Population genetics
Michèle Sale, Ph.D.
Center for Public Health Genomics
msale@virginia.edu
Tel: 982-0368
Additional reading
• Campbell, N.A., Reece, J.B. et al. (2008). Biology. 8th edition.
Benjamin/Cummings Publishing Company, Inc.
http://www.mansfield.ohio-state.edu/~sabedon/campbl23.htm
• A.H. Sturtevant, (2001) A History of Genetics. Cold Spring Harbor
Laboratory Press.
http://www.esp.org/books/sturt/history/contents/sturt-historych-17.pdf
Review of terminology
• Mutation
– A permanent, heritable change in genomic
sequence
• Variant
– Any mutated site, irrespective of frequency
• Allele
– A DNA sequence variant
– All DNA sequences, not just genes, can have
more than one allele
Allele
A C G AA T A T T
A C G A T T A T T
Genotype
A C G AA T A T T
A C G A T T A T T
Genotype
A C G AA T A T T
A C G A T T A T T
Haplotype
A C G AA T A T T
A C G A T T A T T
Haplotype
A C G AA T A T T
A C G A T T A T T
Diplotype
or
Haplogenotype
A C G AA T A T T
A C G A T T A T T
More than 2 alleles at a locus in a population
1/2
1/1
1/3
2/2
1/1
2/2
1/2
1/2
1/1
1/2
1/1
1/2
1/2
1/2
1/2
More than 2 alleles at a locus in a population…
1/2
1/1
1/3
2/2
1/1
2/2
1/2
1/2
1/1
1/2
1/1
1/2
1/2
1/2
1/2
Phenotype vs. Genotype
• Phenotype is the observable
property of an organism; a trait such as
height, weight, medical condition, etc.
• Genotype is the DNA sequence of an
organism at a specific, defined
location.
Population genetics
• The study of allele and genotype
frequencies in a population
What do we mean by a population?
• Population
– A localized group of interbreeding individuals
– Note: For this part of the course – human genetics –we
are dealing with a single species, but many of the
concepts of population genetics apply more broadly
• Gene pool
– A gene pool consists of all alleles at all loci in all
individuals in a population
Allele frequency
• All alleles possess a frequency that is
somewhere between 0.0 and 1.0
• Allele frequency refers to the frequency
of alleles in a gene pool, not in single
individuals
Punnett square
• Used to predict the probability of
possible genotypes of offspring
Punnett square
Punnet
Reginald C. Punnett
• In 1900, Mendel's work was rediscovered by
Carl Correns, Erich Tschermak von
Seysenegg and Hugo de Vries
• William Bateson had Mendel's work
translated into English
• Bateson and Punnett helped established the
new science of genetics at Cambridge
• Mendelism (1905) by Punnett was probably
the first popular science book to introduce
genetics to the public
• Punnett and Bateson co-founded the
Journal of Genetics in 1910
1875 –1967
http://www.dnaftb.org/dnaftb/concept_5/con5bio.html
Explaining the allele frequency
in a population
• The discrete alleles Mendel discovered exist
at some frequency in natural populations
• Biologists wondered how and if these
frequencies would change
• Many thought that the more common
versions of genes would increase in
frequency simply because they were already
at high frequency
Asked by a student
why recessive alleles
don’t disappear from
the population
Godfrey Harold Hardy
1877– 1947
Cambridge mathematician
http://en.wikipedia.org/wiki/G._H._Hardy
Hardy-Weinberg theorem
G.H. Hardy
Wilhelm Weinberg
1862-1937
German physician
•
The Hardy-Weinberg Law states that allele and genotype
frequencies remain constant in succeeding generations in a
population at equilibrium
•
For a two allele system, let:
p = the frequency of the dominant allele (e.g. A)
q = the frequency of the recessive allele (e.g. a)
•
For a population in genetic equilibrium:
p + q = 1 (The sum of the frequencies of both alleles is 100%.)
