Animal breeding

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Course Title: Population Genetics and Genetic
Diversity of Farm Animals (AnGB7012)
Chapter 2: Hardy-Weinberg principle
Birhan Kassa: BDU1500178
Bahir Dar University, Bahir Dar

2. 2. Hardy-Weinberg principle
2.1. The Hardy-Weinberg principle
2.2. Heterozygosity and homozygosity
23. Deviations from The Hardy-Weinberg
expectations
2.4. Sex and the Hardy-Weinberg principle
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3. 2.1. The Hardy-Weinberg principle
Hardy-weinberg principle states that a populations allele and
genotype frequency will remain constant in the absence of
evolutionary mechanisms
Ultimately, the Hardy-weinberg principle model is a
population without evolution under the following conditions
No mutation
No immigration/emigration
No natural sexual selection
A large population
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4. If a population is not in Hardy-Weinberg equilibrium, it can be
concluded that the population is evolving
Evolutionary Mechanisms (will put population out of HW
Equilibrium):
Genetic Drift
Selection
Mutation
Migration
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5. The Hardy Weinberg Theorem deals with Mendelian genetics
in the context of populations of diploid, sexually reproducing
individuals in given set of assumptions
1. Allele frequencies in a population will not change from
generation to generation.
2. If the allele frequencies in a population with two alleles at
a locus are p and q, then the expected genotype
frequencies are p2 , 2pq, and q2 .
This frequency distribution will not change from
generation to generation once a population is in Hardy-
Weinberg equilibrium.
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6. If the frequency of allele A in the population is p and the
frequency of allele a in the population is q,
Then the frequency of genotype AA = p2
The frequency of genotype Aa = 2pq
The frequency of genotype aa = q2
p + q= 1
For a diploid organism (2 chromosomes), (p + q) 2 = 1 = p2 + 2pq +
q2
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7. Hardy-Weinberg Hardy-Weinberg Equilibrium
Single locus with two alleles (A and a)
Fr(A) = p Fr(a) = q p + q = 1
If assumptions of Hardy-Weinberg hold, then we can predict
the genotype freq’s in next generation
Fr(AA) = p2
Fr(aa) = q2
Fr (Aa) = 2pq
p2 + q2 + 2pq = 1
Allele freq.’s in next generation
Fr(A)’ = p’ = [2(Fr(AA)) + 1(Fr(Aa))]/Total
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Total number = 15, frequency of AA = 8/15 (0.53)
Aa = 4/15 (0.27)
aa = 3/15 (0.20)

