Population Genetics Population Genetics

Studying the Distribution of Alleles Studying the Distribution of Alleles and Genotypes in a Population and Genotypes in a Population

Human polymorphism for ABO blood typeHuman polymorphism for ABO blood type

Evolution Evolution

• Change in characteristics of organismsChange in characteristics of organisms• Change in genetic composition (frequency of Change in genetic composition (frequency of

alleles) in a populationalleles) in a population• Population = group of organisms of same Population = group of organisms of same

species occupying a particular geographic species occupying a particular geographic regionregion

• To study evolution: measure changes in allele To study evolution: measure changes in allele frequencies from equilibrium values frequencies from equilibrium values

Hardy-Weinberg EquilibriumHardy-Weinberg EquilibriumAllelic FrequenciesAllelic Frequencies p + q = 1p + q = 1

p = frequency of Ap = frequency of A

q = frequency of aq = frequency of a

Genotypic FrequenciesGenotypic Frequencies pp22 + 2pq + q + 2pq + q22 = 1 = 1

pp22== f(AA), qf(AA), q22= f(aa)= f(aa)

2pq = f(Aa)2pq = f(Aa)

AssumptionsAssumptions Large population size Large population size

Random mating Random mating

No selectionNo selection

No migrationNo migration

No mutationNo mutation

Example Using Example Using Hardy-Weinberg EquilibriumHardy-Weinberg Equilibrium

Problem 1, page 4-1Problem 1, page 4-1 Albinism, a lack of skin pigmentation, is caused by the Albinism, a lack of skin pigmentation, is caused by the

autosomal recessive allele autosomal recessive allele aa. The dominant allele . The dominant allele AA causes causes skin pigmentation. For a particular population, the skin pigmentation. For a particular population, the frequency of albinos is 0.09.frequency of albinos is 0.09.

a.a. What is the frequency of the allele for albinism?What is the frequency of the allele for albinism?

b.b. What is the frequency of the allele for skin pigmentation?What is the frequency of the allele for skin pigmentation?

c.c. What is the frequency of individuals with skin What is the frequency of individuals with skin pigmentation?pigmentation?

d.d. What is the frequency of individuals who are homozygous What is the frequency of individuals who are homozygous for the skin pigmentation allele?for the skin pigmentation allele?

e.e. What is the frequency of individuals who are heterozygous What is the frequency of individuals who are heterozygous for the albino allele?for the albino allele?

.7A

.3a

.7A .3a

.49AA .21Aa

.21Aa .09aa

0.09 q aa ofFrequency

0.42 2pq AaofFrequency

0.49p AA ofFrequency

2

2

0.7q1p

0.3q q

0.09q Albinosof Frequency2

2

Genotypic Frequencies as Related to Allele FrequenciesGenotypic Frequencies as Related to Allele Frequenciesfor Populations in Hardy-Weinberg Equilibriumfor Populations in Hardy-Weinberg Equilibrium

Hardy-Weinberg Equilibrium Hardy-Weinberg Equilibrium Applied to Sex-linked GenesApplied to Sex-linked Genes

• Problem 2a, page 4-1Problem 2a, page 4-1• Colorblindness is an X-linked recessive allele. In a particular Colorblindness is an X-linked recessive allele. In a particular

population in Hardy-Weinberg Equilibrium, 1 in 20 males are colorblind. population in Hardy-Weinberg Equilibrium, 1 in 20 males are colorblind. What is the frequency of colorblind females in this population?What is the frequency of colorblind females in this population?

• Same frequencies of alleles in both gendersSame frequencies of alleles in both genders

.95XB

.05Xb

.95XB .05Xb

.9025 XBXB

0.0025 q XX ofFrequency

0.095 2pq XX ofFrequency

0.9025p XX ofFrequency

2bb

bB

2BB

:offspring female only gConsiderin

0.95q1p

0.05q males Colorblind of Frequency

.0475 XBXb

.0475 XBXb .0025XbXb

Solution to Problem 2a, page 4-1

Hardy-Weinberg Equilibrium Applied to Hardy-Weinberg Equilibrium Applied to Sex-linked GenesSex-linked Genes

• Problem 2b, page 4-1Problem 2b, page 4-1

• In a population that is not in Hardy-Weinberg In a population that is not in Hardy-Weinberg Equilibrium, the frequency of the colorblind allele Equilibrium, the frequency of the colorblind allele is 0.1 in females and 0.7 in males. Considering is 0.1 in females and 0.7 in males. Considering random mating to produce the next generation, random mating to produce the next generation, what proportion of male offspring will be what proportion of male offspring will be colorblind? What proportion of the female colorblind? What proportion of the female offspring will be colorblind?offspring will be colorblind?

