Download Allele Frequencies: Staying Constant

Allele Frequencies:
Staying Constant
Chapter 14
What is Allele Frequency?
How frequent any allele is in a given
population:
– Within one race
– Within one nation
– Within one town/school/research project
• Calculated by genotyping a large sample
of the population
• Or – estimated by phenotype frequency in
entire population (recessive disease only)
Example: PKU allele
Population Genetics
Considers all alleles within a given
population:
• Allele is the version of the gene that a
person carries (Allele frequency)
• Gene pool = all alleles that are possible
within population’s gametes
• Genotype frequency = proportion of the
population that has each type of genotype
• Phenotype frequency = percentage of
population that have phenotype
Bi-allelic Gene
• In bi-allelic gene there are only two alleles
possible
– T or t – for tall or short pea plants
– R or r – for wrinkled or round seeds
• p = frequency of the more common of the
two alleles
• q = frequency of the less common of the
two alleles
Commonly…
• Many genes have more than two alleles
• Most common diseases/disorders are
multifactorial:
– More than one gene – each with more than
two alleles
– Environment and genetics
• Therefore – phenotype will not equal
genotype
Rare cases are still useful…
• Even though most genes and most
diseases don’t follow these rules we are
about to learn
• There are still many cases where these
rules are important and useful for genetics
• Next class we’ll learn some of the
complications
Hardy-Weinberg Equilibrium
Where the allele frequencies stay constant
from one generation to the next
• Often calculated with a bi-allelic gene
(p and q)
Therefore…
• p and q remaining constant
Changing Allele Frequencies
1. Mutation – introduces new alleles into
population
2. Natural Selection – specific alleles are
more likely to be passed down because
they are somehow advantageous
3. Non-random Mating – individuals of one
genotype are more likely to mate with
individuals of same genotype
– Think of an example of this happening?
Changing Allele Frequencies
4. Migration – individuals with specific
genotypes move in or out of a population
5. Genetic Drift – random changes in allele
frequencies
– Caused by random sampling of specific
genotypes
– Often seen in small, isolated populations
Can you think of why?
– Nothing to do with natural selection
Hardy-Weinberg Equilibrium
• Requires that none of these things are
happening in a population:
– No mutation
– No selection
– No migration
– No genetic drift
– Random mating
– Large population
• Obviously this is VERY rare in real life
Hardy-Weinberg Equilibrium
1908
• Hardy – an English mathematician
• Weinberg – a German physician
• Both derived, independently, an algebra
calculation for what happens to allele
frequencies within a population
• Assuming all those false conditions
Hardy-Weinberg Equilibrium
1. If there are only two alleles then the
following must be true:
p+q=1
The frequency of the two alleles added
together must equal the entire population
(a frequency of 1)
Hardy-Weinberg Equilibrium
2. The genotype frequencies can also be
calculated:
p2 + 2pq + q2 = 1
The frequency of each homozygote equals
the frequency of the allele squared
The frequency of heterozygote is 2 times p
times q Product Rule
These three
genotypes
must add
to one
Product
and Addition
Rules
Hardy-Weinberg Equilibrium
1. Allele frequencies add to one:
p+q=1
2. The genotype frequencies can be
calculated from the allele frequencies:
p2 + 2pq + q2 = 1
Hardy-Weinberg Equilibrium
1. Allele frequencies add to one:
p+q+r=1
2. The genotype frequencies can be
calculated from the allele frequencies:
p2 + 2pq + 2pr + 2rq + q2 + r2 = 1
How it was derived:
A (p)
a (q)
A (p)
a (q)
AA
(pp)
Aa
(pq)
Aa
(pq)
aa
(qq)
Frequencies:
Allele A
=p
Allele a
=q
Genotype AA = p2
Genotype Aa = 2pq
Genotype aa = q2
Let’s work through HWE:
• Autosomal recessive trait – (middle finger
is shorter than 2 and 4)
• All we know is this:
In 100 individuals there are 9 that show the
recessive shorter finger
• Use HWE to figure out:
Both allele frequencies
All three genotype frequencies
Let’s work through HWE:
• Know: 9/100 show recessive phenotype
• Calculate:
p=
q=
Homozygous Dominant =
Heterozygous
=
Homozygous Recessive = 0.09
Let’s work through HWE:
• 9/100 = recessive phenotype
• Know this is an autosomal recessive trait
Therefore:
• Recessive phenotype = qq genotype
• q2 = 0.09
Therefore:
• q = 0.3
• p must equal 1 - q = 1 - .3 = 0.7
Let’s work through HWE:
• p = 0.7 and q = 0.3
• Homozygous Dominant = p2
(.7)(.7) = .49 or 49%
• Heterozygous = 2 pq
2(.7)(.3) = .42 or 42%
• Homozygous Recessive = q2
(.3)(.3) = .09 or 9% (which is what we
based all of these calculations on)
Solved HWE:
• Know: 9/100 show recessive phenotype
• Calculate:
p = .7
q = .3
Homozygous Dominant (p2) = 49%
Heterozygous (2pq)
= 42%
Homozygous Recessive (q2) = 9%
• What about in the next generation?
