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.