Today:
Population Genetics
Chapter 17 in 1st edition
Chapter 18 in 2nd edition
A week from Friday (April 24th)
Redo Exams
Consider a locus with two alleles: A and a
In populations, genetic variation
is distributed among individuals
• How can these distributions be described?
• What distributions are expected from
Mendelian inheritance alone?
Allele frequencies are the proportions of
each allele in the population.
Possible diploid genotypes are:
AA, Aa, aa
In a diploid population of N individuals each
individual has two genomes, so there are
2N genomes in the population.
The genotype frequencies are the
proportions of each genotype in the
population
p = the frequency of allele A =
Number of genomes with A allele
Total number of genomes in population
Five major forces that cause
evolution of populations:
Evolution is a change in the
genetic composition of a
population or populations
Changes in allele frequencies
Changes in genotype frequencies
1)
2)
3)
4)
5)
Mutation
Selection*
Random genetic drift
Migration
Nonrandom mating
*Note that natural selection is just one of 5 forces that
causes evolution
1
What happens to allele and genotype
frequencies when there are no forces acting
to change them?
A Simple Case
Consider the probabilities of:
1) individuals with specific genotypes mating
2) the probabilities of each genotype among
their progeny.
• N is the number of diploid individuals
• Individuals are hermaphroditic
• Every individual has an equal chance of
reproducing
• Every individual has an equal chance of
mating with any other individual
• All individuals reproduce at the same time,
then die (discrete generations)
Discrete Generations
Step 1: What are the allele frequencies
in haploid gametes ?
Generation 1  Generation 2  Generation 3
Each generation lives, reproduces and dies together,
no individuals survive from one generation to the next.
Examples: Annual plants, some insects
Simplest Case:
Broadcast Spawning
• Gametes produced by meiosis: each
gamete gets one of the parental alleles
• AA individuals produce all A gametes
• aa individuals produce all a gametes
• Aa individuals produce ½ A gametes and
½ a gametes
Corals Spawning
Common in some marine invertebrates
(bivalves, corals, etc.)
eggs and sperm are released into water and
fertilize at random
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Gametes unite in pairs
• Two haploid gametes combine to make a
diploid egg
• What is the probability of an A allele gamete?
• What is the probability of an a allele gamete ?
• Probability of allele = its allele frequency
Probability of a gamete carrying A = p
Probability of a gamete carrying a = q
What will be the genotype
frequencies in the eggs?
Probabilities of each progeny genotype
depends on allele frequencies
Multiply allele frequencies to get genotype
frequencies (zygote event is intersection of
two gamete events)
For heterozygotes, consider both
combinations that produce heterozygotes
Genotype Probabilities / Frequencies
Probability of AA genotype =
Pr(A sperm and A egg) = p x p = p2
Probability of Aa genotype =
Probability of
[(A sperm and a egg) or
(a sperm and A egg)]
=pxq+
q x p = 2pq
Probability of aa genotype =
Pr(a sperm and a egg) = q x q = q2
Example
•
•
•
•
p = 0.4, q = 0.6
Probability of AA = p2 = 0.16
Probability of Aa = 2pq = 0.48
Probability of aa = q2 = 0.36
Hardy-Weinberg (Castle) Law
p = frequency of allele A
q = (1-p)= frequency of allele a
Regardless of genotype frequencies in parental
population, after one generation of random
mating:
p2 = frequency of AA genotype
2pq = frequency of Aa genotype
q2 = frequency of aa genotype
I
3
Simple population with
random mating:
HW Genotype Frequencies vs. Allele
Frequencies for 2 Alleles
• Allele frequencies don’t change from one
generation to the next
• Genotype frequencies don’t change after
they reach Hardy-Weinberg proportions
Assumptions of HW
What about mating in pairs?
Diploid, hermaphroditic, sexually
reproducing population
Absence of other forces, implies:
Random mating
No immigration / emigration
No selection
No mutation
No genetic drift
If individuals mate in pairs but and
are hermaphroditic:
• Hardy-Weinberg principle still holds
• A few more steps are needed to prove
this…
What if individuals are not
hermaphroditic?
