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Quantitative Genetics
The analysis of traits whose variation is determined by both multiple genes and environmental factors
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In quantitative genetics, you can often predict the underlying genotype from a given phenotype
T/F
False
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Qualitative trait
distinct phenotype observed, controlled by one locus and usually predictable from the genotype
examples: Mendelian inheritance, simple inheritance
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Quantitative Trait
- observed phenotype is controlled by many loci, and effects of each locus are continuous
- often environmental effects are large
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What does the phrase "purely additive" mean when referring to dominance/recessive traits?
- no dominance exists
- the phenotype trait is the cumulative effect of many loci
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Goals of Quantitative Genetics:
Determining how much of the trait is determined by environmental (nurture) vs genetic (nature) components
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QTL
- "quantitative trait loci"
- The underlying locus contributing to genetic variation
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In this image, what does 'a' represent?
'additive gene action'
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Using this image, finish the equation: 2a=
2a=G(Q2Q2)-G(Q1Q1)
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In this image, d measures dominance. What is the value of 'd' if the heterozygote is exactly intermediate to the two homozygotes?
d=0 if the heterozygote is in exact intermediate
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Additive gene action
When the hetero-zygote is the average of the recessive and dominant phenotype
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Complete dominance gene action
- Where the AA homozygote and Aa heterozygote have the same phenotype
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Rewrite this system of equations to solve via matrix algebra:
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- A is the matrix containing all the constant coefficients,
- u is a vector containing the unknown variables,
- v is the matrix product equals some different constant vector
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Write equivalent equations (using only symbols) for this matrix math:
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What is the trace of matrix A?
- Tr(A) is the sum of the elements of the main diagonal running from top left to bottom right of the matrix: Aii
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Properties of Matrix inversion:
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What is another name for a matrix where the determinant = 0?
- Singular matrix
- singular matrices are not invertible!
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What is a synonym for "singular matrix"?
- Rank deficient matrix
- There is linear dependency in the matrix
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What does 'rank' mean in matrix algebra?
- Rank is counting the number of linearly independent rows or columns.
- The minimum of those two thinks is the rank in the dimension of the matrix
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How do you do division in matrix math?
- there is no division, so matrix inverses play an important role to accomplish something analogous to division
- In the following equation we can solve the value of the vector x by multiplying both sides of the equation by A-1
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Epistasis
- circumstance where the expression of one gene is modified (e.g., masked,
- inhibited or suppressed) by the expression of one or more other genes
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If matrix A is a 6 x 7 matrix
And matrix B is a 7 x 3 matrix
What is the dimensions of the product of A*B?
B*A?
- AB= 6x3
- BA= NA!
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What is the product of multiplication of matrices A x B =C?
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What is required for a matrix to have an inverse?
full rank (dimensions of rows= dimensions of columns, and all columns are linearly independent)
Determinant of |A| != 0
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Define: Full rank
dimensions of rows= dimensions of columns, and all columns are linearly independent
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What does this symbol indicate? ⊕
Direct sum
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What is the direct sum of A ⊕ B?
- Resulting matrix size is the dimensions of A plus B with the original matrices on the diagonal
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What is the direct product of A ⊗ B?
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