MBG 3060 Lecture Notes - Lecture 5: Zygosity
2 May 2018
School
Department
Course
Professor
Just as homozygosity increases as population size decreases, homozygosity
across loci in an individual increases as the ancestors of that individual are
more closely related.
Proportion of loci in an individual that have both alleles identical by
descent or state
•
OR proportion of individuals in a population whose alleles at a given
locus are identical by descent or state
•
X - a1
□
1/2 V - a1
!
X - a1
!
W - a1
□
1/2 Y - a1
!
A - a1a2
○
If FA=0,
•
--> Fx= (1/2)2+1+1 = (1/16)
Inbreeding Coefficient:
*see Inbreeding Path Coefficients video
Can generalize to n1generations between a parent and common
ancestor and n2generations between other parent and common
ancestor
•
Fx= (1/2)n1 + n2 +1(1+FA)
•
*as the pedigree gets more complicated, you need to take the pedigree apart
and look at each of the inheritance paths individually
*see course manual for pedigree and paths
•
E -C -B: n1= 2
○
E -A: n2= 1
○
Path 1 -Common ancestor E:
•
E -D -B: n1= 2
○
E -A: n2= 1
○
Path 2 -Common ancestor E:
•
F -D -B: n1 =2
○
F -E -A: n2= 2
○
Path 3 -Common ancestor F:
•
Fx= (1/2)2+1+1 + (1/2)2+1+1 + (1/2)2+2+1 = (5/32)
○
To find Fx, add up unique paths:
•
15.625% of the loci in X are likely to be homozygous by
descent or state
○
This also means that X is 15.625% more likely to be
homozygous at a specific locus
○
This means that indivual X is 5/32 or 15.625% inbred
•
Individuals may have several common ancestor
•
Each one contributes a separate probability that the allele in X are
copies of the same ancestral alleles
•
Sum of [ (1/2)n1+n2+1(1+Fcommon ancestor) ]
○
The total probability of alleles identical by descent and by state is:
•
A genetic relationship tracks the potential for individuals to have
alleles in common
•
Parent and child -0.5
○
Two children with same parents -0.5
○
Two children with the same mother/father -0.25
○
Grandparent and grandchild -0.25
○
Degrees of relatedness:
•
Inbreeding:
A measure of the proportion of the genome shared by X and Y
•
aAB = 1/2 (1 + FA)
○
aAC = 1/4 (1 + FA)
○
aBC = 1/2 (1 + FB)
○
A --> B --> C (direct relatives)
•
aBC = (1/2)2(1 + FA)
○
B <-- A --> C (collateral relatives)
•
Additive Relationship:
Probability both alleles are identical by descent
○
1/2 the additive relationship of the parents
○
Inbreeding coefficient = F
•
FD= 1/2 aBC = (1/2) (1/2)2(1+ FA)
○
Ex. D <-- B <-- A --> C --> D
•
Relationship vs. Inbreeding
To calculate inbreeding, follow all the paths through all the common
ancestors of the parents of the individual for whom you are calculating
inbreeding
To calculate relationships, follow all the paths through all the common
ancestors between the individuals you are calculating the relationships
between.
Establish birth order (A-B-C-D)1.
Make table2.
A B C D
A
B
C
D
Add parents above (use - or … for unknowns)
… … AB AB
A B C D
3.
Put a 1 in diagonal cells and additive relationships in a base
generation
4.
A B C D
A 1 0
B 0 1
C 1
D 1
Off-diagonal entries for row 1 are 1/2 entry in the row corresponding
to the column of the 1st parent + 1/2 entry in row corresponding to
2nd parent (copy to fill out 1st column)
5.
A B C D
A101/2(1+0) 1/2(1+0)
B 0 1
C1/2 1
D1/2 1
Go to next row and begin at diagonal, add 1/2 of the relationships
between parents
6.
