EEB 122: Principles of Evolution, Ecology and Behavior

Lecture 5

 - How Selection Changes the Genetic Composition of Population


Genetics controls evolution. There are four major genetic systems, which are combinations of sexual/asexual and haploid/diploid. In all genetic systems, adaptive genetic change tends to start out slow, accelerate in the middle, and occur slowly at the end. Asexual haploids can change the fastest, while sexual diploids usually change the slowest. Gene frequencies in large populations only change if the population undergoes selection.

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Principles of Evolution, Ecology and Behavior

E&EB 122 - Lecture 5 - How Selection Changes the Genetic Composition of Population

Chapter 1. Introduction [00:00:00]

Professor Stephen Stearns: Today we’re going to talk about Adaptive Genetic Change. And in order to set the stage for this, before I get into the slides, I would like you to consider the following proposition. Every evolutionary change on the planet, that has ever led to something that you think is cool and interesting and is well designed, whether it is the brain of a bat, or the vertebrate immune system, or the beautiful structure of the ribosome, or the precision of meiosis, has occurred through a process of adaptive genetic change. A mutation has occurred that had an effect on a process or a structure and, if it increased the reproductive success of the organism that it was in, it was retained by evolution; and if it did not, it disappeared.

So what we’re talking about today is a look into a very basic mechanism that is operating in all of life and is causing the accumulation of information. Now, these are the keys to the lecture. In the middle of the lecture you’re going to get a couple of slides that have tables and equations on them and stuff like that, and I’ll lead you through one of those tables, and I’ll ask you to go through another one. But they’re not the point. The point is this. There are four major genetic systems, and there are some interesting exceptions to them. But you can capture a big chunk of the variation in the genetics of the organisms on the planet with just four systems. Okay?

They are sexual versus asexual and haploid versus diploid, and those differences make a big difference to how fast evolution occurs. You guys are sexual diploids and you evolve slowly, and your pathogens are asexual haploids and they evolve fast. That’s important, the kind of thing you ought to know.

Now when we get into the equations of population genetics–they’re just algebra–the point is that you can always go find them in a book and you can program them pretty easily, even in simple spreadsheet programs like Excel, and you can understand their basic properties by playing around with them. If you go on the web and go to Google and type Hardy-Weinberg equations, you’re going to get 20 websites around the country where some professor of population genetics has put up some package for students to play with and it’s going to generate all kinds of beautiful pictures and stuff like that.

It’s real easy for you to lay your hands on these tools now. What’s important for you to know is (a) that they are there and represent something important; (b) what their major consequences are; and (c) how to get a hold of them when you need them. I am not going to ask you to repeat the derivation of the Hardy-Weinberg equations on a mid-term. Okay? But I do expect you to know why they’re important and what they’re about.

The third thing that I want you to take home from this lecture is that when adaptive genetic change starts to occur, it is virtually always slow at the beginning, fast in the middle and slow at the end. So that if you are looking at a graph of gene frequencies over time, it looks like an S; and that’s the third thing. That’s it, there’s the lecture, ta-da. Now background to this decision.

When, in 1993, Rolf Hoekstra and I began to put together the first edition of this book, I asked Rolf to be my co-author because he is a population geneticist. He has a marvelously clear mind. He likes those kinds of equations and he’s really good at them. And we, Rolf and I, went around and we asked about fifteen of the leading evolutionary biologists in the world, “What’s important? What should every biologist know about evolution? This is for everybody. This is for doctors and molecular biologists and developmental biologists, everybody. What should they know?” And I said, “Rolf, your job is to figure out the part from population genetics.” And he came back, after about two weeks, and he said, “You know Steve, I don’t think there is anything.”

I was shocked. I said, “Rolf, you’re a population geneticist. This stuff is important, right?” And then he said, “You know, the way we normally teach population genetics, which is as a big bunch of equations that are about drift and frequency change under selection and so forth, most people end up not really needing that. What they need to know is that there are four main genetic systems and that genetic change is slow, fast, slow.”

