 Good morning. First of all, start off, are there any questions? Yes. Okay, so the question had to do with readings. So on the course website, have you been there? There's a place where you actually see the lecture material as it's posted. I believe there should also be the chapter from the Big Thick Campbell Biology textbook. It's also indicated there, remember the readings from the textbook I'm thinking of is just background material. It's not required. It's one of the frustrations with this course is that it's a very expensive book and different people that teach Biology 1A and 1B have different feelings about whether it's required or what types of books to be reading. And frankly, I'm not that impressed by Campbell's Evolution Treatment, so I'm not super enthusiastic about assigning readings from it. Any other questions? Okay, we also had a request, oh, go ahead, yeah, for some things, but no, I don't have the direct correspondence. We could probably work that out, but I don't have them with me. It's certainly not on the top of my head. The problems I need a seventh, yeah, the problems I need a seventh edition for me to be able to make the correspondences, you know, corresponding chapters, I don't have that. They give me, you know, I get free textbooks, but it's the ones they want me to assign to you because they make lots of money off these books, as you can imagine. Other questions? Okay, we had a request, there's a number of people that are hearing impaired that are taking this course, and so we have a person who's signing the, is that right, or I'm sorry? Captioning, okay, captioning these, and so she finds it difficult, like when you come in late, if the door slams, to hear what I'm saying, at least during the slamming portion of the door close, so if you're coming in late, try to, I'm not picking on you, I think, but try to be gentle, and now I'm going to be completely distracted the entire lecture by people coming in and slamming the doors potentially, but it doesn't bother me, but it is hard for her to hear what's going on. So I'm going to continue with the last lecture where we were talking about Darwin and the origin of species. I want to finish that up, then we'll be starting our discussion of population genetics, okay? And I stopped, or the last thing we were saying in the lecture last time, or I was saying in the lecture last time, was, he had this theory that describes adaptation, right, that's natural selection, but a good theory often can bring in other facts as well, it can actually explain more than it was originally intended to explain, and that's true for Darwin's theory of evolution by natural selection as well. And so I spoke a little bit about biogeography, I'll return to that, but some other facts that, and he could also explain the fossil record, so just go through things that Darwin could explain really easily. Well, last lecture I lamented a lot about how incomplete the fossil record is, but what is known about it, and what is known at the time of Darwin's published origin of species is consistent with his theory, okay? And specifically, people had a very good idea of the sequence of, or the progression of organisms in different rock strata, so it was known that trilobites and things from the Paleozoic occur in certain rocks, and the rocks above them had different fossils, and up to the ones, the rocks that were the most recent, they had their own assemblage of fossils, and the fossils in the most recent rocks, the youngest rocks, most closely resembled living species, okay? And that was consistent with, with Darwin's theory. Okay, another thing that he pointed out is that the Linnaean classification system, which by that time had been the standard way that people classified species, was also consistent with the theory of evolution. So I don't know if you should probably know this, the Linnaean hierarchy, but it's kingdom, phylum, order, and species. So every named species on Earth, of course, we're, we're, it's given a genus and a species name, we're Homo sapiens, and the typical thing is you always capitalize the H in the genus, even if it's not starting a sentence, and the species name, oh, Homo sapiens, what am I talking about? And the species name is, is lowercase, okay? Anyways, we're all given a Latin binomial, that's the Latin binomial name, but we're also in a family and order a class of phylum in a kingdom, okay? Like, for instance, the kingdom animalia. And this classification scheme was devised by a Swedish scientist, Linnae, and of course he's very famous in Sweden, even today, he's like their hero there. But this is, this is the Linnaean classification scheme, and it's a hierarchical scheme, okay? There's a hierarchy. Every, you know, a lot of species fall into a, into a kingdom, different phyla, for instance, in a kingdom a bunch of different classes are contained within phyla and so forth. And Darwin pointed out that this scheme, which seemed a natural one to the people at the time, and it's still one that's hard to get rid of, seemed to, seemed to explain, could be easily explained by evolution. That is to say that things that were, that were very closely related, that are very similar and people grouped into, into the same genus, well that was because those things happened to be more closely related to one another, phylogenetically. Phylogeny is a, is a genealogical relationship, so sometimes I say the word phylogeny without, without having to find it, but now I have. A phylogeny represents the relationships of species, and so things in the different genre in the same family, well the argument is that they're similar to one another