Population Genetics

• Genetic variation• Genotype frequencies• Allele frequencies• Hardy-Weinberg Equilibrium• Inferring Evolution• Applying HWE

p2 + 2pq + q2 = 1

p + q = 1

CRCR CWCWCRCW

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

Genetic VariationPhenotype:

the observable characteristics of an organismWhat controls phenotype?

genotype & environmentExamples of pure genotype?Examples of pure environment?

Examples of combination genotype and environment?

Spring brood feeds on oak flowers

Summer brood feeds on oak leaves

Nemoria arizonaria

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

For a given gene, how many alleles might there be in a population?

There can be lots…sometimes dozensExamples of 3 alleles? ABO blood types in humans – 3 alleles (IA, IB, i)

How many alleles can any one diploid individual carry?

Only 2 (diploid!)

For simplicity though, let’s think about a gene for flower color that has only two alleles (CR & CW) that show incomplete dominance…

(need a refresher on incomplete dominance?)

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

Homozygous red flower

Homozygous white flower

Heterozygous pink flower

CRCR CWCW

Now let’s imagine a population of these plants, say 500 plants….

What are the frequencies of the three genotypes and the two alleles in the population?

CRCW

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

Using the alleles CR and CW, what would be the genotype of a…

Calculating genotype fequencies…

Assume that of our 500 plants, 300 had red flowers200 had pink flowers 0 had white flowers

What are the genotype frequencies in the population?

Divide each genotype number by the total plants in the population.

f(red) = 0.6

Now how do we calculate allele frequencies?

f(pink) = 0.4 f(white) = 0.0

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

Calculating allele frequencies

1. Count the number of homozygotes of each type

Each one has two of the same allele, so double each number

2. Count the number of heterozygotes

Each heterozygote has one of each allele, so add that to the earlier number

3. Divide by the total number of alleles…2X the number of individuals (each individual is diploid)

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

How many CR alleles are there in the population?

F(CR) = (2*300) + 200 = 800 = 0.8 1000 1000

Among our 500 plants, there were

300 red, 200 pink, and 0 white

Calculating allele frequencies…

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

In the same way, calculate the frequency of the white allele (CW).

F(CR) = 200 + 2*0 = 200 = 0.8 1000 1000

What’s another way we could have found the f(CW)?

We know that there are only 2 alleles, so their frequencies must add to 1

0.8 + 0.2 = 1

Calculating allele frequencies…

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

So what good is knowing the allele frequencies?

From allele frequencies, we can calculate the expected proportions of homozygotes and heterozygotes…

….if there is no evolution underway.

In other words, we can use this as a test for ongoing evolution!

The expected genotypic frequencies =

The Hardy-Weinberg Equilibrium

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

Calculating Expected Proportions of Homozygotes & Heterozygotes in a Population

If we have just 2 alleles in a population, we denote the frequency of one as “p” and the frequency of the other as “q”.

We already know that p + q = 1…why?

If breeding is random, then the chance that an allele will show up in an offspring depends on its relative frequency in the population.

Next generation genotypic frequencies = p2, 2pq, and q2

p2 pq

pq q2

p q

p

q

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

Hardy-Weinberg Equilibrium Genotypic Frequencies

p2, 2pq, q2

If p=0.8 & q=0.2…

p2 = (0.8)2 = 0.64

2pq= 2(0.8)(0.2) = 0.32

q2= (0.2)2 = 0.04If we multiply these genotypic frequencies by the population size (500), we get HWE predicted numbers of:Red: 320 White: 20Pink: 160

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

How do these predicted numbers compare to what we saw in the actual population?

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

How do these predicted numbers compare to what we saw in the actual population?

In the HWE population, we predicted: 320 red, 160 pink, 20 white In the actual population, we saw: 300 red, 200 pink, 0 white

How is the actual population different from the predicted population?There are fewer red and white than expected, and more pink than expected.What do these differences suggest about evolution in the population?The pink flowers have the highest fitness; natural selection favors them, perhaps because pollinators like them better than red or white.What is the fitness of the white phenotype? White flowered plants have 0 fitnessWhat will happen to the allele frequencies over time if the fitness of the white genotype stays at 0? The white allele is likely to decrease over time in the population.

Can we calculate allele frequencies if the alleles show complete dominance?

With complete dominance, if we can ASSUME HWE, then we can predict genotypic frequencies.

Example: What is the frequency of carriers of PKU in the US population?

PKU is a recessive genetic disease. If we assume HWE, and q = the frequency of the PKU allele, what is the frequency of the PKU phenotype?

If we know that the PKU phenotype occurs in 1 out of 10,000 births, then q2 = 0.0001, and then q =

If q = 0.01, then p =

Then the frequency of heterozygotes is 2pq =

2(.99)(.01) = 0.0198 = ~2% of US population

q2

0.01

0.99

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution.

Check for understanding

If there are 20AA, 56Aa, and 36aa, is the population evolving?

There is a set of homework problems to practice HWE with both incomplete and complete dominance.