So that’s where this lecture came from. It came from somebody thinking deeply about that, and asking lots of people. Now if you like this, there’s a whole field there, there’s a whole bunch of wonderful stuff that you can do. But these are the things that everybody I think should know.

So here’s the outline. I’m going to give you the context, the historical context that led to the concentration on genetics in evolutionary biology. I’ll talk a little about the main genetic systems. Then I’ll run through changes in gene frequencies under selection and, if I have time, I’ll get to selection on quantitative traits. If I don’t get to selection on quantitative traits, it will be because I have engaged in a dialog with you about some interesting puzzles, and that dialog is more important to me than getting to quantitative genetics. Okay?

Chapter 2. History of Genetics [00:05:45]

So here’s how genetics became a key element in evolutionary thought. Darwin did not have a plausible genetic mechanism and he failed to read Mendel’s paper, which came out six years after he wrote The Origin, but before he constructed some of the later editions of his book, and so he reacted by incorporating elements of Lamarck into his later editions. If you read the Sixth Edition of The Origin of Species, it’s got some really Lamarckian statements in it, inheritance of acquired characteristics.

Anybody here know what the problem was with Darwin’s original model? Anybody know how Darwin thought genetics worked in 1859? He had a model of blending inheritance. That meant that he thought that when the gametes were formed, gemmules from all over the body, that had been out there soaking up information about the environment, swam down into the gametes, into the gonads, carrying with them information about the environment into the gametes, and that then when the zygote was formed, that the information from the mother and the information from the father blended together like two liquids.

In other words, he didn’t think of genes as distinct material particles. He thought of them as fluids. Now if I give you a glass of red wine and a glass of white wine, and I pour them together, I get pink wine. And if I take that glass of pink wine and I pour it together with another glass of white wine, I get even lighter pink. And you can see that if I continue this, pretty soon red disappears completely. The problem with blending inheritance is that the parental condition gets blended out and there isn’t really a preservation of information.

That’s why Darwin came under attack. And Mendel wasn’t known, and he resorted to Lamarckianism, and he was wrong. So genetics became an issue. In the year 1900 there was a simultaneous rediscovery of Mendel’s Laws, and at that point people went back and they read Mendel’s paper, and they realized that they had missed this 35 years earlier.

Then the so-called ‘fly group’ of Thomas Hunt Morgan and Sturtevant and Bridges, who were working at Cal-Tech, demonstrated that genes are carried on chromosomes. And enough then was known about cytology, so that we knew that chromosomes had an elaborate kind of behavior, at mitosis and meiosis, and people then, about 1915, showed that in fact the behavior of chromosomes was consistent with Mendel’s Laws. They didn’t know at that point what chromosomes were made out of. They had no notion of the genetic code, but they could establish experimentally that genes were on chromosomes; and that was done by 1915.

However, there were still issues about whether all of this would actually work at the population level. It was not immediately clear that you could take Mendelian genetics and then construct populations out of it, that obeyed Mendel’s Laws, and have natural selection work. To do that actually required a fair amount of math, and the people who did it were Ronald Fisher, J.B.S. Haldane and Sewall Wright, and they did it between about 1918 and 1932.

In so doing, they also invented much of what is now regarded as basic statistics. So Fisher had to invent analysis of variance in order to understand quantitative genetics, and Wright had to invent path coefficients in order to understand how pedigrees translate into patterns of inheritance. So these guys laid the foundations.

As a result of that, genetics really became regarded as kind of the core of evolutionary biology during the twentieth century, and there’s been a tremendous concentration on it. And it is still true that many people will not accept a claim about any evolutionary process unless it can be shown to be consistent with genetics. That’s sort of a Gold Standard. If you can’t do it genetically, if you can demonstrate it’s genetically illogical, then a claim just falls theoretically; you don’t even have to go out and get the data. Therefore, of course, the Young Turks have great joy in discovering cases that don’t fit and come up with epigenetics and lots of stuff like that. At any rate, that’s ahead of you; that’s not today.

