Wisconsin Public Television University Place Genetics Colloquium  James Crow, "The Progress of Genetics From the 1930s to Today"  November 3, 2010 UP514  cc >> Millard Susman: When we were planning the colloquium series for this semester, our objective in designing the colloquium was to celebrate the centennial of the laboratory of genetics, which is to say the centennial of the Department of Genetics, and the 50-year anniversary of the founding of the Department of Medical Genetics. And we specifically designed the colloquium with the thought in mind that we wanted to inspire graduate students, to let you know what a great department we are, a great place to be a geneticist, a great place to learn to be a geneticist. We've been a world leader in the field of genetics for a century. And all the talks in this series are being given by graduates of this department, or by faculty members in the department. And I think for those of you who have been attending the colloquium series, you'll agree that it's been a pretty terrific series of talks. It's my honor today to introduce today's great geneticist, James F. Crow. He's been a member of the laboratory of genetics since 1948, which you will note is well over half the lifetime of the department. (laughter) If we're an outstanding program today, it's largely due to Jim's contributions. He's had a rich career, and I can't begin to give you a full account of everything without using up all of Jim's time. But I can't do justice without using up some of his time. 

So, I'm going to read this, because it's such a busy life, and I'm leaving out an awful lot. Jim got his bachelor's degree in 1937 at Friends University in Kansas, and his PhD in genetics in 1941 at the University of Texas. You'll notice that was right at the beginning of World War II. He then joined the faculty at Dartmouth College, where he taught, get this, genetics, embryology, zoology, comparative anatomy, parasitology, navigation... (laughter) And statistics. So, if you think you have a heavy teaching load... (laughter) Take a look at today's speaker. He moved to Madison in 1948. He's made major contributions in both theoretical and experimental genetics. His early experimental research was on inter-specific hybridization of Drosophila mulleri, and then on DDT resistance in Drosophila. 

Later, pursuing an interest in genetic loads and populations, Jim and his group pioneered work on the impact of minor mutations on the fitness of fly populations. And over the years, his lab worked on non-Mendelian hereditary in flies, including the meiotic drive caused by segregation distortive mutation, and hybrid disgenesis caused by transposable elements. His theoretical work has included work on random drift in small populations, effects of non-random mating, effect of population numbers, models for kin selection. And along with his student Motoo Kimura, Jim worked on evolution involving selectively neutral mutations. He's written papers on the importance of sex, and on determining the mutational component of human diseases. He's a legendary teacher. If you meet someone who got a degree in Life Sciences at our university anywhere in the world, you're likely to hear an unsolicited testimonial to Jim's teaching. Things like, "I took genetics from Jim Crow, the best teacher I had at the university." "The best course I took at the university." "He was rigorous." "Crystal Clear." And, "funny." Jim's book, Genetics Notes, which he wrote to help students follow his own lectures, became popular in genetics courses throughout the country, and was translated into a number of foreign languages. And although he intended it only as supplementary reading, it became the primary textbook for many genetics students. I think it became, more or less, the primary textbook for me. 

With Motoo Kimura, he wrote the book, Introduction to Population Genetics, which was for many years the primary text in the field of population genetics. With Bill Dove, Jim edited the "Perspectives" column in the Journal of Genetics, for more than two decades. Of the 200-plus articles that appeared in "Perspectives" during that time, Jim wrote almost 50. His many graduate students and post-docs have been among the leaders in the field of genetics. And a good many of them are now members of the National Academy of Sciences, and occupy leadership positions everywhere. In addition to his academic activities, Jim has a long list of service activities. He served, for example, on the general advisory committee to the director of NIH. And for many years, he was on the genetics study section of NIH. He served on various national committees on the biological effects of radiation. He chaired the National Academy committee on DNA technology in forensic science. 

He was president of the Genetics Society of America, and the American Society of Human Genetics. He served as chair of our Laboratory of Genetics for a number of years. He was once acting Dean of our medical school, an assignment that he remembers with pain. (laughter) He was once editor of the Journal of Genetics. His many honors include elections in the National Academy of Sciences, the Institute of Medicine, Royal Society of London, the Japan Academy. Last year, he was awarded the 2009 UCSD Merck Life Sciences Lifetime Achievement Award of the University of California at San Diego. So, when some day, when you graduate students are teaching genetics, you may not be able to say that you knew Gregor Mendel. (laughter) Or that you had dinner with Francis Crick, but you'll be able to say that you knew Jim Crow. And that's almost as good. Jim's title, you will notice, has undergone a drastic mutation. 

