Mary Simpson MATH 150 Objectives Understanding how to find the probability of genetic outcomes for situations involving Multiple Traits Linkage Incomplete Dominance Codominance Multiple Allelism ID: 239675
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Slide1
Math of Genetics
Mary Simpson
MATH 150Slide2
Objectives
Understanding how to find the probability of genetic outcomes for situations involving:
Multiple Traits
Linkage
Incomplete Dominance
Codominance
Multiple Allelism
Understanding Hardy Weinberg Equations in relation to population geneticsSlide3
Flashback to High School Biology!
Genetics: the study of the inheritance of traits
Gene: a section of DNA that influences the heredity of a traitSlide4
Flashback to High School Biology!
Genetics: the study of the inheritance of traits
Gene: a section of DNA that influences the heredity of a trait
Chromosome: dense coils of DNA that contain multiple genes
Allele: denotes different versions of the same geneSlide5
Flashback to High School Biology!
Genetics: the study of the inheritance of traits
Gene: a section of DNA that influences the heredity of a trait
Chromosome: dense coils of DNA that contain multiple genes
Allele: denotes different versions of the same gene
Gregor Mendel was a pioneer in geneticsSlide6
Mendelian Genetics
Gregor Mendel (1822-1884)
Studied the inheritance of traits in pea plants Slide7
Mendelian Genetics
Gregor Mendel (1822-1884)
Studied the inheritance of traits in pea plants
Mendel looked for patterns in the inheritance traits from parents with specified traitsSlide8
How Genes Are Inherited
The average human had 46 chromosomes (2 sets of 23)Slide9
How Genes Are Inherited
The average human had 46 chromosomes (2 sets of 23)
Half of these chromosomes come from the mother and half from the father (1 set from each parent)Slide10
How Genes Are Inherited
The average human had 46 chromosomes (2 sets of 23)
Half of these chromosomes come from the mother and half from the father (1 set from each parent)
Because there are two sets of chromosomes, a person inherits two copies of each geneSlide11
How Genes Are Inherited
The average human had 46 chromosomes (2 sets of 23)
Half of these chromosomes come from the mother and half from the father (1 set from each parent)
Because there are two sets of chromosomes, a person inherits two copies of each gene
A person has two alleles for each trait that interact, resulting in the expressed traitSlide12
Inheritance of Single Traits
Dominant Trait: if a gene for the dominant trait (called a dominant allele) is present, it will be expressed
Usually expressed with an uppercase letter (ex. A)
Recessive Trait: this trait will only be expressed in the absence of a dominant allele
Usually expressed with a lowercase letter (ex.
a
)Slide13
Inheritance of Single Traits
Dominant Trait: if a gene for the dominant trait (called a dominant allele) is present, it will be expressed
Usually expressed with an uppercase letter (ex. A)
Recessive Trait: this trait will only be expressed in the absence of a dominant allele
Usually expressed with a lowercase letter (ex.
a
)
Genotype: the combination of two alleles (ex. Aa)
Phenotype: the trait expression that results from a genotypeSlide14
Inheritance of Single Traits
Dominant Trait: if a gene for the dominant trait (called a dominant allele) is present, it will be expressed
Usually expressed with an uppercase letter (ex. A)
Recessive Trait: this trait will only be expressed in the absence of a dominant allele
Usually expressed with a lowercase letter (ex.
a
)
Genotype: the combination of two alleles (ex. Aa)
Phenotype: the trait expression that results from a genotype
Homozygous: genotype with two copies of the same allele (ex. AA, aa)
Heterozygous: genotype with one dominant allele and one recessive allele (ex. Aa)Slide15
Punnett Squares
To form a punnett square, form a grid with the paternal genotype on the top and the maternal genotype down the left sideSlide16
Punnett Squares
To form a punnett square, form a grid with the paternal genotype on the top and the maternal genotype down the left side
In the center sections of the table, combine the paternal and maternal alleles to create all possible genotypes for the offspringSlide17
Punnett Square Example
If we have a mother with genotype aa and a father with genotype Aa
The punnett square would look as follows:
a
a
A
aSlide18
Punnett Square Example
If we have a mother with genotype aa and a father with genotype Aa
The punnett square would look as follows:
a
a
A
A
A
a
a
aSlide19
Punnett Square Example
If we have a mother with genotype aa and a father with genotype Aa
The punnett square would look as follows:
a
a
A
A
a
A
a
a
a
a
a
aSlide20
Punnett Square Example
If we have a mother with genotype aa and a father with genotype Aa
The punnett square would look as follows:
a
a
A
A
a
A
a
a
a
a
a
a
Genotypic Ratio
: a ratio of the number of possible outcomes of each genotype (in this example
1:1
)
Phenotypic Ratio
: ratio of the number of outcomes that will result in different phenotypes (in this example
1:1
)Slide21
Practice Problem
The allele for dark hair (B) is dominant and the allele for light hair (b) is recessive
If a female with genotype Bb and a male with genotype Bb mate, what are the chances that they will have a light haired offspring?Slide22
Practice Problem
The allele for dark hair (B) is dominant and the allele for light hair (b) is recessive
If a female with genotype Bb and a male with genotype Bb mate, what are the chances that they will have a light haired offspring?