Chapter 3. Different Genetic Systems [00:10:56]

The genetic system of a species is really the basic determinant of its rate of change. So we have sexual versus asexual species–there are complications to this–and we have haploid versus diploid, and there are other ploidy levels. Can anybody name me asexual vertebrates; not sexual vertebrates but asexual vertebrates? Anybody ever heard of an asexual vertebrate? Fish, amphibians, reptiles, birds, mammals?

Student: Wasn’t there a recent documentation of a shark? You mentioned it.

Professor Stephen Stearns: I could imagine that a shark might be capable of being asexual. I haven’t heard of that case.

Student: I think it was kind of a [inaudible]

Professor Stephen Stearns: Yes, there are some. There are some asexual lizards. There are some interestingly asexual fish. There are some frogs that manage to be kind of quasi-asexual by using male sperm but then not incorporating it into gametes–excuse me, in the developing baby. So they use it just to stimulate development. There’s one case in captivity of an asexual turkey.

But asexual types are not frequent among vertebrates. They are common in plants. Of course, most bacterial sex is asexual, although bacteria do have a bit of sex. You’re diploid; your adult large form is diploid. Anybody know what group of plants is haploid in the state in which you normally see them in nature, where the big recognizable thing is haploid? I’ll show you one in a minute. I just wanted to check. Mosses; mosses are haploid. Okay, so this is what’s going on with these four systems.

Basically the difference between sexual haploids and sexual diploids is the point in the lifecycle where meiosis occurs. If the adult is diploid and meiosis occurs in gonads in the adults that produce gametes, and then the zygote form develops so that all of the cells in the developing organism are diploid, you get the diploid cycle. If you have the zygote having meiosis immediately, or shortly after being formed, so that the developing young are haploid, then you get a haploid adult. So this is what moss do and this is what we do. Then we have asexual haploids and asexual diploids, and at least in outline they look pretty simple. Asexual diploid, just makes a copy of itself; just goes through mitosis, makes babies. Asexual haploid, same kind of thing.

So those are the four major genetic systems. There are many, many variations on them. So the asexual haploids are things like the tuberculosis pathogen, blue-green algae, the bread mould, the penicillin fungus, cellular slime moulds, and they constitute the bulk of the organisms on the planet.

Sexual haploids are things like moss, and red algae; most fungi are sexual haploids. In this case you can see that’s where the haploid adult is in the lifecycle. There are where the gametes are formed. They are formed up on the head of the adult. You can see the pink and the blue are coding for the male and the female gametes, on different parts of the gametophyte. Then the zygote forms where the sperm gets into an ovule, on the tip of the plant, and then the young actually develop up here. So this is haploid up here and then the spores go out–meiosis has occurred in here and the spores go out as haploid spores. So that is a sexual haploid lifecycle.

The asexual diploids include the dynoflagelates; there are about ten groups of the protoctists–that’s the modern name for what you think of as protozoa, but it also includes some single-celled organisms that have chloroplasts in them–the unicellular algae, some protozoa, some unicellular fungi. There are a lot of multi-cellular animals that are asexual diploids, and this one here, the bdelloid rotifer is one of them. It is called a scandalous ancient asexual. Anybody know why the word ‘scandalous’ is used in this context? Yes? What?

Student: No males.

Professor Stephen Stearns: There are no males; bdelloid rotifers do not have any males, nobody’s ever seen a male bdelloid rotifer. But that’s not the scandal; I mean, if you’re a male you might think it was scandalous. Right? [Laughter] But for an evolutionary biologist, no, that’s not scandalous.

Well it actually has to do with this part of it right here. Almost all asexual organisms on the planet, that are multi-cellular–leaving out the bacteria–but all the multi-cellular ones are derived from sexual ancestors and originated relatively recently, with a few exceptions, and this is one of the exceptions. There is a whole huge body of literature on the evolution of sex that says one of the things that sex is good for is that it allows long persistence.

