutation doesn’t usually have time to occur.

On the other hand, there can also be multiple, identical mutations that occur in different individuals in the same population. That’s unusual, but it does occur, for example in the case of the sickle cell trait. It’s probably relevant that balancing selection is at work in that case, maintaining the allele at an intermediate frequency for an extended period.

There can be multiple mutations with the same phenotype. That’s what happened at lactase worldwide: different, independent mutations confer lactase persistence in Europe and in Africa. In this case, the subpopulations were more or less isolated from one another, and so the first beneficial allele didn’t spread to the second region, leaving time for a different mutation to occur. (Obviously, the probability of this happening depends on how many different mutations would yield the same phenotype. That can vary enormously.)

There can be selection for variants that are already present in the population, so-called selection on standing variation. That’s what happened in the case of selection for greater stature in northern Europe (or perhaps for shorter stature in southern Europe); in this case, hundreds of existing variants, all affecting height, were shifted modestly in frequency, resulting in an overall change.

@Bob_Kurland

To put it another way: considered as a boundary value problem, the initial conditions are not really well defined.

Well, mutation is a stochastic process, at least at the level we’re ever likely to study it, so that’s bound to be the case.

[GJDS]

@Sy_Garte … regulatory networks …"

This is an interesting area that may extend beyond Darwinian thinking. I recall descriptions given in the Nobel Prize award on ways “information is exchanged at a cell wall/membrane (my own words and details can be found at the web page for Nobel Prizes)” – this work shows that specific molecules may adopt configurations that result in particular events within the cell. This speaks to me of very specific and subtle mechanisms that may be part of a vast regulating capacity within living species, at the cellular level. Yet we may read papers such as D. Benjamin Barros, “Natural Selection as a Mechanism “ in Philosophy of Science, Vol. 75, No. 3 (July 2008), pp. 306-322, who state:

“…acknowledging the merit of some of their points but arguing against their central conclusion that natural selection cannot be characterized as a mechanism. Skipper and Millstein’s most important objection centered on the issue of regularity. Natural selection is understood to operate probabilistically, but the leading accounts of mechanisms, proposed respectively by Glennan (1996, 2002) and Machamer, Darden, and Craver (2000; hereafter MDC), appear to be concerned with deterministic mechanisms, that is, those that will always produce a certain outcome if the mechanism is working properly…”

I cannot envisage anything more deterministic as specific molecular configurations that are central to regulating events in a cell. Yet such elegant mechanistic insights appear to contradict stochastic probabilistic notions put forward as a way NS may be hypothesized. I am more inclined to the view that there are a myriad of mechanisms and these testify to the immense complexity of life – and I am not inferring emergence, but rather the need for an actual mechanistic/deterministic account of biological (biochemical) systems.

[Bob_Kurland (Robert J. Kurland, Ph.D.)]

Let me put my thoughts on why it might be important to consider mutation rates by a simple example. You are at liberty to correct incorrect notions, for which I would be grateful. Consider a small region in which one beneficial mutation has occurred. The analysis as in the treatment of lactase persistence is applied to yield an estimate for the coefficient of selection. Now suppose that instead of one mutation having occurred, within a small interval of time several mutations have occurred within different regions. The different regions are far enough apart that no migration occurred during the initial history, but they lie within the region surveyed today. For example mutations occurred in Hungary, Poland, Denmark, Norway. If the present day occurrence of this beneficial allele is analyzed for the coefficient of selection on the assumption of only one mutation having occurred, would it not overestimate the coefficient of selection? If this intuitive notion is not correct, please tell me how it fails.

[Henry (Henry Stoddard)]

My Dear Doctor,

Were you able to review I recommend on the internet to you concerning diabetes? In any case, I would not have minded having you as a science professor. God bless.

[Bob_Kurland (Robert J. Kurland, Ph.D.)]

Henry, thank you for your very kind remarks. I did do a Google search, “Jewish Diabetes Association type 2 diabetes”. There were several sites, and I found the following article of interest, which said that 100 years ago diabetes was thought to be a Jewish disease, but now it is found the prevalence is higher in other ethnic and racial groups: Diabetes and Race–A Historical Perspective
I hope your diabetes symptoms abate. My wife’s symptoms and blood sugar levels are fairly well under control thanks to the four or five drugs she takes, thank the Lord.

[Henry (Henry Stoddard)]

Dr. Kurland,

I enjoy communicating with you. You are a good of God.