The Rise of Human Chromosome 2: Fixation Within a Deme

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This essay is the third of a series authored by Dave Wisker, Graduate Student in Molecular Ecology at the University of Central Missouri.

In previous essays in this series, I have discussed two issues with the fusion that resulted in human chromosome 2: its dicentric nature, and the fusion’s possible effect on fertility. I showed how one extra centromere may not result in inevitable damage to the chromosome during meiosis and mitosis, and demonstrated that the fusion did not necessarily have to result in greatly decreased fertility. Either of those situations would have effectively prevented the fusion from rising in frequency and eventually becoming fixed in the human population. We are now in the position to consider the probability of such a fusion becoming fixed. This essay will examine the fixation probability of the fusion in a small subpopulation, or deme.

The first order of business is to get a better idea of what actual effect the chromosome fusion may have had on fertility. Even though some fusions are known to have little, if any, effect, the fact is many do decrease fitness to some extent. Lande (1979) was of the opinion that fusions which resulted in metacentric chromosomes with arms that were roughly equal in size would not greatly reduce fertility in heterozygotes, and suggested that the heterozygote disadvantage for human chromosome 2 was probably only a few percent for that reason. Bengtsson (1980) and Bengtsson & Bodmer (1976) looked at human population karyotype data to estimate the fitness effect of chromosomal rearrangements. They determined the relative frequencies of de novo and inherited chromosomal rearrangements in all human newborns in a particular region in Britain. The ratio of new mutations to those which have been inherited can give an idea of a rearrangement’s mean fitness effect. The reasoning is simple. If a rearrangement (like a translocation or fusion) appears in a population and isn’t eliminated by drift, then it will exist in most individuals as a heterozygote in the early generations. If the heterozygous state has a drastic effect on fertility, then successfully inherited rearrangements in live born children will be very rare in the population, in roughly the same order of rarity as those which have newly arisen via mutation. So, for any given chromosomal rearrangement, the ratio of new mutations to the total number (inherited plus new mutations) gives a rough estimate of its mean fitness: the higher the ratio, the lower the fitness. Using this reasoning, Bengtsson (1980) reported that reciprocal translocations showed a 30% average decrease in fitness, but for fusions the average decrease in fitness was only around 10% (and lower in some cases). I will therefore use a 10% heterozygote disadvantage as a plausible value for human chromosome 2 in the subsequent calculations below.

Several factors can influence the frequency of a chromosomal rearrangement in a population:

  1. Mutation (recurrence of the same rearrangement)
  2. Emigration/immigration (gene flow between populations/demes)
  3. Natural selection
  4. Genetic Drift
  5. Inbreeding
  6. Meiotic drive (segregation bias at meiosis)

The head-to-head fusion that resulted in human chromosome 2 is extremely rare, so recurring fusions creating significant mutation pressure can most likely be ruled out. For the moment, we will also leave aside emigration/immigration, but will return to it later. That leaves:

  1. Natural selection
  2. Genetic Drift
  3. Inbreeding
  4. Meiotic drive (segregation bias at meiosis)

Hedrick (1981), expanding on earlier work by Sewall Wright and others, developed models for the probability of fixation of chromosomal rearrangements in both very large (essentially infinite) and finite (including very small) populations, where there was a heterozygote disadvantage. For the large population model (which renders the effects of genetic drift and inbreeding negligible), he restricted himself to the effects of selection and meiotic drive.

Meiotic drive is simply a deviation from normal chromosomal segregation frequencies. Under normal segregation, a heterozygote for a chromosome rearrangement will produce 50% of its gametes with the rearrangement, and 50% with the normal karyotype. If there is a bias to segregation, that is, if there is a deviation from 50%, then meiotic drive is said to be occurring.

Hedrick noted that meiotic drive is rarely present in both sexes, so his model restricted its effect to one sex (females). He represented meiotic drive mathematically this way:

The heterozygotes for the rearrangement produce m of the rearrangement and 1-m of the normal karyotype in the gametes. In other words, m is the percentage of gametes carrying the fusion. For normal segregation, then, m =0.5. If there is meiotic drive in favor of the fusion, the value of m will be between 0.5 and 1.