And he is going to speak on this subject, in praise of multiple additive genes. Jim. (applause)  >> Jim Crow: Thank you. One of the reasons I keep giving talks is-- (no audio)  >> Jim... >> Oh. (light laughter)  >> Is that better? (indistinct answers) I guess I'll just have to talk louder. >> That's good. >> Or move it up. (laughter) >> Jim Crow: With Millard's introduction, plus all this, it won't give me any time to talk! (laughter) Which is all right. (laughter) I'll just keep talking, and you tell me when it approaches the right volume. 

(indistinct answers and talking) (laughter) >> That's not as nice! (laughter)  I dearly love attention. (laughter) >> Is that better? >> Yeah. >> Okay. >> Jim Crow: All right. Well, as I said, I've been retired for 25 years, and it's been a happy time on the whole. And as I said, I recommend retirement, but I don't recommend getting old in order to be retired. I've occasionally puttered with research problems during this period, but these have been mainly problems that would've been some interest 40 years ago, and have been largely replaced by other questions in the meantime. But I'm also interested in the fact that with the coming of molecular genetics, there was immediately a lot more attractive things to work on. You could sequence something and get an answer. It may not have been an important answer, but it was definite. 

(laughter) Whereas in population genetics, we worked on important questions, but hardly ever got an answer. (laughter) And one of the things that's happened with the molecular revolution was the abandoning of quite a number of questions in population genetics, just because other things were more attractive. And I suggest that it's time to go back and look at some of these questions, which are still good questions, with a modern viewpoint. And it's with that in mind that I chose the title for today. I'm going to talk about quantitative genetics, which is something we really know a great deal about in one sense, but not nearly enough in the sense that molecular biology could reveal something about. So that will be my objective today.  Here's the problem. In recent years, there's been a lot of study of complex human traits. And most of these are very highly heritable. Heritability is at 0.6 or 0.8, sometimes higher. 

And yet, known loci account for only a tiny fraction, something like 10% of the genetics variance. Why? My guess is that most of the missing heritability is due to many genes with effects too small to be detected by existing molecular methods. It's a strong argument that was made by Nature Genetics just a few weeks ago. There's been a lot of attention recently to selective sweeps, as indicated by the fact that there's reduced variability in the vicinity of a gene, which suggests that that gene has been selectively increased in the recent past. And there's certainly a number of selective sweeps that have been found. But there don't seem to be enough to account for very much of the genetic variance. They're there and they're important, but they're not that big in the overall picture. So I want to say a little bit about human height. It's been the classical subject for quite a few in genetics, ever since the turn of the century. I mean the other century, 1900. 

(laughter) I'm living in the past. It goes back to Karl Pearson and R.A. Fisher. By about 2008, there had been three studies that had identified a total of 54 loci, from three different studies. The three studies were almost non-overlapping, so therefore those 54 are pretty close to the total number. And these account for 9% of the genetic variance. So where's the rest of the 91%? If you had to account for all of those, all the rest of genetic variance, in terms of these genes, it would take about 600 loci. So this suggests that there are at least 600 loci involved with human height. And this is certainly an under-estimate. They have to have a certain minimum, a factor that wouldn't be detected by the systems used. That's the state of affairs in 2008. 

A lot of uncertainty in last two years. Happily, it gives me something to read. So far, there have been 600 variances detected by genome wide association of studies. And altogether, these account for about 10% of genetic variances, so about the same as before. If we include undetected alleles of the same general type, that brings the estimate up to maybe 16% or there about, but it's still a small fraction of the total. These results are interesting to me, because it turns out that quite a number of the genes associated with human height are genes that are already known to have skeletal effects or size effects already. Anyhow, as I said, where does the rest of this variance come from? I think the best guess is there are many loci will still smaller effect, and that's what I want to discuss a bit more about. Polygenic inheritance has been invoked since early in the 20th century. And the real breakthrough in intellectual thought about this question came with R.A. Fisher. Here's a picture of Fisher in 1912. 

