Chapter 23 Population Genetics © John Wiley & Sons, Inc.

Chapter Outline  The Theory of Allele Frequencies  Natural Selection  Random Genetic Drift  Populations in Genetic Equilibrium © John Wiley & Sons, Inc.

Population Genetics  Population genetics studies genes in groups of individual.  It focuses on –Allelic variation among individuals –Transmission of allelic variants from parents to offspring generation after generation –Temporal changes in the genetic makeup of a population due to systematic and random evolutionary forces © John Wiley & Sons, Inc.

The Theory of Allele Frequencies …to predict the frequencies of the genotypes …frequency of each of the gene’s alleles …the frequencies of the different types of homogozygotes and heterozygotes of genes Random mating (no selection) © John Wiley & Sons, Inc.

Estimating Allele Frequencies: The MN Blood Type  The M-N blood type is determined by two alleles of a gene on chromosome 4. –L M produces the M blood type. –L N produces the N blood type. –L M L N heterozygotes have the MN blood type.  After the MN blood groups have been determined for a sample, allele frequencies can be calculated. © John Wiley & Sons, Inc. MN blood groups (glycophorin A=antigen) The M allele encodes Ser at position 1 (Ser-1) and Gly at position 5 (Gly-5) The N allele encodes Leu-1 and Glu-5 Allele : It is the alternative form of a gene for a character producing different effects.

© John Wiley & Sons, Inc. Number of copies of a particular allele Frequencies of an allele: Number of copies of ALL alleles at the locus

Estimation of Allele Frequencies  The total number of alleles is two times the sample size: 2  6129 = 12,258. © John Wiley & Sons, Inc.

 The frequency of the L M allele is 2 times the number of L M L M homozygotes plus the number of L M L N heterozygotes, all divided by the total number of alleles: [(2  1787) ] / 12,258 = © John Wiley & Sons, Inc. f (L M ) = 2n L M L M + n L M L N 2N

The frequency of the L N allele is 2 times the number of L N L N homozygotes plus the number of L M L N heterozygotes, all divided by the total number of alleles: [(2  1303) ] / 12,258 = f (L N ) = 2n L N L N + n L M L N 2N

Allele Frequencies  Letting p represent the frequency of the L M allele and letting q represent the frequency of the L N allele, we estimate that p = and q = , which is the variation of these alleles in this particular population.  Because L M and L N represent 100% of the alleles of this gene, p + q = 1. © John Wiley & Sons, Inc.

The Hardy-Weinberg Principle  The Hardy-Weinberg principle  --describes a mathematical relationship between allele frequencies and genotype frequencies.  --allows the prediction of a population’s genotype frequencies from its allele frequencies. © John Wiley & Sons, Inc.

 Assume that in a population, a particular gene segregates two alleles, A and a, with frequencies of p and q, respectively.  If members of the population mate randomly, the diploid genotypes of the next generation will be formed by the random union of haploid eggs and haploid sperm. © John Wiley & Sons, Inc.

 The probability of producing an AA homozygote is p  p = p 2.  The probability of producing an aa homozygote is q  q = q 2.  A heterozygote may be produced by –an A sperm uniting with an a egg and –an a sperm uniting with an A egg  Each of these events occurs with probability p  q, so the total probability of forming an Aa zygote is 2pq. © John Wiley & Sons, Inc.

Genotypic Frequencies  The predicted frequencies of the genotypes in the population are –AA, …..f (AA)=p 2 –Aa,….f (Aa)=2pq –aa,….f (AA)=q 2  These predicted frequencies can be obtained by expanding the binomial expression (p + q) 2 = p 2 + 2pq + q 2 © John Wiley & Sons, Inc.

f (AA)=p 2 f (Aa)=2pq f (AA)=q 2 allele frequencies genotype frequencies f (L N ) = 2n L N L N + n L M L N 2N f (L M ) = 2n L M L M + n L M L N 2N p= q=p+q = 100 %=1

Hardy-Weinberg Equilibrium  The key assumption underlying the Hardy- Weinberg principle is random mating.  … and no differential survival or reproduction exists among members of the population, the Hardy-Weinberg genotype frequencies persist generation after generation…the genotype is expected to produce p 2 + 2pq + q 2 the population is at equilibrium….  This condition is Hardy-Weinberg equilibrium. © John Wiley & Sons, Inc.

Predicting Genotype Frequencies  With the Hardy-Weinberg principle, allele frequencies can be used to predict the genotype frequencies.  For the MN blood type example, p = and q =  The predicted genotype frequencies are L M L M p 2 = (0.5395) 2 = L M L N 2pq = 2 (0.5395) (0.4605) = L N L N q 2 = (0.4605) 2 = © John Wiley & Sons, Inc.

 Do these predictions fit the data?  First we must calculate the predicted genotype numbers by multiplying the Hardy- Weinberg frequencies by the sample size (6129). GenotypePredicted Number L M L M  6129 = L M L N  6129 = L N L N  6129 = © John Wiley & Sons, Inc.

 Next, we check for agreement between the observed and predicted numbers by calculating a chi-square statistic.  This chi-square has 3 –1 = 2 degree of freedom © John Wiley & Sons, Inc.