For natural selection, Hedrick used standard population genetics nomenclature. He assigned the two homozygous karyotypes fitnesses of 1, and the heterozygote karyotype a fitness of 1-s (to reflect a heterozygote disadvantage). Those familiar with population genetics will recognize s as the selection coefficient, and it reflects the effect on viability and fertility. For the moment, we will not assign any values to m or s, but simply see how they affect the frequency of the fusion. In Hedrick’s paper, p and q are the frequencies of the normal and the fusion karyotypes, respectively.

Hedrick went on to derive the equation that defines the conditions for what is called an unstable equilibrium value for q. Homozygotes for the fusion have normal fertility vs. a selective disadvantage for the heterozygote. As the frequency of the fusion rises, the more copies of the fusion there are in the population, which in turn increases the chance of fusion homozygotes being formed. This creates more individuals who can out-reproduce the heterozygotes, and if there are enough of them, the rise in frequency will take on an inertia of its own. There is a critical frequency for the fusion– the unstable equilibrium frequency–which, once exceeded, will allow the fusion to drive to fixation despite selection against the heterozygote. That is, if the unstable equilibrium frequency is exceeded, a tipping point will be reached where the fusion karyotype will act as if it were under positive selection. The unstable equilibrium frequency (q(e)) depends on both the levels of selection and meiotic drive (s and m, respectively) as follows:

As an example, if we give the heterozygote a 10% fitness disadvantage ( s = 0.1), but keep segregation normal (no meiotic drive, i.e., m = 0.5), we get:

This means that the frequency of the fusion has to reach 0.50 before it can achieve the ‘momentum’ to drive to fixation, even with a relatively low level of selection against the heterozygote. Of course, in a large population, getting to this point is very, very difficult to do. But what happens if we posit a low level of meiotic drive in favor of the fusion (m = 0.6), while keeping the selection against the heterozygote at 0.1? The results are dramatic:

Just a small amount of meiotic drive has lowered the unstable equilibrium point by 90%. The fusion only has to reach a frequency of 0.05 before the combination of forces will automatically drive it to fixation.

I will leave it as an exercise for the reader to plug in various values of s and m. It will soon become clear that moderate to strong selection against the heterozygote will effectively prevent fixation of the fusion in very large populations, regardless of the level of meiotic drive. On the other hand, relatively weak selection can be countered by even moderate meiotic drive.

That is the large, essentially infinite, population model. Of course, in nature, populations are never infinite, and often structured into smaller, locally breeding subpopulations–called demes– with effective population sizes (in many vertebrate species) between 10 and 100 (Wilson, 1975). Presumably, early human or ancestral hominid populations fell under this model, so when we consider the probability of fixation of a chromosomal fusion in early humans, we can assume the fusion arose in a small deme and spread from there. In doing so, however, we have to bring back the two forces we left out when we considered large populations, namely genetic drift and inbreeding.

Genetic drift is present in all finite populations, regardless of size. It is defined as changes in frequency due to chance variations in reproduction that occur in all organisms. Its main effect is to reduce heterozygosity of a population over time. Since loss of heterozygosity has to be made up by an increase in homozygosity, drift actually increases the probability of fixation of one allele (or chromosomal variant). Drift reduces the heterozygosity by 1/2N per generation. Thus the amount of heterozygosity removed per generation is inversely proportional to the population size: as the population size decreases, the proportion of heterozygosity removed by drift increases. This means the frequency of homozygotes of one allele will also increase over time. Which allele eventually becomes fixed is primarily due to chance, but forces like meiotic drive can influence the outcome for one allele over another, as we shall see later.

Inbreeding is another force that has a stronger effect in small populations than in large ones. Inbreeding essentially increases the probability that the gene copies on the two chromosomes of an individual are related by descent. Obviously, if close relatives mate, their offspring will have a greater chance of having genes related by descent than those of offspring from distantly related individuals. It should also be clear that in small, isolated demes, the chances of genes being related by descent is higher than in large populations. Like genetic drift, inbreeding also reduces heterozygosity. To actually calculate its effect, however, requires detailed pedigree information, and since we are dealing with prehistoric populations, the chance of getting that is pretty slim. About all we can say is, the degree of inbreeding in small populations is higher than that in large ones.

With the above background, we are now ready to consider the probability of fixation of the fusion in a single deme.

