1. Mendelian Genetics (Chapter 2, Chapter 4.5)
Assist. Prof. Dr. Betul Akcesme

2. A family portrait with members of four generations
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Why do some of the children look like only one of the parents, while some of the other children look more like the great, great grandparents? What causes the similarities and differences of appearance and the skipping of generations?
Fig. 2.1
GENES!!!

3. Gregor Mendel discovered the basic principles of genetics
Mendel was the first scientist to combine data collection, analysis, and theory to understand heredity
He inferred genetic laws about the appearance and disappearance of traits during different generations
Fig. 2.2

4. Genetics explains the mechanisms that determine the inheritance of traits
Genes are the basic units of heredity
Heredity is the way that genes transmit traits from parents to offspring
Genes are passed from one generation to the next
Genes underlie the formation of every heritable trait, e.g. cleft chin, hair loss, color of hair, skin, and eyes
Some traits are causes by a single change in a single gene, e.g. sickle-cell anemia
Some traits are caused by complex interactions between many genes, e.g. facial features

5. Four general themes of Mendel's work
Variation is widespread in nature and provides for continuously evolving diversity
Observable variation is essential for following genes from one generation to another
Variation is inherited by genetic laws, which can explain why like begets like and unlike (e.g. Fig 2.3) (not only by chance)
Mendel's laws apply to all sexually reproducing organisms

6. Genetic variation exists even within dog breeds
Mendel's laws explain why two black Labradors could have a litter of black, brown, and golden puppies
Fig. 2.3

7. Johann Mendel (1822) born in Heizendorf(Hynčice)
Admitted to Augustinian Monastery of St. Thomas in Brno (1843) –took the name Gregor
From , he attended University of Vienna
Returned to Brno in 1854, where he tought physics and natural science for the next 16 year
He published his findings in 1866,

8. Background to Mendel's work: The historical puzzle of inheritance
Artificial selection was the first applied genetic technique
Purposeful control of mating by choice of parents for the next generation
Domestication of plants and animals was a key transition in human civilization
Domestication of dogs from wolves
Domestication of rice, wheat, barley, and lentils from weed like plants

9. The earliest known record of applied genetics
The earliest known record of applied genetics. In this year-old Assyrian relief from the Northwest
Palace of Assurnasirpal II (883–859 B.C. ), priests wearing bird masks artificially pollinate flowers of female date palms.

10. Desirable traits sometimes disappear and reappear
In 1822, the year of Mendel’s birth, what people in Austria understood about the basic principles of heredity was not much different from what the people of ancient Assyria had understood.
By the nineteenth century, plant and animal breeders had created many strains in which offspring often carried a prized parental trait.

11. Critical questions about selective breeding before Mendel's studies
Concluding remarks by Abbot Cyril Napp at annual meeting of the Moravian Sheep Breeders Society:
Three basic questions must be answered
What is inherited?
How is it inherited?
What is the role of chance in heredity?
Abbot Napp presided over the monastery where Mendel began his seminal genetic experiments in 1864

12. Two other theories of inheritance at the time of Mendel's studies
Inherited features of offspring are contributed mainly by only one parent (e.g. a "homunculus" inside the sperm, Fig 2.6)
Parental traits become mixed and changed in the offspring (i.e. "blended inheritance")
Neither theory could explain why some traits would appear, disappear, and then reappear

13. Figure 2.6 The homunculus: A misconception. Well
into the nineteenth century, many prominent microscopists believed they saw a fully formed, miniature fetus crouched within the head of
a sperm

14. Mendel studied the inheritance of alternative traits in pea plants
Mendel inferred laws of genetics that allowed predictions about which traits would appear, disappear, and then reappear
This work was done in his garden at a monastery
Mendel's paper "Experiments in plant hybrids" was published in 1866 and became the cornerstone of modern genetics
Fig. 2.5