9. Ex: Genetic structure of first generation
Expected Genotype
F(AA): p x p = p2 = 0.8 x 0.8 = 0.64
F(Aa): p x q + q x p = 2pq = 2 x (0.8 x
0.2) = 0.32
F(aa): q x q = q2 = 0.2 x 0.2 = 0.04
p2 + 2pq + q2 = 0.64 + 0.32 + 0.04 = 1
Allele Frequencies
F (A)= p = 0.8
F (a) = q = 0.2
p + q = 1
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10. Expected Allele Frequency at second Generation
p = AA + Aa/2 = 0.64 + (0.32/2) = 0.8
q = aa + Aa/2 = 0.04 + (0.32/2) = 0.2
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11. Calculating Allele Frequencies from number of Individuals
Genotypes AA Aa aa
# of individuals 120 60 35
#A = (2 x AA) + Aa = 240 + 60 = 300
#a = (2 x aa) + Aa = 70 + 60 = 130
 Proportion A = 300/total = 300/430 = 0.70
 Proportion a = 130/total = 130/430 = 0.30
 A + a = 0.70 + 0.30 = 1
 Proportion AA = 120/215 = 0.56
 Proportion Aa = 60/215 = 0.28
 Proportion aa = 35/215 = 0.16
 AA + Aa + aa = 0.56 + 0.28 +0.16 = 1
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12. Example: estimate frequency of a disease allele in
a population
 Phenylketonuria (PKU) is a metabolic disorder that
results from homozygosity for a recessive allele
 Individuals that are homozygous for the deleterious
recessive allele cannot break down phenylalanine, results
in build up
 à mental retardation
 The occurrence of PKU is 1 per 10,000 births
 How many carriers of this disease in the
population?
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13. Rare deleterious recessives often remain in a
population because they are hidden in the
heterozygous state (the “carriers”)
Natural selection can only act on the homozygous
individuals where the phenotype is exposed
(individuals who show symptoms of PKU)
We can assume HW equilibrium if:
There is no migration from a population with different
allele frequency
Random mating
No genetic drift
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14. So, let’s calculate HW frequencies
The occurrence of PKU is 1 per 10,000 births
(frequency of the disease allele):
q2 = 0.0001
q = sqrt(q2 ) = sqrt(0.0001) = 0.01
The frequency of wildtype (normal) alleles is:
p = 1 – q = 1 – 0.01 = 0.99
The frequency of carriers (heterozygotes) of the
deleterious allele is:
2pq = 2 x 0.99 x 0.01 = 0.0198
or approximately 2% of the U.S. population
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15. 2.2. Heterozygosity and homozygosity
Homozygosity is the condition of having two identical alleles
at the same locus (AA, aa) and Homozygous: of an organism
in which both copies of a given gene have the same allele.
Heterozygous: of an organism which has two different alleles
of a given gene. In Heterozygous, the only allele that is
expressed is the dominant trait. The recessive is present, but its
expression is hidden.
Heterozygosity is of major interest to breeders of genetic
variation in natural populations
High heterozygosity means lots of genetic variability.
Low heterozygosity means little genetic variability.
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16. Recessive: able to be covered by a dominant trait.
Dominant: a relation ship between alleles of gene, in which one
allele masks the expression of another gene with the same locus.
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17. Often, we will compare the observed level of
heterozygosity to what we expect under Hardy-
Weinberg equilibrium (HWE)
If the observed heterozygosity is lower than expected,
we seek to attribute the discrepancy to forces such as
inbreeding
If heterozygosity is higher than expected, we might
suspect an isolate-breaking effect (the mixing of two
previously isolated populations)
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18. DEVIATION from Hardy-Weinberg Equilibrium Indicates
that EVOLUTION is happening
2.3. Deviations from The Hardy-Weinberg
expectations
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19. Violations of the Hardy–Weinberg assumptions can cause
deviations from expectation.
How this affects the population depends on the assumptions that
are violated
deviation from the Hardy-Weinberg equilibrium denotes the
evolution of a species
Random mating: The HWP states the population will have the
given genotypic frequencies (called Hardy-Weinberg
proportions) after a single generation of random mating within
the population.
When violations of this provision occur, the population will not
have Hardy-Weinberg proportions.
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20. Three such violations are:
Inbreeding, which causes an increase
in homozygosity for all genes
Assortative mating, which causes an increase
in homozygosity only for those genes involved in the
trait that is assortatively mated (and genes in linkage
disequilibrium with them)
Small population size, which causes a random change in
genotypic frequencies, particularly if the population is
very small
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21. Selection:
In general, causes allele frequencies to change, often quite rapidly,
while directional selection eventually leads to the loss of all alleles
except the favored one, some forms of selection, such as balancing
selection, lead to equilibrium without loss of alleles.
Mutation:
Mutation will have a very subtle effect on allele frequencies.
Mutation rates are of the order 10−4 to 10−8, and the change in
allele frequency will be, at most, the same order.
Migration:
Migration genetically links two or more populations together.
In general, allele frequencies will become more homogeneous
among the populations.
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22. A X2 goodness-of-fit test can be used to determine if a
population is significantly different from the
expectations of Hardy-Weinberg equilibrium
If we have a series of genotype counts from a
population, then we can compare these counts to the
ones predicted by the Hardy-Weinberg model
O = observed counts, E = expected counts, sum across
genotypes
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Testing for Deviation from Hardy-Weinberg Expectations