Getting back to Phil Hedrick’s paper (previously cited), he synthesized the effects of drift with natural selection and meiotic drive, and worked out the probabilities of fixation for chromosomal variants with various population sizes, which he summarized in Table 2. Here are some interesting illustrative values:

Population size: 40 individuals

s: 0.3 m: 0.5 (no meiotic drive): Probability of fixation: 10 -5

m: 0.6 (low level meiotic drive): Probability of fixation: 0.0002

s: 0.1 m: 0.5 (no meiotic drive): Probability of fixation: 0.00046

m: 0.6 (low level meiotic drive): Probability of fixation: 0.045

Population size: 20 individuals

s: 0.3 m: 0.5 (no meiotic drive): Probability of fixation: 0.00008

m: 0.6 (low level meiotic drive): Probability of fixation: 0.0015

s: .01 m: 0.5 (no meiotic drive): Probability of fixation: 0.0056

m: 0.6 (low level meiotic drive): Probability of fixation: 0.068

Population size: 10 individuals

s: 0.3 m: 0.5 (no meiotic drive): Probability of fixation: 0.0039

m: 0.6 (low level meiotic drive): Probability of fixation: 0.017

s: 0.1 m: 0.5 (no meiotic drive): Probability of fixation: 0.026

m: 0.6 (low level meiotic drive): Probability of fixation: 0.102

It should be clear from these selected values that low values of meiotic drive increase the probability of fixation considerably in small populations, just like it does in large ones. For low selection (i.e, s = 0.1) the probability ranges from 4.5 % to 10 % for various population sizes; however, moderate values of selection against the heterozygote keep the probability well below 1%, with low meiotic drive. Table 2 also shows that moderate selection against the heterozygote with very high values of meiotic drive, say 0.8 or 0.9, has probabilities of fixation between 10 and 20% .

So the question is, does meiotic drive for chromosomal fusions occur in humans? The answer is yes. Pardo-Manuel de Villena and Sapienza (2001) have shown that, in human female heterozygotes, ~60% of the balanced gametes contain fusions. This translates to an m value of 0.6. So, for humans at least, the level of meiotic drive is low.

Looking back at Hedrick’s paper, and using the values for s and m which are reasonable for humans, even with a population of 40 individuals, the probability of fixation within a deme is 4.5%, and for ten individuals it is 10%. This is not very high, but well within the realm of possibility. It should be very clear then, that modern evolutionary theory can provide a naturalistic explanation for how fixation can occur within a deme. What is left is to consider the probability of fixation beyond the deme to the species itself. That will be the subject of the final essay in this series.

References

  • Bengtsson BO (1980). Rates of karyotypic evolution in placental mammals. Hereditas 92: 37-47.
  • Bengtsson BO and WF Bodmer (1976). The fitness of human translocation carriers. Ann. Hum. Genet London 40: 253-257.
  • Hedrick P (1981). The establishment of chromosomal variants. Evolution 35(2): 322-332.
  • Lande, R (1979). Effective deme sizes during long term evolution estimated from rates of chromosomal rearrangement. Evolution 33(1):234-251.
  • Pardo-Manuel de Villena F and C Sapienza (2001). Transmission ratio distortion in offspring of heterozygous female carriers of Robertsonian translocations. Hum. Genet. 108: 31-36.
  • Wilson, EO (1975). Sociobiology: The New Synthesis Belknap Press, Cambridge MA.

24 Comments

Dave Wisker’s previous posts on the rise of chromosome 2 are The Dicentric Problem and The Fertility Problem.

Thanks, RBH!

I’m in the Dunnellon, FL library, and I’m not sure about the email I sent, but here is the same tip:

In posts, we support equations via <eqn></eqn> tags that will accept any LaTeX formatted equation. If you need help converting the equations, I’m sure the math people on the email list can help you with the format.

Dave,

I will be hearing a bit about this from Ken Miller (again) tonight. He’s giving the annual Brown University Club in New York “Meeting of Minds” lecture.

Thanks for a great series of posts.

Best,

John

I hope this doesn’t count as off-topic since this thread is specifically about fixation.

I have a question regarding chromosome 2’s vestigial centromere. Would it have to have been deactivated at the time of the fusion event or is a chromosome with two functioning centromeres viable?

Also, many thanks to Art Hunt for the publishing help.

I’m probably the least likely person to try answering this since my own knowledge about chromosomal structure is minimal. But I am inclined to suspect that that vestigial centromere was deactivated at - or soon after - the fusion event:

Dean Wentworth said:

I hope this doesn’t count as off-topic since this thread is specifically about fixation.