We see that sexual things have been in a sexual state on the Tree of Life for a long time, and the asexual things have branched off of it, and we don’t see very many ancient ones. The reason for that–we’ll come to that, when we get to the evolution of sex–is that both because of mutations and because of pathogens, sex repairs damage and defends the organism against attack. So this is a low maintenance, poorly defended organism, and it looks like it’s been around without sex for perhaps 300 million years. The scandal is we don’t know how it did it. Okay? That’s why it’s called a scandalous ancient asexual. Yes, that’s a very intellectual definition of scandal; I agree.

Okay, sexual diploids. You guys are sexual diploids, this bee is a sexual diploid, and that flower is a sexual diploid. They have this kind of lifecycle, as is sketched here, the one that I talked about earlier. So about twenty animal phyla are sexual diploids. Many plants, most multi-cellular plants are, and there are some algae protozoa and fungi that are sexual diploids. They include the malaria and sleeping sickness pathogens. There are some things that don’t fit; the sexual diploid part doesn’t fit, for malaria and sleeping sickness.

The things that are alternating between being haploid and diploid, with neither one dominating, are mushrooms, microsporidian parasites, which are things that are actually quite common in many insects, and the malaria–malaria has a very complex lifecycle. So it is haploid inside your red blood cells, it’s diploid at a certain point in a mosquito, and it’s moving back and forth.

The things that alternate sexual and asexual reproduction: there are some rotifers, some cnidarians, some water fleas, some annelids. There’s a great little annelid that lives in the bottom of the Harbor of Naples in Italy, and it actually does everything. It can be asexual–the same species–it can be asexual; it can be born as a female and turn into a male; it can be born as a male and turn into a female; and it can be born as both and do both. So some things are really flexible, but most things aren’t. And the timing of sexuality and asexuality is an important part of the lifecycle of all of these things.

Last fall, for example, there were huge jellyfish blooms over much of the world’s oceans, and that’s part of a complex lifecycle in which there is an asexual phase on the floor of the ocean, that builds up what looks like a stack of dinner plates, and then the top plate flips off and turns into a jellyfish. It goes off as a jellyfish and has sex and makes larvae, and then goes down and turns into an asexual thing on the bottom that makes stacks of dinner plates. So there’s a lot of variety out there. All of these things probably evolved from an asexual haploid; and we say that because we believe that the bacterial state was the ancestral condition.

Chapter 4. Math of Genetics [00:20:45]

Okay, now genetics constrains evolution, and genetics is doing something to evolutionary thought which is about what chemistry does to metabolism and structure, and is about what physics does to chemistry. Okay? There’s a broad analogy there. If you want to understand molecular and cell biology, you learn a lot of chemistry. If you want to understand some evolution, then you need to learn a little bit about how genetics constrains evolution, and so you need a little math. So I’m going to give you some simple math, and here’s some terminology to soak up.

So we’re going to represent these ideas by symbols. We’re going to call alleles Aa. So those are two alleles at one locus; a little exercise of genetic terminology. We’re going to let p be the frequency of A1, and q the frequency of A2. And frequency just means the following: some traits are Mendelian, which means that they’re easily recognized in the phenotype.

One of the Mendelian traits in humans is the ability to curl your tongue. I am a tongue curler. Okay? How many of you can curl your tongues? Okay, let’s say it’s about 45. How many of you cannot curl your tongues? Let’s say it’s about 30. So the frequency of tongue curling is going to be–I’m just making up the numbers, right?–45 divided by 75. That’s how we get the number. And by the way, the frequency of the other one is going to be 1 minus that frequency, because p plus q is equal to 1; and we’ll let s be the selection coefficient, which is measuring the reproductive success of the organism carrying this trait, the difference that it makes.

And if we look at the genetic change in asexual haploids, basically what one does is make a table of the process; and it is moving from young, in the present generation, through the adult stage, to young in the next generation. So we try to go through one generation. This is an active Cartesian reduction. We’re taking a complex process and breaking it down into the parts that are essential for the thing that we’re thinking about.