B
b
B
bSlide23
Practice Problem
The allele for dark hair (B) is dominant and the allele for light hair (b) is recessive
If a female with genotype Bb and a male with genotype Bb mate, what are the chances that they will have a light haired offspring?
B
b
B
B
B
b
b
bSlide24
Practice Problem
The allele for dark hair (B) is dominant and the allele for light hair (b) is recessive
If a female with genotype Bb and a male with genotype Bb mate, what are the chances that they will have a light haired offspring?
B
b
B
B
B
B
b
b
B
b
b
bSlide25
Practice Problem
The allele for dark hair (B) is dominant and the allele for light hair (b) is recessive
If a female with genotype Bb and a male with genotype Bb mate, what are the chances that they will have a light haired offspring?
B
b
B
B
B
B
b
b
B
b
b
b
To have light hair the genotype must be bb
There is only a 1/4 chance of that, therefore the chance is 25%Slide26
Inheritance of Two Traits
Looking at the inheritance of two traits is called a dihybrid crossSlide27
Inheritance of Two Traits
Looking at the inheritance of two traits is called a dihybrid cross
To set up the punnett square you have to look at all possible combinations of maternal and paternal DNASlide28
Inheritance of Two Traits
Looking at the inheritance of two traits is called a dihybrid cross
To set up the punnett square you have to look at all possible combinations of maternal and paternal DNA
You use those 4 combinations from each parent to set up the punnett squareSlide29
Practice Problem
We will look at the inheritance of brown and black fur and coarse and soft fur in hamsters
Brown fur (B) and soft fur (S) are dominantSlide30
Practice Problem
We will look at the inheritance of brown and black fur and coarse and soft fur in hamsters
Brown fur (B) and soft fur (S) are dominantSlide31
Practice Problem
We will look at the inheritance of brown and black fur and coarse and soft fur in hamsters
Brown fur (B) and soft fur (S) are dominant
If the mother has genotype
BBss
and the father has genotype
BbSs
, what is the chance that an offspring will have brown coarse fur?Slide32
Practice Problem Cont.
If the mother has genotype
Bbss
and the father has genotype BbSs, what is the chance that an offspring will have brown coarse fur?
BS
Bs
bS
bs
Bs
Bs
bs
bsSlide33
Practice Problem Cont.
If the mother has genotype
Bbss
and the father has genotype BbSs, what is the chance that an offspring will have brown coarse fur?
BS
Bs
bS
bs
Bs
Bs
Bs
Bs
Bs
Bs
Bs
Bs
Bs
Bs
bs
bs
bs
bs
bs
bs
bs
bs
bs
bsSlide34
Practice Problem Cont.
If the mother has genotype
Bbss
and the father has genotype BbSs, what is the chance that an offspring will have brown coarse fur?
BS
Bs
bS
bs
Bs
B
BS
s
B
Bs
s
B
bS
s
B
bs
s
Bs
B
BS
s
B
Bs
s
B
bS
s
B
bs
s
bs
b
BS
s
b
Bs
s
b
bS
s
b
bs
s
bs
b
BS
s
b
Bs
s
b
bS
s
b
bs
sSlide35
Practice Problem Cont.
If the mother has genotype
Bbss
and the father has genotype BbSs, what is the chance that an offspring will have brown coarse fur?
