# Hardy-Weinberg Equilibrium: Combining Darwinian Evolution and Mendelian Genetics to Study Population Genetics

## Transcript of Part 1: Hardy-Weinberg Equilibrium: Combining Darwinian Evolution and Mendelian Genetics to Study Population Genetics

00:00:15.13 Back in the early 1900s, 00:00:17.06 a couple of scientists named 00:00:19.12 G. H. Hardy and Wilhelm Weinberg 00:00:21.26 started thinking that Darwin's theory of natural selection, 00:00:25.00 survival of the fittest, 00:00:26.21 and Mendel's ideas about inheritance of genes 00:00:29.12 could be combined to help us understand 00:00:31.14 how populations evolve. 00:00:34.07 They were interested in understanding... 00:00:36.05 one, what is the frequency of specific alleles in a population? 00:00:39.25 So, what fraction of the total number of alleles 00:00:42.16 are dominant, capital B, 00:00:44.04 or recessive, lowercase b? 00:00:46.24 And two, as the organisms mate 00:00:49.09 and have offspring over many generations, 00:00:51.28 whether the frequency of those alleles 00:00:54.12 changes over time. 00:00:56.13 So, if you start out with 60% of the alleles being capital B 00:01:02.02 and 40% being lowercase b. 00:01:05.12 After the people mate, 00:01:08.09 are there still 60% capital B and 40% lowercase b? 00:01:12.11 Notice also that the allele frequencies 00:01:14.11 -- 0.6 and 0.4 -- 00:01:16.07 add up to 1. 00:01:18.00 This is a key aspect of learning how to solve 00:01:20.17 Hardy-Weinberg equilibrium problems, 00:01:22.18 so keep it in mind for later. 00:01:24.25 Hardy and Weinberg postulated 00:01:27.01 that if the allele frequencies 00:01:28.29 did not change over time, 00:01:30.16 then the population was in equilibrium. 00:01:32.29 We would say that such a population 00:01:35.06 is in Hardy-Weinberg equilibrium. 00:01:37.25 In contrast, if the allele frequencies 00:01:40.00 do change over time, 00:01:41.16 the population is not in Hardy-Weinberg equilibrium. 00:01:46.08 For a population to be in Hardy-Weinberg equilibrium 00:01:50.24 -- so, for the allele frequencies to not change over time -- 00:01:53.20 there are five criteria that must be met. 00:01:56.09 These are, number one, 00:01:57.25 the population must be large; 00:01:59.26 number two, no mutations occur; 00:02:03.04 number three, no migration into or out of the population, 00:02:07.08 also called gene flow; 00:02:10.03 number four, mating must be random; 00:02:12.10 and number five, no natural selection can occur. 00:02:16.04 If these five criteria are met, 00:02:18.04 the population is in Hardy-Weinberg equilibrium. 00:02:21.18 Evolution is not occurring at that locus, 00:02:24.11 and the allele frequencies 00:02:26.23 will remain the same over time. 00:02:29.19 If you calculate allele frequencies 00:02:31.10 and find that they have changed over time, 00:02:33.25 you can say that the population is not in Hardy-Weinberg equilibrium, 00:02:37.13 meaning that it has evolved. 00:02:40.25 Let's go through two related examples 00:02:42.23 of Hardy-Weinberg equilibrium problems, 00:02:45.08 and learn both how to calculate allele and genotype frequencies, 00:02:49.23 as well as to start thinking about why 00:02:52.15 a population may or may not be evolving. 00:02:55.22 Example number one... 00:02:57.18 you are studying the coat color locus 00:02:59.17 for a population of 100 squirrels 00:03:01.21 living in a forest along the coast of California. 00:03:05.13 The dominant allele, capital B, gives black fur, 00:03:11.16 while lowercase b, the recessive allele, 00:03:13.14 gives white fur and is recessive. 00:03:15.06 In population genetics, we call the frequency of the dominant allele "p" 00:03:18.27 and the frequency of the recessive allele "q". 