We have genotype frequencies–for genotypes A1 and A2 they’re p and q–and we have relative fitnesses up here. The only place that selection is making any difference, on this whole page that’s in front of you, is right here. And basically what–our placing that there is an act that means the following. We are only going to think about the case in which there is some difference in the juvenile survival of A2; it’s different from A1. If it makes it to adulthood, there’s no difference; we don’t put that down in the table. So this is a case where we’re just–you know, it’s a special case–we’re just looking at the juvenile survival difference between A1 and A2. What happens?

Well it changes the frequencies of A1 and A2 in the adults. Basically it changes them by reducing the number of A2s. Some of them have died out; that’s 1 minus s, that’s what the 1 minus s is doing. You can take these expressions here and you can simplify them so they look like this–it’s just a little bit of algebra–and because these are the frequencies in the adults, the young in the next generation have exactly those frequencies, because there is no selective difference in the adult stage. Okay? That’s what that table means.

Now a little bit about this. This little process that I’ve gone through, which probably looks like remarkably simplistic bookkeeping to you, is actually the part of doing applied mathematics which is the most difficult. It is the translation of a process into something analytically simple, that you can deal with. In the act of doing it, you make certain assumptions to simplify the situation, and by writing them down it helps you to remember what assumptions you made and what thing you’re actually looking at.

We’re not looking at all of evolution here, we’re looking at a very special case; we’re looking at asexual haploids where selective differences only occur in juveniles. What happens is you get a change in the gene frequencies of the adults that result from that process, and then that exact change is passed on to the next generation. So that’s the part of this process that I want you to remember. You can go look this stuff up any time. You don’t need to memorize that. You can program this as recursion equations and apply them repeatedly. Okay?

Now let’s do it for sexual diploids. In the sexual diploids, you’ve already been exposed to the Hardy-Weinberg Law, this p2 2pq q2 law. In order to get it, we have to assume random mating in a big population. The reason you need the big population is so that those p’s and q’s are actually accurate measures. In a small population they’re noisy, but in a big population they are good stable estimates. And if there’s random mating, that means that matings are occurring in proportion to the frequency of each type.

So you get a Punnet diagram like this. You have the probability of one of these alleles occurring; and one parent is going to p, the other allele in that parent q. Same for the other parent. These are the possible zygotes that will result from that. This one has probability p2; this one has probability q2; and these two together have probability 2pq. That’s just simple basic probability theory.

Now, the important thing about the Hardy-Weinberg Law is that it implies that there’s no change from one generation to the next. The gene frequencies under Hardy-Weinberg don’t change. That means that the information that’s been accumulated on what works in the population doesn’t change for random reasons. If it’s going to change, it’s going to change because that big population is going to come under selection. Okay?

That means that replication is accurate and fair, at the level of the population, just as it is at the level of the cell. Now, of course, gene drift is going on, but we’re not so worried here about gene drift, because gene drift is affecting things that aren’t making a difference to selection, and we’re building models of selection. What Hardy-Weinberg does is tell you if there isn’t any drift, if there isn’t any mutation, if there isn’t any selection, if there isn’t any migration in the population, and if you don’t have a high mutation rate, things are going to stay the same. So if they’re changing, one of those things is making a difference. Okay? And that gives us a baseline.

So it gives us a baseline to see the process of selection occurring, but it also means that random mating in large populations preserves information on what worked in the past. So you don’t have to invent everything all over again. And a note for future lectures, these are also the conditions that remove conflict by guaranteeing fairness. So basically the Hardy-Weinberg situation is one in which everything that was in the population last generation has exactly the same chance of getting into the next generation, in proportion to its frequency; nothing is going to change.

Okay, here’s a genetic counseling problem, and I’m going to take a little time on this. We go back to John and Jill. They’ve fallen in love, they want to get married, but they’re worried. John’s brother died of a genetic disease, and that is a nasty one. It’s recessive, it’s lethal, it kills anybody that carries it before they can reproduce. That’s fact one. Jill doesn’t have any special history of this disease in her family, but that history’s not well known, and so we estimate the probability that Jill carries the disease from the frequency of deaths in the general population, and that frequency is 1%; to make it easier for you to calculate. Okay?