Phenotypic Ratio 6:6:2:2
BS
Bs
bS
bs
Bs
B
BS
s
B
Bs
s
B
bS
s
B
bs
s
Bs
B
BS
s
B
Bs
s
B
bS
s
B
bs
s
bs
b
BS
s
b
Bs
s
b
bS
s
b
bs
s
bs
b
BS
s
b
Bs
s
b
bS
s
b
bs
sSlide36
Practice Problem Cont.
If the mother has genotype
Bbss
and the father has genotype BbSs, what is the chance that an offspring will have brown coarse fur?
Phenotypic Ratio 6:6:2:2
BS
Bs
bS
bs
Bs
B
BS
s
B
Bs
s
B
bS
s
B
bs
s
Bs
B
BS
s
B
Bs
s
B
bS
s
B
bs
s
bs
b
BS
s
b
Bs
s
b
bS
s
b
bs
s
bs
b
BS
s
b
Bs
s
b
bS
s
b
bs
sSlide37
Practice Problem Cont.
If the mother has genotype
Bbss
and the father has genotype BbSs, what is the chance that an offspring will have brown coarse fur?
Phenotypic Ratio 6:6:2:2
Out of the sixteen possible genetic combinations, 6 result in brown, coarse fur
6/16= .375 = 37.5%
BS
Bs
bS
bs
Bs
B
BS
s
B
Bs
s
B
bS
s
B
bs
s
Bs
B
BS
s
B
Bs
s
B
bS
s
B
bs
s
bs
b
BS
s
b
Bs
s
b
bS
s
b
bs
s
bs
b
BS
s
b
Bs
s
b
bS
s
b
bs
sSlide38
Linkage
Linked genes are those found on the same chromosomeSlide39
Linkage
Linked genes are those found on the same chromosome
This means that these traits should not follow the same pattern of inheritance because the traits cannot be independently assorted into gametesSlide40
Linkage
Linked genes are those found on the same chromosome
This means that these traits should not follow the same pattern of inheritance because the traits cannot be independently assorted into gametes
In terms of a punnett square, having two linked traits would be treated like having a single traitSlide41
Linkage
Linked genes are those found on the same chromosome
This means that these traits should not follow the same pattern of inheritance because the traits cannot be independently assorted into gametes
In terms of a punnett square, having two linked traits would be treated like having a single trait
Mendel was lucky that each of the traits he studied had genes that were not linkedSlide42
Incomplete Dominance
Incomplete dominance means that the dominant allele will not completely dominant the recessive alleleSlide43
Incomplete Dominance
Incomplete dominance means that the dominant allele will not completely dominant the recessive allele
In many cases this means that heterozygous individuals will have intermediate phenotypesSlide44
Incomplete Dominance
Incomplete dominance means that the dominant allele will not completely dominant the recessive allele
In many cases this means that heterozygous individuals will have intermediate phenotypes
This will not alter genotypic ratios, but it will alter phenotypic ratiosSlide45
Practice Problem
T
he allele for white flowers (R) is dominant, but it’s dominance incomplete
The allele for red flowers (r) is recessiveSlide46
Practice Problem
T
he allele for white flowers (R) is dominant, but it’s dominance incomplete
The allele for red flowers (r) is recessive
What are the possible phenotypes of the offspring of two plants with genotypes Rr and Rr?Slide47
Practice Problem
T
he allele for white flowers (R) is dominant, but it’s dominance incomplete
The allele for red flowers (r) is recessive
What are the possible phenotypes of the offspring of two plants with genotypes Rr and Rr?
R
r
R
rSlide48
Practice Problem
T
he allele for white flowers (R) is dominant, but it’s dominance incomplete
The allele for red flowers (r) is recessive
What are the possible phenotypes of the offspring of two plants with genotypes Rr and Rr?
R
r
R
RR
Rr
r
Rr
rrSlide49
Practice Problem
T
he allele for white flowers (R) is dominant, but it’s dominance incomplete
The allele for red flowers (r) is recessive
What are the possible phenotypes of the offspring of two plants with genotypes Rr and Rr?
R
r
R
RR
Rr
r
Rr
rr
RR will have white flowers
rr will have red flowers
Rr will have pink flowers (intermediate between white and red)Slide50
Practice Problem
If we mated two of that same type of flowers with the genotypes, RR and Rr, what is the probability that the offspring will have pink flowers?Slide51
Practice Problem
If we mated two of that same type of flowers with the genotypes, RR and Rr, what is the probability that the offspring will have pink flowers?