And another one in 1924. He grew a beard in the meantime, which you see. And the purpose for him growing the beard, he told me, was he felt the students didn't respect him, so he grew a beard. (laughter) Fisher decided-- First, he wanted to get into the war, but his eyesight prevented him from being elected, so he took whatever job he could get, which was teaching. And he was a lousy teacher. Some of you have heard Fisher lecture. He writes on the blackboard in a barely detectable size. And he pays no attention to whether the audience is understanding or not. And for that matter, I don't think he paid any attention to who the audience was. He was here some years ago. 

He often came to Madison. He was here and he gave two lectures. One on the auto-tetraploid inheritance and on the auto-octoploid inheritance, and one on smoking and lung cancer. And as fate would have it, Fisher got in the wrong auditorium. And for the small auditorium, he lectured on lung cancer. For the big auditorium, he lectured on octoploid. (laughter) There weren't but two or three people in the audience that had the slightest idea of what he was talking about. (laughter) And those two or three couldn't have cared less. So it was just a total failure. (laughter) But what did happen during that period was far from a total failure. 

He decided to develop a theory on inheritance, which he did. And it's still our standard for the subject. He tried to get it published, with no success for a long time at least. He tried through various publications in London, in England, and finally published in the Royal Society of Edinburgh, which at that time was the jumping off place. And that's where it was finally published, and not until 1918, several years after the work was done. But what's this all about? If there are a large number of factors, it's useless to try to identify individual factors, at least it was in the past. And so, sort of by analogy with thermodynamics, Fisher grew up in physics, incidentally, he decided to develop a theory about the way quantitative genetics works, based on Mendelian inheritance. And yet, the quantities that you measure are not individual means, but deducible quantities from behavior of the individual genes. So it turns out that the convenience from the standpoint of population quantitative genetics, are standard quantities of statistics, means, variances, co-variances. And Fisher showed that by making assumptions about the inheritance, you could derive formulas for the variances and co-variances. 

And then, for example, from the use of correlations between relatives, you could predict the result of breeding experiments. And these worked remarkably well. It's fair to say that one of the reasons they worked remarkably well is that the errors of measurement in the effects were so great that everything looked like it was working well. (laughter) But at least they were the standard procedures for breeding tests. And they still are. They've been refined, of course. Now, this study of quantitative genetics led to quite a bit of theory. And one of the ideas of Fisher's fundamental theory of natural selection, which says that the rate of change of population mean is related to the genetic variance, by which he means the additive genetic variance. Another way of stating this is it's a measure of how fast variability is used up. Because in selection, you change the infrequencies and the variance decreases. 

So for a number of years, people talked about this as if selection reduces genetic variance. And yet, the empirical evidence is otherwise. There are a large number of experiments that have run for a long time with no diminishing of the genetic variance. And the best example is the Illinois Corn experiment. It started at the turn of the still earlier century, and ran all through the 20th century-- Yes, it started in 1800, continued through the 1900s, and it's still going on. It's now been well over 100 generations. The selection was for high and low oil content of corn. There's also protein content, but the oil is a little more spectacular. And yet, there was no reduction in variance in the high line, despite using only 12 ears each generation. So there's enough stored genetic variability, possibly with new mutations, to keep that going for this 400 years of selection. 

And the analysis of this done by Cathie Laurie, somebody you remember was a post-doc fellow here a few years ago. She showed that the effects are almost entirely additive. Here's just a picture. You can see, there's a difference between the low line and the high line, about 32-fold. And although the low line is decreasing in variance, it has an obvious explanation, it can't go below zero. And the decreases variability in that direction. But in the high line, the variance is just as great as it was in the beginning. So as far as this experiment is concerned, there's no diminishing variance with long-time selection. And furthermore, that's in agreement with most other people's experiments in recent years. Often, a population will reach a plateau in the sense that you can't get any further with it. 