What’s the probability that they will have a child that dies from this disease in childhood? The probability is .03. Your problem is not to tell me .03, your problem is to tell me why did I use that equation? Okay? So take a look at that equation for a minute, take a look at that problem, and let’s go through and pull it apart. Can anybody see why either the two-thirds or the one-quarter is in the equation?

Student: We know that his brother has a recessive version of the lethal gene, and therefore John is either heterozygous–doesn’t look like it’s dominant, looks like it’s recessive. So if he is heterozygous or homozygous recessive, then he’s carrying the gene; which is what we’re worried about. So there’s a two-thirds chance that he is either carrying it or actually has the disease.

Professor Stephen Stearns: That’s correct. The only slip you made in expressing that is that we know that if they are going to have a child that has the defect, they both must be heterozygous, and so we’re concentrating specifically on what’s the probability that they’re heterozygous. You then gave me that probability. Does anybody have a problem seeing why the probability that John is a heterozygote is two-thirds, rather than 50%; excuse me, that the baby is a heterozygote is two-thirds? Yes?

Student: So we’re going to keep him as a [inaudible].

Professor Stephen Stearns: Yes, you do. Okay. This is for the baby. Okay? If John is a heterozygote and if Jill is a heterozygote, they can have either a homozygous recessive, and that one will die before birth; they can have a homozygous dominant, perfectly healthy; or they can have a heterozygote. The probability of the homozygote recessive is 25%, the probability of the homozygous dominant is 25%, and the probability of the heterozygote is 50%.

But, the probability that John and Jill will have a baby that dies from this disease in childhood is going to be therefore this one-quarter. This two-thirds is going to be the probability that John is a heterozygote. How do we know that John–John’s parents were both heterozygotes?

Student: They had a recessive son.

Professor Stephen Stearns: They had a recessive son. John’s parents had to be heterozygotes. Therefore, given that John’s parents were heterozygotes, his probability is two-thirds. We know he survived to adulthood; the other 25% died. So of those who survived to adulthood, two-thirds are heterozygotes and one-third are homozygotes.

Student: Why can’t one be homozygote recessive and the other one be heterozygous? [Inaudible].

Professor Stephen Stearns: Because if one, the parent–if one parent was a homozygote, it could only have been homozygous dominant, because it survived to adulthood, to have a child. And if the other parent was a heterozygote, the only possibilities for the children are both heterozygotes; and that wasn’t the case, because John’s brother died. Okay? So this is the probability that John is a heterozygote. This is the probability that if John and Jill have a baby, it will have the problem. What’s this thing in the middle–2 times 0.9 times 0.1?

Student: [Inaudible]

Professor Stephen Stearns: Right. That’s the probability that Jill is a heterozygote, and we get that from here. The square root of 1% is .1. 1 minus .1 is .9. This is q and this is p and this is 2pq. Okay? Where did we get this from? That’s in Jill’s part of the population. Those are the baby–oh you’ve got it.

Student: The probability has to be out of the entire population, and the long-term population, they can’t reproduce–[inaudible].

Professor Stephen Stearns: Right. So we have to correct the percentages for the ones that have died. Yes, you got it. Do you see how much goes into dissecting an equation like that? But because we’ve set up the logical apparatus, we can go through a sequence of steps and say, “Okay, first we know they both have to be heterozygous. Then, if they are both heterozygous, the probability that Jack is, is two-thirds; the probability that Jill is, is 2pq, corrected for the fact that 1% have died. She has survived, so we have to correct for that. Then this is the probability that their baby has the disease.” That’s the kind of process that one goes through when thinking about population genetics.

This is the table for sexual diploids that reflects this kind of thinking. It is more complicated because now we have to keep track of both the haploid and the diploid condition. So we have these haploid gametes, with frequencies p and q. We have the diploid zygotes. Then another process comes in.

