# The evolution of populations & Hardy- Weinberg Equilibrium FRIDAY, SEPTEMBER 5, 2014

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The evolution of populations & Hardy-Weinberg Equilibrium

Friday, September 5, 2014Warm-upWhat do you think is the most important component in order for evolution to occur? (Hint: think about the definition of evolution).

HomeworkBe a leader assignment due Monday, September 8!Directions: Solve your problem on a separate sheet of paper and staple it to your given worksheet slip. Hand it in on Monday.Be prepared to show your group how you solved the problem!Lamarck vs. Darwin

Inheritance of acquired characteristicsNatural selection4

Evolution is change in the genetic composition of a population from generation to generationBut what is a more concise definition for evolution that will help us determine quantitatively if evolution is occurring??

Evolution is the change in allele frequencies over timeHow can we measure allele frequencies?How can we track changes in allele frequencies over time?

Genetic variation exists in the population (this is key for evolution to occur!)Certain alleles produce traits that are more adaptive, i.e., promote greater survival and reproductionThese alleles get passed on to the next generationEvolution is the change in allele frequencies in a population over generationsPopulation: group of individuals of the same species that live in the same area and interbreed, producing fertile offspring.Gene pool: genetic makeup of a population

9Evolution is the change in allele frequencies in a population over generationsMechanisms that cause allele frequency change:Natural selectionGenetic driftGene flowMutationNon-random matingOnly natural selection causes adaptive evolution

10Mini genetics review

Alleles are different versions of that geneExample:

Combinations of allelesExample for a population in which alleles for a gene are R or rHomozygous recessive: rrHomozygous dominant: RRHeterozygous: Rr

Skittles gene poolNow, how do we measure changes in allele frequencies in populations over time?

First, we must know the starting pointWhat are the allele frequencies in the population right now?We cannot measure change unless we know the initial state.Use Hardy-Weinberg Principle to quantify evolution

Godfrey Harold "G. H." HardyWilhelm WeinbergThe idea is to track allele frequenciesAAAAAAAAAAAaAaAaaaaaWhat is the frequency of allele A?What is the frequency of allele a?The idea is to track allele frequenciesAAAAAAAAAAAaAaAaaaaaThe frequency for allele A = 13/20 or 0.65The frequency for allele a = 7/20 or 0.35

AAAAAAAAAAAaAaAaaaaaGeneration 1?Generation 2Hardy-Weinberg PrincipleAllele frequencies of alleles and genotypes in a population will remain constant from generation to generation if all assumptions are met

A gene pool that remains constant is said to be in Hardy-Weinberg equilibriumAAAAAAAAAAAaAaAaaaaaGeneration 1?Generation 2AAAAAAAAAAAaAaAaaaaaGeneration 1A0.65a0.35A0.65AA0.42Aa0.23a0.35Aa0.23aa0.12Generation 2AAAAAAAAAAAaAaAaaaaaf(A) = 0.65f(a) = 0.35A0.65a0.35A0.65AA0.42Aa0.23a0.35Aa0.23aa0.12f(A) = ?f(a) = ?AAAAAAAAAAAaAaAaaaaaf(A) = 0.65f(a) = 0.35A0.65a0.35A0.65AA0.42Aa0.23a0.35Aa0.23aa0.12f(A) = 0.65f(a) = 0.35Allele frequencies did not change, thus no evolution.23The Hardy-Weinberg PrincipleAllele frequencies in a population will remain constant if ALL of the following conditions are met:The population is infinitely largeIndividuals mate randomlyNo gene flowNo natural selectionNo mutationsIf all conditions are met, then NO evolution. Allele frequencies will remain constant. This is the null hypothesis. The Hardy-Weinberg equation: p2 + 2pq + q2 = 1

A0.65a0.35A0.65AA0.42Aa0.23a0.35Aa0.23aa0.12Understanding the equationAAAAAAAAAAAaAaAaaaaap2 + 2pq + q2 = 1p is the frequency of the dominant allele (A) = 0.65q is the frequency of the recessive allele (a) = 0.35

p2 + 2pq + q2 = 1p is the frequency of the dominant allele (A) = 0.65q is the frequency of the recessive allele (a) = 0.35

p = f(AA) + f(Aa)p = 0.5 + 0.3 = 0.65q = f(aa) + f(Aa)q = 0.2 + 0.3 = 0.35 Understanding the equationAAAAAAAAAAAaAaAaaaaaUsing p and q from generation 1, solve for frequencies of predicted genotypes in generation 2 using HW Understanding the equationA0.65a0.35A0.65AA0.42Aa0.23a0.35Aa0.23aa0.12p2 + 2pq + q2 = 1p is the frequency of the dominant allele (A) = 0.65q is the frequency of the recessive allele (a) = 0.35

