# 1 migrant needed to prevent genetic divergence

By Razib Khan | January 26, 2012 2:09 am

In the survey below I asked if you knew about how many migrants per generation were needed to prevent divergence between populations. About ~80 percent of you stated you did not know the answer. That was not totally surprising to me. The reason I asked is that the result is moderately obscure, but also rather surprisingly simple and fruitful. The rule of thumb is that 1 migrant per generation is needed to prevent divergence.*

It doesn’t tell you much in and of itself of course. But if you think about it you can inject that fact into all sorts of other population genetic phenomena. For example, to have selection across two populations which is not reducible to selection within those populations (i.e., inter-demic selection) you need group-level genetic differences. These differences can be measured by the Fst statistic. In short the value of Fst tells you the proportion of variation which can be attributed to between-group differences (e.g., Fst across human races is ~0.15). For natural selection to have any adaptive effect you also need heritable variation. If you have lots of heritable variation selection can be weaker, while if you have little heritable variation selection has to be very strong (see response to selection). Fst is a rough gauge of heritable variation when you are evaluating group level differences. An Fst of 1.0 would imply that the groups are nearly perfectly distinct at the loci of interest, while an Fst of 0.0 would imply that the groups are not genetically distinct at all. With no distinction selection would have no efficacy in terms of driving adaptation. All this is a long way to saying that the 1 migrant rule is one reason that evolutionary biologists take a skeptical position in relation to group selection. It tends to quickly erase the variation which group selection depends upon.

To make it concrete here is the equation which you use to generate the equilibrium F statistic:

In this formula N = the population size, and m = the proportion of migrants within the population within a given generation. Nm then works out to be the number of migrants in any given generation. So 1 migrant per generation would mean for 1,000 individuals m = 0.001. For 100, the m = 0.01. To see the power of a given number of migrants per generation on long term Fst, the measure of between population difference, I’ve plotted some computed results below (Fst y-axis, Nm on the x-axis).

This should make intuitive sense. If there is no migration (gene flow) between populations then over the long term they become perfectly distinct. As you increase migration naturally that is going to homogenize differences between populations. But I suspect the question you may still have is how is it that only a few individuals are necessary in even large populations to prevent differentiation?

Here the intuition is simple. In a neutral scenario between-population differences emerge as gene frequencies change over time. The generation to generation change is inversely proportional to population. This is simply the sample variance or transmission noise. The expected deviation is going to be proportional to 1/N, where N is the population (2N for diploid). As N gets rather large you converge upon zero. So as the population gets very large there is less and less divergence which may occur in one given generation. In contrast you have a lot of generation to generation variation, and rapid change in frequency, in a small population. So why only 1 migrant? In a large population 1 migrant does not effect much change, but much change is not necessary. In a small population it has much more impact, but the generation to generation change is also much bigger. These two dynamics work at cross purposes so that the number of migrants needed remains relatively insensitive to population size.

* This is the result derived from population genetics, some ecological geneticists have made the case that you may actually need 10 migrants, 1 being the lower boundary.

Image credit: Wikipedia

CATEGORIZED UNDER: Population Genetics
• http://www.scribd.com/doc/74944514/ Robert Dole

Does the less recombination-prone DNA (X, Y, mtDNA) still do this?

• Charles Nydorf

Thanks for explaining this.

• jb

OK, this makes intuitive sense for a neutral scenario, where two populations are under the same selective pressures, and the only force working to separate them is genetic drift. But the question doesn’t specify a neutral scenario, it simply asks how many migrants per generation are required to prevent the divergence of two unspecified populations, so it sounds like this should include, let’s say, a species with a large population living in a rain forest and another large population on an arid savanna. It’s not at all intuitively clear to me that one migrant per generation would prevent divergence in this scenario!

• wijjy

One small point, N is Ne here, the effective population size, which will be considerably smaller than the census population size. The proportion of migrants per generation needs to be proportionally larger by the ratio of the real to the effective population size.

This also means that – to answer the first post – that the Y chromosome and mtDNA will diverge by more than the autosomes (if we ignore sex biased migration) as only one Y chromosome migrates for every four autosomes, so Fst for the Y can be much larger.

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

a species with a large population living in a rain forest and another large population on an arid savanna. It’s not at all intuitively clear to me that one migrant per generation would prevent divergence in this scenario!

selection will keep the adaptive locus/loci different.

• jb

Yes, and that was my point. The question and answer as stated seem misleading to me, because they make it sound like one migrant per year is enough to stop any two interfertile populations from diverging, when, in fact, if selection pressures are different, populations can diverge drastically even with substantial migration. Clearly for any situation there will always be some level of migration that will prevent divergence, but it will often be much higher than one migrant per generation.

The question should make it clear that we are only talking about the neutral scenario, not the general case of any two populations.

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

The question should make it clear that we are only talking about the neutral scenario, not the general case of any two populations.

yes, but the vast majority of cases are probably neutral. so its a good null. this is usually brought up in conservation genetics fwiw.

• Robert Hymes

Surely this has to be one migrant per generation who’s _successful in reproducing_, no? But in many populations the chance of an individual’s successfully reproducing is very low. So degree of contact and number of “migrants” in the strict sense might need to be much higher than one per generation, no? Or is this already the technical sense of the word “migrant” in population genetics? In which case pardon my ignorant comment.

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

#8, i didn’t want to get into the issue of ‘effective population,’ but this is the effective migration rate. i might clarify effective population in a separate post. i wanted to keep this simple, though these questions and concerns are all useful.