23. Genotype No.
AA 260
Aa 180
aa 360
Example: Testing for HWE
Step 1: Calculate observed allele frequency
Fr(100) = (2*260 + 1*360)/(2*800) = 0.55 (= p)
Fr(125) = (2*180 + 1*360)/(2*800) = 0.45 (= q
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24. Genotype No. Expected
AA 260 p2*N=242
aa 180 q2*N=162
Aa 360 2*p*q*N=396
Step 2: Calculate expected genotype number
Testing for HWE
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25. Genotype Observed Expected Stat
AA 260 242 1.34
aa 180 162 2.00
Aa 360 396 3.27
Step 3: Compare observe to expected
X2 = Σ (O-E)2/E=6.61 df = 1
crit = 3.84
Conclusion: Population deviates from HWE fewer
heterozygotes than expected
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26. In general, the factors that are assumed to be non-
operative under HWE are hardly realised in the living
systems.
The living system (populations or organisms) are
structured (non-random entities) and are influenced
by multiple and interactive factors that operate
through space and time.
With the help of HW equilibrium it is possible to
investigate and estimate the effect of these individual
forces that change gene frequency in populations..
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27. Generally change in gene frequency is affected by
Natural selection:
Stabilizing
Disruptive
Directional
Genetic drift
Founder effect
Bottleneck effect
Gene flow
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28. Natural Selection
When natural selection occurs, variation of traits in a
population changes over time
3 patterns of changes due to natural selection
Stabilizing
Disruptive
Directional
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29. 1. Stabilizing selection
Individuals with average forms of a trait has the
highest fitness and the extreme values have lower
fitness
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30. 2. Disruptive selection
Selection where both extreme traits are considered
more fit for the environment than the intermediate
trait
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31. 3. Directional selection
Individuals in a population with one extreme trait
have higher fitness than the average trait
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32. Example
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33. Genetic drift
Causes deviation from equilibrium
Genetic drift change in agene pool due to enhance
The smaller the population, the greater the
impact it has on the population
oFounder effect
oBottleneck effect
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34. Founder effect
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35. Bottleneck effect
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36. Gene flow
Gaining or losing when individuals move into or out
of population
Immigration: introduce genetic variation in to a
population
Emigration: reduce introduce genetic variation
in to a population
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37. Mutation
A mutation is a change in an organism’s DNA.
A new mutation that is transmitted in gametes can
immediately change the gene pool of a population by
substituting the mutated allele for the older allele.
For any single locus, mutation alone does not have
much quantitative effect on a large population in a
single generation.
An individual mutant allele may have greater impacts
later through increases in its relative frequencies as a
result of natural selection or genetic drift.
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38. While mutations at an individual locus is a rare event, the
cumulative impact of mutations at all loci can be
significant.
– Each individuals has thousands of genes, any one of
which could experience a mutation.
– Populations are composed of thousands or millions of
individuals that may have experienced mutations.
Over the long term, mutation is very important to
evolution because it is the original source of genetic
variation that serves as the raw material for natural
selection.

39. The variation among individuals in a population is a combination of
inheritable and non-heritable traits.
Phenotype, the observable characteristics of an organism, is the
cumulative product of an inherited genotype and a multitude of
environmental influences.
For example, these butterflies are genetically identical at the loci for
coloration, but they emerge at different seasons.
Only the genetic component of variation can have
evolutionary consequences as a result of natural selection.
– This is because only inheritable traits pass from
generation to generation.
1. Genetic variation occurs within and between populations

40. Both quantitative and discrete characters contribute to
variation within a population.
Quantitative characters are those that vary along a
continuum within a population.
– For example, plant height in our wildflower population
includes short and tall plants and everything in between.
– Quantitative variation is usually due to polygenic
inheritance in which the additive effects of two or more
genes influence a single phenotypic character.
Discrete characters, such as flower color, are usually
determined by a single locus with different alleles with
distinct impacts on the phenotype.