I have a question regarding chromosome 2’s vestigial centromere. Would it have to have been deactivated at the time of the fusion event or is a chromosome with two functioning centromeres viable?

Hi Dean,

I discuss this in the “Dicentric Problem” link that RBH provided in the first comment.

Dave, John, and RBH

Thanks. I didn’t do my homework. Worse than that, a title like The Dicentric Problem didn’t even sink in.

Most embarrassing of all, I just reread the first paragraph, which clearly addressed my question and pointed me to the appropriate source.

These articles are great.

I tend to just read and appreciate when there is actual discussion of science (*unless I have a point or question about science*). But the appreciation is there.

John Kwok said:

Dave,

I will be hearing a bit about this from Ken Miller (again) tonight. He’s giving the annual Brown University Club in New York “Meeting of Minds” lecture.

Thanks for a great series of posts.

Best,

John

Hi John,

You lucky dog. I’ve always wanted to hear Miller speak in person.

Dave Wisker said:

Under normal segregation, a heterozygote for a chromosome rearrangement will produce 50% of its gametes with the rearrangement, and 50% with the normal karyotype.

This must make sense with mammalian gametogenesis somehow. With just meosis you’d end up with 50% new chromosome and 50% aneuploid. ?

Mike said:

Dave Wisker said:

Under normal segregation, a heterozygote for a chromosome rearrangement will produce 50% of its gametes with the rearrangement, and 50% with the normal karyotype.

This must make sense with mammalian gametogenesis somehow. With just meosis you’d end up with 50% new chromosome and 50% aneuploid. ?

Would that be in the first generation with the rearrangement?

Yes, sorry. “Heterozygote for the rearrangement.” not “with the rearrangement.”

Since human chromosome 2 is a fusion of corresponding ape chromosomes 2p and 2q, would the heterozygous karyotype be considered aneuploid? There wouldn’t be any duplication or deletion of genetic material.

I assume that during meiosis in an individual heterozygous for the fusion, a gamete would either get a set of 2p and 2q or a single 2, not some combination like 2p and 2.

Mike said:

Dave Wisker said:

Under normal segregation, a heterozygote for a chromosome rearrangement will produce 50% of its gametes with the rearrangement, and 50% with the normal karyotype.

This must make sense with mammalian gametogenesis somehow. With just meosis you’d end up with 50% new chromosome and 50% aneuploid. ?

Actually, any heterozygote for the fusion

Mike said:

Mike said:

Dave Wisker said:

Under normal segregation, a heterozygote for a chromosome rearrangement will produce 50% of its gametes with the rearrangement, and 50% with the normal karyotype.

This must make sense with mammalian gametogenesis somehow. With just meosis you’d end up with 50% new chromosome and 50% aneuploid. ?

Would that be in the first generation with the rearrangement?

Any heterozygote for the fusion will produce approximately 50% fusion and 50% normal gamets

Mike said:

Mike said:

Dave Wisker said:

Under normal segregation, a heterozygote for a chromosome rearrangement will produce 50% of its gametes with the rearrangement, and 50% with the normal karyotype.

This must make sense with mammalian gametogenesis somehow. With just meosis you’d end up with 50% new chromosome and 50% aneuploid. ?

Would that be in the first generation with the rearrangement?

You bring up a great point. There will be some aneuploid gametes produced, given the 10% fertility disadvantage. However, of the remaining balanced gametes, there should be a roughly 50/50 split of fusion and normal, assuming no meiotic drive.

Does that address your question?

Hi Mike,

That last comment was mangled. This is the nly part that should have been published:

You bring up a great point. There will be some aneuploid gametes produced, given the 10% fertility disadvantage. However, of the remaining balanced gametes, there should be a roughly 50/50 split of fusion and normal, assuming no meiotic drive. Does that address your question?

Sorry about that. You asked a great question.

Hi Dean,

Dean Wentworth said:

Since human chromosome 2 is a fusion of corresponding ape chromosomes 2p and 2q, would the heterozygous karyotype be considered aneuploid? There wouldn’t be any duplication or deletion of genetic material.

I assume that during meiosis in an individual heterozygous for the fusion, a gamete would either get a set of 2p and 2q or a single 2, not some combination like 2p and 2.