•
For genotype frequencies,
(p + q)2 = 1, or
p2 + 2pq + q2 = 1
•
The three terms of this binomial expansion indicate the
frequencies of the three genotypes:
p2 = frequency of AA (homozygous dominant)
2pq = frequency of Aa (heterozygous)
q2 = frequency of aa (homozygous recessive)
Hardy Weinberg Equilibrium
Genotype frequency
p2 + 2pq + q2 = 1
Allele frequency
G.H. Hardy
• “… I should have expected the very
simple point which I wish to make to
have been familiar to biologists”
Hardy-Weinberg Equilibrium
• Given the appropriate conditions, it
takes only a single generation to reach
Hardy-Weinberg equilibrium
Reaching HWE
Most extreme situation (takes 2 generations):
Start with two population with different fixed alleles:
AA AA
AA
AA
AA
aa
x
AA
Aa
AA
Aa
aa
aa
aa
aa
Aa
Aa
AA
aa
Aa
Aa aa
Aa
Aa
Aa
Aa
Aa
Aa
Aa
Aa
aa
AA
Aa
AA
aa
Aa
Aa
aa
Calculating allele frequencies
– Remember that a diploid organism has two (not necessarily
different) alleles at each locus
– The frequency of an allele within a population is equal to the
number of alleles of a given type within the population divided
by the total number of alleles found at a given locus
– Thus, if:
• 200 A alleles and
• 400 a alleles
are found within a given population, then the frequency of
A alleles is 200 / (200 + 400) = 1/3 = 0.33
– If this is a diploid population, how many individuals are in this
population?
300
Calculating allele frequencies from genotype frequencies
•
•
Genotype frequency information can be used to calculate allele
frequency
If a population has
– 100 Aa individuals
– 200 aa individuals, and
– 300 AA individuals
then the number of
A alleles is 100*1 + 300*2 = 700;
the number of a alleles is 100*1 + 200*2 = 500;
the frequency of A therefore is 700 / (500 + 700) = 7/12 = 0.58
•
•
Remember diploid individuals contribute two alleles from each
locus to the gene pool (hence the *2 in the above calculations)
How many diploid individuals are present in the above example?
600
Calculating genotype frequencies from allele frequencies
•
If the frequency of allele A is 0.4 and that the frequency of allele a is 0.6, what is the
frequency of genotypes AA, Aa, and aa?
– For a locus for which only two alleles are present in a population:
• p2 + 2pq + q2 = 1 = (p + q)2
–
Substitute p for the frequency of A (i.e., in this example p = 0.4) and q for the
frequency of a (i.e., in this example q = 0.6)
• Frequency AA = p * p = p2
• Frequency aa = q * q = q2
• Frequency Aa = p * q + q * p = 2pq
• Frequency AA = 0.4 * 0.4 = 0.16
• Frequency aa = 0.6 * 0.6 = 0.36
• Frequency Aa = 0.4 * 0.6 + 0.6 * 0.4 = 0.48
–
Keep in mind that:
• p + q = 1, i.e.
• p=1–q
• q=1–p
Calculating genotype frequencies
from allele frequencies
– If a has a frequency of 0.01, then
• Frequency AA = 0.99 * 0.99 = 0.98
• Frequency Aa = 2 * 0.99 * 0.01 = 0.02
• Frequency aa = 0.01 * 0.01 = 0.0001
– In this example there are 200 times more heterozygotes carrying the
recessive allele than there are recessive homozygotes
– As recessive alleles become rare, many more carriers of this allele
will be heterozygotes rather than homozygotes
Hardy-Weinberg equilibrium
only holds true if:
•
•
•
•
•
No mutation
Large population
No migration
No selection
No selective mating
(Note: It is possible that balanced mutation and
selection could exist)
Hardy-Weinberg equilibrium
only holds true if:
•
•
•
•
•
No mutation
Large population
No migration
No selection
No selective mating
Mutation
•
•
•
•
•
•
•
•
•
Changes allele frequency since it involves the conversion of one allele into
another allele
Doesn’t play a large direct role in changing allele frequency because mutation
rates per locus tend to be low
Mutations rarely affect phenotype
However, all allelic variation ultimately has a mutational origin
Mutation rates differ between species and between different regions of the
genome of a single species, e.g. CpG islands
Mutation rate may change in response to environmental stress, e.g. UV
damage
It is estimated that a human DNA sequence differs from that of one's parents
at about 100 nucleotide positions
These sites generally represent germline mutations that have arisen during the
production of gametes in the parental generation
The human mutation rate is higher in the male germ line (sperm) than the
female (egg cells)
Hardy-Weinberg equilibrium
only holds true if:
•
•
•
•
•
No mutation
Large population
No migration
No selection
No selective mating
Evolution
• Evolution:
– Change over time (many definitions!)