We can have a selective difference–I made a +S here; I made a -S in the last one. I made that change deliberately, just so that you’d see it as arbitrary; because we can make S negative or positive itself. Right? S doesn’t have to be a positive number; neither does H. Anybody have an idea what H might be in there for? It’s in there to represent something that’s going on in genetics. Yes?

Student: Is it heritability?

Professor Stephen Stearns: No it’s not heritability, in this context. Okay? Yes?

Student: Is it the Marsh’s coefficient for being heterozygous? [Inaudible]

Professor Stephen Stearns: Not in this context. Good idea, but no. What is it about that heterozygote that doesn’t necessarily have anything to do with selection? H expresses dominance. It expresses the degree to which A1 is covering up A2 in the phenotype.

Dominance itself is not something that’s always there. If there isn’t any dominance, then the heterozygote is just exactly halfway in the phenotype between the two homozygotes. So H is a little mathematical symbol that allows us to deal with situations in which either there’s a lot of dominance or none at all. If H = 0, there’s no dominance. Okay? No excuse me, the way it’s set up, if H = 0, then A1, A2 is just exactly like A1, A1, and there is dominance. So we have to make H something non-zero, in order to express deviations from dominance, the way this one is set up.

At any rate, the–what’s going on here is essentially the same kind of selection process. There is a selective difference, which is disadvantaging A2. So A2 doesn’t survive as well as A1. When it is in the heterozygous form, it may do better, if there’s some dominance. And that results in a more complicated set of equations.

W here is defined as this big term. We have basically the adults being p2, 2 pq times 1 plus hs. And A2, A2 has a frequency of q2 times 1 plus s, which is the selection coefficient over here. So q is changing the most, and to the degree that A2 can be seen in the heterozygote, it will also be affected by s, but it won’t be affected if there is complete dominance. Okay? So if h is zero, there’s no effect of selection on the heterozygote; this term cancels out. The result of that is that you get these frequencies forming the next generations.

Now there a couple of ways of setting up this whole derivation, and in the Second Edition of the book, Box 4.1 and Box 4.2 do it a little bit differently. You might want to just step through those things in section. The goal here is not to memorize how to derive the equations, or to memorize the equations. Because, as I’ve said, you can always pick them up in a book, or pull them off the web, and you can find programs that will do it all the time. The goal is to understand what it is that population geneticists are thinking about when they set it up this way, and what power it gives them.

So let me just show you what happens when you program these recursion equations. By the way, they’re called recursion equations because they give us the frequency in the next generation as a function of the frequency in this generation. So they form kind of a Markov chain. They allow us to calculate next time from this time; that’s something computers are really good at.

Chapter 5. Rates of Change in Different Genetic Types [00:40:42]

So this is the take-home message of all that analysis: you look at genetic change, in asexual haploids, sexual diploids, and it’s slow at the beginning, fast in the middle; it’s slow at the end. The haploids change faster than the diploids, and the dominants change faster than the recessives. So let’s step through that and see if you can tell me why this is the case.

First let’s take the asexual haploids, or haploids of any kind. Why is it that haploids change gene frequencies faster, for given selection pressures, than do diploids? Yes?

Student: The entire gene–all the genes are inherited. It’s not all [inaudible]; it’s sort of a complete replication of them, the order.

Professor Stephen Stearns: Well that is what a haploid is, but that doesn’t explain why it’s faster. The statement is true, but it’s not an answer to my question. Another try. Yes?

Student: Well all the [inaudible], the bad genes die off. [Inaudible]

Professor Stephen Stearns: Okay, that’s going in the right direction, but I think it can be expressed even more clearly. Yes?

Student: [Inaudible]

Professor Stephen Stearns: That’s interesting. That actually gets into the evolution of sex. I’m actually thinking though about an answer that has more to do with developmental biology and not so much to do with sex, at this point. Um, actually I think that, uh, your answer is partially correct, but it’s more complicated than what I was looking for. [Laughs] Yes?

Student: Is it that all asexuals can reproduce?

