EEB 122. Principles of Evolution, Ecology and Behavior?

Lecture 06.?The Origin and Maintenance of Genetic Variation

https://oyc.yale.edu/ecology-and-evolutionary-biology/eeb-122/lecture-6

We're going to talk about the origin and maintenance of genetic variations.?The reason we're interested in this is that there cannot be a response to natural selection, and there cannot be any history recorded by drift, unless there's genetic variation in the population.?

The classical view?was that?there wasn't very much genetic variation out there and that evolution was actually limited by the rate at which genetic variation was created.?Since 1965, with the discovery of protein isozymes, and especially now, since the discovery of ways to sequence DNA very cheaply, we know that's not true.?There is a tremendous amount of genetic variation in nature.?So since about 1975, 1980, due to a series of studies?on the Galapagos finches,?the guppies in Trinidad,?mosquitofish in Hawaii, and?the world's fish populations responding to being fished, we know that evolution can be very fast when there's strong selection acting on large populations that have lots of genetic variation.?

So really the rate of evolution--and, for example, the issue of climate change and global warming--will all the species on earth be able to adapt fast enough to get--to persist in the face of anthropogenic change on the planet??Is there?enough genetic change to adapt?

So the outline of the lecture today basically is this.?

• Mutations are the ultimate origin of all genetic variation.

• Recombination has a huge impact on variation.

• So what that means basically is that sexual populations have the potential to be much more variable than asexual populations--there is lots of genetic variation in natural populations.

• Then we will run through four mechanisms that can maintain variations in single genes, and briefly mention the maintenance of variation in quantitative traits.?

Mutations are where these genetic differences come from, and they can be changes in the DNA sequence or changes in the chromosomes, and in the chromosomes they can be changes in how many chromosomes there are in the form of chromosomes or in aspects of chromosome structure.?Most of the mutations that occur naturally are mutations that are occurring during DNA replication.?

The probability that a cancer will emerge in a tissue is directly proportional to the number of times cells divide in that tissue; which is why cancers of epithelial cells (skin,?lungs, and in the lining of your gut)are much more common than cancers of cells that do not divide (heart muscle). And that's because every mitotic event is a potential mutation event.?

The kinds of DNA sequence mutations are point mutations; there can be duplications, and in the chromosomes as well there can be inversions and transplacements that go on. Genes can be moved around from one chromosome to another. They can actually be turned around so that they are in the opposite reading direction, along the chromosome.?

There's good reason to think that an intermediate mutation rate is optimal. If the mutation rate is too low, then the descendants of that gene cannot adapt to changed conditions. If it's too high, then all the accumulation of information on what has worked in the past will be destroyed by mutation; which is what happens to pseudogenes that are not expressed.?

Now a gene that controls the mutation rate will evolve much more easily in an asexual organism than in a sexual species because sexual recombination uncouples the gene for the benefits of the process.?Recombination, instead of keeping genes?on the same chromosome,?will actually end up putting genes?into a different body.?So in a sexual organism the gene that's controlling the mutation rate becomes disassociated from the genes whose mutations it might try to control.?So it is much more plausible that we will see genes that are controlling mutation rates evolving in organisms like bacteria and viruses than it is that we will see mutations that control mutation rates evolving in us.?

How frequent is a mutation? So the per nucleotide mutation rate in RNA is about 10^-5; in DNA it's 10^-9.?DNA is a remarkably stable molecule.?The per gene rate of mutation in DNA is about one in a million; so this is like per meiosis. The per trait mutation rate is about 10^-3?to 10^-5. The rate per prokaryotic genome is about 10^-3, and per eukaryotic genome it's between .1 and 10.?

Now what is your mutation rate? Well each of you has about four mutations in you that your--new things, your parents didn't have, and about 1.6 of those are deleterious.?Mutations?happened fifty times more in males than in females.?There are many more cell divisions between the formation of a zygote and the production of a sperm than there are between the formation of a zygote and the production of an egg. The result of that is that there are more mutations in the?sperm of older males;?they've lived a longer time.?