The heterozygote karyotype isn’t aneuploid, but some gametes will be, given that segregation is affected (but not greatly) by the fact the “normal” two chromosomes must align correctly with the fused chromosome. In some cases the alignment will not be right and some gametes will be produced either missing some chromosomes or having extra copies. It is these aneuploid gametes that are presumably responsible for the 10% loss of fitness for the heterozygote.

It’s proven to be quite popular. I heard from the Brown Club president that there are a lot of people trying to get in, and it’s been completely sold out since last Friday morning. Ken’s due back here early next month to speak at a World Science Festival panel discussion on the relationship between science and religion (I believe it’s the same one that Jerry Coyne has mentioned at his personal blog recently.), so I suggested that maybe some of those who’ve RSVPed might wish to attend that instead:

Dave Wisker said:

John Kwok said:

Dave,

I will be hearing a bit about this from Ken Miller (again) tonight. He’s giving the annual Brown University Club in New York “Meeting of Minds” lecture.

Thanks for a great series of posts.

Best,

John

Hi John,

You lucky dog. I’ve always wanted to hear Miller speak in person.

Hi Dave,

I admit that this is a little off topic, but I just came from Ken’s talk. I asked him about Jerry Coyne’s recent essay critical of NCSE’s - and other scientific/science advocacy organizations - efforts at reaching some kind of “accommodation” with religion. He doesn’t see that activity to be anything more than to tell devout Christians, Jews, Muslims and others that they can accept valid science like evolution and still retain their deeply-held religious beliefs. He also said something remarkable, suggesting that those who believe in a religious faith that can’t be tolerant of modern science, should reconsider their acceptance of such a faith, and indeed, be prepared to discard it. The talk focused on the ongoing political battles between those who are scientifically literate and evolution denialists, and of course, reviewed such “notable” features of ID as “irreducible complexity” (using of course both Behe’s “mousetrap” and bacterial flagellum models), and compelling evidence for evolution such as the fish to tetrapod transition, and even, a quick reference to the newly announced early Cenozoic primate fossil from Germany.

Regards,

John

Dave Wisker said:

John Kwok said:

Dave,

I will be hearing a bit about this from Ken Miller (again) tonight. He’s giving the annual Brown University Club in New York “Meeting of Minds” lecture.

Thanks for a great series of posts.

Best,

John

Hi John,

You lucky dog. I’ve always wanted to hear Miller speak in person.

Dave, thanks for the article. I’ll get back to reading it, but I’ll mention something that coincidentally involves a comment I just left you on the other thread. I first heard Ken Miller’s “Gov. Huckabee, you are a primate” quote at a talk he gave in Philadelphia last Darwin Day. There he showed slides of the chromosome 2 fusion and asked for a show of hands of how many in the audience had heard of that before. Even though there appeared to be many college science majors and scientists in the audience, less than half, and possibly as little as 1/4, raised our hands. While that fraction is rather depressing, without excellent work like yours and that which you cite, it would be zero.

Thanks, Frank. The point you make is exactly why I wrote the essays. ID proponents like Luskin and Jonathan Wells count on the basic scientific naivete of the public. It enables them to make the ridiculous pronouncements they do because they know most people do not have the background to realize what they are saying is incorrect. Human Chromosome 2 is a great example. To refute Luskin’s throwaway line about how it could not become fixed via Darwinian means takes a lot of time, and requires a knowledge of some sophisticated biology (population genetics and cytogenetics) that the public simply does not possess.

I can only hope these essays give lay people some tools to see through these cynical ID arguments. Knowledge is power.

Frank J,

Well I didn’t hear the Huckabee quote from Ken last night. However, he did review the political situtation and it’s rather sobering to think that there have been anti - evolution efforts with regards to public school science education in forty four of the fifty states in the last few years. He did warn that the next “battleground” will be in Texas, simply because the State Board of Education will meet next spring to review textbooks so that they conform with their newly enacted standards (including of course Ken and Joe Levine’s popular biology textbook). He did acknowledge that he regards LA as a loss on our side, in light of Bobby Jindal’s signing of his state’s DI-crafted “Academic Freedom” bill.

Best,

John

P. S. Just a note to Texans who may be reading this. I strongly encourage them to vote to ensure that their State Board of Education has a majority that is pro-science. So by all means I hope they’ll defeat those candidates who aren’t, including, of course, the Xians who claim to be fellow “Republicans”.

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