because, and they're grouped together in the same family because they're, they're each other's closest relatives, they're very closely related at least. Okay. Oh, and this is something you, you should know. There's actually an easy way of remembering, you may have learned this from high school, at least this is how I learned it. You know, King Philip came over from German shores, somebody, you probably have a different one, I know there's a number of them out there. What's that? All right, well I don't, we don't need to hear any of this, but King Philip came over from German shores, works, so anyway the Linnaean classification scheme is, is consistent with what is known about evolution, and then of course biogeography, that is to say how species are distributed on the earth, and the, the basic observation, this is what I ended with, is, there we go, I can't, don't have the ability to use a pointer here, so I'm going to use this, this one that's hard to see in the, in the projections, but anyways, that, that species that are closely related to, that are, that are similar in habits, the same area of earth, so this, an example is New World and Old World Monkeys, this is what I ended with, basically you have a lot of monkeys called New World Monkeys, the Platyrines that live in the New World South Africa, South America rather, and they all have three premolars, and they have the Old World Monkeys, the Caterine Monkeys that live in Europe, Africa, Asia, and they have two premolars. The reason why you have these two groups distributed not randomly, right, is because the Platyrines have their common ancestor on, in the New World, in South America probably, whereas the Caterine Monkeys have their common ancestor in the New World, in the Old World. There's another, other types of observations that Darwin made, so for instance, the distribution on islands as species is quite peculiar, okay, and it can best be explained by different islands having a history of colonization. So oceanic islands for instance, these are islands that often are formed by volcanoes, that is to say a volcano finally pops above the surface of the ocean, once it does that you have new land that can be colonized by plants and animals. Oceanic islands have a very low diversity of kinds, so for instance, there's only 29 bird species on the Glopkos versus if you just go to the Berkeley campus you can see over 100. There's a bias of the types of birds, so you have a bunch of different finches on the Glopkos islands, right, whereas here you have all sorts of different groups of species represented on the Berkeley campus. It's also the case that the most similar kinds of, to the oceanic island forms, so for instance the closest relative of the birds on the Glopkos are found on the South American mainland. They're not found in Africa, they're not found in Europe, they're found on the west coast of South America, okay, and that's true for the turtles as well. The closest relatives of the Glopkos tortoises, giant tortoises is, is it the Chaco tortoise, but it's a South American tortoise, okay, which is kind of interesting. The argument being that the reason why the closest relative to the Glopkos birds or turtles is, is found in South America is that's where they're colonized from. These islands were colonized by turtles and birds that came from South America. And there's also a real bias of types of species that are found in oceanic islands, so for instance you see lots of plants and insects and birds and some reptiles, but what you don't find is amphibians, freshwater fish, usually you don't see mammals unless they're reintroduced later like they were on the Glopkos like rats, and you don't see most types of reptiles. The argument is that some of these types of species can actually traverse oceans quite easily and others can't. So for instance, amphibians have a real hard time tolerating saltwater, as do freshwater fish as you might imagine. Tortises are quite hard, hardy animals. You can probably throw a tortoise into the ocean and it'll survive for a month. It's not a very pleasant thing to do to the tortoise, but they can live for a long time without food and water. We have a tortoise, like I said, that wanders in our backyard and we just leave for weeks at a time and he just eats the grass, doesn't eat water because he gets all his moisture from the grass. Birds are obviously good dispersers. Plants are quite good dispersers and Darwin did all sorts of very interesting experiments in a study where he'd take different seeds from different plants. In fact, he wrote to all sorts of different farmers, can I get seeds of this type of prop or that type of plant and he'd just drop them into saltwater and he'd leave them in there for months at a time and they'd take them out and see if they germinate. And his argument was that many of these plant species, they're seeds which you're made after months in the water and he made little calculations about how far a seed could disperse in the oceanic currents in a month or two months. So anyways, the argument is that a lot of these islands can be explained as having a history and the subsequent, the fact that you have lots of turtles that are very close related to one another or birds that are close related to each other is that the speciation happened within those lucky survivors that got to the island. So that's why you have so many different types of finch, for instance, on the Glopkos. Okay, this is a little bit, some other things that Darwin could explain. This is the only figure in the origin of species. And it shows a sort of branching tree representing the relationships of some