Females have a mutation?screen that males do not.?In human development, and in mammal development, egg production pretty much stops in the third month of embryonic development, at which point all the women in this room had about seven million eggs in their ovaries.?Since then oocytic atresia, which means the killing of oocytes, has reduced the number of eggs in your ovaries down by nearly seven million. When you began menstruating you had about 1500 eggs in your ovaries. You've gone from seven million down to 1500. When you were born you had gone from seven million down to one million; you'd lost six million of them before you were even born. It appears to be a quality control mechanisms, ensuring that the oocytes that survive are genetically in really good shape.?

Now if we had a real eukaryotic genome that had free recombination--which we don't have--and unlimited crossing over--which we don't have--then the number of possible zygotes is about 315,000?or 350,000.?(Crossing over happens more frequently the farther genes?are apart on a chromosome, and it doesn't happen very often when they're close together.)?Well the number of fundamental particles in the universe is only 10131. That means that in the entire course of evolution the number of genetic possibilities that are present?have never been realized. There is a huge portion of genetic space that remains unexplored, simply because there hasn't been enough time on the planet for that many organisms to have lived.?

The chromosome number of the species itself evolves?fairly dynamically. There are actually some populations within a single species that have a different chromosome number than other populations within that species, and when individuals from those two populations meet and mate with each other, the offspring often run into developmental difficulties because of this difference in chromosome number.?

Crossing over also generates a lot of genetic diversity. And the amount of crossing over can be adjusted. Inversions will block crossing over. You take a chunk of chromosome and flip it around, so that in the middle of the chromosome the gene sequences are reversed, and in that section of the chromosome the inversion causes mechanical difficulties. It actually changes the shape of the chromosomes when they line up next to each other, and it inhibits crossing over during meiosis.?

We could wave a magic wand over a moderately large sexual population, completely shut off mutation, and the impact of recombination on the standing genetic diversity in that population would create so many new diverse combinations of genes that it would take about 1000 generations before we would even notice that mutation has been shut off.?I said mutation is the origin of all genetic diversity; and that's true. But once mutation and evolution have been going on for awhile, so much genetic diversity builds up in populations that you can actually shut off mutation and?evolution will keep going for quite a while. After 1000 generations it'll run out of steam and stop; but it takes quite awhile.?

After 1965, with electrophoresis, the impact of Clement Markert's work, and Dick Lewontin, and his colleague Hubby, we've recognized that there's a lot of molecular variation. This concept that each species has a certain genomic type is no longer tenable. There's just a tremendous number of different kinds of genomes out there. Since 1995, we've had a lot of DNA sequence variation and now we've got genomics.?Once we had the human genome, it was clear that we could then look for places in genomes that had single nucleotides, that were different, between one person and another; these are called single nucleotide polymorphisms.?

Now if you take this and you then use the tools of phylogenetic analysis to ask what kind of historical structure is there in this data set, this is what you get. You can see the emergence of mankind from Africa--this is thought to have happened about 100,000 years ago.?We paused for awhile in the Middle East, before we broke out. We were in the Middle East up until about 50,000 years ago, and then there was a group that went into Europe, and other groups then split off from that and set off into Asia. And about probably 40,000 years ago people went to Papua New Guinea and Australia, and probably somewhere around between say 15 and 20,000 years ago, a group of people headed off over the Bering Straight for North America, to become Native Americans, and then another group diversified in East Asia. So there is a huge amount of information in the history of genetic variation.?

Selection and drift can both explain the maintenance of genetic variation.?It's extremely difficult to answer, in any specific case, whether the pattern you see is because of a history of natural selection or because of a history of drift. Both of them are capable of generating quite a few patterns, and those patterns overlap.?So here are four situations that can maintain genetic variation in principle:

1. there can be?a balance between mutation and drift;

2. there can be?a balance between mutation and selection;

3. there can be heterosis or over-dominance;

4. there can be negative frequency dependence.

We're going to be dealing with equilibria.?We do it because the periods during which things are in balance may be pretty long, compared to those in which they're dynamically changing.?We do know that in terms of our immune genes that we share certain polymorphisms with chimpanzees. Those appear to have been things that evolved in terms of disease resistance before humans and chimps speciated, about five to six million years ago. So certainly that genetic variation is five to six million years old.?

The fixation probability of a mutation is the probability that it will spread and be fixed in the population. That's equal to its frequency, at any point in time.?The fixation probability is the probability that out of all of the mutations that might arise, most of which drift out, this one will be fixed; and that's a small number.?