But always, as equally often, that has a spurious kind of explanation, -- for example, or something else that lends itself to genetic analysis, rather than loss of genetic variability. And one of the evidences with the genetic variability is still there, it's how effective selective in reverse direction is. And almost every experiment of this sort demonstrates that by that kind of very simple experiment. So why does long-time selection experiments not exhaust the variance? One explanation is mutation, and maybe that's the reason. But I also think it's necessary to postulate mutation. Maybe the environment is changing. But this seems to happen even with a constant environment. One way I like to look at this is to say, well, for one thing, with multiple factors, a small change in gene frequency of a large number of alleles still is a big change in the phenotype. And so, we can have a big change in height or any other kind of quantitative trait with rather small changes in gene frequency, and practically no decrease in the variance. But if there is a decrease in the variance, I think we can account for that and explain why it hasn't diminished, because in those experiments where it does turn out that the effect is due to a relatively small number of factors, like some of the quantitative traits in cattle. 

 I'm sorry, I don't remember my own thought! So I'll go on. (laughter) If you select the genes that are contributing to the variance at a particular time, or those with the intermediate frequencies, variances to a half, the greater the contribution to the variance. And as you select genes with frequencies of a half, go to flat, in which case the variance decreases. At the same time, there were other genes though that have been unused up until this time that have very low frequencies, and their infrequencies increased. And what you have in effect then, is a sort of a steady state. There's a certain amount of variance that persists, but it's a different gene. It has the stability of a waterfall, rather than actual particles remaining stable. I think that, plus the fact that there's really not much change in gene frequency anyhow, accounts for the fact that you select for a long time and simply don't run out of the genetic variance. So that particular myth, actually some of the greatest geneticists perpetuated the myth. One is one I admire very much, Alan Robertson. 

And he bet quite a theory based on this now wrong assumption. So, my general conclusion is that most complex traits show a great deal of additive genetic variance. And there's a nice article about this in 2008 by Bill Hill. And one thing that's found both experimentally, and I think you'd expect it theoretically, is that the smaller the effect, the greater the additivity. One way to think of this, for myself at least, is to say that the small things are additive and for the same reason that Taylor's theorem works, the same reason that the first two terms of the first term of Taylor's theorem works. Anything that's small enough becomes additive. And I think that's true of genes, too. But anyhow, there's an abundance of experimental evidence with the large variant effect of an individual gene, the more likely it is to have dominance and epistasis. And the smaller the effect, the more likely it is to be additive. So there's some advantages in additive genes, and with a large number of them. 

One advantage of multiple factor inheritance is its fine tuning. If you have many factors affecting a trait, each do a very small bit about it. Then there's an optimum value that can be achieved. And if there are large genes with larger effects, you couldn't do this. And with additive effects, if they are additive, then effectiveness of selection is maximized, because the most effective methods population structure for rapid evolution, rapid selection of change, is to have everything additive. Dominance and epistasis impede the process, and therefore, if you don't have them, it goes better.  Even if there is variance caused by dominance and epistasis, it turns out that the contribution to parent-offspring correlation comes entirely from the additive form anyhow. If you do ordinary variance analysis with epistatic variance, you find that there's a small component to parent-offspring correlation from the epistatic variance. If the population is in linkage equilibrium, that works out. But what Kimura showed one time, remarkably, he showed that for loosely linked loci, which is what I'm concerned with, after a few generations of selection, there's just enough linkage disequilibrium introduced by selection to cancel the epistatic variance. 

So the net effect is that epistasis does not contribute to parent-offspring correlation, and therefore doesn't contribute to the effectiveness or non-effectiveness of selection. It gives me a bit of pure poetic justice, because animal breeders and plant breeders have been ignoring epistasis all along. Mainly, because they didn't know how to deal with it, or they couldn't deal with it. But actually, they've been doing the right thing. If they tried to correct for epistasis, they probably would've made poorer predictions than they made by not doing it. I don't have, maybe some of you do, an intuitive explanation as to why this has to work this way. I simply have to grind it out. But it certainly comes out of any analysis of this. That's not the whole story though. Here's a picture of it. 

If you look at this, this is the graph of the change in gene frequency over a period in time. And the solid line is the actual change. It's also the genetic variance, and they're the same. And if I include epistasis, I get the dotted line. And you see, for the first generation, or the first few generations, including epistasis does work. But after about 20 generations in this particular sample, the population reaches a stage in which the epistatic variance, as I said, exactly cancels the -- variance exactly cancels the epistatic variance. The trouble with that was that it was a -- story. It was done by Kimura, much to my surprise, much to everybody's surprise, I think. And I'll show you a little bit about him. This is a nice picture of him, made when he was here as a student, or when he was here to get an honorary degree. 