15. Keys to the success of Mendel’s experiments: What did Mendel do differently from those who preceded him?
1-Pure-breeding lines of peas (Pisum sativum)
Breeding could be done by cross-fertilization or selfing
Large numbers of progeny produced within a short time
Traits remained constant in crosses within a line (pure breeding)
2- Inheritance of alternative forms of traits
Antagonistic pairs of "either-or" traits: e.g. purple or white, yellow or green Discrete traits vs continuous traits
3- make reciprocal crosses, reversed the traits of the male and female parents,
4- Brilliant experimentalist
Planned experiments carefully
Controlled the plant breeding
Analyzed results mathematically
Because the progeny of these reciprocal crosses were similar, Mendel demonstrated that the two parents contribute equally to inheritance.
“It is immaterial to the form of the hybrid,” he wrote, “which of the parental types was the seed or pollen plant.”
Fifth, with large numbers of plants, counted all offspring, subjected his ndings to numerical analysis, and then compared his results with predictions
based on his models. He was the rst person to study inheritance in this manner, and no doubt his background in physics and mathematics contributed to this quantitative approach. Mendel’s careful numerical analysis revealed patterns of transmission that re ected basic laws of heredity.
Mendel was a brilliant practical experimentalist.
When comparing tall and short plants, for example, he made sure that the short ones were out of the shade of the tall ones so their growth would not be
stunted. Eventually he focused on certain traits of the pea seeds themselves, such as their color or shape,rather than on traits of the plants arising from the seeds. In this way, he could observe many more individuals from the limited space of the monastery garden, and he could evaluate the results of a cross in a single growing season.

16. Mendel's experimental organism: The garden pea
a) Pea plants with white fl owers. (b) Pollen is produced in the
anthers. Mature pollen lands on the stigma, which is connected to the ovary (which becomes the pea pod). After landing, the pollen grows a
tube that extends through the stigma to one of the ovules (immature seeds), allowing fertilization to take place. (c) To prevent self-fertilization,
breeders remove the anthers from the female parents (here, the white fl ower) before the plant produces mature pollen. Pollen is then transferred
with a paintbrush from the anthers of the male parent (here, the purple fl ower) to the stigma of the female parent. Each fertilized ovule becomes
an individual pea (mature seed) that can grow into a new pea plant. All of the peas produced from one fl ower are encased in the same pea pod,
but these peas form from different pollen grains and ovules
Fig. 2.7

17. Mendel studied seven antagonistic pairs of traits in peas
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Three antagonistic pairs of traits are shown at right
Note that each hybrid resembles only one of the parents: the dominant trait
Figure 2.8 The mating of parents with antagonistic traits produces hybrids. Note that each of the hybrids for the
seven anta gonistic traits studied by Mendel resembles only one of the parents. The parental trait that shows up in the hybrid is known
as the “dominant” trait.
Antagonistic Pairs
Fig. 2.8

19. Monogenic vs. polygenic traits
Discontinuous (discrete) traits: traits with only a few possible phenotypes that fall into discrete classes
Continuous (quantitative) traits -do not fall into discrete classes; a segregating population will show a continuous distribution of phenotypes, a trait that has a quantitative value (yield, IQ)

20. Genetic Analysis According to Mendel
In early 1865, Gregor Mendel presented a paper entitled “Experiments on Plant Hybrids” before the Natural Science Society of Brünn.
Describes the transmission of visible characteristics in pea plants,
defines unseen but logically deduced units (genes) that determine when and how often these visible traits appear,
analyzes the behavior of genes in simple mathematical terms to reveal previously unsuspected principles of heredity.

21. Monohybrid crosses revealed units of inheritance and the law of segregation
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Mendel crossed pure-breeding lines that differed in only one trait, e.g. seed color
Also did reciprocal crosses
Examined phenotypes of F1 progeny and F2 progeny
F1 progeny have only one of the parental traits
Both parental traits reappear in F2 progeny in a 3:1 ratio
These results disproved the blending hypothesis
Figure 2.9 Analyzing a monohybrid cross. Cross-pollination of pure-breeding parental plants produces F 1 hybrids, all of which
resemble one of the parents. Self-pollination of F 1 plants gives rise to an F 2 generation with a 3:1 ratio of individuals resembling the two
original parental types. For simplicity, we do not show the plants that produce the peas or that grow from the planted peas.
Fig. 2.9

22. Traits have two forms that can each breed true
Mendel proposed that each plant carries two copies of a unit of inheritance
Traits have two forms that can each breed true
Trait that appears in F1 progeny is the dominant form
Trait that is hidden in the F1 progeny is the recessive form
Progeny inherit one unit from the maternal parent and the other unit from the paternal parent
Units of inheritance are now known as "genes"
Alternative forms of a single gene are "alleles"
Individuals with two different alleles for a single trait are "monohybrids"

23. Mendel's law of segregation
Two gametes, one from each parent, unite at random at fertilization
The two alleles for each trait separate during gamete formation
Figure 2.10 The law of segregation. (a) The two identical alleles of pure-breeding plants separate (segregate) during gamete
formation. As a result, each pollen grain or egg carries only one of each pair of parental alleles. (b) Cross-pollination and fertilization
between pure-breeding parents with antagonistic traits result in F 1 hybrid zygotes with two different alleles. For the seed color gene,
a Yy hybrid zygote will develop into a yellow pea.
Fig. 2.10a
Fig. 2.10b