hypothetical species. This isn't the relationships of any specific species, but he's using this as a as a graphic way for the reader to see what he means by phylogeny or relationships. And besides, you know, besides being able to explain the Linnaean hierarchy, he could also explain what was known what are known as homologous structures in different species. So this is the classic example you'll see over and over again, in any textbook illustrating homology. So homology is a similarity in the structure in different organisms that's caused by a common ancestry. So he could explain homology, better write that on the board. This is a free free thing that falls out of out of his theory. And the argument is that in a lot of vertebrates, you see this pattern where you have a forelimb, you have two sets of limbs forelimbs and hind limbs, the forelimb has a pattern where you have one bone, followed by two bones, followed by a bunch of small bones and some long bones. Right? We all know I mean, a lot of you guys are going to be going off to medical school. I'm sure you'll learn the names of the parts, but that's the pattern you see, right? One bone, two bones, a bunch of little bones. And you see that in different species. Here's a mole. Here's a horse. Here's a dolphin. There's a bat. Okay, one bone, followed by two bones, followed by a bunch of fused small bones with five long skinny bones. Okay. Why do we have the similar pattern in different vertebrates? Well, the argument is their ancestor had that same pattern as well. Now, that is, this is something that was understood even at Darwin's time. At Darwin's time that people really start to understand the anatomy of different organisms, things were being shipped to London from all over the world at the time. And people were starting to understand the similarities and the structures across different species. And also, they were starting to understand the development of the species, which all, which all, you know, how a single cell turns into a full adult organism. I'll get to that in a second. Now, we also have examples of modern homology. I just want to give you an idea of what I mean by that. So here's some different species. And what I have listed along here on this table are different genes. So this is the alpha enolase. I don't know what that one is. This is probably called modulin. These are all just the names of different genes. And you'll see here they have a Psi at the end. These are what are called pseudo genes. What is a pseudo gene? Well, it's a gene that was replicated. You take a functioning gene, you replicate it, you put it elsewhere in the genome. And there's a number of mechanisms by which this can occur. But one of two things can happen when that replication occurs, when that duplication occurs. Either you have a functioning version of this gene, right? In which case, you have two copies of this functioning gene, and then you have the opportunity for the functions of the two genes to diverge. And that's one of the main arguments for why we have so many different types of genes function in ourselves. We have a history of duplication and then functional specialization. But the other thing that can happen, and far more commonly what happens, is the replicated gene is not functional. It doesn't have all the bits and pieces that tell that this bit needs to be transcribed and translated. So what happens then to this little replicated piece of DNA? Well, natural selection doesn't care about it anymore, right? And the normal copy of the gene, if you break a protein, if you change an amino acid that's coded for in the normal piece of DNA, you probably break the protein, right? And natural selection tends to eliminate those types of mutations from the population. In this replicated bit of DNA, if you change a nucleotide there, natural selection doesn't care. It doesn't have any function at all, right? So what happens is these pseudo genes start to become more and more like the background bit of the genome. In fact, after a certain amount of time, they're very difficult to even recognize, even identify as being pseudo genes because there's no signature that would allow you to actually represent or recognize that this little bit of DNA is similar to this functional bit of DNA. Now is that clear? What I mean by a pseudo gene? This is one of the few times where I wish I had, there's a clicker system. This is where I would have asked you a question and you would have been able to respond. I would have known whether you understood it. But I think it's pretty clear. So these are different pseudo genes and notice the pattern that you see these pseudo genes, the sharing among these different species. So for instance, in human chimps and grill, you have this specific alpha NLase psi 1 gene. It's estimated age in which the duplication occurred is about 11 million years ago. Here you have this Comodulin 2 pseudo gene 3. It is thought to have diverged about 36 million years ago and notice the pattern is sharing. There's more species, including hamsters, or no, that's monkey, including this monkey here that has that pseudo gene. The argument is that this pattern is consistent with what's known in the phylogeny. That is to say, the human chimp and griller, each of these closest relatives. This pattern isn't, is it? Actually, it's arangatang is up there as well. There's some uncertainty about the relationships of grills and arangs and with humans and chimps. But you have the great apes here, then you have primates here, right? So you see this pattern of sharing in which some species might have the pseudo genome, some might not. This pattern is also