genetics anton 10.16. mathematical concepts eigenvalues and eigenvectors diagonalization of a matrix...
TRANSCRIPT
![Page 1: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/1.jpg)
Genetics
Anton 10.16
![Page 2: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/2.jpg)
Mathematical concepts
• Eigenvalues and Eigenvectors• Diagonalization of a Matrix• Intuitive Understanding of Limits
• Probability
![Page 3: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/3.jpg)
Genotypes
![Page 4: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/4.jpg)
Genotypes
A = dominant trait
a = recessive trait
![Page 5: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/5.jpg)
Genotypes
Aa
![Page 6: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/6.jpg)
Genotypes
A = brown eyes
a = blue eyes
AA =
Aa =
aa =
brown eyes
brown eyes
blue eyes
![Page 7: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/7.jpg)
Probability of Inheritance
Genotype ProbabilityAA ¼ Aa ½ aa ¼
![Page 8: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/8.jpg)
Probability of Inheritance
![Page 9: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/9.jpg)
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?
![Page 10: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/10.jpg)
Example: Autosomal Inheritance
• Each plant is fertilized with another plant of genotype AA.
![Page 11: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/11.jpg)
Example: Autosomal Inheritance
AA:
Aa:
aa:
![Page 12: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/12.jpg)
Example: Autosomal Inheritance
where and
![Page 13: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/13.jpg)
Example: Autosomal Inheritance
![Page 14: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/14.jpg)
Example: Autosomal Inheritance
Can you calculate ?Can you calculate ?
![Page 15: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/15.jpg)
Example: Autosomal Inheritance
• If prove that .
![Page 16: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/16.jpg)
Example: Autosomal Inheritance
Diagonalization of matrix Eigenvalues: Eigenvectors:
![Page 17: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/17.jpg)
Example: Autosomal Inheritance
Eigenvalues:
Eigenvectors:
![Page 18: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/18.jpg)
Example: Autosomal Inheritance
𝐷𝑛=[1 0 0
0120
0 0 0]𝑛
=[1𝑛 0 0
0 ( 12 )𝑛
0
0 0 0𝑛]=[ 1 0 0
0 ( 12 )𝑛
0
0 0 0]
![Page 19: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/19.jpg)
Example: Autosomal Inheritance
1
![Page 20: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/20.jpg)
Example: Autosomal Inheritance
![Page 21: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/21.jpg)
X-linked Inheritance
Carries gene Does not
carry gene
![Page 22: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/22.jpg)
Probability of X-linked Inheritance
A AA AA AA
A aa Aa aa
![Page 23: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/23.jpg)
Probability of X-linked Inheritance
A aA a
A AA A
![Page 24: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/24.jpg)
Probability of X-linked Inheritance
![Page 25: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/25.jpg)
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.
![Page 26: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/26.jpg)
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
![Page 27: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/27.jpg)
Example 2: X-linked InheritanceParents
(A, AA) (A, Aa)
Offspring
(A, AA) 1 1/4
(A, Aa) 0 1/4
(A, aa) 0 0
(a, AA) 0 1/4
(a, Aa) 0 1/4
(a, aa) 0 0
![Page 28: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/28.jpg)
Example 2: X-linked InheritanceParents
(A, AA) (A, Aa) (A, aa)
Offspring
(A, AA) 1 1/4 0
(A, Aa) 0 1/4 0
(A, aa) 0 0 0
(a, AA) 0 1/4 0
(a, Aa) 0 1/4 1
(a, aa) 0 0 0
![Page 29: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/29.jpg)
Example 2: X-linked Inheritance
Parents(A, AA) (A, Aa) (A, aa) (a, AA) (a, Aa) (a, aa)
Offspring
(A, AA) 1 1/4 0 0 0 0
(A, Aa) 0 1/4 0 1 1/4 0
(A, aa) 0 0 0 0 1/4 0
(a, AA) 0 1/4 0 0 0 0
(a, Aa) 0 1/4 1 0 1/4 0
(a, aa) 0 0 0 0 1/4 1
![Page 30: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/30.jpg)
Example 2: X-linked Inheritance
Solve where
![Page 31: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/31.jpg)
Example 2: X-linked Inheritance
Solve where
![Page 32: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/32.jpg)
Example 2: X-linked Inheritance
𝟎𝒏→∞
![Page 33: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/33.jpg)
Example 2: X-lined Inheritance
![Page 34: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/34.jpg)
Example 2: X-linked Inheritance
𝑥(𝑛)→[1 2 /3 1 /30 0 00 0 0
2 /3 1/3 00 0 00 0 0
0 0 00 0 00 1/3 2 /3
0 0 00 0 01/3 2/3 1
]𝑥(0)
![Page 35: Genetics Anton 10.16. Mathematical concepts Eigenvalues and Eigenvectors Diagonalization of a Matrix Intuitive Understanding of Limits Probability](https://reader033.vdocuments.us/reader033/viewer/2022061618/56649e235503460f94b1000d/html5/thumbnails/35.jpg)
Example 2: X-linked Inheritance
Initial Parents , i.e. , then