24. The Punnett square is a simple way to visualize the segregation and random union of alleles
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Each F1 hybrid produces two kinds of gametes in a 1:1 ratio
F2 progeny
3:1 ratio of phenotypes
1/4 will breed true for the dominant trait
1/2 will be hybrids
1/4 will breed true for the recessive trait
Figure 2.11 The Punnett square: Visual summary of a cross. This Punnett square illustrates the combinations that can arise
when an F 1 hybrid undergoes gamete formation and self-fertilization. The F 2 generation should have a 3:1 ratio of yellow to green peas.
Fig. 2.11

25. Mendel’s law of segregation encapsulates this general principle of heredity:
The two alleles for each trait separate(segregate) during gamete formation, and then unite at random, one from each parent, at fertilization.

26. Mendel's results and the Punnett square reflect the basic rules of probability
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Product rule: probability of two independent events occurring together is the product of their individual probabilities
What is the probability that event 1 AND event 2 will occur?
P(1 and 2) = probability of event 1 X probability of event 2
Sum rule: probability of either of two mutually exclusive events occurring is the sum of their individual probabilities
What is the probability that event 1 OR event 2 will occur?
P(1 or 2) = probability of event 1 + probability of event 2
Consecutive coin tosses are obviously independent events; a
Thus, the probability of a given combination is the product of their independent probabilities.
For example, the probability that both coins will turn up heads is

27. Applying probability to Mendel's crosses
From a cross of Yy x Yy peas
What is the chance of getting YY offspring?
Chance of Y pollen is 1/2
Chance of Y ovule is 1/2
Chance of Y pollen and Y ovule uniting is 1/2 x 1/2 = 1/4
What is the chance of getting Yy offspring?
Chance of Y pollen uniting with y ovule is 1/2 x 1/2 = 1/4
Chance of y pollen uniting with Y ovule is 1/2 x 1/2 = 1/4
Chance of either event happening is 1/4 + 1/4 = 1/2
In the analysis of a genetic cross, the product rule multiplies probabilities to predict the chance of a particular
fertilization event. The sum rule adds probabilities to predict the proportion of progeny that share a particular trait
such as pea color.

28. Mendel did further crosses to verify the law of segregation
F2 plants were selfed to produce F3 progeny
All of the green F2 peas were pure breeding
1/3 of the yellow F2 peas were pure breeding
2/3 of the yellow F2 peas were hybrids
Fig. 2.12

29. Definitions of commonly used terms
Phenotype is an observable characteristic (e.g. yellow or green pea seeds)
Genotype is a pair of alleles in an individual (e.g. YY or Yy)
Homozygote has two identical alleles (e.g. YY or yy)
Heterozygote has two different alleles (e.g. Yy)
The heterozygous phenotype defines the dominant allele (e.g. Yy peas are yellow, so the yellow Y allele is dominant to the green y allele)
A dominant allele with a dash represents an unknown genotype (e.g. Y− stands for either YY or Yy) h

30. Genotype vs phenotype in homozygotes and heterozygotes
From a cross of Yy x Yy peas
Genotypes in F2 progeny are in 1:2:1 ratio (1/4 YY, 1/2 Yy, 1/4 yy)
Phenotypes in F2 progeny are in 3:1 ratio (3/4 yellow, 1/4 green)
Fig. 2.13

31. A testcross can reveal an unknown genotype
Is the genotype of an individual with a dominant phenotype (e.g. Y−) heterozygous (Yy) or homozygous (YY)?
Solution: Testcross to homozygous recessive (yy) and examine progeny
Figure 2.14 How a testcross reveals genotype. An
individual of unknown genotype, but dominant phenotype, is
crossed with a homozygous recessive. If the unknown genotype is
homozygous, all progeny will exhibit the dominant phenotype,
(cross A). If the unknown genotype is heterozygous, half the progeny
will exhibit the dominant trait, half the recessive trait (cross B).
Fig. 2.14

33. What monohybrid cross reveal?
Each plant possess 2 genetic factors (alleles) coding for a character/trait
The 2 alleles in each plant separate when gametes are formed, and 1 allele goes into each gamete
The concept of dominance (RR, Rr–dominant phenotype; rr–recessive phenotype)
2 alleles of an individual plant separate with equal probability into the gametes (3:1 ratio)

