Math of Genetics

1. Math of Genetics Mary Simpson MATH 150

2. 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

3. 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

4. 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

5. 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

6. Mendelian Genetics • Gregor Mendel (1822-1884) • Studied the inheritance of traits in pea plants

7. 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

8. How Genes Are Inherited • The average human had 46 chromosomes (2 sets of 23)

9. 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)

10. 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

11. 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

12. 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)

13. 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

14. 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)

15. 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

16. 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

17. Punnett Square Example • If we have a mother with genotype aa and a father with genotype Aa • The punnett square would look as follows:

18. Punnett Square Example • If we have a mother with genotype aa and a father with genotype Aa • The punnett square would look as follows:

19. Punnett Square Example • If we have a mother with genotype aa and a father with genotype Aa • The punnett square would look as follows:

20. 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)

21. 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?

22. 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?

23. 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?

24. 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?

25. 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%

26. Inheritance of Two Traits • Looking at the inheritance of two traits is called a dihybrid cross

27. 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

28. 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

29. 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

30. 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

31. 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?

32. 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?

33. 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?

34. 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?

35. 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

36. 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

37. 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%

38. Linkage • Linked genes are those found on the same chromosome

39. 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

40. 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

41. 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

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

43. 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

44. 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

45. Practice Problem • The allele for white flowers (R) is dominant, but it’s dominance incomplete • The allele for red flowers (r) is recessive

46. 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?

47. 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?

48. 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?

49. 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)

50. 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?