41. Polymorphism occurs when two or more discrete
characters are present and noticeable in a population.
The contrasting forms are called morphs, as in the red-
flowered and white-flowered morphs in our wildflower
population or the butterflies in the previous slide
Human populations are polymorphic for a variety of
physical (e.g., freckles) and biochemical (e.g., blood
types) characters.
Polymorphism applies only to discrete characters, not
quantitative characters, such as human height, which varies
among people in a continuum.

42. Population geneticists measure genetic variation both at
the level of whole genes and at the molecular level of DNA
Gene diversity measures the average percent of gene loci
that are heterozygous.
In the fruit fly (Drosophila), about 86% of their 13,000
gene loci are homozygous (fixed)
About 14% (1,800 genes) are heterozygous.

43. Nucleotide diversity measures the level of difference in
nucleotide sequences (base pair differences) among
individuals in a population.
In fruit flies, about 1% of the bases are different
between two individuals.
Two individuals would differ at 1.8 million of the 180
million nucleotides in the fruit fly genome.
Humans have relatively little genetic variation.
Gene diversity is about 14% in humans.
Nucleotide diversity is only 0.1%.
• You and your neighbor have the same nucleotide at
999 out of every 1,000 nucleotide sites in your DNA.

44. Geographic variation results from differences in genetic
structure either between populations or between
subgroups of a single population that inhabit different
areas.
Often geographic variation results from natural selection
that modifies gene frequencies in response to
differences in local environmental factors.
Alternatively, genetic drift can lead to chance variations
among populations.
Geographic variation can occur on a local scale, within a
population, if the environment is patchy or if dispersal of
individuals is limited, producing subpopulations.

45. Geographic variation in the form of graded change in a
trait along a geographic axis is called a cline.
Clines may reflect direct environmental effects on
phenotype, but also genetic differences along the cline.
For example, average size of yarrow plants (Anchillea), gradually
decreases with increasing variation.
Although the environment
affects growth rate directly
to some extent with
altitude, common garden
experiments have
demonstrated that
some of the variation
has a genetic basis.
Fig. 23.8

46. In contrast to clines, isolated populations typically
demonstrate discrete differences.
For example, populations of
house mice were first intro-
duced to the island of
Madiera in the 15th century,
but isolated populations
developed that were
separated by mountains.
Some isolated populations
have evolved differences
in karyotypes probably
through genetic drift.
Fig. 23.9

47. New alleles originate only by mutation.
Mutations are changes in the nucleotide sequence of
DNA.
Mutations of individual genes are rare and random.
Mutations in somatic cells are lost when the individual
dies.
Only mutations in cell lines that produce gametes can be
passed along to offspring.
2. Mutation and sexual recombination generate genetic
variation

48. Most point mutations, those affecting a single base of
DNA, are probably harmless.
– Most eukaryotic DNA does not code for proteins and
mutations in these areas are likely to have little impact on
phenotype.
– Even mutations in genes that code for proteins may lead to
little effect because of redundancy in the genetic code.
– However, some single point mutations can have a significant
impact on phenotype.
• Sickle-cell disease is caused by a single point mutation.

49. Mutations that alter the structure of a protein enough to
impact its function are more likely to be harmful than
beneficial.
– A random change is unlikely to improve a genome that
is the product of thousands of generations of
selection.
– Rarely, a mutant allele may enable an organism to fit
its environment better and increase reproductive
success.
– This is especially likely if the environment is changing
– These mutations may be beneficial now.
• For example, mutations that enable HIV to resist
antiviral drugs are selected against under normal
conditions, but are favorable under drug treatment.

50. Chromosomal mutations, including rearrangements of
chromosomes, affect many genes and are likely to disrupt
proper development of an organism.
– However, occasionally, these dislocations link genes
together such that the phenotype is improved.
Duplications of chromosome segments, whole
chromosomes, or sets of chromosomes are nearly always
harmful.
– However, when they are not harmful, the duplicates
provide an expanded genome.
– These extra genes can now mutate to take on new
functions.