A B C D
A101/2(1+0) 1/2(1+0)
B011/2 1/2
C1/2 1/2 11/2
D1/2 1/2 1/2 1
Tabular Method
Diagonal elements: ii = 1 + Fi
•
Off diagonal elements: ij = aij
•
Therefore,
aAD = (1/2) + (1/2)2
•
aAC = (1/2)
•
aBC= (1/2)
•
aCD = (1/2) + (1/2)2
•
aBD = (1/2) + (1/2)2
•
FD= 1/2 and aAC= (1/2)2
•
Example: B --> C --> D; C <-- A --> D
… … AB AC
A B C D
A101/2 3/4
B011/2 1/4
C1/2 1/2 1 + (1/2)(0)
= 1
3/4
D3/4 1/4 3/4 1+(1/2)(1/2)
= 5/4
*the quantity that is added to the diagonal elements of the table is 1/2 the
relationship between the individual's parents which is equal to the level of
inbreeding in the individual
Ex. Mating of Full Siblings
*see pedigree in course manual
… … AB AB CD CD
A B C D E F
A101/2 1/2 1/2 1/2
B011/2 1/2 1/2 1/2
C1/2 1/2 11/2 3/4 3/4
D1/2 1/2 1/2 13/4 3/4
E1/2 1/2 3/4 3/4 1+1/4 3/4
F1/2 1/2 3/4 3/4 3/4 1+14
Sum over all the paths from parents through all common
ancestors
○
FZ= Sum [ (1/2)n1 + n2 +1(1+FA) ]
○
Inbreeding:
•
Sum over all paths between x and y, both directly and through
common ancestors
○
'a'xy = Sum [ (1/2)n(1+FA)]
○
FZ= 0.5axy
○
Relationsihp:
•
Summary of Path Coefficients:
1 + FX= 1 + 1/2 aparents
FD= 0
aCD = 1/2
5. Individual Inbreeding & Relationships
Friday,*March*3,*2017
3:22*PM
Just as homozygosity increases as population size decreases, homozygosity
across loci in an individual increases as the ancestors of that individual are
more closely related.
Proportion of loci in an individual that have both alleles identical by
descent or state
•
OR proportion of individuals in a population whose alleles at a given
locus are identical by descent or state
•
X - a1
□
1/2 V - a1
!
X - a1
!
W - a1
□
1/2 Y - a1
!
A - a1a2
○
If FA=0,
•
--> Fx= (1/2)2+1+1 = (1/16)
Inbreeding Coefficient:
*see Inbreeding Path Coefficients video
Can generalize to n1generations between a parent and common
ancestor and n2generations between other parent and common
ancestor
•
Fx= (1/2)n1 + n2 +1(1+FA)
•
*as the pedigree gets more complicated, you need to take the pedigree apart
and look at each of the inheritance paths individually
*see course manual for pedigree and paths
•
E -C -B: n1= 2
○
E -A: n2= 1
○
Path 1 -Common ancestor E:
•
E -D -B: n1= 2
○
E -A: n2= 1
○
Path 2 -Common ancestor E:
•
F -D -B: n1 =2
○
F -E -A: n2= 2
○
Path 3 -Common ancestor F:
•
Fx= (1/2)2+1+1 + (1/2)2+1+1 + (1/2)2+2+1 = (5/32)
○
To find Fx, add up unique paths:
•
15.625% of the loci in X are likely to be homozygous by
descent or state
○
This also means that X is 15.625% more likely to be
homozygous at a specific locus
○
This means that indivual X is 5/32 or 15.625% inbred
•
Individuals may have several common ancestor
•
Each one contributes a separate probability that the allele in X are
copies of the same ancestral alleles
•
Sum of [ (1/2)n1+n2+1(1+Fcommon ancestor) ]
○
The total probability of alleles identical by descent and by state is:
•
A genetic relationship tracks the potential for individuals to have
alleles in common
•
Parent and child -0.5
○
Two children with same parents -0.5
○
Two children with the same mother/father -0.25
○
Grandparent and grandchild -0.25
○
Degrees of relatedness:
•
Inbreeding:
A measure of the proportion of the genome shared by X and Y
•
aAB = 1/2 (1 + FA)
○
aAC = 1/4 (1 + FA)
○
aBC = 1/2 (1 + FB)
○
A --> B --> C (direct relatives)
•
aBC = (1/2)2(1 + FA)
○
B <-- A --> C (collateral relatives)
•
Additive Relationship:
Probability both alleles are identical by descent
○
1/2 the additive relationship of the parents
○
Inbreeding coefficient = F
•
FD= 1/2 aBC = (1/2) (1/2)2(1+ FA)
○
Ex. D <-- B <-- A --> C --> D
•
Relationship vs. Inbreeding
To calculate inbreeding, follow all the paths through all the common
ancestors of the parents of the individual for whom you are calculating
inbreeding
To calculate relationships, follow all the paths through all the common
ancestors between the individuals you are calculating the relationships
between.