R
R
R
rSlide52
Practice Problem
If we mated two of that same type of flowers with the genotypes, RR and Rr, what is the probability that the offspring will have pink flowers?
R
R
R
RR
RR
r
Rr
RrSlide53
Practice Problem
If we mated two of that same type of flowers with the genotypes, RR and Rr, what is the probability that the offspring will have pink flowers?
R
R
R
RR
RR
r
Rr
Rr
2/4 or 50% chanceSlide54
Codominance
Codominance: when heterozygotes have the phenotypes associated with each allele (because both alleles are dominant)Slide55
Codominance
Codominance: when heterozygotes have the phenotypes associated with each allele (because both alleles are dominant)
The best example is blood type
There are three alleles for blood type (I
A
, I
B
, i)Slide56
Codominance
Codominance: when heterozygotes have the phenotypes associated with each allele (because both alleles are dominant)
The best example is blood type
There are three alleles for blood type (I
A
, I
B
, i)
I
A
and I
B
are codominant, so if a person has genotype I
A
I
B
, they will have type AB blood
I
A
i, results in type A, I
B
i in type B and ii in type OSlide57
Practice Problem
What are the possible blood types of offspring of parents with genotypes I
A
i and I
B
I
BSlide58
Practice Problem
What are the possible blood types of offspring of parents with genotypes I
A
i and I
B
I
B
I
B
I
B
I
A
iSlide59
Practice Problem
What are the possible blood types of offspring of parents with genotypes I
A
i and I
B
I
B
I
B
I
B
I
A
I
A
I
B
I
A
I
B
i
I
B
i
I
B
iSlide60
Practice Problem
What are the possible blood types of offspring of parents with genotypes I
A
i and I
B
I
B
I
B
I
B
I
A
I
A
I
B
I
A
I
B
i
I
B
i
I
B
i
I
A
I
B
will result in type AB
I
B
i will result in type B Slide61
Practice Problem
What is the chance that a mother with genotype I
B
i and a father with genotype I
A
i will have a child with type O blood?Slide62
Practice Problem
What is the chance that a mother with genotype I
B
i and a father with genotype I
A
i will have a child with type O blood?
I
B
i
I
A
iSlide63
Practice Problem
What is the chance that a mother with genotype I
B
i and a father with genotype I
A
i will have a child with type O blood?
I
B
i
I
A
I
A
I
B
I
A
i
i
I
B
i
iiSlide64
Practice Problem
What is the chance that a mother with genotype I
B
i and a father with genotype I
A
i will have a child with type O blood?
I
B
i
I
A
I
A
I
B
I
A
i
i
I
B
i
ii
1/4 or 25%Slide65
Multiple Gene Inheritance
Multiple Gene Inheritance: there is more than one gene that controls the expression of a traitSlide66
Multiple Gene Inheritance
Multiple Gene Inheritance: there is more than one gene that controls the expression of a trait
Example: Pepper Color
Pepper color is controlled by two different genes
The first gene controls the expression of red pigment
The dominant allele (R) indicates the presence of red pigment
The recessive allele (r) indicates the absence of red pigmentSlide67
Multiple Gene Inheritance
Multiple Gene Inheritance: there is more than one gene that controls the expression of a trait
Example: Pepper Color
Pepper color is controlled by two different genes
The first gene controls the expression of red pigment
The dominant allele (R) indicates the presence of red pigment
The recessive allele (r) indicates the absence of red pigment
The second gene controls the expression of either green (G) or yellow (g) pigmentSlide68
Multiple Gene Inheritance
If red pigment is expressed, the pepper will be red, regardless of the second gene. Slide69
Multiple Gene Inheritance
If red pigment is expressed, the pepper will be read, regardless of the second gene.
If the red pigment is absent, you must look to the second gene to determine colorSlide70
Multiple Gene Inheritance
If red pigment is expressed, the pepper will be red, regardless of the second gene.
If the red pigment is absent, you must look to the second gene to determine color
What would the color of a pepper with the genotype
Rrgg
be?Slide71
Multiple Gene Inheritance
If red pigment is expressed, the pepper will be read, regardless of the second gene.
If the red pigment is absent, you must look to the second gene to determine color
What would the color of a pepper with the genotype
Rrgg
be?
