Selection

1
Lecture 20
Selection
2
Selection for quantitative traits
3
Selection for quantitative traits 1) Estimate
merit (BVs)
4
Selection for quantitative traits 1) Estimate
merit (BVs) 2) Determine accuracy of
estimation
5
Selection for quantitative traits 1) Estimate
merit (BVs) 2) Determine accuracy of
estimation 3) Predict response to
selection
6
Assessment of Genetic Merit
7
Assessment of Genetic Merit
Ancestors Sire Dam Sibs Sibs Indivi
dual (i) Progeny Future Descendants
8
Assessment of Genetic Merit
Every animal shares genes in common with animal i.
Ancestors Sire Dam Sibs Sibs Indivi
dual (i) Progeny Future Descendants
9
What building is at the East end of tower
road? 0.02 pts
10
Genetic Evaluation Examples
11
Genetic Evaluation Examples
-- combine all information weighted
appropriately for the source -- degree of
relatedness is important
12
Genetic Evaluation Examples
1) n records on one animal, i or a relative
13
Genetic Evaluation Examples
1) n records on one animal, i or a
relative 2) 1 record on each of q equally
related relatives
14
Bell Ranch, New Mexico
15
Lecture 20
Selection Estimating BVs
16
Genetic Evaluation Examples
1) n records on one animal, i or a
relative 2) 1 record on each of q equally
related relatives 3) pedigree index
17
Estimation of BVs
18
Estimation of BVs
-- obtained as a regression of a phenotypic
deviation
19
Estimation of BVs
-- obtained as a regression of a phenotypic
deviation Phenotypic deviation -- records
deviated from a mean
20
Estimation of BVs
-- obtained as a regression of a phenotypic
deviation Phenotypic deviation -- records
deviated from a mean Regression -- BV on
the phenotypic deviations
21
1) Records on Animal j
Want BV of animal i
(if own record j i)

22
1) Records on Animal j
(if own record j i)
Regression coefficient bBVi on Pj aij
n h2 1 (n - 1) r
23
1) Records on Animal j
(if own record j i)
Regression coefficient bBVi on Pj aij
n h2 1 (n - 1) r aij relationship of i
and j h2 heritability of the trait r
repeatability of the trait
24
1) Records on Animal j
EBVi bBVi on Pj ? (Pjk - ?k) n k
record number 1 to n
25
1) Records on Animal j
EBVi bBVi on Pj ? (Pjk - ?k) n k
record number 1 to n
Example 1 8 pups Mean 7 2 10
8 3 9 9
26
1) Records on Animal j
EBVi bBVi on Pj ? (Pjk - ?k) n k
record number 1 to n Special Case j i n
1 regression h2 EBVi h2 (Pi - ?)
27
1) Records on Animal j
EBVi bBVi on Pj ? (Pjk - ?k) n k
record number 1 to n Special Case j i n
1 regression h2 EBVi h2 (Pi - ?) --
Remember h2 proportion of total variation due
to variation in BVs --
28
1) Records on Animal j
As n increases the regression gets larger. h2
.25 r .50 aij 1
29
1) Records on Animal j
As n increases the regression gets larger. h2
.25 r .50 aij 1 n regression 1 .25
0
30
1) Records on Animal j
As n increases the regression gets larger. h2
.25 r .50 aij 1 n regression 1 .25
0 2 .330
31
1) Records on Animal j
As n increases the regression gets larger. h2
.25 r .50 aij 1 n regression 1 .25
0 2 .330 3 .375 4 .400 ? h2/r
32
1) Records on Animal j
As n increases the regression gets larger. h2
.25 r .50 aij 1 n regression 1 .25
0 2 .330 3 .375 4 .400 ? h2/r
.08
33
1) Records on Animal j
As n increases the regression gets larger. h2
.25 r .50 aij 1 n regression 1 .25
0 2 .330 3 .375 4 .400 ? h2/r
.08 .045 .025 .50 Important
34
Question

• Which Tompkins County water falls was used in the
  filming of the old Tarzan films?
• What is the name of the state park at the south
  end of Seneca Lake?
• Which of the following parks is the largest in
  acres Adirondacks, Yellowstone, Yosemite or
  Glacier?

35
Answers
Taughannock Falls
Watkins Glen State Park
Adirondacks
36
2) Records on q relatives
(q number of relatives)
37
2) Records on q relatives
(q number of relatives)
a) all q relatives are equally related to i
38
2) Records on q relatives
(q number of relatives)
a) all q relatives are equally related to
i b) all q relatives are equally related among
themselves
39
2) Records on q relatives
(q number of relatives)
a) all q relatives are equally related to
i b) all q relatives are equally related among
themselves i individual j one relative j
second relative
40
2) Records on q relatives
(q number of relatives)
a) all q relatives are equally related to
i b) all q relatives are equally related among
themselves i individual j one relative j
second relative
sire (i) 1 2 j j q q half sibs
41
2) Records on q relatives

Pj average of q relatives records
42
2) Records on q relatives

Pj average of q relatives records aij
relationship of i to any relative
43
2) Records on q relatives

Pj average of q relatives records aij
relationship of i to any relative ajj
relationship of j to any other relative
with a record
44
Regression for EBV
45
Regression for EBV
one record on each of q relatives bbvi on Pi
(aij/ ajj)q q ?
46
Regression for EBV
one record on each of q relatives bbvi on Pi
(aij/ ajj)q q ? where ?
(1/ ajj) - h2 h2
47

EBVi bBVi on Pj (Pj - ?)