Establish birth order (A-B-C-D)1.
Make table2.
A B C D
A
B
C
D
Add parents above (use - or … for unknowns)
… … AB AB
A B C D
3.
Put a 1 in diagonal cells and additive relationships in a base
generation
4.
A B C D
A 1 0
B 0 1
C 1
D 1
Off-diagonal entries for row 1 are 1/2 entry in the row corresponding
to the column of the 1st parent + 1/2 entry in row corresponding to
2nd parent (copy to fill out 1st column)
5.
A B C D
A101/2(1+0) 1/2(1+0)
B 0 1
C1/2 1
D1/2 1
Go to next row and begin at diagonal, add 1/2 of the relationships
between parents
6.
A B C D
A101/2(1+0) 1/2(1+0)
B011/2 1/2
C1/2 1/2 11/2
D1/2 1/2 1/2 1
Tabular Method
Diagonal elements: ii = 1 + Fi
•
Off diagonal elements: ij = aij
•
Therefore,
aAD = (1/2) + (1/2)2
•
aAC = (1/2)
•
aBC= (1/2)
•
aCD = (1/2) + (1/2)2
•
aBD = (1/2) + (1/2)2
•
FD= 1/2 and aAC= (1/2)2
•
Example: B --> C --> D; C <-- A --> D
… … AB AC
A B C D
A101/2 3/4
B011/2 1/4
C1/2 1/2 1 + (1/2)(0)
= 1
3/4
D3/4 1/4 3/4 1+(1/2)(1/2)
= 5/4
*the quantity that is added to the diagonal elements of the table is 1/2 the
relationship between the individual's parents which is equal to the level of
inbreeding in the individual
Ex. Mating of Full Siblings
*see pedigree in course manual
… … AB AB CD CD
A B C D E F
A101/2 1/2 1/2 1/2
B011/2 1/2 1/2 1/2
C1/2 1/2 11/2 3/4 3/4
D1/2 1/2 1/2 13/4 3/4
E1/2 1/2 3/4 3/4 1+1/4 3/4
F1/2 1/2 3/4 3/4 3/4 1+14
Sum over all the paths from parents through all common
ancestors
○
FZ= Sum [ (1/2)n1 + n2 +1(1+FA) ]
○
Inbreeding:
•
Sum over all paths between x and y, both directly and through
common ancestors
○
'a'xy = Sum [ (1/2)n(1+FA)]
○
FZ= 0.5axy
○
Relationsihp:
•
Summary of Path Coefficients:
1 + FX= 1 + 1/2 aparents
FD= 0
aCD = 1/2
5. Individual Inbreeding & Relationships
Friday,*March*3,*2017 3:22*PM
Document Summary
Just as homozygosity increases as population size decreases, homozygosity across loci in an individual increases as the ancestors of that individual are more closely related. Proportion of loci in an individual that have both alleles identical by descent or state. Or proportion of individuals in a population whose alleles at a given locus are identical by descent or state. Can generalize to n1 generations between a parent and common ancestor and n2 generations between other parent and common ancestor. *as the pedigree gets more complicated, you need to take the pedigree apart and look at each of the inheritance paths individually. E - c - b: n1 = 2. E - d - b: n1 = 2. Fx = (1/2)2+1+1 + (1/2)2+1+1 + (1/2)2+2+1 = (5/32) This means that indivual x is 5/32 or 15. 625% inbred. 15. 625% of the loci in x are likely to be homozygous by descent or state.