00:03:22.24 The sum of these allele frequencies 00:03:26.02 -- all the alleles in the population -- 00:03:28.02 must equal 1. 00:03:30.06 Now, let's relate this to the genotypes, 00:03:32.11 which is the probability of having an individual 00:03:35.21 that is homozygous dominant, 00:03:37.09 that is, having one allele to be capital B 00:03:40.20 and the other, also, a capital B, 00:03:42.02 is p times p. 00:03:44.05 That equals p^2. 00:03:46.11 The probability of being heterozygous, 00:03:48.25 having one capital B 00:03:51.04 and one lowercase b, 00:03:52.28 is 2 times p times q. 00:03:55.23 And the probability of being homozygous recessive 00:03:58.25 is q times q, 00:04:01.08 which equals q^2. 00:04:03.25 The sum of the genotype frequencies 00:04:06.02 must also equal 1, 00:04:07.26 which is this equation: 00:04:09.24 p^2 + 2pq + q^2 = 1. 00:04:15.09 Now, back to your squirrels. 00:04:17.11 You find that 20 of the 100 squirrels have white fur, 00:04:21.16 which corresponds to 0.2. 00:04:25.05 White fur is homozygous recessive, 00:04:28.20 so we know that these squirrels have the same genotype: 00:04:31.09 little b little b. 00:04:33.18 Since we know that q^2 is the genotype frequency 00:04:36.15 of homozygous recessive 00:04:38.15 -- little b little b -- 00:04:40.00 we know that 0.2 equals q^2. 00:04:43.22 We can solve for q 00:04:46.11 by taking the square root of 0.2, 00:04:48.16 which gives us q equals 0.45. 00:04:52.24 Since p plus q equals 1, 00:04:55.16 we can easily solve for p, 00:04:58.02 which is 0.55. 00:05:03.02 These squirrels breed and, in a second generation, 00:05:04.25 you go back to the forest 00:05:07.06 and want to determine if the population 00:05:09.10 is in Hardy-Weinberg equilibrium. 00:05:11.16 You count and see that 40 of the 200 squirrels 00:05:15.05 in this generation have white fur. 00:05:17.15 This means that the frequency 00:05:19.20 of the recessive genotype, 00:05:21.02 q^2, is 0.2. 00:05:23.12 We can now easily solve for q, 00:05:25.09 the recessive allele frequency, 00:05:27.08 so q equals 0.45. 00:05:29.21 We can easily solve for p, 00:05:32.21 which is 0.55. 00:05:34.14 Based on these equations, 00:05:36.11 let's see if our population is in Hardy-Weinberg equilibrium. 00:05:39.22 We started with p equals 0.55 00:05:42.18 and q equals 0.45 00:05:45.09 in the first generation. 00:05:47.28 And we calculated that p equals 0.55 00:05:51.13 and q equals 0.45 00:05:53.27 in the second generation. 00:05:56.26 So, the allele frequencies did not change over time. 00:05:59.27 This means we can accept the Hardy-Weinberg equilibrium null hypothesis 00:06:04.19 and say that, yes, this population 00:06:07.13 is in Hardy-Weinberg equilibrium 00:06:09.07 and has not undergone evolution. 00:06:12.21 Example number two... 00:06:14.07 you are also studying a population of squirrels 00:06:16.13 that live on a nearby beach. 00:06:18.27 In the first generation, 00:06:20.14 they had p equals 0.55 00:06:22.24 and q equals 0.45. 00:06:26.13 In the second generation, 00:06:28.24 you find that the frequency of the dominant allele, 00:06:31.11 p, is 0.7, 00:06:34.02 and the frequency of the recessive allele, 00:06:36.17 q, is 0.3. 00:06:38.22 This population of squirrels on the beach 00:06:41.03 is not in Hardy-Weinberg equilibrium 00:06:43.00 since the allele frequencies 00:06:45.07 did change over generations. 00:06:47.11 So, we reject the null hypothesis 00:06:49.21 and can say that this population evolved. 00:06:52.12 Now, what factors caused this population 00:06:54.26 to undergo evolution? 