34. Monohybrid cross –Summary 1

35. Monohybrid cross –Summary 2

36. Mendel's dihybrid crosses revealed the law of independent assortment
Mendel tested whether two genes in dihybrids would segregate independently
First, he crossed true-breeding yellow round peas with true-breeding green wrinkled peas to obtain dihybrid F1 plants:
YY RR x yy rr  F1 Yy Rr
Then, the dihybrid F1 plants were selfed to obtain F2 plants:
F1 Yy Rr x F1 Yy Rr  F2
Mendel asked whether all the F2 progeny would be parental types (yellow round and green wrinkled) OR
would some be recombinant types (yellow wrinkled and green round)?

37. A dihybrid cross produces parental types and recombinant types
Each F1 dihybrid produces four possible gametes in a 1:1:1:1 ratio
Yy Rr  1/4 Y R, 1/4 Y r,
1/4 y R, 1/4 y r
Four phenotypic classes occurred in the F2 progeny:
Two are like parents
Two are recombinant
Fig. 2.15

38. Independent assortment in crosses of F1 dihybrids produces a 9:3:3:1 phenotype ratio
Note that in these F2 progeny, there is a 3:1 phenotype ratio of dominant to recessive forms
Fig. 2.15

39. Mendel's law of independent assortment
During gamete formation, different pairs of alleles segregate independently of each other
Y is just as likely to assort with R as it is with r
y is just as likely to assort with R as it is with r
The law of independent assortment. In a dihybrid cross, each pair of alleles assorts independently during
gamete formation. In the gametes, Y is equally likely to be found with R or r (that is, Y R = Y r ); the same is true for y (that is, y R = y r ).
As a result, all four possible types of gametes ( Y R , Y r , y R , and y r ) are produced in equal frequency among a large population.
Fig. 2.16

40. To find the probability that two independent events such as yellow and round will occur simultaneously in the same plant, you multiply as follows

41. Following crosses with branched-line diagrams
Progeny phenotypes for each gene are shown in different columns
This gives the same ratios as seen in the Punnett square in Fig 2.15
Following crosses with branched-line diagrams. A branched-line diagram, which uses a series of columns
to track every gene in a cross, provides an organized overview of all possible outcomes. This branched-line diagram of a dihybrid cross
generates the same phenotypic ratios as the Punnett square in Fig. 2.15, showing that the two methods are equivalent
Fig. 2.17

42. Testcrosses on dihybrids
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Testcross dihybrids to individuals that are homozygous for both recessive traits
Fig. 2.18

43. Law of independent assortment
The law of independent assortment states that the alleles of genes for different traits segregate independently of each other during gamete formation.

44. Mendel's laws can be used to predict offspring from complicated crosses
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To calculate the possible number of gamete genotypes from a hybrid, raise 2 to the power of the number of different traits
Aa Bb Cc Dd  24 = 16 kinds of gametes
Aa Bb Cc Dd x Aa Bb Cc Dd  16 x 16 = 256 genotypes
To do a Punnett square with this cross involving four genes, you would need 16 columns and 16 rows
An easier way is to break down a multihybrid cross into independently assorting monohybrid crosses

45. Predicting proportions of progeny from multihybrid crosses – example 1
Cross Aa Bb Cc Dd x Aa Bb Cc Dd
What proportion of progeny will be AA bb Cc Dd?
Aa x Aa  1/4 AA
Bb x Bb  1/4 bb
Cc x Cc  1/4 Cc
Dd x Dd  1/4 Dd
So, the expected proportion of AA bb Cc DD progeny is:
1/4 x 1/4 x 1/2 x 1/2 = 1/64

46. Predicting proportions of progeny from multihybrid crosses – example 2
Cross Aa Bb Cc Dd x Aa Bb Cc Dd
How many progeny will show the dominant traits for A, C, and D and the recessive trait for B?
Aa x Aa  3/4 A−
Bb x Bb  1/4 bb
Cc x Cc  3/4 C−
Dd x Dd  3/4 D−
So, expected proportion of A− bb C− D− progeny is:
3/4 x 1/4 x 3/4 x 3/4 = 27/256

47. The science of genetics began with the rediscovery of Mendel's work
Mendel published his monumental breakthrough in understanding heredity in 1866, but hardly anyone paid attention to his work!
In 1900, three scientists independently rediscovered and acknowledged Mendel's work
Fig. 2.19

48. Mendelian inheritance in humans
Many heritable traits in humans are caused by interaction of multiple genes and so don't show simple Mendelian inheritance patterns
In 2009, there were ~ 4300 single-gene traits known in humans
See Table 2.1 for some of the common single-gene traits
Even with single-gene traits, determining inheritance pattern in humans can be tricky
Long generation time
Small numbers of progeny
No controlled matings
No pure-breeding lines
Although many human traits clearly run in families, most do not show a simple Mendelian pattern of inheritance.
Not necessarily, because eye color is infl uenced by more than one gene.