consistent with there being an underlined history. Now, I want to mention a little bit about what was known about developmental biology. You guys can walk out if you want tomorrow or Thursday, rather, I guess. So where was I? So number five. His theory was consistent with what was known at the time about development. So the observation was that very disparate species, things that are quite different looking as adults, go through very similar patterns in their early embryogenesis. For instance, a lot of species undergo a process called gastrulation, which is sort of the turning inside out of the developing embryo. A lot of vertebrates, all vertebrates, have a notochord that forms and it forms in a very specific way. There's an invagination of folding over of cells along the dorsal part of the developing embryo. That's something that shared across species look quite different. Our Darwin says, look, one way of explaining why we have these very similar patterns of development among really different looking species is because they all shared a common ancestor that had that same pattern of development. Now, since then, this is one of the most fabulous success stories probably in modern biology. We've learned that these patterns of similarities go much deeper and much wider than we ever imagined possible. So you don't have to remember this, first of all, right? So if this looks complicated, don't worry. I just want to make a general argument. If you're interested in developmental biology, and it's really a fascinating field, there are specialized courses that molecular cell biology teaches on developmental biology, which is fascinating. But one thing that's known is how, for instance, the drosophila, the the fruit fly, people study that for well a century now, and a lot is known about how drosophila develops. Basically what happens is you have an embryo and you have some genes that are expressed early on that set up the segmented pattern of the embryo, and then what you have is specific genes that are turned on in certain segments, okay? These genes that are turned on in different segments are called homeotic genes, okay? And the interesting thing about these homeotic genes is there's several of them, and you can imagine that it's almost like a light board. Which genes are turned on? Which of these homeotic genes are turned on in a certain segment have it affect downstream, and other genes that turn that segment into an antenna, or a wing, or whatever, right? But that's these homeotic genes that give different segments of the drosophila its identity. You're ahead. You're the tail segment. You're a wing segment, okay? And so this is just showing some of these different homeo box genes, so homeotic genes, the antena pedia complex, so there's a labial gene, there's a deformed gene, there's sex coms reduced, and showing where these genes are normally expressed. And the one cool thing, I love these, these, the mutations in these genes cause crazy mutation, crazy phenotype. So for instance, everybody knows, perhaps you don't, that flies have two wings, one pair of wings, right? So you have a, usually you have this pattern where you have four wings, and these hind wings are typically called halt years. They're just little tiny stubs that are called balancing organs. They just go up and down, counter to the wing motion. Here's an example where, in one of these homeotic genes, where this, where the third thoracic segment, that's this one, looks just like the second one, okay? So you have the, it's basically the expression turns posterior segments to make them look more like anterior segments. Here's another crazy mutation, homeotic mutation, which turns the antenna into legs, right? That's a weird thing, okay? But they're, they're cool mutations. Well here is the homeo, so it turns out that vertebrates, we have homeotic genes as well. We don't call them homeotic genes, we call them hawks genes, because they're discovered independently, but they're the same genes, they're homologous. That is to say, our common ancestor of flies and humans had homeotic genes. And interestingly, they have the same pattern, we're, you know, there's genes that are expressed early on that set up the segmented pattern in humans, we're segmented, believe it or not. But also these homeotic genes are expressed, you know, in different regions of the body. And mutations in these genes have the same effect as they do in Drosophila, that is to say, they make posterior segments look more like anterior segments. So here's an example in which the hind brain expands, because it's making this segment back here look more like the brain right here. So here's the normal phenotype, here's the mutant form, phenotype. Okay, so that's another thing that Darwin could explain real easily, developmental patterns. Number six, he could easily explain vestigial and rudimentary structures. So here, if you, these are, if you go to like the Cal Academy of Sciences, they have a big whale. And I believe it's whale skeleton rather. And I believe they actually have suspended, they've actually included the pelvic bones in this whale. So typically what happens if you see a whale skeleton, if it's done right, they'll basically suspend from wires in about the right place where they would be in the interior part of the whale, where these pelvic bones are. What these are, is these are the rudimentary parts of their hind limb, hind limbs, right? You have the bones of the pelvis followed by just the rudimentary parts of the femur. That's all there is left. So why are these bones there? They don't serve any purpose at all in the whale. The argument here is that