Math of genetics
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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 to

Genes that the Hardy Weinberg Equilibrium Applies To

  • Tongue Rolling (dominant)


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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