00:06:56.22 To answer this, think about the five criteria 00:06:59.21 for Hardy-Weinberg equilibrium, 00:07:01.11 and let's come up with some ideas 00:07:03.07 as to which of these criteria were not met. 00:07:06.04 Number three: no migration 00:07:08.16 into and out of the population. 00:07:10.07 Maybe the water level went down, 00:07:12.17 so some white squirrels living on the coast 00:07:14.29 could come from shore 00:07:16.28 and start living on the island. 00:07:19.00 Number five: no natural selection can occur. 00:07:22.20 Maybe the white squirrels 00:07:25.00 stood out more against the sand 00:07:26.24 than the black squirrels, 00:07:28.13 so they were more noticeable to predators 00:07:30.11 and got eaten. 00:07:32.11 Now, let's do a third example 00:07:34.14 to see how we can use the Hardy-Weinberg equilibrium idea 00:07:37.01 to solve population genetic problems. 00:07:40.19 You can use the Hardy-Weinberg equilibrium 00:07:42.11 to solve population genetic problems 00:07:45.08 if you assume that the population 00:07:46.26 is in Hardy-Weinberg equilibrium. 00:07:49.11 Let's say that you are now studying eye color 00:07:51.28 in a population of squirrels. 00:07:53.19 You have either brown eyes or blue eyes, 00:07:55.13 and you know that blue is recessive. 00:07:59.04 You look at all of your squirrels 00:08:00.20 and find that 4% of the population has blue eyes. 00:08:04.24 How can you figure out, 00:08:06.25 A, the frequency of the brown eye allele, 00:08:08.25 and B, what percentage of the population 00:08:11.29 is heterozygous for this trait? 00:08:15.00 Assuming the population follows Hardy-Weinberg equilibrium, 00:08:17.27 let's solve A and B. 00:08:20.24 To solve A, let's start with the information 00:08:23.05 that 4% of the population has blue eyes. 00:08:26.17 This is telling you the frequency 00:08:28.17 of the recessive genotype: blue eyes. 00:08:31.09 So, we know that 0.04 equals q^2. 00:08:35.11 We can easily solve for q, 00:08:37.16 the frequency of the recessive allele, 00:08:39.04 which is 0.2. 00:08:41.11 Therefore, given that p plus q equals 1, 00:08:45.27 we know that p equals 0.8. 00:08:49.16 This is the allele frequency of brown eyes. 00:08:53.15 To solve B, 00:08:55.07 let's use the equation p^2 + 2pq + q^2 = 1. 00:09:01.13 The frequency of the heterozygous genotype is 2pq, 00:09:05.07 so 2 times 0.8 times 0.2 00:09:10.04 equals 0.32. 00:09:13.09 To get the percentage, 00:09:15.26 we can multiply by 100. 00:09:17.15 So, 32% of the population of squirrels 00:09:19.26 is heterozygous at the eye color locus. 00:09:23.09 Overall, Hardy-Weinberg equilibrium 00:09:26.27 is a way to apply Mendelian genetics 00:09:29.04 -- the idea that traits like coat and eye color in squirrels 00:09:33.17 get inherited -- 00:09:35.20 to large populations, 00:09:37.15 and to figure out whether that trait is undergoing evolution. 00:09:39.28 Through this lesson, you have learned 00:09:42.14 how to calculate genotype and allele frequencies 00:09:44.15 over several generations 00:09:46.06 and use these calculations to determine 00:09:48.05 if a population is or is not 00:09:50.07 in Hardy-Weinberg equilibrium. 00:09:53.15 If the population is in Hardy-Weinberg equilibrium, 00:09:56.01 you can use Hardy-Weinberg equilibrium 00:09:58.05 to solve population genetics problems. 00:10:01.01 On the other hand, if the population 00:10:03.01 is not in Hardy-Weinberg equilibrium, 00:10:05.09 we can start thinking about what selective pressures 00:10:07.19 might be in place 00:10:09.22 that are causing evolution 00:10:12.13 and anticipate how these selective pressures 00:10:14.03 may shape future generations. 00:10:17.29 This video has been provided to you by Youreka Science 00:10:20.11 and iBiology, bringing the world's best biology to you.