Genetic distinctiveness vs. genetic diversity

By Razib Khan | November 28, 2011 1:20 am


Meeting the Taino

In the comments below a few days ago someone expressed concern at the diminishing of genetic diversity due to the disappearance of indigenous populations. My response was bascally that it depends. The issue here is whether that disappearance is due to assimilation, or extinction. If a given population is genetically absorbed into another, obviously their genetic diversity is by and large maintained. What disappears are the specific genotypes, the combinations of gene pairs, which are distinctive to that given group. This is the same dynamic at the heart of the ‘disappearing blonde gene’ meme. Unless there is selection at the loci which encode or predispose one to blonde hair the ‘gene’ isn’t going anywhere. Rather, the implicit issue here is that blonde people are intermarrying with non-blonde people, and if the genetic variant has a recessive expression then the frequency of the trait will decrease. Populations with a high degree of homozygosity at the ‘blonde loci’ are distinctive in a very particular manner, but they’re no more or less ‘diverse’ than other populations which don’t manifest the same tendency.

A toy example will suffice. Take two populations, A and B, and one locus, 1, with two variants, X and x. Assume that the two populations are the same size. At locus 1 population A is 100% X, and population B is 100% x. In a diploid scenario then all the individuals in population A will be XX, and in B will be xx. When you add A + B you get a frequency of X of 0.5, and of x of 0.5 (since the two populations are balanced in size).

 

Now imagine a scenario where all individuals in population A pair up with someone in population B (assume sex balance in both populations). In the first generation, F1, all the offspring will be heterozygote Xx (hybrids). The frequency of X and x will be 0.5 still, as in the previous generation. But no individual now reflects the genotype of the parental populations, as all individuals are heterozgyote. At the level of alleles, specific genetic variants, you’ve go the same diversity (X and x at locus 1). But at the level of genotype there’s a huge shift. Two genotypes (XX and xx) no longer exist, but a novel one is now fixed in the population (Xy).


A novel combination

Finally, in the F2 generation, the offspring of F1, Hardy-Weinberg will reassert itself. 25% of the genotypes will be XX, 25% xx, and 50% Xx, due to p2 + 2pq + q2 = 1. In this scenario some of the distinctiveness of the parental and F1 generations in terms of genotype are evident, but the diversity in the allelic sense of the parental and F1 states remains the same, X = 0.5 and x = 0.5. Observe that if you’re looking at genotypic diversity the F2 generations are actually more diverse than the parental (because Xy is a different genotype). In other words, in some ways the aggregation of various distinct populations may increase diversity by generating novel combinations.

This is not to deny that a very specific historically contingent form of diversity in terms of distinctness of particular groups is threatened today. That’s why it was important that the HGDP was overloaded with threatened groups like the Bushmen, Kalash, and Pygmies. These populations may be assimilated soon, and with that assimilation it will be more difficult to extract out historically very important information which will inform us about the human past.

But another issue is extinction instead of assimilation. Wouldn’t this eliminate a lot of genetic variation? Perhaps. I actually considered this issue a few years back with the Star Trek reboot. If you haven’t watched the film, there’s a major spoiler next. So basically on the order of ~10,000 Vulcans survived the destruction of their planet. Culturally the preservation was rather good, because the Vulcan elders, who are the repositories of the culture, were saved. In this way a fully fleshed Vulcan culture could easily reemerge out of the genocide. On the other hand, the vast majority of Vulcans died. Isn’t ths population bottleneck a genetic catastrophe? It depends. If the Vulcans who survived are a relatively random assortment of the population genetically, then the disaster isn’t that bad in terms of genetic diversity.

To get some idea of why, consider the statistic of heterozygosity. This measures the extent of heterozygote states, where the two gene copies differ at a locus, across the population. It’s a proxy for genetic diversity, as more allelic diversity produces more heterozygosity.

The decay of heterozygosity over time due to random genetic drift (without mutation) can be modeled like so:

Ht = H0(1 – 1/(2N))t

The variable “t” is simply the generation time, from an initial time. H0 refers to the initial heterozygosity, and Ht is simply the value at a given time out from that initial value. The N is effective population size. This formula can be used to model population bottlenecks. The Vulcan population reduction from one on the order of billions to 10,000 was basically a massive population bottleneck. The decrease in heterozygosity that you’d expect would be:

Ht = (1 – 1/(2*10,000))1

Ht = 0.99995 of the initial value. Basically almost nothing. Why? Because 10,000 turns out to be a relatively large population. This makes some intuitive sense. If you have a sample size of 10,000, and it’s representative, sample variance isn’t going to be that high. If you have an infinite number of coin flips so that the ratio of heads and tails is 50:50, reducing that to 10,000 flips isn’t going to result in much of a deviation from 50:50.