The fixation time is how long it takes to become fixed in generations, or?on average how long it takes for this process to occur.

• If this is frequency here, it can go from 0 to 1, on the Y axis, and if this is time, on the X axis, this can be many thousands of generations.

• And the fate of most neutral alleles, when they come into the population, will be to increase in frequency for a little while and then drift out. They have low probability of being fixed because when they first originate they're very rare, and the probability of eventual fixation is just directly equal to their frequency. So in a big population most mutations disappear.?But every once in awhile one will drift through, and when it reaches frequency 1.0, it's fixed.

• Now for a neutral allele, the fixation rate is just equal to the mutation rate. That doesn't depend on population size. The probability of fixation?is equal to the current frequency. For a new mutation,?that's 1/2N, to be fixed, and 1-1/2N?to be lost. That means that most of them are lost. N is the population size. N is a big number.

• Because there are 2N copies of the gene in the population, and if mu is mutation rate, that means in each generation there are 2mu new mutations, and for each of them the probability of fixation is 1/2N. So the rate of fixation of new mutations is about 2mu times 1/2N, which is equal to the mutation rate. That's about 10^-5?to 10^-6?per gene, and that means the molecular clock is ticking once every 100,000 to once every 1,000,000 generations per neutral gene.

• The fixation rate doesn't depend on the population size, and that's because the probability that a mutation will occur in a population depends upon how many organisms are there. You can think of all of their genomes out there as being a net spread out to catch mutations--the bigger then net, the more the mutations are in any given generation--and that will just exactly compensate for the fact that it takes them longer to get fixed. The bigger the population, the longer this process takes. But the bigger the population, the more of these are actually moving through to fixation. Those two things exactly compensate.

• In a small population most of them are lost. The few that do reach fixation, reach it rapidly, and in large populations more new mutations are fixed, but each one does it more slowly. Those things compensate, and the fixation rate doesn't depend on population size, if you're looking at the whole genome. The number of differences fixed over the whole genome doesn't depend on the size of the population.?

Now there is a technical concept in evolutionary genetics called?effective population size, and that is the size of a random mating population, that is not changing in time, whose genetic dynamic would match those of the real one under consideration.?We take a real population and then transform it into something that's really easy to calculate.?The factors that will have to come into consideration are variation in family size, inbreeding, variation in population size, and variation in the number of each sex that is breeding.?

There are about 100,000,000 female cattle in North America. They are fertilized by four males, on average, through artificial insemination. So there are four bulls that are inseminating 100,000,000 cows. Genetically speaking, how big is the population? It's just about 16.?So by restricting one sex to a very small number, we have restricted one pathway that the genes can go through to get to the next generation. Every time one of those genes goes through a female and goes into a baby and grows up the next generation, it's going to go back through the male side of the population?as you go through the generations.?

So that's the basis of a mutation-drift balance. The amount of genetic variation in a population, in a mutation-drift balance, is just a snapshot of the genes that are moving through it.?

Now the second possibility for a mechanism that will maintain genetic variation is a balance between mutation and selection.?

• Mutation brings things into the population. Selection takes them out. So if we had a haploid population, with N individuals, and we have a mutation rate mu, we're getting Nmu new mutations each generation. The key idea is that if there is a mutation selection balance, then the number going in equals the number going out; that's what would keep this mechanism balancing the amount of genetic variation in the population.

• If the mutant individuals have a lower fitness than the non-mutants, and if q is the frequency of the mutants, then selection is taking out NSq mutants per generation. And at equilibrium, with the number coming in equal to the number going out,?and that gives us an equilibrium frequency of the mutation rate divided by the selection coefficient. It's a very simple result.

• And if you do the same kind of thinking for a diploid population, you get that the equilibrium frequency will be the square root of the mutation rate, divided by selection for recessives, and the same as it is for haploids for dominance.?

There are rare human genetic diseases, such as phenylketonuria--that's the inability to metabolize phenylalanine. It has a frequency of about 1 in 200,000, in Caucasians and Chinese. It is probably in selection mutation balance. It's at low frequency but it's present in a population. People with it suffer a selective disadvantage. It keeps mutating and coming back in, and it keeps getting selected out. The result is balance?and it's pretty rare.

