Transcript P(X b )

Population Genetics
Studying the Distribution of Alleles
and Genotypes in a Population
Human polymorphism for ABO blood type
Evolution
• Change in characteristics of organisms
• Change in genetic composition (frequency of
alleles) in a population
• Population = group of organisms of same
species occupying a particular geographic
region
• To study evolution: measure changes in allele
frequencies from equilibrium values
Hardy-Weinberg Equilibrium
Allelic Frequencies
p+q=1
p = frequency of A
q = frequency of a
Genotypic Frequencies
p2 + 2pq + q2 = 1
p2= f(AA), q2= f(aa)
2pq = f(Aa)
Assumptions
Large population size
Random mating
No selection
No migration
No mutation
Example Using
Hardy-Weinberg Equilibrium
Problem 1, page 4-1
Albinism, a lack of skin pigmentation, is caused by the
autosomal recessive allele a. The dominant allele A
causes skin pigmentation. For a particular population, the
frequency of albinos is 0.09.
a. What is the frequency of the allele for albinism?
b. What is the frequency of the allele for skin pigmentation?
c. What is the frequency of individuals with skin
pigmentation?
d. What is the frequency of individuals who are homozygous
for the skin pigmentation allele?
e. What is the frequency of individuals who are heterozygous
for the albino allele?
Frequency of Albinos  q2  0.09
q  q2  0.3
p  1  q  0.7
.7A
.3a
.7A
.49AA
.21Aa
.3a
.21Aa
.09aa
Frequency of AA  p 2  0.49
Frequency of Aa  2pq  0.42
Frequency of aa  q2  0.09
Genotypic Frequencies as Related to Allele Frequencies
for Populations in Hardy-Weinberg Equilibrium
Hardy-Weinberg Equilibrium
Applied to Sex-linked Genes
• Problem 2a, page 4-1
• Colorblindness is an X-linked recessive
allele. In a particular population in HardyWeinberg Equilibrium, 1 in 20 males are
colorblind. What is the frequency of
colorblind females in this population?
• Same frequencies of alleles in both
genders
Solution to Problem 2a, page 4-1
Frequency of Colorblind males  q  0.05
p  1  q  0.95
Considering only female offspring :
.95XB
.05Xb
.95XB .9025 XBXB
.0475 XBXb
.05Xb
.0025XbXb
.0475
XBXb
Frequency of XB XB  p 2  0.9025
Frequency of XB Xb  2pq  0.095
Frequency of Xb Xb  q2  0.0025
Hardy-Weinberg Equilibrium Applied to
Sex-linked Genes
• Problem 2b, page 4-1
• In a population that is not in Hardy-Weinberg
Equilibrium, the frequency of the colorblind allele
is 0.1 in females and 0.7 in males. Considering
random mating to produce the next generation,
what proportion of male offspring will be
colorblind? What proportion of the female
offspring will be colorblind?
• Genders do not have the same allele frequencies
Females
Males
q
0.1
0.7
p
0.9
0.3
Solution to Problem 2b, page 4-1
Considering only female offspring:
P(colorblind female) = P(Xb) from female x P(Xb) from male
P(colorblind female) = 0.1 x 0.7 = 0.07
.9XB
.1Xb
.3XB
.27XBXB
.03 XBXb
.7Xb
.63 XBXb
.07 XbXb
Considering only male offspring:
P(colorblind male) = P(Xb from female) = 0.1
Y
.9XB
.1Xb
.9 XBY
.1 XbY
Perturbations of
Hardy-Weinberg Equilibrium
Genetic Drift
Changes in allele
frequency due to small
population sizes
Causes of Genetic Drift
1. Population is reduced in size due to
limitations in resources
2. Founder Effect: small group of individuals
starts a new population
3. Population Bottleneck: population size
decreased by chance
Perturbations of
Hardy-Weinberg Equilibrium
Non-Random
Mating
Alters the genotypic
frequencies of a
population
Inbreeding
• Mating between close relatives is called
inbreeding.
• Inbreeding increases the probability of
homozygosity by descent: becoming
homozygous by inheriting two copies of the
same allele from one ancestor.
• Homozygosity by descent is calculated as
(1/2)n where n=number of ancestors in the
common pathway.
A1/A2
A1/A2
or A2/A3
Matching allele
A1 or A2
or A2/A2
From male parent
½ x ½ x ½ = 1/8
Matching allele
A3 or A4
A2/A3 or A2/A4
or A3/A3
From female parent
½ x ½ x ½ = 1/8
P(homozygosity by descent) = 1/8 + 1/8 = 1/4
or (1/2)3 + (1/2)3 = 1/4
Additional Problems Involving
Inbreeding
• Problem 3, page 4-1
• What is the probability of homozygosity
by descent of the offspring of a
a.parent child - mating?
b.aunt-nephew or uncle-niece mating?
c.first cousin mating?
Solutions to Inbreeding
Problems
• Problem 3a, page 4-1: 1/4
• Problem 3b, page 4-1: 1/8
• Problem 3c, page 4-1: 1/16
Perturbations of
Hardy-Weinberg Equilibrium
Natural
Selection
Increases the frequency
of genotypes with higher
fitness
Perturbations of
Hardy-Weinberg Equilibrium
Migration
Can add new alleles,
remove alleles or change
allele frequency
Hardy-Weinberg Equilibrium
Applied to Migration
• Problem 2c, page 4-1
• Twenty percent of the males in a certain
population are colorblind. A representative
group of 1000 migrates to a small, isolated
island where there are already 1000
individuals where 30% of the males are
colorblind. What is the frequency of colorblind
males and females in the new mixed
population immediately after immigration?
Assume both populations are in HardyWeinberg Equilibrium at all times.
Solution to Problem 2c, page 4-1
Assume 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 = 0.25
F(XbXb) = q2 = 0.0625
Perturbations of
Hardy-Weinberg Equilibrium
Mutation
Alters allele frequency,
causes formation of new
genotypes