• Dan

I find this amazing!

I guess the lesson here is that genetic drift is very weak for large populations.

• http://washparkprophet.blogspot.com ohwilleke

In the random, phenotypically neutral case this rule of thumb is right. But, of course, migration between groups, groups of humans anyway, is not random. It is a quintessentially selective event driven by a careful, semiconscious weighting of phenotypic traits (and often evaluation of unexpressed genotypic traits that are inferred to be likely to be present from people related to the migrant).

So, for traits that either have a selectively meaningful phenotype (or inferrable genotype) or are statistically associated with a selectively meaningful phenotype (or inferrable genotype), intergroup migration will often be assortive and enhance rather than reduce divergence between the two populations.

For example, suppose that there is a genotype associated with the Big Five personality trait conscientiousness which has a fairly high level of heritability, and that two populations – herders for whom conscientiousness has little value as a phenotype, and farmers for whom it is an extremely valueable phenotype live side by side and sometimes exchange brides. A farmer with an unconscientious daughter is likely to try to marry her off to a herder in a community where she would be more highly valued than in her own. The herder with a conscientious daughter may be likely to try to marry her off to a farmer who may value her more than the men in his community.

Of course, it doesn’t have to be bride exchange immediately. People who have the Big Five trait of openness to experience may preferrentially move to Vermont, while people who do not may preferrentially move to New Hampshire. Brown eyed brunettes born in Sweden where they are considered “un-Swedish looking” and perhaps unattractive, may preferrentially migrate to Germany where they are better appreciated. People born in the mountains who lack adaptations necessary for them to have healthy pregnancies and deliveries at high altitudes may migrate to lowlands, while people in lowlands who are adapted to high altitude may be more likely to stay in a community away from home after successfully having a child there. Afro-Caribbeans have historically intentionally tried to pedigree their descendants to a maximum degree of European admixture that undoes the gene pool sharing that took place at their birth.

Taken to an extreme, this can speed up the process of sympatric speciation.

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

Afro-Caribbeans have historically intentionally tried to pedigree their descendants to a maximum degree of European admixture that undoes the gene pool sharing that took place at their birth.

this illustrates the problem with your argument. humans don’t have a automatic genotyping system. they use coarse predictors. as i noted above, unless the trait is a prefect reflection of the whole genome selection is going to drive differentiation on a subset of loci.

• ryan

The easy theoretical counter to the fact that migration quickly diminishes the variation on which group selection is the possibility that group selection pressure may be extremely high, so that it would act to find, advantage and quickly fix relatively small differences in group genetic profile.

And indeed, that seems to correspond fairly well to at least some situations in recent human history and to putative situations in human prehistory, in which weaker groups would be wiped out, despite having some very adaptive individuals.

I’m not necessarily advocating this position. Just putting forth as a possible case in which your point about the difficulty of group selection in a setting of limited divergence can be overcome.

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

And indeed, that seems to correspond fairly well to at least some situations in recent human history and to putative situations in human prehistory, in which weaker groups would be wiped out, despite having some very adaptive individuals.

be specific, don’t be general. what situations are you thinking of?

• ryan

I don’t think it’s absurd here to mention the holocaust. (Godwin’s Law shouldn’t apply here, since I’m not calling anyone a Nazi.) Or to use a similar example, Katyn – thousands of presumably quite adaptively fit individuals wiped out because of the group they were a part of. (I use “weaker groups” strictly in a sense of what actually happened – and not any higher “ideal” sense of group weakness or strength.)

In general, I’d argue that war is and has been like this typically for centuries – that men lose because their flank is turned, through little fault of their own as individuals, and so fitness in the sense of successful reproduction has in great part depended on both the luck of what group you happened to belong to and to group dynamics that may well be partially genetically determined. One’s reproductive success may have depended in great degree on producing brave brothers and cousins and on belonging to a group predisposed to a high degree of loyalty along “fictive kinship” lines.

Obviously there are many other aspects of fitness, and in addition to competing against other groups, humans compete against other individuals in their own group, fellow villagers, cousins, sibling rivalry, etc.

It’s hard for me to understand why geneticists are so resistant to SOME degree of group fitness, since species individuals are aggregations of cooperative cells and genes that clearly survive and reproduce in large part dependent on whether the other genes and cells around them are adaptive and successful.

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

I don’t think it’s absurd here to mention the holocaust. (Godwin’s Law shouldn’t apply here, since I’m not calling anyone a Nazi.) Or to use a similar example, Katyn – thousands of presumably quite adaptively fit individuals wiped out because of the group they were a part of. (I use “weaker groups” strictly in a sense of what actually happened – and not any higher “ideal” sense of group weakness or strength.)

these are very weak to worthless examples from what i can tell. but be explicit about your genetic parameters. group selection is not just one group killing another.

It’s hard for me to understand why geneticists are so resistant to SOME degree of group fitness

do you know the math? if you don’t, then it may be hard. the math isn’t hard btw in a technical sense. but if you don’t know the basics you shouldn’t be offering up your opinion on the issues (or at least just say you’re lay person’s perspective blah, blah).

• ryan

Fair enough. I feel I have a good intuitive sense of the math – following your argument and understanding which direction the arrows point given certain gene flows. I don’t have time to work it out fully for myself just now. You’ve given a fuller account of your view in your more recent post on monogamy (monogyny?) which is really interesting. I do recognize that you’ve got a much more solid understanding of the math. So I’m writing back here only by way of disengaging respectfully given time constraints. I love the blog and only venture to comment every now and then.

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

#17, understood.

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