these, these, these vestigial structures here are there only because the common ancestor of whales happened to have hind legs. It was a vertebra that used to be on land. They moved to water. And now I mentioned last time that there are examples of whales that have hind limbs, right? They're about 50 million years old. But this is all that we modern whales don't have hind limbs. I imagine that they were sort of, if they did, they would be just a drag, sort of speak, they would actually slow down the whale. And here this is a, I don't want to call it a vestigial structure, but this is an example, something was discovered in the 1960s of a homologous structure that's shared across all of life. Okay? And that is the, the so-called universal genetic code. Now it turns out the universal genetic code, there's variations on it, small variations, like in the human mitochondria or vertebrate mitochondria, there's a slightly different variant of the genetic code. But for the most part, all different organisms, bacteria, humans, everything share this code. And basically all this is, is remember the, the basic stories you have your, your proteins are coded for in the DNA, right? And every triplet of nucleotides is, codes for one amino acid in the protein. So the typical thing that happens is you have that DNA transcribed into messenger RNA and the messenger RNA is often spliced and then read by a translational machinery to, to form proteins. You know, if you're not familiar with that, don't worry, you should be familiar with it if you took high school biology, but if you're not, it's not important. The main point is that each amino acid in a protein is coded for by a triplet of nucleotides in the DNA. And so you can imagine there's 64 possible triplets for, raise the third power, four times four times four. There's 20 different amino acids. There's some redundancy in the genetic code meaning that there's some triplets that code for the same amino acid, sometimes up to six different triplets that'll code for the same amino acid, but it's shared. That's a remarkable thing. And the interesting thing is we can easily imagine a different genetic code, right? Now if we were to change the genetic code willy-nilly right now, every one of our proteins wouldn't work and that would be a very bad mutation. But early on when the genetic code must have first evolved there were probably different ways you could have had a genetic code that would have been equally good. It's just it's sort of in some ways it's just an arbitrary chance that this genetic code was chosen and not some other by evolution. But the main point is this is something that's been conserved for billions of years. Okay. Are there any questions up to this point right now? I want to turn my attention so that's all I want to say about the Darwin and the origin of species, right? It was a lot to, you know, two lectures worth of material, actually more than two. I wanted to give you the background on the basic ideas. But from now on and give you an idea for why Darwin is, is, you know, is like a set of certifiable great man. And he actually had a huge influence in modern biology. That said that the field has changed a lot since Darwin, okay? The field, I mean Darwin had no idea about inheritance. He said that things that offspring resembled parents, but that's about all he could do. He didn't know why they resemble parents, right? And in fact, it was, you know, some people argued, well, you know, this is a great theory, but it depends critically on how inheritance works. How does it work? And in some of the later editions of the origin of species, Darwin came up with a theory that just was, was flat wrong, all right? So actually the earlier editions of the origin of the species are the more interesting ones to read because they don't have this, this wrong theory in it about how inheritance works. Interestingly, you've all heard of Gregor Mendel, who's the father of Mendelian genetics, you know, he's of genetics. Darwin did have a copy of the famous 1865 manuscript that Mendel wrote in his office, right? And it's always been a great speculation about whether he read it or not. Now I'd heard as a grad student that he'd never read it because in the old days, you know, they would come to, you could, you could tell the publisher, look, I want this manuscript sent to these different people, they'd send it to these different people for you, and they'd send it in what's called the uncut state where you'd have to sort of slice the front edge so you could actually open it up. And I'd heard that it was unsliced or unopened, but I'd talked like two years ago to Darwin's scholar, that's where I always told students, which was wrong, turns out, turns out it was, it was sliced. He could have potentially read it. So it's possible he read it and didn't understand the ramifications of what he'd read, or it's possible it was just in his office, and like a lot of things in your office, in my office at least, I haven't even looked at. Okay? So, so there's great speculation, but in any case he didn't, he didn't see, he didn't understand he had the wrong theory of inheritance. But the theory itself has survived several great discoveries in biology, the first of which is this discovery of genetics and inheritance, how it actually works. The theory not only survived it, but it became stronger. In fact, the stuff I'll be talking about, population genetics, is basically how Mendelian genes act in populations. Okay? And the modern view of evolution is that evolution has changed in gene frequencies over time. Okay? So the theory became stronger after the discovery of Mendelian