51. Because microorganisms have very short generation times,
mutation generates genetic variation rapidly.
– In an AIDS patient, HIV generates 1010 new viruses per
day.
– With its RNA genome, mutation rate is higher than DNA
genomes.
– This combination of mutation and replication rate will
generate mutations in the HIV population at every site in
the HIV genome every day.
• In the face of this high mutation rate, single-drug
treatments are unlikely to be effective for very long
and the most effective treatments are multiple drug
“cocktails.”
–It is far less probable that mutations against all the
drugs will appear in individual viruses in a short
time.

52. In organisms with sexual reproduction, most of
the genetic differences among individuals are
due to unique recombinations of the existing
alleles from the population gene pool.
– The ultimate origin of allelic variation is past
mutations.
Random segregation of homologous
chromosomes and random union of gametes
creates a unique assortment of alleles in each
individual.
Sexual reproduction recombines old alleles into
fresh assortments every generation.

53. The tendency for natural selection to reduce variation is countered by
mechanisms that preserve or restore variation, including diploidy and
balanced polymorphisms.
Diploidy in eukaryotes prevents the elimination of recessive alleles via
selection because they do not impact the phenotype in heterozygotes.
– Even recessive alleles that are unfavorable can persist in a population
through their propagation by heterozygous individuals.
– Recessive alleles are only exposed to selection when two parents carry
the same recessive allele and these are combined in one zygote.
– This happens only rarely when the frequency of the recessive allele is
very low.
– Heterozygote protection maintains a huge pool of alleles that may not be
suitable under the present conditions but that could be beneficial when
the environment changes.
3. Diploid and balanced polymorphism preserve variation

54. Balanced polymorphism maintains genetic diversity in a
population via natural selection.
One mechanism in balance polymorphism is heterozygote
advantage.
– In some situations individuals that are heterozygous at a
particular locus have greater survivorship and
reproductive success than homozygotes.
– In these cases, multiple alleles will be maintained at that
locus by natural selection.
Heterozygous advantage maintains genetic diversity at the
human locus for one chain of hemoglobin.
– A recessive allele causes sickle-cell disease in
homozygous individuals.
– Homozygous dominant individuals are very vulnerable to
malaria.
– Heterozygous individuals are resistant to malaria.

55. • The frequency of the sickle-cell allele is highest
in areas where the malarial parasite is common.
– The advantages of heterozygotes over homozygous
recessive individuals who suffer sickle-cell disease
and homozygous dominant individuals who suffer
malaria are greatest here.
– The sickle-cell allele
may reach 20% of
the gene pool, with 32%
heterozygotes resistant
to malaria and 4% with
sickle-cell disease.

56. • A second mechanism promoting balanced
polymorphisms is frequency-dependent selection.
• Frequency-dependent selection occurs when the reproductive
success of any one morph declines if that phenotype becomes
too common in the population.
– The relationships between parasites and their hosts often
demonstrate this type of relationship.
• Hosts often vary in their defense against parasites and
parasites in their ability to infect hosts.
– Those parasites that are capable of infecting the most
common host type will increase in abundance.
– The rarer host types will increase as the genetic frequencies
in the parasite population shifts.
– These shifts in genetic frequencies among hosts and among
parasites maintain variation in both populations.