If allele frequencies are same in males and
females  Hardy-Weinberg proportions
are reached after one generation
If allele frequencies are different in males
and females  Hardy-Weinberg
proportions are reached after two
generations
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The Hardy-Weinberg (HW)
Principle in Practice
How to Tell if Genotype Frequencies
are in Hardy-Weinberg Proportions
• Despite needing assumptions, in most cases genotype
frequencies are very close to HW proportions
• HW is robust to small deviations from the assumptions
(e.g. typical mutations rates or levels of natural selection)
• Even when deviations occur, they go away after ~1
generation of random mating
• Large deviations from HW indicate something interesting
is going on!
• Often the cause of HW deviations is non-random mating
• Need a statistical test for expected counts,
Chi-Square is often used
• Expected genotype frequencies are based
on estimated allele frequencies
• Estimation of allele frequencies eliminates
one degree of freedom for each indepdent
allele frequency estimated
Chi-Square Test of
Hardy-Weinberg Equilibrium
1. Estimate Allele Frequencies
Are these genotype counts significantly different
from those expected for genotype frequencies in
Hardy-Weinberg proportions?
Calculated Expected Genotype Frequencies
According to Hardy-Weinberg
Calculate 2:
Observed Counts - Expected
There is 3 – 1 – 1 = 1 degree of freedom,
1 degree of freedom was lost when p was estimated
(q is just 1- p, so no degree of freedom was lost for q)
5
Determine if 2 is significant
• 2 = 7.16 with 1 degree of freedom
What can cause deviations from
Hardy-Weinberg Proportions?
Violation of the assumption of absence of
these other forces:
non-random mating
immigration / emigration
selection
mutation
genetic drift
p < 0.01, difference IS significant
Nonrandom Mating is a Common Cause of
Deviation from Hardy-Weinberg Proportion
Mate choice can be based on:
1) The level of genetic relatedness
• Inbreeding (preference for relatives)
• Outbreeding (preference for non-relatives)
2) The level of physical resemblance
• Assortative mating (mate with similar)
• Disassortative mating (mate with dissimilar)
Inbreeding
Nonrandom Mating
• Inbreeding is the mating of individuals that
are more closely related than would be
expected by chance
• Outbreeding is the mating of individuals
that are genetically more distantly related
than would be expected by chance
Figure 23.14
• Inbreeding leads to an increase in
homozygosity (proportion of homozygotes)
• Inbreeding is measured by the inbreeding
coefficient (F)
– The probability that two alleles in an individual
are identical because of their inheritance from a
single allele in an ancestor
• Probability that individual IV-1 inherits the A1 allele
from both her maternal and paternal ancestors is:
– P = (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) = 0.016 or 1/64
• However, she could be homozygous for A2, A3, or A4
• Therefore, the inbreeding coefficient is:
– F = (1/64) x 4 = 1/16
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Inbreeding Depression
Inbreeding does not change allelic frequencies
– However, it does change genotypic frequencies
Because inbreeding increases the frequency of
homozygotes, it can have a profound effect on the
expression of deleterious phenotypes
• Inbreeding depression is the reduction in
fitness due to inbreeding
• The increased frequency of homozygotes
expressing deleterious recessive alleles
results in a lowered mean fitness for the
inbred population
States in which 1st cousin
marriages are banned
Should Cousins Marry?
• In the US, laws banning first cousin
marriages date to the Civil War
• Similar laws were not passed in Europe
• Marriage of first cousins common in some
societies
• How great is the risk of first cousin
marriages?
2002 Study by National Society of
Genetic Counselors
• See paper on course website
• Risks were smaller than assumed
– 1.7-2% above background risk for birth defects
– 4.4% for pre-reproductive mortality
• Similar to risk for women over 40 having children
• Smaller than risk (50%) for people with known
autosomal dominant disorders (e.g. Huntington
disease)
Closer look at forces that affect the
amount and distribution of genetic
variation, and thus cause evolution:
1)
2)
3)
4)
5)
Mutation
Selection
Random genetic drift
Migration
Nonrandom mating
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Genetic Drift
Change in Allele Frequencies
• A change in the genetic composition of a
population due to the random sampling of
gametes that produce zygotes
• Leads to changes in allele and genotype
frequencies.
Genetic drift changes allele frequencies randomly
exact outcomes cannot be predicted
only probabilities of outcomes
Progressive loss of alleles:
random but directional
Eventual outcomes of genetic drift
How strong is genetic drift?
