The Mathematics of Evolution: The Lactase Persistent Gene

Thank you for the video reference Beagle Lady.

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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.

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“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.

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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. :grinning: 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.

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.

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?

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.

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.

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@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.

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.

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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.

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.

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Dr. Kurland,

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

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