genetics. It became stronger still when people discovered the structure of DNA, and of course today, we have full genome sequences. It's almost impossible to understand a genome without evolution. Why would we have parasitic elements in our genome, for instance, which we do, lots of them, except to say that it's just a spread of selfish genetic elements through the genome. So the theory has become stronger, not weaker, with each discovery in modern biology. Now, what was the reaction to the origin of species immediately afterwards? Well, I would argue that most scientists accepted the fact of evolution, that is that species change over time. They said, look, you've masked a lot of evidence, and I believe that part of it. What they didn't necessarily agree with Darwin was his most original contribution, which was natural selection. A lot of people argued at that time, especially in the late 1800s, that there must be some other mechanisms that's causing adaptation in addition to natural selection. And they also disagreed with Darwin about the pattern of evolution. So remember, you have some trait here in time. And Darwin argued that you should see very gradual change in a trait. And he explained gaps in the evolution of some trait as basically due to the imperfection of the fossil record. Other people said, well, why does it have to be continuous like that? Why does it have to be gradual and continuous? Why couldn't it be sort of punctuated by very rapid bursts of change? So this would be an example of a period of very rapid change before which you had stasis and after which you had stasis. Actually, this would be the rapid change. Rapid change. This would be the stasis. So some people argued that this might be a pattern as well. That would be perfectly valid. In fact, this would also be consistent with the fossil record, what was known of it at the time. And in fact, what's known for most species today. Now, I think just as an aside, I think the modern understanding is that rates change. Some traits evolve very rapidly. Some don't change very much at all. So it depends on the characteristic you're looking at. But at the time, people debated Darwin about the pattern as well. I did mention that Darwin did not have a convincing mechanism for inheritance. And some people did criticize the theory for that very reason. But it turns out, 1865, he had Mendel's discovery. 35 years of basically his work was ignored. So he discovers basically how inheritance works. His discovery is ignored for 35 years. And it's rediscovered in about 1900. And so that's when the modern field of genetics was born, essentially. It's about 1900. Now, from our perspective, what do we need to know? We need to know that there's locus, a locus, which is sometimes called a gene. And there's different variants at a locus, which we call alleles. Now, what is a locus? It can mean a bunch of different things. So it could be a full gene. But today, nowadays, with sequencing being as cheap as it is, it's often what's called a SNP, or a SNP locus. A SNP is a single nucleotide position in the genome that potentially varies, where you see some organisms have an A there. Others might have a C, G, or T. So today, the resolution of a locus, what we mean by a locus, can be down to a single nucleotide, which, of course, is as small as you can make a locus. Everybody know what I meant by a nucleotide? But you have chromosomes that are made of DNA. And it's a one-long strand. And the nucleotides are usually abbreviated A, C, G, or T. And so a gene is usually one segment of that chromosome as a specific set of nucleotides, A, C, Gs, and T's, and that the different variants at that locus that are present in a population are called alleles. And like I said, the smallest locus can be a single nucleotide change, where maybe some species have an A here, and others have a C there. That's the smallest. So you have parts of the chromosomes, and you have variants. You have another thing you should know is genotype. That is the specific combination of alleles that some individual has at a locus. And remember, we're diploid species. That is to say, we have two copies of every gene, one from mom, one from dad. So the genotype is actually described as a pair. The two alleles you have, the allele you have for mom and the allele you have from dad. So for instance, in Mendel's notation, you might have the big A allele might be one of the alleles that's possible at some locus. And so if you've got the same variant of the allele from mom and from dad, then you'd be called big A, big A, and this is called a homozygous individual. Another possibility is you've got one variant of the allele from mom and another variant of the allele from dad. And these individuals are called heterozygous. And of course, you can have this pattern as well, little A, little A, be homozygous for the other variant of the allele. This is all stuff you probably have heard of, but I was making certain you've got it. So that's the genotype. These are the different possible genotypes when you have two different alleles in a population. And the other thing you should know is the phenotypes. This is the thing that's actually visible to you as a scientist, directly visible by eye. This is the trait. So it could be, for instance, little A, little A is an eye color. Maybe you have blue eyes if you have little A, little A. And brown eyes if you have big A, big A. And maybe you have brown eyes if you have big A, little A. So that would be an example of a phenotype, the thing you actually see. Blonde hair would be a phenotype. Brown eyes, blue eyes. Your height is a phenotype. I think that'll