Here's a picture I like better. It shows him in his greenhouse. When we wrote a book together, that was in the days where you got 360 yen to the dollar. And the yen bought a lot more than it does now. There was enough in his royalties to fix a little greenhouse at his house. So we used that to work on orchids. Every Sunday, he worked on his orchids, and you couldn't see him on Sunday.  Can't resist being personal, but I will anyhow. But Kimura had the habit of naming his orchid clones after friends, or people he admired, sometimes both. And the one that he named after me turned out to be a prize winner. 

(laughter) So I've found my name better known in orchid circles than in genetics. (laughter) It's nice to have a double reputation in this town. You might think that's about as far as you can go with this problem. That doesn't take into account Nagylaki, who's another post-doc of mine. I'll tell you a little bit about him, too. He was a theoretical physicist to begin with. And he worked with Feynman, a great physicist at CalTech and made quite a distinguished record for himself.  He decided that he couldn't compete with Feynman. Of course, 99.99% of the population feels the same way about this. Most of the rest of them are not bothered by it, but he was. 

(laughter) He wanted to be the best. So he read a textbook on population genetics, the one by C.C. Li, which in fact, is pretty elementary. And he decided that that's an interesting subject, I can get out in a hurry on that. So he switched from physics to population genetics. And the subject has never been the same since. He brought a whole collection of skills, I guess I should say, that enabled him to solve the kind of problems that the rest of us can only admire. He generalized Kimura's results to any number of loci, any linkage map, as long as the linkage was loose, as long as recombination was larger than the selective differences, any amount of dominance, any amount of epistasis. There can be time dependence on the fitnesses. And I guess almost any other variable I can think of. It turns out that under these most general conditions, after a few generations, you attain a disequilibrium and then the population moves as if it were linkage equilibrium. 

I probably said it backwards. You attain a certain level of disequilibrium that's stable, and then the population moves as if it were linkage equilibrium. So the very simple additive theory, going back to Fisher and others, works remarkably well, and now we have some justification for it. One of the side effects of having students like Kimura and Nagylaki is you have a totally undeserved reputation as a mathematician. We weren't very careful in distinguishing who did the math in our papers. I even fooled Haldane, unintentionally. But he wrote a letter one time and said he'd discovered a new theorem that maybe the French mathematicians knew about it, and maybe some Americans, but certainly no biologists would. He said, "Except for hotshots like Crow." (laughter) I preserved that. Little did he know, of course. All right, so much for additive selection, and so much for selection that imitates the additive, even though the underlying gene action may be quite complicated. 

The form of selection that's most effective is truncation selection. By which I mean that the individuals are ranked in some order, and everybody above that particular amount is selected, or is well preserved as they can be. And it's a particularly effective way to remove harmful mutations. It does it with a little cost to the population. This can happen only with sexual reproduction. And the person who really capitalized on this idea was Alex Kondrashov. I'll tell you a little bit about him, too. This has become awfully personal. But I discovered this too, but I didn't develop it carefully, the way he did. And when we discovered each other had done the same thing, we decided we had to get together some time. 

But he was in Russia at that time and couldn't get out. So, we corresponded rather extensively. I never thought I'd ever see him. Then, one evening he appeared in Madison. He had a sudden opportunity to leave, and he had to leave quickly, and he couldn't take any belongings with him. So he got himself to Madison somehow. He borrowed money part of the way. He called me up. So, I kept him on -- to work with. Then later on, he finally was able to immigrate and he now is one of the faculty at the University of Michigan. 

His son, incidentally, is on the program here on Friday afternoon, a seminar on using mathematical models for developing biological theory.  One of the consequences of truncation selection is that it sort of makes genetic load not very relevant. Haldane developed the concept that he called genetic load, or what other people call genetic load. He developed it. I developed it too, but I was 20 or 30 years later than Haldane in this. (laughter) But what he showed is that the impact of mutation on the population is related to the frequency of the mutation and not the individual effects. You can argue this way, that if I have a mutation that causes a lethal effect, it effects one person. The gene is gone and there's one person killed. If I have a gene that causes a 1% effect on 100 people. A 1% effect, on the average, that will effect 100 people before it's eliminated. 

