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

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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.

This Talk

Speaker: Youreka Science

Audience:

Educators of H. School / Intro Undergrad
General Public
Educators of Adv. Undergrad / Grad
Student
Researcher
Educators

Recorded: June 2017

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Talk Overview

Hardy-Weinberg equilibrium combines the concepts of Darwinian evolution and Mendelian genetics to explain and study population genetics. This Youreka Science video provides an overview of allele and genotype frequency, and explores the criteria that make a population be in Hardy-Weinberg equilibrium. This video will help you understand how to use Hardy-Weinberg equilibrium to solve population genetic problems.

Speaker Bio

Youreka Science

Youreka Science was created by Florie Mar, PhD, while she was a cancer researcher at UCSF. While teaching 5th graders about the structure of a cell, Mar realized the importance of incorporating scientific findings into classroom in an easy-to-understand way. From that she started creating whiteboard drawings that explained recent papers in the scientific literature… Continue Reading