Let’s look at the effect of population bottlenecks of 20 generations at various values of N. The x axis shows generation time, while the y axis illustrates the proportion of the initial heterozyosity which remains.

This is not to downplay the impact of bottlenecks and demographic stochasticity. Rather, it’s to suggestion that population genetic diversity is relatively resistant to a crash in numbers. The extinction of small tribal groups is a tragedy, but genetically it may not be as much of a problem as we think. Even in groups such as the Bushmen with a great deal of genetic diversity it is likely that most of that diversity is already found within non-Bushmen populations.

Image credits: Ian Beatty and Lesley-Ann Brandt.

CATEGORIZED UNDER: Human Genetics, Human Genomics
  • Charles Nydorf

    Ashkenazic Jews are an example of a group that has undergone at least one bottleneck and yet maintains the degree of heterozygosity of an average European population.

  • jb

    The members of many small threatened groups are extremely vulnerable to common outside diseases (measles, etc.), and this makes it difficult for them to fully enter the modern world (which eventually they are going to have to do — they can’t stay on the reservation forever, and most don’t even want to). Modern medical technology is helpful, but the best long term solution is genetic assimilation into the wider population.

    So it would be good if it were more widely understood that this is not the same as extinction — that these people will still have children and grandchildren and so on in the general population, just like anyone else. The loss of distinctive cultures and languages is a little unfortunate, not because they have any practical importance, but because they are part of our history, and tell us something about who we were and who we can be. But still, nothing morally wrong is happening when the members of a small group choose to become part of a larger world.

    BTW, I read somewhere recently that European haplotypes are surprisingly common even among American Indians who consider themselves to be full blooded. For me the question is reversed — how would it be possible for any Indian group to have survived to the present day without picking up European genes for disease resistance?

  • http://blogs.discovermagazine.com/gnxp Razib Khan

    Ashkenazic Jews are an example of a group that has undergone at least one bottleneck and yet maintains the degree of heterozygosity of an average European population

    that’s a reason why it’s asserted by some that they haven’t gone through a genetic bottleneck.

    For me the question is reversed — how would it be possible for any Indian group to have survived to the present day without picking up European genes for disease resistance?

    zero contact? but then there is malaria in some regions….

  • omar

    “how would it be possible for any Indian group to have survived to the present day without picking up European genes for disease resistance?”
    I am not an expert on this, but it is likely that the epidemics would in fact select out those American Indians (Native Americans) who were lucky enough to already have the appropriate genetic makeup. Resistant alleles from Europeans would have spread more gradually into the Native population. But I have not looked this up. Does anyone have more specific information about this question?

  • Charles Nydorf

    There is good evidence for bottlenecks in Ashkenazic demographic history. Perhaps, this population had an even higher level of heterozygosity in pre-bottleneck times.

  • http://blogs.discovermagazine.com/gnxp Razib Khan

    #5, that’s why i said genetic bottleneck. demographic bottleneck != genetic bottleneck. on occasion people explain jewish genetic peculiarities as due to the bottleneck, but their genetic bottleneck is probably not sufficient to explain the phenomenon.

  • Nador

    Your model shows how much is lost as a function of population size due to random drift in a population of constant size. It is not entirely intuitive for me, how it translates to the loss in case of drastic population decrease. So i thought about a quick way to guess the chance of losing some rare variants in such a pop. collapse.
    So let assume there are N copies of a certain gene (N/2 is the pop. size). Let the number of a rare allele be A. If the population collapses to a new size of n/2 then the chance of having k copies of this allele is given by hyper-geometric distr. : P(copy # = k)= bin(A,k)*bin(N-A, n-k)/bin(N, n), where bin is the binomial coeff. I started to rewrite it with the Stirling formula, but still seemed too complicated, so, since N is big compared to n anyway, one can use binomial distribution instead. So we have binomial(n, A/N), and since i am lazy as hell i will replace it with poisson: Poi(A*n/N), so the chance of having k copies in the new, reduced population is P( k)=exp(-A*n/N)*(A*n/N)^k/k!. The chance of extinction is given by k=0 , that is exp(-A*n/N).
    In your example you had the population reduce from N/2= 10^9 to n/2= 10^4. So a rare variant of a f= A/N=10^-4 original frequency has about 36% chance of going extinct. For f=5E-4 it is 0,67%. So clearly those alleles are threatened whose reciprocal of frequency is less than the new population size.