RedSlide72
Multiple Gene Inheritance
If red pigment is expressed, the pepper will be red, regardless of the second gene.
If the red pigment is absent, you must look to the second gene to determine color
What would the color of a pepper with the genotype
Rrgg
be?
R
ed
What about
rrGgSlide73
Multiple Gene Inheritance
If red pigment is expressed, the pepper will be read, regardless of the second gene.
If the red pigment is absent, you must look to the second gene to determine color
What would the color of a pepper with the genotype
Rrgg
be?
R
ed
What about
rrGg
GreenSlide74
Hardy Weinberg Principle
Looks at the frequency of alleles in a population
The Principle makes several important assumptions:
There is not natural selection regarding the gene in question
There is no genetic drift
There is no gene flow
There is no mutation
Random mating with respect to the gene in question is occurringSlide75
Hardy Weinberg Principle
Hardy Weinberg Equation:
p
2
+ 2pq + q
2
= 1
p + q = 1Slide76
Hardy Weinberg Principle
Hardy Weinberg Equation:
p
2
+ 2pq + q
2
= 1
p + q = 1
p
=allele frequency of the dominant allele
q
=allele frequency of the recessive alleleSlide77
Hardy Weinberg Principle
Hardy Weinberg Equation:
p
2
+ 2pq + q
2
= 1
p + q = 1
p
=allele frequency of the dominant allele
q
=decimal version of the recessive allele
p
2
is the frequency of the homozygous dominant genotype
q
2
is the frequency of the homozygous recessive genotype
2pq is the frequency of the heterozygous genotypeSlide78
Genes that the Hardy Weinberg Equilibrium Applies To
Tongue Rolling (dominant)Slide79
Genes that the Hardy Weinberg Equilibrium Applies To
Tongue Rolling (dominant)
Free (dominant) v. Attached (recessive) EarlobesSlide80
Genes that the Hardy Weinberg Equilibrium Applies To
Tongue Rolling (dominant)
Free (dominant) v. Attached (recessive) Earlobes
Hand Clasping
Left thumb over right (dominant)
Right thumb over left (recessive)Slide81
Genes that the Hardy Weinberg Equilibrium Applies To
Tongue Rolling (dominant)
Free (dominant) v. Attached (recessive) Earlobes
Hand Clasping
Left thumb over right (dominant)
Right thumb over left (recessive)
Widow’s Peak (dominant)Slide82
Genes that the Hardy Weinberg Equilibrium Applies To
Tongue Rolling (dominant)
Free (dominant) v. Attached (recessive) Earlobes
Hand Clasping
Left thumb over right (dominant)
Right thumb over left (recessive)
Widow’s Peak (dominant)
Mid-Digital Hair (dominant)Slide83
Using the Hardy Weinberg Equations
If the frequency of the recessive allele for sickle cell anemia is .4 in a population of 100,000
The dominant allele has a frequency of .6
Individuals that are heterozygous for this allele have a higher resistance to malaria
How many members of the population would have the increased resistance to malaria?Slide84
Using the Hardy Weinberg Equations
If the frequency of the recessive allele for sickle cell anemia is .4 in a population of 100,000 people
The dominant allele has a frequency of .6
How many members of the population would have the increased resistance to malaria?
Heterozygous Frequency = 2pqSlide85
Using the Hardy Weinberg Equations
If the frequency of the recessive allele for sickle cell anemia is .4 in a population of 100,000 people
The dominant allele has a frequency of .6
How many members of the population would have the increased resistance to malaria?
Heterozygous Frequency = 2pq
2pq = 2 * 0.4 * 0.6 = .48Slide86
Using the Hardy Weinberg Equations
If the frequency of the recessive allele for sickle cell anemia is .4 in a population of 100,000 people
The dominant allele has a frequency of .6
How many members of the population would have the increased resistance to malaria?
Heterozygous Frequency = 2pq
2pq = 2 * 0.4 * 0.6 = .48
48,000 people would have increased malaria resistanceSlide87
Homework
What is the probability that a father with genotype
Hhpp
and a mother with genotype
HHPp
will have offspring that have the dominant phenotype for both traits?
If the allele frequency for blue eyes in a population is 0.35 and that allele is recessive, what is the frequency of heterozygous individuals in the population?