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Math of Genetics. 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

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Math of genetics

Math of Genetics

Mary Simpson

MATH 150


Objectives
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 genetics


Flashback to high school biology
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


Flashback to high school biology1
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


Flashback to high school biology2
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 genetics


Mendelian genetics
Mendelian Genetics

  • Gregor Mendel (1822-1884)

  • Studied the inheritance of traits in pea plants


Mendelian genetics1
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 traits


How genes are inherited
How Genes Are Inherited

  • The average human had 46 chromosomes (2 sets of 23)


How genes are inherited1
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)


How genes are inherited2
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


How genes are inherited3
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 trait


Inheritance of single traits
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)


Inheritance of single traits1
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


Inheritance of single traits2
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)


Punnett squares
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


Punnett squares1
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 offspring


Punnett square example
Punnett Square Example

  • If we have a mother with genotype aa and a father with genotype Aa

    • The punnett square would look as follows:


Punnett square example1
Punnett Square Example

  • If we have a mother with genotype aa and a father with genotype Aa

    • The punnett square would look as follows:


Punnett square example2
Punnett Square Example

  • If we have a mother with genotype aa and a father with genotype Aa

    • The punnett square would look as follows:


Punnett square example3
Punnett Square Example

  • If we have a mother with genotype aa and a father with genotype Aa

    • The punnett square would look as follows:

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)


Practice problem
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?


Practice problem1
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?


Practice problem2
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?


Practice problem3
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?


Practice problem4
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?

To have light hair the genotype must be bb

There is only a 1/4 chance of that, therefore the chance is 25%


Inheritance of two traits
Inheritance of Two Traits

  • Looking at the inheritance of two traits is called a dihybrid cross


Inheritance of two traits1
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


Inheritance of two traits2
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 square


Practice problem5
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


Practice problem6
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


Practice problem7
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 BBssand the father has genotype BbSs, what is the chance that an offspring will have brown coarse fur?


Practice problem cont
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?


Practice problem cont1
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?


Practice problem cont2
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?


Practice problem cont3
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


Practice problem cont4
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


Practice problem cont5
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%


Linkage
Linkage

  • Linked genes are those found on the same chromosome


Linkage1
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


Linkage2
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


Linkage3
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 linked


Incomplete dominance
Incomplete Dominance

  • Incomplete dominance means that the dominant allele will not completely dominant the recessive allele


Incomplete dominance1
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


Incomplete dominance2
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 ratios


Practice problem8
Practice Problem

  • The allele for white flowers (R) is dominant, but it’s dominance incomplete

  • The allele for red flowers (r) is recessive


Practice problem9
Practice Problem

  • The 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?


Practice problem10
Practice Problem

  • The 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?


Practice problem11
Practice Problem

  • The 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?


Practice problem12
Practice Problem

  • The 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?

RR will have white flowers

rr will have red flowers

Rr will have pink flowers (intermediate between white and red)


Practice problem13
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?


Practice problem14
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?


Practice problem15
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?


Practice problem16
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?

2/4 or 50% chance


Codominance
Codominance

  • Codominance: when heterozygotes have the phenotypes associated with each allele (because both alleles are dominant)


Codominance1
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 (IA, IB, i)


Codominance2
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 (IA, IB, i)

  • IA and IB are codominant, so if a person has genotype IAIB, they will have type AB blood

  • IAi, results in type A, IBi in type B and ii in type O


Practice problem17
Practice Problem

  • What are the possible blood types of offspring of parents with genotypes IAi and IBIB


Practice problem18
Practice Problem

  • What are the possible blood types of offspring of parents with genotypes IAi and IBIB


Practice problem19
Practice Problem

  • What are the possible blood types of offspring of parents with genotypes IAi and IBIB


Practice problem20
Practice Problem

  • What are the possible blood types of offspring of parents with genotypes IAi and IBIB

IAIB will result in type AB

IBi will result in type B


Practice problem21
Practice Problem

  • What is the chance that a mother with genotype IBi and a father with genotype IAi will have a child with type O blood?


Practice problem22
Practice Problem

  • What is the chance that a mother with genotype IBi and a father with genotype IAi will have a child with type O blood?


Practice problem23
Practice Problem

  • What is the chance that a mother with genotype IBi and a father with genotype IAi will have a child with type O blood?


Practice problem24
Practice Problem

  • What is the chance that a mother with genotype IBi and a father with genotype IAi will have a child with type O blood?

1/4 or 25%


Multiple gene inheritance
Multiple Gene Inheritance

  • Multiple Gene Inheritance: there is more than one gene that controls the expression of a trait


Multiple gene inheritance1
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


Multiple gene inheritance2
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) pigment


Multiple gene inheritance3
Multiple Gene Inheritance

  • If red pigment is expressed, the pepper will be red, regardless of the second gene.


Multiple gene inheritance4
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


Multiple gene inheritance5
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?


Multiple gene inheritance6
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?

    • Red


Multiple gene inheritance7
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?

    • Red

  • What about rrGg


Multiple gene inheritance8
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?

    • Red

  • What about rrGg

    • Green


Hardy weinberg principle
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 occurring


Hardy weinberg principle1
Hardy Weinberg Principle

  • Hardy Weinberg Equation:

    • p2 + 2pq + q2 = 1

    • p + q = 1


Hardy weinberg principle2
Hardy Weinberg Principle

  • Hardy Weinberg Equation:

    • p2 + 2pq + q2 = 1

    • p + q = 1

    • p=allele frequency of the dominant allele

    • q=allele frequency of the recessive allele


Hardy weinberg principle3
Hardy Weinberg Principle

  • Hardy Weinberg Equation:

    • p2 + 2pq + q2 = 1

    • p + q = 1

    • p=allele frequency of the dominant allele

    • q=decimal version of the recessive allele

    • p2 is the frequency of the homozygous dominant genotype

    • q2 is the frequency of the homozygous recessive genotype

    • 2pq is the frequency of the heterozygous genotype



Genes that the hardy weinberg equilibrium applies to1
Genes that the Hardy Weinberg Equilibrium Applies To

  • Tongue Rolling (dominant)

  • Free (dominant) v. Attached (recessive) Earlobes


Genes that the hardy weinberg equilibrium applies to2
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)


Genes that the hardy weinberg equilibrium applies to3
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)


Genes that the hardy weinberg equilibrium applies to4
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)


Using the hardy weinberg equations
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?


Using the hardy weinberg equations1
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


Using the hardy weinberg equations2
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


Using the hardy weinberg equations3
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 resistance


Homework
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?


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