57. • Aspects of this teeter-totter of frequency-
dependent selection can be seen in the host-
parasite between clones of aquatic snails and a
parasitic worm.
– In these snails which reproduce asexually, the most
common snail clones suffer the higher infection
rates than the least
common clone,
suggesting
frequency-
dependent
selection.
Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings
Fig. 23.11

58. • Some genetic variations, neutral variation, have
negligible impact on reproductive success.
– For example, the diversity of human fingerprints
seems to confer no selective advantage to some
individuals over others.
– Much of the protein and DNA variation detectable
by methods like electrophoresis may be neutral in
their adaptive qualities.
• The relative frequencies of neutral variations
will not be affected by natural selection.
• Some neutral alleles will increase and others will
decrease by the chance effects of genetic drift.
Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings

59. • There is no consensus on how much genetic
variation can be classified as neutral or even if
any variation can be considered truly neutral.
– It is almost impossible to demonstrate that an allele brings
no benefit at all to an organism.
– Also, variation may be neutral in one environment but not in
another.
– Even if only a fraction of the extensive variation in a gene
pool significantly affects an organism, there is still an
enormous reservoir of raw material for natural selection and
adaptive evolution.
KSJ : This is typical selectionist phrases! The opposite could be said
for all points above. In short, most mutations will have a negative
effect on the organism. Survival of a mutation (i.e. Allele is thus
coupled to neutral or near-neutral properties.

60. Migration:
A population could out of HWE with a lot of migration
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61. Example
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62. 3/23/2023 62

63. 3/23/2023 63
• Mutation
• Changes to an organism’s DNA
• Most common way to introduce novel genotypic and
phenotypic variance.
• Some are unfavorable or harmful and are quickly
eliminated from the population by natural
selection.
• Some are beneficial and will spread
• Some do not do anything and can linger,
unaffected by natural selection

64. • Nonrandom mating
1. Mate choice
• Natural selection picks traits that lead to more
mating for an individual
• Assortative mating = individual’s preference to
mate with partners who look the same
2. Physical location
• In large populations spread over vast geographic
distances, not all individuals will have equal access
to one another
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65. • Environmental variance
• Human skin color
• Temperature-dependent sex determination in reptiles
• Geographical variation in environmental conditions
• Can produce clines
• Phenotype of a species' populations varies
gradually across an ecological gradient (ie.
Bergmann’s Rule)
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66. 2.4. Sex and the Hardy-Weinberg principle
Where the A gene is sex-linked
The heterogametic sex (e.g., mammalian males; avian
females) have only one copy of the gene (and are
termed hemizygous),
The homogametic sex (e.g., human females) have two
copies. The genotype frequencies at equilibrium
are p and q for the heterogametic sex
but p2, 2pq and q2 for the homogametic sex.
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67. For example, in humans red-green colorblindness is
an X-linked recessive trait.
In western European males, the trait affects about 1 in 12,
(q = 0.083) whereas it affects about 1 in 200 females
(0.005, compared to q2 = 0.0070), very close to Hardy-
Weinberg proportions.
If a population is brought together with males and
females with different allele frequencies, the allele
frequency of the male population follows that of the
female population because each receives its X
chromosome from its mother.
The population converges on equilibrium very
quickly.
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68. 3/23/2023 68
If allele frequencies differ between the sexes, it takes two generations of
random mating to attain Hardy-Weinberg equilibrium.
Sex-linked loci require multiple generations to attain equilibrium because
one sex has two copies of the gene and the other sex has only one.

69. Consider a sex-linked locus in a species where females are XX
(homogametic) and males are XY (heterogametic).
Suppose f(a) is initially unequal in females and males.
(1) Because each female receives an X chromosome from both parents in
generation n, the female f(a) in generation n+1 is the mean of the male and
female f(a) in generation n.
(2) Because each male in receives an X chromosome only from the female
parent in generation n, the frequency of the allele f(a) in females of
generation n automatically determines f(a) in males in generation n+1.
The male f(a) therefore "chases" the female f(a) in the preceding
generation until they reach approximate equality.
In this example, note that frequencies are within 1% of each other in the
seventh generation, even when the initial frequencies are completely
divergent.
Note that, because females contribute two X chromosomes each and males
one X each, the mean f(a) for a sex-linked locus is a constant (2 x f(a) + 1
x f(a)) / 3 . In this case, (2x1 + 1x0) = 0.6667 and remains constant.
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