49. Some of the most common single-gene traits caused by recessive alleles in humans
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Disease
Effect
Incidence of Disease
Thallassemia (chromosome 16 or 11)
Reduced amounts of hemoglobin; anemia, bone, and spleen enlargement
1/10 in parts of Italy
Sickle-cell anemia (chromosome 11)
Abnormal hemoglobin; sickle-shaped red cells, anemia, blocked circulation; increased resistance to malaria
1/625 African-Americans
Cystic fibrosis (chromosome 7)
Defective cell membrane protein; excessive mucus production; digestive and respiratory failure
1/2000 Caucasians
Tay-Sachs disease (chromosome 15)
Missing enzyme; buildup of fatty deposit in brain; buildup disrupts mental development
1/3000 Eastern European Jews
Phenylketonuria (PKU) (chromosome 12)
Missing enzyme; mental deficiency
1/10,000 Caucasians
Table 2.1

50. Some of the most common single-gene traits caused by dominant alleles in humans
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Disease
Effect
Incidence of Disease
Hypercholesterolemia (chromosome 19)
Missing protein that removes cholesterol from the blood; heart attack by age 50
1/122 French Canadians
Huntington disease (chromosome 4)
Progressive mental and neurological damage; neurologic disorders by ages
1/25,000 Caucasians
Table 2.1

51. Human Genealogy
Genealogy(Greek, “genea”= generation, “logos” = knowledge): the study of families and the tracing of their lineages and history

52. In humans, pedigrees can be used to study inheritance
Pedigrees are orderly diagrams of a family's relevant genetic features
Includes as many generations as possible (ideally, at least both sets of grandparents of an affected person)
Pedigrees can be analyzed using Mendel's laws
Is a trait determined by alternate alleles of a single gene?
Is a trait dominant or recessive?

53. Symbols used in pedigree analysis
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Symbols used in pedigree analysis. In the simple pedigree at the bottom, I. 1 is the father, I.2 is the mother, and II.1 and II.2 are their sons.
The father and the first son are both affected by the disease trait.
They could not determine whether the allele causing the disease depicted at the bottom of Fig is dominant or recessive
solely on the basis of the simple pedigree shown. The data are consistent with both possibilities. If the trait is dominant, then the father and the affected son are heterozygotes,
while the mother and the unaffected son are homozygotes for the recessive normal allele. If instead the trait is recessive, the father and affected son are homozygotes
for the recessive disease-causing allele, while the mother and the unaffected son are heterozygotes.
Fig. 2.20

54. A vertical pattern of inheritance indicates a rare dominant trait; e
A vertical pattern of inheritance indicates a rare dominant trait; e.g Huntington disease
Every affected person has at least one affected parent
Mating between affected person and unaffected person is effectively a testcross
Fig. 2.21

55. How to recognize dominant traits in pedigrees
Three key aspects of pedigrees with dominant traits:
Affected children always have at least one affected parent
As a result, dominant traits show a vertical pattern of inheritance
the trait shows in every generation
Two affected parents can produce unaffected children, if both parents are heterozygotes
Table 2.2

56. A horizontal pattern of inheritance indicates a rare recessive trait; e.g. cystic fibrosis
Parents of affected individuals are unaffected but are heterozygous (carriers) for the recessive allele
Fig. 2.22

57. How to recognize recessive traits in pedigrees
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Four keys aspects of pedigrees with recessive traits:
Affected individuals can be the children of two unaffected carriers, particularly as a result of consanguineous matings
All the children of two affected parents should be affected
Rare recessive traits show a horizontal pattern of inheritance
Recessive traits may show a vertical pattern of inheritance if the trait is extremely common in the population
Table 2.2

