# Population Genetics p + q = 1 p2 + 2pq + q2 = 1 Genetic variation

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Population Genetics p + q = 1 p2 + 2pq + q2 = 1 Genetic variation
Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution. Population Genetics Genetic variation Genotype frequencies Allele frequencies Hardy-Weinberg Equilibrium Inferring Evolution Applying HWE p + q = 1 CRCR CWCW CRCW p2 + 2pq + q2 = 1

Genetic Variation Phenotype:
Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution. Genetic Variation Phenotype: the observable characteristics of an organism What controls phenotype? genotype & environment Examples of pure genotype? Examples of pure environment? Examples of combination genotype and environment? Nemoria arizonaria Spring brood feeds on oak flowers Summer brood feeds on oak leaves

(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. For a given gene, how many alleles might there be in a population? There can be lots…sometimes dozens Examples 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?)

Using the alleles CR and CW, what would be the genotype of a…
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… Homozygous red flower Heterozygous pink flower Homozygous white flower CRCR CRCW 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?

Calculating genotype fequencies…
Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution. Calculating genotype fequencies… Assume that of our 500 plants, 300 had red flowers 200 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

Calculating allele frequencies
Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution. Calculating allele frequencies Count the number of homozygotes of each type Each one has two of the same allele, so double each number Count the number of heterozygotes Each heterozygote has one of each allele, so add that to the earlier number Divide by the total number of alleles…2X the number of individuals (each individual is diploid)

Calculating allele frequencies…
Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution. Calculating allele frequencies… Among our 500 plants, there were 300 red, 200 pink, and 0 white How many CR alleles are there in the population? F(CR) = (2*300) = = 0.8

Calculating allele frequencies…
Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution. Calculating allele frequencies… In the same way, calculate the frequency of the white allele (CW). F(CR) = *0 = = 0.8 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 = 1

The Hardy-Weinberg Equilibrium
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

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

Hardy-Weinberg Equilibrium Genotypic Frequencies
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 = 0.04 If we multiply these genotypic frequencies by the population size (500), we get HWE predicted numbers of: Red: White: 20 Pink: 160 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
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 fitness What 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.

Learning target: I can calculate genotype and allele frequencies and use the Hardy-Weinberg equilibrium to test for evolution. 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 = , and then q = If q = 0.01, then p = Then the frequency of heterozygotes is 2pq = 2(.99)(.01) = = ~2% of US population q2 0.01 0.99

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.

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