  2 =  1 degree of freedom  The critical value for 2 degree of freedom is  Conclusions: –The predicted genotype frequencies are in agreement with the observed frequencies. –In this population, the M-N genotypes are in Hardy-Weinberg proportions. © John Wiley & Sons, Inc.

Predicting Allele Frequencies from Genotype Frequencies  In the United States, the incidence of the autosomal recessive disorder phenylketonuria (PKU) is about  The incidence of PKU represents the frequency of mutant homozygotes in the population. © John Wiley & Sons, Inc.

 Homozygous mutant individuals should occur with a frequency equal to the square of the mutant allele frequency, q.  q 2 =  Taking the square root, q = 0.01  Because p + q = 1, we know that p =  p = 0.99 and q = 0.01  The frequency of heterozygous carriers is 2pq = 2(0.99)(0.01) =  p+q=100%, p=99%; q=1%; © John Wiley & Sons, Inc.

The Hardy-Weinberg Principle for X-Linked Genes  For X-linked genes, allele frequencies are estimated from the frequencies of the genotypes in males. © John Wiley & Sons, Inc.

Example: Color Vision SexGenotype Frequency Phenotype Males X 1 Y p = 0.88 Normal vision X 2 Y q = 0.12 Color blind Females X 1 X 1 p 2 = 0.77 Normal vision X 1 X 2 2pq = 0.21 Normal vision X 2 X 2 q 2 = 0.02 Color blind © John Wiley & Sons, Inc. f (X 1 X 1 )= f (X 2 X 2 )= f (X 1 X 2 )= f (X 1 Y)= f (X 2 Y)= Genotype Frequency Allele f (X 1 )=p f (X 2 )=q X 1 Y=C X 2 Y=c

Genes with Multiple Alleles  For genes with multiple alleles, the Hardy-Weinberg genotype proportions are obtained by expanding a binomial expression. © John Wiley & Sons, Inc.

Example: A-B-O Blood Type  The A-B-O blood types are determined by three alleles, I A, I B, and I, with frequencies p, q, and r, respectively.  Genotypes can be calculated by expanding the trinomial (p + q + r) 2 = p 2 + q 2 + r 2 + 2pq + 2qr + 2pr © John Wiley & Sons, Inc.

Blood TypeGenotype Frequency AI A I A p 2 I A i2pr BI B I B q 2 I B i2qr ABI A I B 2pq Oi ir 2 © John Wiley & Sons, Inc. =f (I A I A ) =f (I i I i ) Frequency G A f (I A )=p f (I b )=q f (I i )=r Phenotype =f (I B I B )

Exceptions to the Hardy- Weinberg Principle  Nonrandom mating  Unequal survival  Population subdivision  Migration  It will disrupt Hardy-Weinberg equilibrium © John Wiley & Sons, Inc.

Nonrandom Mating  Nonrandom mating includes –Consanguineous mating (mating between genetically related individuals) –Assortative individuals (mating between individuals with similar phenotypes)  Both consanguineous mating and assortative mating reduce the frequency of heterozygotes and increase the frequency of homozygotes compared to the Hardy-Weinberg genotype frequencies.  The effects of consanguineous mating can be quantified using the inbreeding coefficient, F.  F=1 Self-fertilization © John Wiley & Sons, Inc.

Unequal Survival  If zygotes produced by random mating have different survival rates…. Heterozygotes == Homozygotes  A sample of 200 adults yielded the following data: GenotypeObserved NumberExpected Number A 1 A A 1 A A 2 A © John Wiley & Sons, Inc.

Population Subdivision  Single interbreeding unit,---non homogenous  There are no mating restrictions at all  It is panmictic.  Panmixis implies that any member of the population is able to mate with any other member.  In nature, populations may be subdivided due to geographical or ecological barriers that may be correlated with genetic differences. © John Wiley & Sons, Inc.

Migration  The introduction of genes by recent migrations can alter allele and genotype frequencies within a population and disrupt Hardy-Weinberg equilibrium. © John Wiley & Sons, Inc.

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Random Genetic Drift Allele frequencies change unpredictably in populations because of uncertainties during reproduction. Genetic drift, the random change of allele frequencies in populations. It is due to uncertainties in Mendelian segregation. Non-Mendelian inheritance: Gene conversion: mismatch repair Extranuclear DNA

Random Changes in Allele Frequencies C c C c CC Cc cCcc Offspring’s probability for CC is 1/2 x 1/2=1/4 2 offspring is 1/16 Offspring’s probability for cc is 1/2 x 1/2=1/4 2 offspring is 1/16 Offspring’s probability for CC and Cc is 1/4 x 1/2 x 2=1/4=4/16 Offspring’s probability for cc and Cc is 1/2 x 1/4 x 2=1/4=4/16 of population

Factors Contributing to Random Genetic Drift  There is always uncertainty as to which allele a given offspring will receive.  There is random variation in the number of offspring that a parent produces. © John Wiley & Sons, Inc.

The Effects of Population Size  In large populations, the effect of genetic drift is minimal.  In small populations, genetic drift may be the primary evolutionary force.  The effect of population size is determined by monitoring the frequency of heterozygotes, or the heterozygosity of a population over time. © John Wiley & Sons, Inc.

p=q=0.5 N=4 H  1/2N