get us started. Oh, and then you have this pattern of what we call dominance, Mendelian dominance. And so this is the idea that sometimes the phenotype is completely determined by just having at least one copy of an allele. So for instance, in the example I just gave with brown eyes and blue eyes, brown would be called, is said to be the dominant allele. Because all you need is one copy of that allele to have the trait, the phenotype. So this big A here would be the heterozygous and the homozygous individuals to have a big A allele would have the brown eyes. A is said to be dominant to little A. Big A is said to be dominant to little A. OK, so I think that's all I wanted to say for the background. So population genetics, I've been describing it as the mathy part of evolution. So population genetics is the study of Mendelian genes in populations. So hopefully you know what a gene is, or a Mendelian gene. What is a population? Well, a population is a group of individuals, all of which can mate with one another. And the usual argument is that there's what's called random mating. Now, I don't know what you're thinking right now. This isn't like a fraternity party or anything like that. This is the idea that your mate choice doesn't depend on the gene that's in question. So one way of thinking about it, which would be kind of a weird way of thinking about it, but the individual you mate with is sort of like a lottery. If you're a female, you give all the males a lottery ticket, numbered from one to whatever, one million or something. And then you roll some dice that would determine which of those million tickets you're going to mate. This isn't how people really do it clearly, but that would be one way of thinking about random mating. So often I like to sort of make my populations as little circles. There's our population. And they have individuals in the population all randomly mating with one another. And they're at least potentially isolated from other such populations. So every species is composed of at least one population. At least one population. But you can imagine there's other populations as well, and there's some amount of interchange between the populations. This is the view I'm going to start to build up. Now the population is a very slippery idea. There's this ideal variant of the population that you can think of a population as a model for what's really happening. And scientists are always very interested in devising models. What is a model? It's just an abstract way of thinking about a process. And usually the key components of a model, in fact, the way you make a model useful to scientists, is you want to extract the most basic parts of the phenomenon you're trying to study. You don't try to do everything. You don't try to explain every single aspect of the phenomenon you're studying. You only take those parts you think are most important, and you put it into the model. So from our perspective, a population is a model for what's really happening. We realize in practice that things are much more complicated than that, but it's a model. Now it turns out that, even though this is a model, it's not a perfect description of what happens within a species, it doesn't usually matter very much. In practice, what a population is, is whatever organisms you have in hand. So you'll often hear people, not evolutionary biologists necessarily, but you'll often hear statements such as the population of San Francisco. So when people talk like that, they don't believe that San Francisco is a population of randomly mating individuals isolated from other such populations, not like people from San Francisco don't come to the East Bay, for instance. It's just, it's an administrative convenience to talk about in that way. And for lots of purposes, thinking about populations in that way are perfectly fine. So we'll talk a lot about populations, but keep in mind there's a difference between what a model is in theory or what a population is in theory and what people do in practice. Often you'll, you know, in this building, for instance, you'll have people studying gophers and they'll be studying populations of gophers that appear on, or that occur on different hills or mountain slopes, for instance. It's perfectly valid to think about populations in that sense. So that's what a population is. Okay. So I talked about also about all this stuff, genotypes, phenotypes, alleles. The last thing I want to mention are allele frequencies. As you might imagine, an allele frequency is just the frequency of some particular allele in a population of organisms. And the modern view of evolution is that, you know, evolution occurs through changes in allele frequencies in a population. So it's probably important enough to repeat. Evolution changes in allele frequencies in a population. Okay. Now the question is, what are the forces that cause allele frequencies to change? And that's what I'm going to be talking about in the next couple of lectures. One of them, of course, is natural selection. If one of the alleles is favored, that is to say, individuals that bear that allele have a better chance of surviving or reproducing, then that allele will tend to increase in frequency over time. But it is worth thinking about what happens to allele frequencies in the absence of any other evolutionary force. What just happens if you just have random mating going on? What happens to allele frequencies when only random mating occurs? And it turns out the theory that tells us what happens to allele frequencies only in the presence of random mating is called Hardy-Weinberg. Okay. Basically, this is the first math result that was