  • http://blogs.discovermagazine.com/gnxp Razib Khan

    Your model shows how much is lost as a function of population size due to random drift in a population of constant size. It is not entirely intuitive for me, how it translates to the loss in case of drastic population decrease.

    please note that the assumption in the model is that the initial generation had a very large population, and then a drastic decrease, which persisted for 20 generations. so the heterozygosity estimates ARE for drastic population size decreases, especially when you go from large to N = 60.

    you are correct that lots of rare variants will disappear. the key is that heterozygosity is measuring the total variance, and the rare alleles aren’t necessarily going to contribute that much to that. rare alleles are coming and going in terms of mutation and extinction in many populations.

  • Nador

    Somehow that assumption is still not obvious for me from the text, but if it so, then well, i calculated a bit for fun.
    [edit - sorry, beginning to see what was meant. Let's magnanimously subscribe it to using a foreign language.]
    [It still seems your model describes how much is lost after the collapse due to small pop. size - i. e. taking N1=N0 new sample of the N0 existing one - not during the collapse. But fortunately N0 is not that relevant. I more or less did away with it too.]

  • http://blogs.discovermagazine.com/gnxp Razib Khan

    #9, basically imagine an infinite population being sampled down to a finite size. that’s basically what the first “step” in the model is. so the intuition i’m trying to get across is sampling down to 10,000 from 7 billion would still preserve the vast majority of the genetic variance (7 billion being ~ infinite population size for purposes of genetic drift).

  • Nador

    Yes, and the cutoff frequency of preserved genes is 1/new pop. size. The rarer ones are likely lost, the others not.

  • http://washparkprophet.blogspot.com ohwilleke

    The flip side of the Vulcan scenario is that we have a great many populations (e.g. Native Americans, Australian Aborigines, Papuans, Andamanese) that have incredibly reduced genetic diversity, implying one of two things (or both):

    1. Very deep population bottlenecks – low hundreds or less, not thousands.

    2. Founding populations that are really just extended, inbred families as much as anything else.

  • Neran

    So it would be good if it were more widely understood that this is not the same as extinction — that these people will still have children and grandchildren and so on in the general population, just like anyone else.

    It is the same as extinction – the groups do go extinct:

    http://dienekes.blogspot.com/2011/10/taino-are-extinct.html

    Having “children and grandchildren and so on in the general population” doesn’t mean they aren’t going extinct. And it isn’t “just like anyone else” in this scenario. Implicit in this scenario is that the groups are not “just like anyone else” in the general population, but are “small threatened groups”.

    But still, nothing morally wrong is happening

    Well this just boils down to what you consider is “morally wrong”.

  • jb

    Well this just boils down to what you consider is “morally wrong”.

    What I actually said was: “But still, nothing morally wrong is happening when the members of a small group choose to become part of a larger world”.

    I think this pretty much speaks for itself. But if you really do believe it’s immoral for the members of group to make such a decision, I’d be interested in hearing your argument.

    Also, from the point of view of the people most deeply involved, it makes a rather big difference whether they do or do not have children and grandchildren.

  • teo

    About the ” disapearing blonde gene”. I observed surpisingly at kindergarden level – balkan country – an amazing number of blonde kids, much larger then the number of blonde parents. the country was much blonder previously and the ones interested in this considered it as happening due to recessive genes. The difference between parents and kids was pretty surpising because the reverse is considered normal.
    The subject attracted my attention because I observed it first in my family. Pretty large number of ancestors being blonde and then a rapidly decreasing number and hmmm then the entire extended family started having pretty blonde or light brown kids. And now at kindergarden level the discrepancy is incredible. The explanation seems to me pretty obvious. The dark brown or dark hair parents were pumped up with blonde genes. Maybe if you will find the time and it might seem interesting you could approach this subject at an academic level. I personally would be very interested to see an analysis.
    Recessive or not few generation after the mixing starts blond hair starts apearing again in large numbers. I haven’t observed the same rate with coloured eyes. Brown seems to rule for the time being.

  • Neran

    I think this pretty much speaks for itself.

    I don’t think that it speaks for itself. There are lots of assumptions behind something as vague as “choose to become part of a larger world”.

    Also, from the point of view of the people most deeply involved, it makes a rather big difference whether they do or do not have children and grandchildren.

    Well I don’t see how this is relevant to what I said, which is that having children and grandchildren doesn’t mean they aren’t going extinct. There are probably lots of things that would make a difference upon their mental states. Whether or not they’re addicted to heroin or alcohol, for example.

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Gene Expression

This blog is about evolution, genetics, genomics and their interstices. Please beware that comments are aggressively moderated. Uncivil or churlish comments will likely get you banned immediately, so make any contribution count!

About Razib Khan

I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. In relation to nationality I'm a American Northwesterner, in politics I'm a reactionary, and as for religion I have none (I'm an atheist). If you want to know more, see the links at http://www.razib.com

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