p = f(AA) + f(Aa)p = 0.5 + 0.3 = 0.65q = f(aa) + f(Aa)q = 0.2 + 0.3 = 0.35 Generation 2p = f(A) = 0.65q = f(a) = 0.35Understanding the equationA0.65a0.35A0.65AA0.42Aa0.23a0.35Aa0.23aa0.12Generation 2p = f(A) = 0.65q = f(a) = 0.35p2 + 2pq + q2 = 1p is the frequency of the dominant allele (A) = 0.65q is the frequency of the recessive allele (a) = 0.35

p = f(AA) + f(Aa)p = 0.5 + 0.3 = 0.65q = f(aa) + f(Aa)q = 0.2 + 0.3 = 0.35 p2 = the predicted frequency of genotype AA = 0.422pq = the predicted frequency of genotype Aa = 0.46q2 = the predicted frequency of genotype aa = 0.1230

The Hardy-Weinberg equation: p2 + 2pq + q2 = 1

What is the frequency of alleles B and b?Allele Frequenciesred = 0.36, white = 0.16red = 0.6, white = 0.4red = 0.5, white = 0.5Allele frequencies cannot be determined unless the population is in equilibrium.Red short-horned cattle are homozygous for the red allele, white cattle are homozygous for the white allele, and roan cattle are heterozygotes. Population A consists of 36% red, 16% white, and 48% roan cattle. What are the allele frequencies?33Answer: bAllele Frequenciesred = 0.36, white = 0.16red = 0.6, white = 0.4red = 0.5, white = 0.5Allele frequencies cannot be determined unless the population is in equilibrium.Red short-horned cattle are homozygous for the red allele, white cattle are homozygous for the white allele, and roan cattle are heterozygotes. Population A consists of 36% red, 16% white, and 48% roan cattle. What are the allele frequencies?34Answer: bLets see another exampleWe sampled 200 individuals from a population:128 individuals have the AA genotype53 individuals have the Aa genotype19 individuals have the aa genotype

What are the genotype frequencies?

Lets see another exampleWe sampled 200 individuals from a population:128 individuals have the AA genotype (0.64)53 individuals have the Aa genotype (0.26)19 individuals have the aa genotype (0.10)

What are the allele frequencies?Genotype frequenciesLets see another exampleWe sampled 200 individuals from a population:128 individuals have the AA genotype (0.64)53 individuals have the Aa genotype (0.26)19 individuals have the aa genotype (0.10)

p = AA + (Aa) = 0.64 + (0.26) = 0.77q = aa + (Aa) = 0.10 + (0.26) = 0.23

Genotype frequenciesAllele frequenciesLets see another exampleWe sampled 200 individuals from a population:128 individuals have the AA genotype (0.64)53 individuals have the Aa genotype (0.26)19 individuals have the aa genotype (0.10)

p = AA + (Aa) = 0.64 + (0.26) = 0.77q = aa + (Aa) = 0.10 + (0.26) = 0.23p + q = 0.77 + 0.23 = 1.0p2 + 2pq + q2 = (0.77)2 + 2(0.77)(0.23) + (0.23)2 = 1.0Genotype frequenciesAllele frequenciesLets work through another exampleAlbinism (aa) occurs on average 1 in 20,000 individuals in North America.

What is the frequency of the A and a allele in this population?

Lets work through another exampleAlbinism (aa) occurs on average 1 in 20,000 individuals in North America. What is the frequency of the A and a allele in this population?

The Hardy-Weinberg equation: p2 + 2pq + q2 = 1

q2 = f(aa) = 1/20,000 = 0.00005 q2 = 0.00005q = 0.007 (frequency of a in the population)

p = 1 qp = 1 0.007 p = 0.993 (frequency A in the population)

p2 + 2pq + q2 (0.993)2 + 2(0.993)(0.007) + (0.007)2 = 1.0

p2 = 98.6% (AA)2pq = 1.4% (Aa)q2 = 0.005% (aa)40The Hardy-Weinberg PrincipleAllele frequencies in a population will remain constant if ALL of the following conditions are met:The population is infinitely largeIndividuals mate randomlyNo genetic migration and mutationNo natural selectionNo mutationIf ALL conditions are met, then theres NO evolution. Allele frequencies will remain constant. The Hardy-Weinberg equation: p2 + 2pq + q2 = 1AAAAAAAAAAAaAaAaaaaaf(A) = 0.65f(a) = 0.35A0.65a0.35A0.65AA0.42Aa0.23a0.35Aa0.23aa0.12What will happen if these assumptions are not met?The population is infinitely largeIndividuals mate randomlyNo genetic migration and mutationNo natural selectionf(A) = 0.65f(a) = 0.3542Exit TicketWhat is the Hardy-Weinberg formula, and what does each component represent?Work on Clover Study