And I'm saying that a system of mutation cost accounting equates 100 individuals exposed to a 1% risk, as equivalent to one that's exposed to 100% risk. On that kind of bookkeeping, you can equate the effect on fitness and mutation to the mutation rate. And for many years, we regarded it as placing a limit on how much selection there could be. But it's a rather severe limit, and it's been rather troublesome for a number of years. The person who first saw, as far as I know, that there was a better way to look at this, and that was John Sved. He pointed out that with truncation selection, there's no such limitation. It's a little hard to try to explain why, and I'm not sure I fully understand why. But it's clearly true in any case. Here's Haldane, the inventor of this particular theory. When he was in Madison, this picture was taken in Madison, he was here in I guess the last year or so of his life. 

He had discovered he had carcinoma of the rectum. And some of you may have been alive at this time. This was in the '60s. He wrote a poem that was published in the Atlantic Monthly. It started, I wish I had the voice of Homer To sing of rectal carcinoma... (laughter) And he made it rhyme. But the other one he said, if I can remember, I liked even better. I can't find it. Here it is. So now I am like two-faced Janus The only god Who sees his own anus (laughter) He had a colostomy, which led him to write this poetry. 

The curious thing is, although he was here, he never said a word about this. And yet, I'm certain that he knew about it and was just keeping it to himself. He was on his best behavior in Madison, I'm happy to say. He could be very nasty when he wanted to be. But here, he was happy. Maybe that's what a carcinoma does to you. But as I said, it's long known that truncation selection is the most efficient form of selection. And it also is the most efficient method of removal of harmful genes. Another way of saying this is maybe a little more intuitive, is that if you have a certain cutoff point, all the individuals above that cutoff point have a larger amount of harmful genes, and you therefore eliminate these genes in bunches. So with one genetic death, you can eliminate almost any, with no obvious upper limit, any number of genes at the same time. 

So although Haldane's genetic load theory is a beautiful theory, I think it's probably irrelevant, and that truncation selection solves the problem. The problem is, does nature truncate? It certainly doesn't do it in a very strict way. -- individuals bring the population up and selecting or rejecting all of them above this particular level. So for a long time I, personally at least, didn't accept this as very important. And then finally it dawned on me, and I was working with Kimura at the time. First, a little bit about this. This is what I mean by truncation selection. In this diagram, there's a truncation point indicated by "C". And on this diagram, all the individuals in the shaded area are say, selected, retained in the population. And all the ones in the unshaded areas are rejected. 

And there will be a mean of the selected group, larger than the mean of the populous as a whole. And we have a nice theory, as long as everything is normally distributed, as to how intense the selection is for a given level of truncation. What turned out, however, is that by experimenting with this a bit, and mostly just ignoring the studies, I was able to see that the truncation doesn't have to be exact at all. It can be very crude, as this diagram here. It was intentionally drawn to be crude. That shows that it can have just an approximate truncation. And it turns out that that's almost as effective. I can have the diagonal line here, running over three or four standard deviations, and still retain about 80% or 90% of the effective removal of deleterious genes. So for me, at least, it changed my mind on this subject entirely. I think it's unrealistic for nature to truncate sharply. 

But I think it's very, very realistic for nature to truncate approximately. Almost every population, of any organism that you're interested in, there's some density regulation. There's always over-production and differential mortality. And happily now, I realize it doesn't have to be a sharp truncation to have all these convenient statistical properties of truncation selection.  So as I just said on the other slide, something like this crude truncation selection could well have happened in resource-limited environments, such as our ancestors lived in. So maybe the reason why we've tolerated as many mutations as we can is because we've practiced this form of selection in the past, and to some extent maybe still are.  I would like to note that as Kondrashov pointed out, that if you're going to use selection as a way of eliminated harmful genes, and do this by truncation selection, that will work only if there's sexual reproduction, because you have to re-scramble the genes every generation. And with truncation selection, as I say here, if the genes with similar effects are selected together, eliminated together, and thus generating the equivalent of epistasis. And this can be very extreme. I like to call this quasi-epistasis. 