Practical Applications of HWE
1. Genotyping error
– If your genotypes are grossly off of the
expected from HWE calculations
2. Artificial Selection
3. Population Genetics
– Determining genetic risk in different
populations
4. Disease risk
5. Forensic Biology
Genotyping Error
Are genotypes present in expected proportions
with allele frequencies?
Allele freq.
p(1) =
0.62
q(2) =
0.38
Expected:
Genotype
1/1
1/2
2/2
Observed
123
131
50
304
Expected
116.9
143.2
43.9
304
1/1 = p2 * total # genotypes
1/2 = 2pq * total # genotypes
2/2 = q2 * total # genotypes
HWE Calculations:
CHI2:
2.207
df:
1
p-value:
0.137
Artificial Selection
This is the human act of purposely selecting
certain traits over others:
• Changing phenotype frequencies
• Agriculture
– What examples can you think of?
• Pure breed dogs (other animals)
• HWE calculations will tell you:
– How many mating pairs to set up
– How many generations to get desired result
Population Genetics
• Estimate genotype frequency from
phenotype frequency
• Based on known percentage of population
that shows a recessive phenotype
• That percent must be homozygous for the
recessive allele right? (q2)
• What are problems here?
– Multifactorial, more than two alleles, etc
Disease Risk
Couple wants to know their risk of having a
child with a specific disease
• If one (or both) parents have phenotype in
question – run genetic tests
• If neither have phenotype then question is
about being a carrier (2pq)
• Based on population genetics calculations
and therefore their assumptions
Disease Risk
Couple wants to know their risk of being
carriers for disease (2pq)
• Population genetics tells us how frequent
phenotype is in population
• That’s q2
• Square root – calculate q
• Calculate p
• Calculate 2 pq – That’s carrier frequency
Carrier Frequencies:
X-linked is different…
• Females follow same HWE formula:
p2 + 2pq + q2 = 1
• Males however only carry one allele:
Therefore
• In males phenotype frequency is allele
frequency (not genotype)
• Therefore frequency of recessive
phenotype gives you q, not q2
Forensic Biology
Using biology to add to the forensics of a
crime scene
• Although we all share 99.9 percent of our
DNA with every other human
• That 0.1 % equals about 3 million base
pairs of difference
• Product rule means that this can ID more
than there are humans on the planet
Forensic Biology
Identifying individuals with DNA:
1. Genotype a few polymorphisms (~10)
2. All on different chromosomes
3. All highly polymorphic
– More than two alleles
– More alleles, more information per
polymorphism
4. Match to crime scene
– Or body, or baby to father in paternity
Forensic Biology
Identifying individuals with DNA:
• Match to crime scene
– Or body, or baby to father in paternity
•
•
•
Calculating the chance of seeing the
DNA profile is calculated based on
Hardy-Weinberg Equilibrium
Exact calculations depend on how
frequent alleles are in given population
How likely genotypes will be
Polymorphisms:
• SNPs:
– Single Nucleotide Polymorphism
– More common, but only have two alleles
• RFLPs:
– Restriction Fragment Length Polymorphism
– Many alleles
• Microsatellites:
– Polymorphic repeats in non-coding sequence
– Most alleles possible (avg. around 8)
How is HWE involved?
• Determine genotype of individual
• Use HWE to calculate probability of seeing
specific genotype:
– Het. = 2pq = 2(.6)(.4) = 0.36
– Homo = q2 = (.25)(.25) = 0.0625
• Then use product rule to calculate final
probability that another person has the
same combination of genotypes:
– (.36)(.06) = 0.0225 or 2.25% chance
HWE and Product Rule:
Genotype Five Bi-allelic
Polymorphism
Het = 2pq = 2(.6)(.3)
= .36
Het = 2pq = 2(.5)(.3)
= .30
Het = 2pq = 2(.15)(.8) = .24
Homo = q2 = (.2)(.2)
= .04
Het = 2pq = 2(.80)(.18) = .29
HWE and Product Rule:
= .36
(.36)(.3)(.24)(.04)(.29) = 0.00031
= .30
= .24
= .04
= .29
Or 1/3,226
Therefore, the chance of this matching
the wrong person is 1/3,226
Summary
• Hardy-Weinberg Equilibrium(HWE) states:
p+q=1
p2 + 2pq + q2 = 1
• HWE is unlikely to exist in a real
population
• But it is still useful for many fields of
genetics – know how and when to use it
• Know how to calculate it for biallelic genes
Next Class:
• Read Chapter Fifteen
• Homework – Chapter Fourteen Problems;
– Review: 1, 2, 3, 5
– Applied: 1, 2, 6, 7, 11
• Happy Halloween!