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Genetics

Genetics. Anton 10.16. Mathematical concepts. Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability. Genotypes. Genotypes. A = dominant trait a = recessive trait. Genotypes. A. a. Genotypes. A = brown eyes a = blue eyes.

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Genetics

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  1. Genetics Anton 10.16

  2. Mathematical concepts • Eigenvalues and Eigenvectors • Diagonalization of a Matrix • Intuitive Understanding of Limits • Probability

  3. Genotypes

  4. Genotypes A = dominant trait a = recessive trait

  5. Genotypes A a

  6. Genotypes A = brown eyes a= blue eyes AA = Aa= aa = brown eyes brown eyes blue eyes

  7. Probability of Inheritance

  8. Probability of Inheritance

  9. Example: Autosomal Inheritance • A population of plants consists of some distribution of genotypes AA, Aa, and aa. • Each plant is fertilized with another plant of genotype AA. • What is the distribution of genotypes AA, Aa, and aa after n generations?

  10. Example: Autosomal Inheritance • Each plant is fertilized with another plant of genotype AA.

  11. Example: Autosomal Inheritance AA: Aa: aa:

  12. Example: Autosomal Inheritance where and

  13. Example: Autosomal Inheritance

  14. Example: Autosomal Inheritance Can you calculate ? Can you calculate ?

  15. Example: Autosomal Inheritance • If prove that .

  16. Example: Autosomal Inheritance Diagonalization of matrix Eigenvalues: Eigenvectors:

  17. Example: Autosomal Inheritance Eigenvalues: Eigenvectors:

  18. Example: Autosomal Inheritance

  19. Example: Autosomal Inheritance

  20. Example: Autosomal Inheritance

  21. X-linked Inheritance Carries gene Does not carry gene

  22. Probability of X-linked Inheritance A A A a A AA AA a Aa aa

  23. Probability of X-linked Inheritance A a A a A A A A

  24. Probability of X-linked Inheritance

  25. Example 2: X-linked inheritance In-breeding: • Begin with a male and female. • Select two of their offspring, one male and one female, and mate them. • Select two of the resulting offspring, one male and one female, and mate them. • Etc.

  26. Example 2: X-linked Inheritance

  27. Example 2: X-linked Inheritance

  28. Example 2: X-linked Inheritance

  29. Example 2: X-linked Inheritance

  30. Example 2: X-linked Inheritance Solve where

  31. Example 2: X-linked Inheritance Solve where

  32. Example 2: X-linked Inheritance

  33. Example 2: X-lined Inheritance

  34. Example 2: X-linked Inheritance

  35. Example 2: X-linked Inheritance Initial Parents , i.e. , then

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