Professor Stephen Stearns: No, it’s not that all of the asexuals can reproduce. Many of them die as juveniles. It has to do with haploidy versus diploidy. Yes?

Student: Then if the organism has the allele that’s different, it’s going to best.

Professor Stephen Stearns: Yes.

Student: And that’s when this other comes along.

Professor Stephen Stearns: Every gene is expressed, and there’s no dominance covering up any hidden genetic information. The genes are exposed to selection, in haploids. Yes?

Student: So why is that faster than a dominant zygote, [inaudible]?

Professor Stephen Stearns: Good. We’ll find out as we go through the next questions. Okay? So the haploids are faster than a dominant diploid because–?

Student: [Inaudible]. That’s why it’s a recessive gene.

Professor Stephen Stearns: Basically, yes. The heterozygotes react like the dominant, but contain the recessive. And so if you’re measuring the rate of evolution as the rate at which the dominant takes over the population, it’s carrying along in the heterozygotes a bunch of recessives. Okay? They’re doing just as well as it is. So development, which is covering up the difference between the two, is actually giving the recessives an advantage and slowing down the rate at which the dominant can take over. Okay?

Recessive diploid; I think that you now see why that would be the slowest. If we have an advantageous recessive gene, it gets slowed down by the fact that when it’s in the heterozygote, its effects are being covered up by the other allele. Okay, why is it S-shaped? Why is the trait–let’s do it for a dominant diploid sexual. Okay? Slow at the beginning, fast in the middle, really slow at the end. Let’s concentrate on first why this is really slow at the end, and then we can also look at why a recessive diploid sexual is really slow at the beginning.

What do you have to think about in order to pull the answer out of that diagram? What proportion of the population is in heterozygous form, as you get near the end? If you’re a dominant diploid sexual and you’re at a frequency of .9, 81% of you are going to be dominant homozygotes; 18% of you are going to be heterozygotes; and 1% of you are going to be recessive. There are eighteen times as many heterozygotes as there are recessive homozygotes. Selection, at that point, is trying to eliminate that 1% of recessive homozygotes. It can’t touch the 18%.

If you carry that process over, where we’re dealing with .01 and .99, it gets even more extreme. A tinier and tinier fraction of that population is a recessive homozygote. A larger and larger fraction of the remaining recessive alleles are tied up in heterozygotes, where selection can’t operate. So this thing just slows way down. It gets harder and harder to get rid of the disadvantageous alleles, because a larger and larger proportion of them–not an absolute number but a larger proportion of them–are hidden in the heterozygotes.

The same thinking describes why evolutionary change in a recessive diploid, where the recessive gene has the advantage, is very slow at the beginning. If a new recessive mutation comes into the population, it’s a very low frequency. Its frequency is 1 divided by the number of individuals in the population. The only things it can mate with are dominant forms. All of its babies are heterozygotes.

So at the beginning selection can’t operate on it at all. Only after two heterozygotes manage to get together and mate, which means they must have come to fairly high frequency, will they have a baby that is a recessive homozygote that selection will operate on. So it takes awhile to get this going. And because of dominance, it takes a long time to build up to the point where it accelerates. But then at the end it’s fast, because at the end the thing that’s being selected is the recessive, and it speeds up as it goes through.

Okay, I thought this would happen, uh, it’s time for class to end, and I’m just getting to quantitative genetics, and so I’m going to let you pick up quantitative genetics from the lecture notes and from the reading. I do want to indicate as potential paper topics though that quantitative genetics has got some of the most interesting questions that we encounter in evolutionary biology, and that it includes questions like the heritability of intelligence, the heritability of SAT scores–those are all things where the apparatus you need to analyze the issue is given to you by quantitative genetics.

And there is a good paper on this, and I have put it up on the course website, under Recommended Readings; there’s now a folder called Recommended Readings, PDFs of Recommended Readings. You can find this paper and some other ones in there, if that’s something that strikes your fancy. Go take a look at the title and abstract. So this is the summary of today’s lecture. And the next time we’re going to talk about the origin and the maintenance of genetic variation.

[end of transcript]

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