• Allele frequency hits 0 – allele is lost
• Allele frequency hits 1 – “fixation”
• If an allele has a frequency of p, the
probability that it will reach fixation is p
• Assumptions:
• If N is the size of a “breeding population”
of diploid individuals
• The “strength” of genetic drift is 1/2N
• Large populations → genetic drift is weak
• Small populations → genetic drift is strong
– no selection, mutation* or migration
*mutation can introduce new alleles
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Why genetic drift is important
• Genetic drift always occurs (no population
is infinitely large)
• Genetic drift causes evolution without
natural selection or adaptation
• Loss of genetic variation in small
populations can be severe:
• The allele that is fixed by genetic drift is random,
not because it is advantageous
• In contrast, selection provides an advantage for a
specific allele or genotype, and is not random
• Random genetic drift is an important consideration
in the conservation of endangered species
– Example: Florida panther, Puma concolor coryi
– causes inbreeding
– less potential to adapt (evolve)
Natural Selection
• Genotypes differ in fitness, which
influences rates of survival and
reproduction
• Differences in fitness change allele or
genotype frequencies
The Concept of Fitness
• Absolute fitness refers to the average
reproductive rate of individuals with the
same genotype
• Relative fitness refers to a genotype’s
ability to survive and reproduce relative to
other genotypes in the population
• Consider a hypothetical genotype of wolf
spider
Relative fitness
in diploid, sexual population
Fitness of genotype AA is WAA
Fitness of genotype Aa is Waa
Fitness of genotype aa is Waa
• Fecundity is the number of offspring born to an average
female with a specific genotype
• Survival is the proportion of those offspring that survive to
sexual maturity
• Fitness is expressed as fecundity times survival
Scaled to 1.0 (fitness are relative)
– Standardized relative to the genotype with the highest fitness
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Models of Selection
Selection can act in three main ways:
1) Directional selection acts to continuously remove
individuals from one end of the phenotypic distribution
2) Stabilizing selection acts to remove individuals at
both ends of the phenotypic distribution
3) Disruptive selection works by favoring the individuals
at the phenotypic extremes over those in the middle of
the phenotypic distribution
Industrial melanism
Figure 23.3
Industrial melanism
• darkening of butterflies and moth in 19th
century Western Europe
• discovered by amateur butterfly collectors
• burning of coal  black soot on trees
• melanism – dark pigmentation
Increase in frequency
of melanic allele
H.B.D. Kettlewell
• 20th century lepidopterist experimented
with peppered moths
• in clean areas
– light colored lichen
– light colored moths
• in sooty areas
– lichen died
– tree trunks dark
– moths dark
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Kettlewell’s experiments
• moths that matched tree trunks were
camouflaged
• birds less likely to eat camouflaged moths
Heterozygote superiority
Stabilizing Selection
Heterozygote advantage (a form of stabilizing selection)
occurs when the heterozygote is the fittest genotype
Heterozygote superiority
WAA < WAa > Waa
Heterozygote genotype can never be fixed – heterozygotes
always produce 1/2 homozygous progeny
Mean fitness population fitness =
p2 WAA +2pq WAa + q2 Waa
Selection will move allele frequencies to point that
maximizes mean population fitness
Sickle Cell Anemia
Normal Blood Cells
Sickle Blood Cells
• Most common in people of African or
Mediterranean descent
• Abnormal hemoglobin (the protein that
transports oxygen and carbon dioxide in blood)
• Caused by a mutation in one of the hemoglobin
genes
• Red blood cells become deformed and break
11
Sickle Hemoglobin forms Long
fibers in Red Blood Cell
Sickle Cell Hemoglobin:
A Single Amino Acid is Changed in the  chain
Valine instead of
glutamic acid
Distribution of sickle-cell allele
Hemoglobin has 4 polypeptide chains:
2 identical  chains
2 identical  chains
The sickle cell allele confers
resistance to malaria
Alleles:
HbS – sickle cell allele
HbA – normal allele
Genotypes and Phenotypes:
HbS HbS – severe anemia, malaria resistant
HbA HbA – no anemia, malaria susceptible
HbA HbS – mild anemia, malaria resistant
Distribution of malaria
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Distribution of malaria and
sickle-cell allele
Sickle-cell heterozygote advantage
HardyWeinberg
Death due to
SSA
Death due to
malaria
Fitness w/
malaria
AA
AS
SS
0.71
0.21
0.02
0
+
+++
+++
+
+
0.88
1.0
0.14
Summary of sickle-cell anemia
• heterozygotes have mild anemia, and
resistance to malaria
• in malarial areas, sickle cell allele is
maintained by heterozygote advantage
• outside of malarial areas, sickle cell allele
is eliminated
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