Genetics Anton 10.16

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

Genotypes

A = dominant trait a = recessive trait

Genotypes A a

A = brown eyes a = blue eyes AA = Aa = aa = brown eyes blue eyes

Probability of Inheritance GenotypeProbability AA¼ Aa½ aa¼

Probability of Inheritance

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?

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

Example: Autosomal Inheritance

X-linked Inheritance Carries gene Does not carry gene

Probability of X-linked Inheritance AA A AA Aa a Aaaa

Probability of X-linked Inheritance Aa Aa AA AA

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.

Example 2: X-linked Inheritance Parents (A, AA) Offspring (A, AA)1 (A, Aa)0 (A, aa)0 (a, AA)0 (a, Aa)0 (a, aa)0

Example 2: X-linked Inheritance Parents (A, AA)(A, Aa) Offspring (A, AA)1 1/4 (A, Aa)0 1/4 (A, aa)00 (a, AA)0 1/4 (a, Aa)0 1/4 (a, aa)00

Example 2: X-linked Inheritance Parents (A, AA)(A, Aa)(A, aa) Offspring (A, AA)1 1/40 (A, Aa)0 1/40 (A, aa)000 (a, AA)0 1/40 (a, Aa)0 1/41 (a, aa)000

Example 2: X-linked Inheritance Parents (A, AA)(A, Aa)(A, aa)(a, AA)(a, Aa)(a, aa) Offspring (A, AA)1 1/40000 (A, Aa)0 1/401 0 (A, aa)0000 1/40 (a, AA)0 1/40000 (a, Aa)0 1/410 0 (a, aa)0000 1/41

Example 2: X-linked Inheritance

Example 2: X-lined Inheritance

Example 2: X-linked Inheritance