– A process that results in heritable changes in a
population spread over many generations
• The two most important forces of
evolution are:
– Genetic drift
– Selection
Genetic drift
•
•
•
•
•
•
Varies with population size
If a population is finite in size – as all populations are – and if a
given pair of parents have only a small number of offspring, then
the frequency of an allele/genotype will not be exactly
reproduced in the next generation because of sampling error
Each generation is an independent event
Results in a random increase or decrease in the frequency of a
given allele
The final result is that the population eventually drifts to p=1 or
p=0. After this point, no further change is possible; the
population has become homozygous.
This problem increases in magnitude as population sizes become
smaller
Genetic drift
https://www3.nationalgeographic.com/genographic/population.html
Genetic drift
https://www3.nationalgeographic.com/genographic/population.html
Genetic drift
https://www3.nationalgeographic.com/genographic/population.html
Genetic drift
https://www3.nationalgeographic.com/genographic/population.html
Genetic drift
https://www3.nationalgeographic.com/genographic/population.html
Genetic drift
https://www3.nationalgeographic.com/genographic/population.html
Fixed allele
• A locus for which only a single allele
exists for an entire gene pool
• The frequency of a fixed allele within a
gene pool is 1.0
• An allele with a frequency of 0.0 is said
to be extinct
• Remember: this allele may still exist in
other populations!
Some types of genetic drift
• Two situations in which the effects of
genetic drift are particularly dramatic
include
– Bottleneck
– Founder effect
Bottleneck
• Population bottlenecks occur when a population's size is
reduced for at least one generation, e.g. via a natural
disaster
• Sampling error means the allele frequencies of the new
population are not likely to match the allele frequencies
in the original population
• Because genetic drift acts more quickly to reduce genetic
variation in small populations, undergoing a bottleneck
can reduce a population's genetic variation by a lot, even if
the bottleneck doesn't last for very many generations
• The longer a population remains at a reduced size, the
greater the effect of genetic drift on allele frequency
• Ultimately, the result of genetic bottlenecks is the loss of
allelic variation, i.e., the fixing of alleles
http://cgland.inha.ac.kr/bbs/special/life-ori33.gif
Example of a genetic bottleneck:
Bubonic plague
Europe
One village: Surrey Heath
http://blue.utb.edu/paullgj/geog3320/lectures/populationgeography.html
http://www.chobham.info/medieval.htm
Founder effect
• Occurs when a new colony is started by a few members of
the original population (founders)
New population may have:
• Reduced genetic variation from the original population
• A non-random sample of the genes in the original
population (sampling error)
• Term is frequently used when a deleterious allele can be
traced to a founder or founders
http://www.blackwellpublishing.com/korfgenetics/figure.asp?chap=07&fig=Fig7-8
Example of a founder effect:
Polydactyly in the Old Order Amish
•
•
•
Lancaster county, Pennsylvania Old Order Amish founded by a
small number of German immigrants: about 200 individuals
High concentrations of rare inherited disorders, especially recessive
Ellis-van Creveld syndrome (a form of dwarfism)
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–
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–
•
•
Short stature
Polydactyly (extra fingers or toes)
Abnormalities of the nails and teeth
A hole between the two upper chambers of the heart in about half the affected
individuals
Traced back to one couple, Samuel King and his wife, who came to
the area in 1744
In 1964, almost as many persons were known in this one kindred as
had been reported in all the medical literature up to that time
http://www.pbs.org/wgbh/evolution/library/06/3/l_063_03.html
Example of a founder effect: Glaucoma
caused by myocilin mutations
Hardy-Weinberg equilibrium
only holds true if:
•
•
•
•
•
No mutation
Large population
No migration
No selection
No selective mating
Gene flow (migration) between
populations
• Transfer of alleles from one population into another
• Movement of an allele into or out of a population changes
allele frequency (either increasing or decreasing allele
frequency)
Hardy-Weinberg equilibrium
only holds true if:
•
•
•
•
•
No mutation
Large population
Isolation from other populations
No selection
No selective mating
Natural selection
•
•
•
•
•
•
•
Acts on an individual’s phenotype, which is exposed to the environment
Individuals with favorable phenotypes are more likely to survive and
reproduce than those with less favorable phenotypes
Indirectly adapts a population to its environment by increasing (or
maintaining) favorable genotypes in the gene pool
Selection acting at the haploid stage reduces allele frequency directly
Selection acting at the diploid stage reduces the contribution of genotypes
to the gene pool
The effect of natural selection is to reduce the absolute number of
genotypes or alleles
If the environment should change, selection responds by favoring
phenotypes (genotypes) adapted to the new conditions, but the degree of
adaptation can be extended only within the realm of the genetic
variability present in the population or through the occurrence of new
mutations
Selection: Sickle cell anemia
•
Sickle cell anemia is a heritable blood disease that
can cause red blood cell destruction and poor blood
flow, resulting in a lack of oxygen to the body's
tissues and damage.