• Genders do not have the same allele frequenciesGenders do not have the same allele frequencies

FemalesFemales MalesMales

qq 0.10.1 0.70.7

pp 0.90.9 0.30.3

Solution to Problem 2b, page 4-1Considering only female offspring: P(colorblind female) = P(Xb) from female x P(Xb) from maleP(colorblind female) = 0.1 x 0.7 = 0.07

.3XB

.7Xb

.9XB .1Xb

.27XBXB .03 XBXb

.63 XBXb .07 XbXb

.9XB

.1Xb

Y

.9 XBY

.1 XbY

Considering only male offspring: P(colorblind male) = P(Xb from female) = 0.1

Perturbations of Perturbations of Hardy-Weinberg EquilibriumHardy-Weinberg Equilibrium

Genetic DriftGenetic Drift Changes in allele Changes in allele frequency due to small frequency due to small population sizespopulation sizes

Causes of Genetic Drift Causes of Genetic Drift

1.1. Population is reduced in size due to Population is reduced in size due to limitations in resourceslimitations in resources

2.2. Founder Effect: small group of individuals Founder Effect: small group of individuals starts a new populationstarts a new population

3.3. Population Bottleneck: population size Population Bottleneck: population size decreased by chance decreased by chance

Perturbations of Perturbations of Hardy-Weinberg EquilibriumHardy-Weinberg Equilibrium

Non-Random Non-Random MatingMating

Alters the genotypic Alters the genotypic frequencies of a frequencies of a populationpopulation

InbreedingInbreeding

• Mating between close relatives is called Mating between close relatives is called inbreeding.inbreeding.

• Inbreeding increases the probability of Inbreeding increases the probability of homozygosity by descent: becoming homozygosity by descent: becoming homozygous by inheriting two copies of the homozygous by inheriting two copies of the same allele from one ancestor.same allele from one ancestor.

• Homozygosity by descent is calculated as Homozygosity by descent is calculated as (1/2)(1/2)nn where n=number of ancestors in the where n=number of ancestors in the common pathway.common pathway.

From male parentFrom male parent ½ x ½ x ½ = 1/8½ x ½ x ½ = 1/8

From female parent From female parent ½ x ½ x ½ = 1/8½ x ½ x ½ = 1/8

p=1/2

P(homozygosity by descent) = 1/8 + 1/8 = 1/4 P(homozygosity by descent) = 1/8 + 1/8 = 1/4 or (1/2)or (1/2)33 + (1/2) + (1/2)3 3 = 1/4= 1/4

or A2/A3

or A2/A2

A1/A2

Matching alleleA1 or A2

p=1/2

p=1/2

A4/A4

Matching allele A3 or A4

p=1/2

p=1/2

or A3/A3

A2/A3 or A2/A4

A1/A2

Additional Problems Involving Additional Problems Involving InbreedingInbreeding

• Problem 3, page 4-1Problem 3, page 4-1

• What is the probability of homozygosity What is the probability of homozygosity by descent of the offspring of a by descent of the offspring of a

a.a.parent child - mating?parent child - mating?

b.b.aunt-nephew or uncle-niece mating?aunt-nephew or uncle-niece mating?

c.c. first cousin mating?first cousin mating?

Solutions to Inbreeding Solutions to Inbreeding ProblemsProblems

• Problem 3a, page 4-1: 1/4Problem 3a, page 4-1: 1/4

• Problem 3b, page 4-1: 1/8Problem 3b, page 4-1: 1/8

• Problem 3c, page 4-1: 1/16Problem 3c, page 4-1: 1/16

Perturbations of Perturbations of Hardy-Weinberg EquilibriumHardy-Weinberg Equilibrium

Natural Natural SelectionSelection

Increases the frequency Increases the frequency of genotypes with higher of genotypes with higher fitnessfitness

Perturbations of Perturbations of Hardy-Weinberg EquilibriumHardy-Weinberg Equilibrium

MigrationMigration Can add new alleles, Can add new alleles, remove alleles or change remove alleles or change allele frequencyallele frequency

Hardy-Weinberg EquilibriumHardy-Weinberg Equilibrium Applied to Migration Applied to Migration

• Problem 2c, page 4-1Problem 2c, page 4-1• Twenty percent of the males in a certain Twenty percent of the males in a certain

population are colorblind. A representative group population are colorblind. A representative group of 1000 migrates to a small, isolated island where of 1000 migrates to a small, isolated island where there are already 1000 individuals where 30% of there are already 1000 individuals where 30% of the males are colorblind. What is the frequency of the males are colorblind. What is the frequency of colorblind males and females in the new mixed colorblind males and females in the new mixed population immediately after immigration? population immediately after immigration? Assume both populations are in Hardy-Weinberg Assume both populations are in Hardy-Weinberg Equilibrium at all times.Equilibrium at all times.

Solution to Problem 2c, page 4-1Assume males represent half of each population.

0.2 x 500 = 100 colorblind males migrate 0.3 x 500 = 150 colorblind males in receiving population

q = 100 + 150/1000 = 0.25

F(XbY) = q = 0.25F(XbXb) = q2 = 0.0625

Perturbations of Perturbations of Hardy-Weinberg EquilibriumHardy-Weinberg Equilibrium

MutationMutation Alters allele frequency, Alters allele frequency, causes formation of new causes formation of new genotypesgenotypes