The third mechanism that will maintain selection in natural populations is a balance of selective forces; that is, where the heterozygote is better than either homozygote. And there is a classic, famous case, and it's always discussed in this context, and it's interesting that it's the one that's always discussed in this context, and the answer is it's been hard to find more. That's sickle cell anemia.?

Now this is the normal heterozygote which is susceptible to malaria. The heterozygote is resistant to malaria, and the sickle cell homozygote is anemic and sick. And it sets up this kind of relative fitness.?So the fitness of the heterozygote is going to be higher than the fitness of either homozygote. And you can then set--the equilibrium frequency is going to be the one where P prime is equal to p; in other words, the frequency in the next generation is just the same as the frequency in this generation.?

At what frequency does that happen? Well it happens when these little equations are satisfied. And the interesting thing, when you look at them, is that the selection coefficient has dropped out of them. The equilibrium frequency doesn't depend on the selection pressure, it depends on how frequently the gene is expressed in a heterozygote. So it depends really on the heterozygote advantage.?

Now the real situation is more complicated than this. There are several such sickle alleles. They're changing frequency. The equilibrium assumption doesn't really apply out there in Nature, but it does give us a rough rule of thumb for how much to expect, and as soon as people who have sickle cell anemia move out of areas with malaria, it takes quite awhile for that allele to disappear from the population.?

The fourth mechanism is a balance of selection forces, so that, for example, for A2, when A2 is 0, it has high fitness here, and as it increases in frequency,?its fitness drops,?according to this equation. Now the frequencies of A1 are just reversed along this axis. A1 is 1.0 here, and it's 0 here. A1 has low frequency--has low fitness when it's at high frequency, and high fitness at low frequency. A2 has high fitness at low frequency; low fitness at high frequency. So both of them do better when they are rare. And I think that you can see intuitively from this diagram that at equilibrium they will stop changing when their fitnesses are exactly the same.?

Now there are some interesting examples of this sort of thing. One is Ronald Fisher's classical argument on why 50:50 sex ratios are so common; why in many populations we see half females and half males. The deviations from that are interesting. This kind of thing happens with evolutionary stable strategies, and those are the solution to many problems within evolutionary game theory. They are also called Nash equilibria, under certain circumstances, and they are important in economics and political science as well.?

And the tremendous amount of genetic variation in the immune system is thought to exist for reasons of frequency dependent selection; basically pathogen resistant genes gain advantage when they are rare, because when they're common, the pathogens evolve onto them. They are more or less sitting ducks; they're a stable evolutionary target. But as they become more common and more and more pathogens evolve onto them, and those organisms get sicker and sicker, the ones that are rare have an advantage. And then as they start to increase in frequency, the same process occurs; the same process, it continues again, and after awhile you've got hundreds of genes, each of which is advantageous at low frequency, and none of which are advantageous at high frequency.?

If we look at quantitative traits, such as birth weight--here's a classical example. This is for babies born in the United States in the 1950s and 1960s, and this is the percent mortality for babies of different weights. You can see that there's stabilizing selection that's operating to stabilize birth weight right at about 7 pounds, and there's variation around it. And you might wonder, why is there any variation around that? Why don't all babies have the optimal birth weight??

1. One is that there are evolutionary conflicts of interest between mother and infant, and father and mother, over how much should be invested in the infant, and these lead to some variation.

2. And there's mutation selection balance. So that this is a trait which is probably determined by hundreds of genes, and at each of those genes mutations are coming into the population, and at each of those genes there is a mutation selection balance, and when you add that up, over hundreds of genes, you get quite a range of variation.

3. Some of this variation is also due to developmental effects of the environment; variations in the mother's diet and other parts of her physiological condition during pregnancy.?

The origin and maintenance of genetic variation are key issues; mutations are the origin. Recombination has huge impact. There's a tremendous amount of genetic variation in natural populations. Remember that data from the HapMap Project on us, on humans, and that all of the differences that you have, in single nucleotide polymorphisms, from the person sitting next to you, and how you share them with people who have had a similar history since we came out of Africa.?

We can explain the maintenance of this variation by various kinds of mechanisms, principally for balance between mutation and drift, between mutation and selection, and by some kind of balancing selection, either heterosis or frequency dependent selection. And we think that variation in many quantitative traits--human birth weight, human body size, athletic performance, lots of other things--is probably maintained by mutation selection balance, as well as by other factors.?