•
Persons who inherit the mutant hemoglobin gene
from each parent develop sickle cell anemia.
•
But those who inherit the variant gene from only
one parent, and a normal gene from the other, are
merely carriers of the sickle cell trait (dubbed
heterozygous) who often display no signs of the
disease.
http://www.dartmouth.edu/~toxmetal/TXQAfe.shtml
•
Heterozygous individuals are resistant to malaria.
The beneficial aspects of the variant gene ensure its
continued natural selection, despite the risk of
disease if the gene is inherited from each parent.
Selection: Sickle cell anemia
https://www3.nationalgeographic.com/genographic/population.html
Stabilizing (purifying) selection
•
•
•
Genetic diversity decreases as the population stabilizes on a particular trait
value
Extreme values of the character are selected against
This is probably the most common mechanism of action for natural selection
•
Example: human birth weight
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–
–
–
Babies of low weight lose heat more quickly are more likely to become ill from infections,
experience high rates of pulmonary and ocular problems, etc.
Babies of large body weight are more difficult to deliver through the pelvis
However, improvements in neonatal care have increased survival of low birthweight infants
Rising rates of Caesarean sections in developed nations; many reasons, may include larger
size babies (improved nutrition, higher rates of diabetes)
Other types of selection
•
•
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Directional selection: Selection against only one phenotypic extreme
Diversifying selection (disruptive selection): Selection against the
intermediate form
Sexual selection (sexual dimorphism, secondary sexual
characteristics)
– Phenotypic differences between males and females (other than
sexual organs); referred to as sexual dimorphisms or secondary
sexual characteristics
– Sexual dimorphisms often are involved in mate procurement
Intrasexual selection: Direct competition among individuals of one
sex (usually the males in vertebrates) for mates of the opposite sex
Intersexual selection (mate choice): Any trait that increases the
attractiveness of an individual to members of the opposite gender will
confer a selective advantage
Hardy-Weinberg equilibrium
only holds true if:
•
•
•
•
•
No mutation
Large population
Isolation from other populations
No selection
No selective mating
Correlation between spousal height
Dad’s height (cm)
Tall men with tall
wives!
Women with shorter
spouses
Mom’s height (cm)
Non-random (assortative) mating
• Positive assortative mating (of alike
individuals) tends to increase
homozygosity (more likely to share the
same alleles)
• Negative assortative mating (of unlike
individuals) tends to increase
heterozygosity
http://anthro.palomar.edu/synthetic/synth_8.htm
http://anthro.palomar.edu/synthetic/synth_8.htm
http://anthro.palomar.edu/synthetic/synth_8.htm
Review
• HWE
– Can be reached within one (or two) generations
– Can be used to calculate allele and genotype frequencies under
conditions of equilibrium
• Mechanisms of microevolution
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–
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Mutation
Genetic drift (e.g. bottlenecks, founder effect)
Gene flow between populations (migration)
Nonrandom mating
Selection
END
Questions?