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Lecture 10

HMB265H1 Lecture Notes - Lecture 10: Monte Carlo Method, Allele Frequency, Genetic Linkage

Human Biology
Course Code
Maria Papaconstantinou

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Lecture 10 Population Genetics
Tuesday, October 10th, 2017 3pm-5pm
Hartwell et al. Ch. 12 pp. 415-433
Hardy-Weinberg Equilibrium
Hardy-Weinberg Calculations
Genetic Drift
Natural Selection
Application of Population Genetics
Population Genetics
Population genetics: the study of the genetics of
a population and how the alleles vary with time
Population: an interbreeding group of the same
species within a given geographical area
Gene pool: the collection of all alleles in the
members of the population
Gene flow: alleles can move between populations
when individual migrate and mate
Phenotype Frequencies Vary in Different Populations
E.g., Phenylketonuria (PKU) is a heritable metabolic disorder, and an autosomal recessive trait
Meeting the Challenge
1908 independent discovery
Godfrey Harold “G.H.” Hardy Wilhelm Weinberg
1877 1947 1862 1937
Genetic composition of a population is the collection of all genotypes in a
Gene pool is the collection of all alleles in the members of this population
We can relate individual genetic processes to populations by investigating some
phenomena, which affect the allelic and genotypic frequencies in these populations
o Mating patterns random or inbreeding
o Migration patterns movement of individuals between populations,
resulting in gene flow (movement of alleles between populations)
o Mutation source of genetic variation, creating new alleles
o Recombination source of genetic variation, new allelic combinations
o Natural selection differences in fitness based on genotypes
o Genetic drift random fluctuations in allelic frequencies
Phenotypic frequencies vary in different populations
o Proportion of individuals in a population that express a particular phenotype
Frequencies of PKU varies between different populations
Random mating resulted in an equilibrium distribution of genotypes
This equilibrium distribution is known as the HWE
The Hardy-Weinberg law correlates allele and genotype frequencies.
If certain assumptions were met, allele frequencies, genotype frequencies, and
phenotype frequencies would remain constant over time and between generations
Last tutorial for this session is
Monday (next week), based on
lectures 8, 9, and 10 linkage,
recombination, and population
One more LearnSmart assignments,
and all six Connect Assignments due
the day of the midterm
Up to now, we were focusing on genetics at the individual level, but most organism don’t live in
isolation, rather in populations
There are questions about the genetic composition of populations that can’t be answered fully by
knowledge of individual genetic processes
Look at how genotypic and allelic frequencies vary or remain constant, and apply population
genetics to real-world problems
find more resources at
find more resources at

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The Hardy-Weinberg Law
The Hardy-Weinberg law clarifies the relation between
genotype and allele frequency within a generation AND
from one generation to the next.
Five assumptions must be met for a population to be at
Hardy-Weinberg equilibrium:
1. Infinitely large population
2. Individuals mate at random
3. No new mutations appear in gene pool
4. No migration into or out of population
5. No genotype-dependent differences in ability to survive
and reproduce
All natural populations violate one or more assumptions
of Hardy-Weinberg law.
However, equations derived based on assumptions are
remarkably robust
Hardy-Weinberg law can be used as a null model
The Hardy-Weinberg Law: Allelic Frequencies
Allele Frequencies
Count both chromosomes of each individual
Allele frequencies affect the genotype frequencies, the
frequency of each type of homozygote and heterozygote in
the population
No genetic drift
No inbreeding
No new mutations
No gene flow
No natural selection
Random mating doesn’t always occur, migration occurs very frequently,
natural selection is inevitable, mutations are constantly arising, and genetic
drift affects smaller populations, etc.
Real populations violate many assumptions, but equations are robust and can
be used to examine and generate estimates of genotypic and phenotypic
frequencies in real populations
Can be used as a null model
Often assign p to dominant allele and q to recessive allele, but not
All allele frequencies must equal 1 (entire collection of alleles in the
All genotypic frequencies must equal 1 (also)
Number of copies of a particular allele divided by total number of
alleles in that population
You must count both chromosomes of each individual
o In diploids, two alleles per gene are carried (autosomal in
both, X-linked in females; males are hemizygous)
Genotypic frequency is the proportion of each genotype in the
In the absence of a fitness difference or other major deviations from Hardy-
Weinberg assumptions, neither recessive phenotypes will go extinct, simply
because their phenotypes are caused by recessive alleles.
Frequencies of alleles and genotypes that produce these phenotypes will
stay constant over time
One and only one HWE exists for a specific set of allele frequencies p
and q, but different values of p and q imply different HWEs
If p = 0.8 and 1 = 0.2, at HWE, the AA genotype is the most frequent of
the three possible genotypes the frequency of AA homozygotes = p2 =
0.64, while the frequency of Aa heterozygotes is 2pq = 0.32, and that of
aa homozygotes is only q2 = 0.04
When q is small, most of the a alleles are carried by heterozygotes
The frequency of heterozygotes is highest (50%) when p = q = 0.5
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The Hardy-Weinberg Law: Calculations
Step 1: Calculate the allele frequency of gametes
Step 2: Use gamete allele frequency to calculate genotype frequencies in the zygotes of the next generation
Using product rule for independent events of a sperm with one allele
fertilizing an egg of the same or different allele
From parental allelic frequencies, you can calculate the genotypic
frequencies of the next generation
If A-carrying sperm fertilize A-carrying eggs, AA zygotes will be
o Since genotype of sperm is independent of the genotype of
the egg it fertilizes, apply the product rule and multiple the
frequency of A sperm (p) by the frequency of A eggs (p) to
find the frequency of AA zygotes: p x p = p2
The frequency of aa zygotes among the progeny, which must result
from fertilization of a-carrying eggs (q) by a-carrying sperm (q), is the
product of q x q = q2
Aa zygotes result either from the fertilization of A eggs by a sperm,
with a frequency of p x q = pq, or from the fertilization of a eggs by A
sperm, also occurring at a frequency of q x p = qp
o Total frequency of Aa zygotes is pq + pq = 2pq
If we replace the gametes from the two single parents with the male and
female gametes produced by the population as a whole, then this is a
metaphorical representation of the sperm produced by all breeding males
along the top and of effs produced by all breeding females along the left.
Random mating among the different genotypes in the population is
equivalent to the random combination of the gametes produced by all
the individuals in the population
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