48

EBVi bBVi on Pj (Pj - ?) Example PHS progeny
test of a male

49

EBVi bBVi on Pj (Pj - ?) Example PHS progeny
test of a male ajj 1/4 aij 1/2 aij
2 1 4 ajj ajj

50
regression h2 ? q 10 q
40 .10 .25 .50
51
regression h2 ? q 10 q
40 .10 39 .41 1.01 .25 .50
52
regression h2 ? q 10 q
40 .10 39 .41 1.01 .25 15 .80 1.45 .50

53
regression h2 ? q 10 q
40 .10 39 .41 1.01 .25 15 .80 1.45 .50
7 1.17 1.78
54
regression h2 ? q 10 q
40 .10 39 .41 1.01 .25 15 .80 1.45 .50
7 1.17 1.78 -- The more progeny, the
higher the regression.
55
regression h2 ? q 10 q
40 .10 39 .41 1.01 .25 15 .80 1.45 .50
7 1.17 1.78 -- The more progeny, the
higher the regression. -- The higher the h2, the
higher the regression.
56
3) Pedigree Index

57
3) Pedigree Index
EBVi 1/2 ( EBVsire i EBVdam i)
58
3) Pedigree Index
EBVi 1/2 ( EBVsire i EBVdam i) Remember ETA
1/2 EBV, so EBVi ETAsire i ETAdam i
59
Lecture 21
Accuracy
60
Accuracy
-- measures of how well the BV of an animal is
estimated
61
Accuracy
-- measures of how well the BV of an animal is
estimated rBV,EBV theoretical correlation
between BV and EBV
62
Accuracy
-- measures of how well the BV of an animal is
estimated rBV,EBV theoretical correlation
between BV and EBV aij bBVi on Pj
63
Accuracy
-- measures of how well the BV of an animal is
estimated rBV,EBV theoretical correlation
between BV and EBV aij bBVi on Pj --
Accuracy ranges from 0 to 1 and the higher the
value, the more accurate the estimate.
64
Repeated Records
65
Repeated Records rBV, EBV aij aij n
h2 1 (n - 1) r
66
Repeated Records rBV, EBV aij aij n
h2 1 (n - 1) r aij n
h2 1 (n - 1) r
67
Repeated Records
For n 1 gt aij h2
68
Repeated Records
For n 1 gt aij h2 h2 aij 1 .09 .3 .49
.7 individual
69
Repeated Records
For n 1 gt aij h2 h2 aij 1 1/2 .09 .3 .1
5 .49 .7 .35 individual full sib
or parent
70
Repeated Records
For n 1 gt aij h2 h2 aij 1 1/2 1/4 .09 .3
.15 .075 .49 .7 .35 .175 individual full
sib or half sib or parent grandparent
71
Accuracy n records on i itself rBV,EBV
aij nh2 1 (n - 1) r
Assume h2 .25, r .50, and aij 1.
72
Accuracy n records on i itself
Records Accuracy 1 .50
73
Accuracy n records on i itself
Records Accuracy 1 .50 2 .57
74
Accuracy n records on i itself
Records Accuracy 1 .50 2 .57 3 .61 4 .63
? .71
75
Accuracy n records on i itself
Records Accuracy 1 .50 2 .57 3 .61 4 .63
? .71
.07
76
Accuracy n records on i itself
Records Accuracy 1 .50 2 .57 3 .61 4 .63
? .71
.07 .04 .02
77
Accuracy n records on i itself
Records Accuracy 1 .50 2 .57 3 .61 4 .63
? .71
.07 .04 .02 from h2/r
78
Summary 1) Accuracy increases as n
increases.
79
Summary 1) Accuracy increases as n
increases. 2) Increases at a diminishing
rate.
80
Summary 1) Accuracy increases as n
increases. 2) Increases at a diminishing
rate. 3) Limit is aij h2 /r as n gt ?
81
3) Limit is aij h2 /r as n gt ? Note
82
3) Limit is aij h2 /r as n gt ? Note h2
?2BV / ?2P r (?2G ?2PE) / ?2P
83
3) Limit is aij h2 /r as n gt ? Note h2
?2BV / ?2P r (?2G ?2PE) / ?2P h2
?2BV r ?2G ?2PE
84
3) Limit is aij h2 /r as n gt ? Note h2
?2BV / ?2P r (?2G ?2PE) / ?2P h2
?2BV r ?2G ?2PE -- If ?2D ?2I ?2PE are
large relative to ?2BV limit is lower. --