ever made in the field of population genetics. Weinberg was a German physician. And he, in 1908, gave a lecture on what happens just in the presence of random mating. And Hardy, I don't know if you know who Hardy is, but he was a very famous mathematician in Cambridge, I believe. If you've ever seen Good Will Hunting, the genius guy who's really good at math, well, that movie was based on a real-life guy who was just like that from around the time of World War I, named Indian mathematician named Ramonajan. And basically, it came out of nowhere with all these great ideas. Hardy was the one who discovered this guy and brought him to England. And they had a lot of fun proving things. But he was a famous number theorist. And I would imagine that the theory I'm going to describe to you that Hardy did was probably a piece of cake form, right? No thought at all. But it describes what happens to allele frequencies only with random mating. And it's worthwhile asking why this is interesting. One historical reason why this is interesting is because people who had different ideas of how genetics worked back then, some of those ideas, including Darwin's, would have resulted in variation in a population being lost. So for instance, Darwin had this idea of blending inheritance, kind of like mixing paints. And so if you take a green paint and a yellow paint, oh, what do you get when you mix green and yellow? I just forget. But you get some other intermediate color, right? And the idea is if you take that intermediate color and then mix it together, you get the same color back out. The idea is with blending inheritance, you tend to lose variation. You lose the extremes, right? So if you used to have this type of variation in a population, if genetics worked by sort of a blending principle, which it doesn't. But if it did, after each generation, you get less and less variation. And some theoretical types pointed out that Darwin's theory, natural selection would have a real problem if genetics really worked this way, that it was blending. It turns out it's not. It's particulate. You have individual genes that are segregating in the population. But the question is, what happens to these alleles in a population? Do some of them leave? Do they get reduced in frequency and others increase naturally? This theory tells us what happens. And the bottom line is that allele frequencies don't change through the action of a random mating. So let's go ahead and work this out. On page 473 of the 8th edition, I think it's on page 456 of the 7th edition. They give an example of Hardy-Weinberg frequencies in a population. And this is basically what you do. So in this example, we have a phenotype. I'm going to do this right. So I'm going to erase some more board over here so I have some room. OK, so we have a phenotype. And in this case, the phenotype is for flower color. So you either have red flowers, pink, or white. Now, in this particular instance, the genotype is determined by the phenotype. Or you can actually say that. The genotype determines the phenotype. But if you know the phenotype, you know the genotype. So in this case, you have a allele called CR. Now, you'll notice this in the literature if you ever start to read it at some point. But alleles are named however you want. So as long as you're the discoverer of the allele. So if you discover a new allele, you get the name of how you want. So whoever discovered this red allele for the flowers named it C, superscript R. You just live with it. So if you're CR, CR, you have red flowers. If you're CR, CW, you have white flowers. And if you're CW, CW, you also have pink flowers. And you have white flowers if you're CW, CW. I think I misspoke. But if I did. So as I said, there's a one to one correspondence between genotype and phenotype. That's not always the case. The example I gave earlier where we have brown eyes and blue eyes, you can't necessarily tell the genotype from the phenotype. If I told you what's a genotype if you have brown eyes, well, you could either be a heterozygous or homozygous. You don't know which. Now in this particular population, we have a count, an observed count for the number of individuals of each genotype, or each phenotype, for that matter. There are 320 individuals that are red. You have 160 individuals that are pink. You have 20 individuals that have the white phenotype. That's just the raw count of the number of individuals in the population of each genotype. This count, of course, through some very complicated higher math will allow us to get the genotype frequencies. So let's go through this. So what is the frequency of the CRCR genotype? Well, it's just 320 divided by the total number of individuals in the population. It's 320 plus 160 plus 20. That total is 500, like I said. So we get that. So that's going to be 0.64. And we can get the genotype frequency of the heterosegous individuals as 160 divided by 500. That's 0.32. And then you have 20 divided by 500. That's 0.04. OK, so so far, we haven't done anything. We've just written down some numbers. This is the only math we've had to do, and presumably you guys are at Berkeley. That's not so difficult. Now, this is where we can start to, this is where we'll end right here. From either the counts or the genotype frequencies, we can calculate the allele frequencies. I'm going to abbreviate those as FCR and FCW. Often, you'll see these allele frequencies as described as P or Q, if you've seen this before. Now, this is where I will, next lecture, I will finish up the discussion of Party Weinberg, and then we'll start talking about natural selection and other evolutionary forces.