I think it's maybe the most important, could be the most important form of epistasis in nature. The genes are acting additively. The epistasis is not generated by gene action at all. It's generated by selection, by the way selection is operating on the populations. And as I said, selection reproduction permits genes with similar effects to be eliminated in bunches. And I think we've gone a long way toward solving some of the troublesome problems. I like to call this quasi-epistasis, because it's equivalent to very strong epistasis. But as I said, the epistasis is not from gene interaction, but from the way selection works. And I re-emphasize it requires Mendelian segregation and recombination, in other words, sexual reproduction. And to me, the possibility of carrying out this form of selection is one of the strongest reasons for having Mendelian inheritance and sexual reproduction in the natural populations. 

To say a little more, I've emphasized that the genes are not necessarily active additively, but the net effect is as if they were. And as I said, with many genes, with individual small effects, it allows fine tuning. But another thing that this permits with multiple factors is with a really small amount of existing variability, by recombining the genes in the population, you go way beyond the extremes of that population. So there's a tremendous potential variability with very little existing variance. And with additivity, selection is very efficient. The selection doesn't depend very much on how many factors there are. It's their being additive that seriously matters. And with truncation selection, harmful genes are more efficiently eliminated. It's the most efficient form of selection as far as I understand it, is by truncation on genes that are active additively. If there's so much additivity in nature, how come? I've obviously shown you that I'm impressed with the fact that there are a lot of variabilities of this sort, and I think we need to be dealing with it. 

Why do we have so much additivity? I think it evolves. One way of looking at this, if you have a population with a number of individuals in it, and the favorable ones survive. Now, if the genes are additive, those that survive transmit a large fraction of their -- to survive. If they're not additive, it transmits a smaller fraction of it. Since the ones that contribute the greater amount of additivities come from the survivors, -- selected, therefore you have selection in favor of additive genes. I like this argument, because it doesn't depend on group selection, which is the usual way of arguing for this. I think there are probably more subtle things happening, that I'm not saying. I believe that evolution tends to produce greater and greater additivity. So we should not be surprised to find that such inheritance prevailing in nature. So what? My conclusion. 

Multiple factors permit a fine adjustment. And most quantitative traits are largely additive. If they're not additive, they interact in such a way that additivity is the net effect. If traits are additive selection is efficient. Truncation selection, or approximate as well, quasi-truncation selection is the most efficient way to eliminate harmful alleles. And as I emphasized at the beginning, we can select for a long time without exhausting genetic variance. As I've suggested, I don't know yet, I think additivity evolves, and has been favored by selection in the past. I want to say just a little bit more. I said at the beginning that these are questions that are left over from the quantitative genetics work in the past, they were left unsolved. I think, what do we need to further these problems? We clearly need more theory. 

There's an obvious gap in the theory. And that is a theory in which close linkage is taken into account. We have a theory of loose linkage, and we have a theory with complete linkage. We have nothing too much in between. And there's quite a bit of nature that's involved with reasonably tight linkage. I think further study of phenotypes, per se, is not likely to be fruitful. I think we've found most of them that have large effects. And the phenotype that we're interested in, the individual genes are too small to be ultimately detected, so it's rather fruitless to search for them. And most people have given up on that search, I think. It's probably better to start with the DNA itself, and work up from that, and see what the effects are, and see if you can infer from the DNA what's happening at the phenotypic level. 

I've just been reading, it's in today's Nature, or the Nature that I got today, about the 1,000 genomes project. It seems to be that that's offering real promise for getting something interesting. These are an attempt to sequence 1,000 different genomes, from seven different populations throughout the world. And their preliminary reports revealed a few new things. They also revealed a lot that we already knew. But it shows definitely, that some of the things we thought we knew, in fact probably really are correct. One of the things that comes out of this study is that there's a greater impact of multiple repetitions of genes of very small effect. Duplications and deficiencies are relatively infrequent, comparative -- mutations. But they maybe more out of proportion to the numbers in importance, maybe important after -- the numbers. And one that I found most intriguing was that one of the regions where there was a considerable amount of repetition of the genes is in a region that's known to be associated already with skeletal formation. 

I'm sorry, I'm talking about -- traits now, one that's already associated with -- traits. I don't think this is going to be an easy task, because we're dealing largely with genes whose individual frequencies don't change very much. And the individual effects are too small to be detected by ordinary methods. I think it's up to ingenuity of a new generation of geneticists to figure out how to deal with this problem. I will follow the standard custom in acknowledging my sources of support. (laughter) Thank you very much. (applause)