58. The chromosome theory of inheritance (4.5)
Walter Sutton – 1903, chromosomes carry Mendel's units of heredity
Two copies of each kind of chromosome
Chromosome complement is unchanged during transmission to progeny
Homologous chromosomes separate to different gametes
Maternal and paternal chromosomes move to opposite poles
Fertilization of eggs by random encounter with sperm
In all cells derived from fertilized egg, half of chromosomes are maternal and half are paternal
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59. How the chromosome theory of inheritance explains Mendel's law of segregation
Table 4.4a
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60. How the chromosome theory of inheritance explains Mendel's law of independent assortment
Table 4.4b
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61. Validation of the chromosome theory
Prior to 1910, the chromosome theory of inheritance was supported by two circumstantial lines of evidence
Sex determination associates with inheritance of particular chromosomes
Events in mitosis, meiosis, and gametogenesis ensure constant numbers of chromosomes in somatic cells
This theory confirmed and validated by:
Inheritance of genes and chromosomes correspond in every detail
Transmission of particular chromosome coincides with transmission of traits other than for sex determination
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62. Nomenclature for Drosophila genetics
Gene symbol identified by abnormal phenotype
Wild-type allele denoted with superscript +
Recessive mutant allele denoted with lowercase
e.g. gene symbol for white gene is w
wild-type allele (w+) specifies brick-red eyes
mutant allele (w) specifies white eyes
Dominant mutant allele denoted with upper case
e.g. gene symbol for bar eyes is Bar
wild-type allele (Bar+) specifies normal eye
mutant allele (Bar) specifies abnormal eyes

63. The Drosophila white gene is located on the X chromosome
T. H. Morgan (1910) discovered a white-eyed Drosophila mutant and did a series of crosses
Fig. 4.19
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64. Crisscross inheritance occurs with X-linked recessive traits
See cross D – daughters inherit the phenotype of their fathers, sons inherit the phenotype of their mothers
Fig. 4.19
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65. Rare mistakes in meiosis helped confirm the chromosome theory
C. Bridges found 1/2000 male progeny of white females have red eyes
Hypothesized that red-eyed males arise from mistakes in chromosome segregation (nondisjunction) during meiosis in white-eyed females
Fig. 4.20a
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66. Rare mistakes in meiosis helped confirm the chromosome theory (cont)
Chromosome segregation in an XXY female
The three sex chromosomes pair and segregate in two ways, producing progeny with unusual sex chromosome complements
Fig. 4.20b
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67. Example of an X-linked trait in humans
(Top) View of the world to a person with normal color vision
(Bottom) View of the world to a person with red-green colorblindness
E. B. Wilson – 1911, assigned gene for this trait to the X chromosome
Fig. 4.21
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68. An example of a pedigree for an X-linked recessive trait: Hemophilia
Fig. 4.22a
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69. An example of a pedigree for an X-linked dominant trait: Hypophosphatemia
Fig. 4.22b
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70. Observed and Expected ratios
If two individuals of known genotype are crossed, certain ratios are expected based on the Mendelian principles
The ratios of genotypes and phenotypes actually observed among the progeny may deviate from these expectations
Chance plays a critical role in genetic crosses

71. Observed and expected ratios
To evaluate the role of chance in producing deviations between observed and expected values, you use statistical test called chi- square test (χ2)
This test provides information about how well observed values fit expected values
The chi-square test can be used to evaluate whether deviations between observed and expected numbers are due to chance or other significant factor.

72. Null Hypotesis
no real difference between the measured values (or ratio) and the predicted values (or ratio). Any apparent difference can be attributed purely to chance.
REJECTED
NOT REJECTED
If the null hypothesis fails to be rejected, any observed deviations
are attributed to chance.
If it is rejected, the observed deviation from the expected result is judged not to be attributable to chance alone.
P value less than 0.05
P value Greater than 0.05

75. For the 3:1 ratio, n = 2, df = 1 For the 9:3:3:1 ratio, n = 4 df = 3.
you must initially determine a value called
the degrees of freedom (df), which is equal to n - 1, where
n is the number of different categories into which the data are divided, (the number of possible outcomes).
For the 3:1 ratio, n = 2, df = 1
For the 9:3:3:1 ratio, n = df = 3.

77. a) Graph for converting X2 values to p values.
(b) Table of X2 values for selected values of df and p. 2 values that lead to a p value of 0.05 or greater (darker blue areas) justify failure to reject the null hypothesis. Values leading to a p value of less than (lighter blue areas) justify rejecting the null hypothesis. For example, the table in part (b) shows that for X2 = 0.53 with 1 degree of freedom, the corresponding p value is between 0.20 and The graph in (a) gives a more precise p value of 0.48 by interpolation. Thus, we fail to reject the null hypothesis.

78. END of LECTURE!!
Hartwell 4e( Pages 13-34)
Hartwell 4e (Pages )
Klug 11e ( 90-92)