Report to the Genetic Evaluation Board - September 2001
Correction of LPI Parent Average for inbreeding
depression on potential matings
Jalal Fatehi, Filippo Miglior and Paul Boettcher
Introduction
Accurate genetic selection programs identify animals with superior genetic
potential. Using genetically superior sires and reproductive biotechnologies (such as
artificial insemination, embryo transfer, embryo splitting, in-vitro fertilization and
embryo transfer) can disperse certain genotypes throughout the population and increase
the number of inbred or genetically similar animals. Inbreeding is caused by the mating
of relatives. Phenotypic performance and survivability decline due to inbreeding because
of decrease in heterozygosity and increase in frequency of deleterious recessive genes.
This phenomenon is defined as inbreeding depression. Smith et al. (1998) reported that
the relative net income adjusted for opportunity cost for fluid and manufacturing milk
price in USA registered Holstein cows was depressed by $24.43 and $21.78 per 1%
inbreeding. In a study done by Weigel and Lin (2000), using a computerized mate
selection program to control inbreeding, a decrease in inbreeding by 1.8 and 2.8%
increased lifetime profit by $37.37 and $59.77 in Holsteins and Jerseys, respectively.
Recently CDN has developed an inbreeding calculator, which is freely available
on the CDN web site. Given a sire and a dam, the inbreeding calculator computes the
inbreeding coefficient of the potential progeny and the progeny Parent Average for LPI.
The objective of this study was to estimate the inbreeding depression on the
genetic performance of Canadian Holstein cows in order to provide an LPI parent
average adjusted for the expected inbreeding depression.
Materials and Methods
Inbreeding depressions were calculated for the cow's LPI and its components.
Although the probability of getting superior offspring can be increased by mating parents
with superior breeding values, there is no control over the Mendelian sampling of genes
which actually determines the genetic makeup of the offspring. Therefore, in this study,
inbreeding depression was investigated on the basis of the Mendelian sampling effect. A
data set was created combining different information including cow, sire, and dam
proofs. All the records from the animals with unknown parents, and with missing values
for the traits were eliminated from the data. Records were restricted to Holstein cows
born from 1990 to 1995 (6 years) due to the highest number of test day records for
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Report to the Genetic Evaluation Board - September 2001
protein. Traits of interest were LPI, milk, fat and protein production, conformation,
capacity, mammary system, feet and legs, udder depth, herd life, somatic cell score, and
milking speed. Proofs for the traits from cows, sires, and dams were utilized for the
calculation of Mendelian Sampling terms on the basis of the following formula:
 Sire EBV for trait (X)  Dam EBV for trait (X) 
Mendelian Sampling for trait (X)  Cow EBV for trait (X)  

2


Calculated inbreeding coefficients were obtained for each cow by merging the
information provided in a file from Canadian Dairy Network (CDN). The total number of
cows, sires, and dams involved in this study were 222,685, 3,196, and 169,099,
respectively.
The analysis was performed using the GLM procedure in SAS and the following
model:
y    B  1XR  2 XF  e
where,
y = calculated Mendelian sampling for a trait in the analysis,
 = overall mean,
B = fixed effect of cow's birth year,
1 = linear regression of dependent variable y on reliability,
2 = linear regression of dependent variable y on inbreeding coefficient,
XR = continuous variable representing reliability,
XF = continuous variable representing inbreeding coefficient,
e = random residual.
The approach in calculating inbreeding depression was to investigate the changes
in average Mendelian Sampling caused by a 1% increase in inbreeding among the cows
born from 1990 to 1995 in this study.
The inbreeding coefficient was also fitted as a classification variable (5 classes as
shown in Table 1) to test the presence of any curvilinear effect of inbreeding depression.
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Report to the Genetic Evaluation Board - September 2001
Results and Conclusions
The levels of inbreeding by birth year for Canadian Holstein cows were presented
in Table 1. All the animals were partially inbred. The minimum, maximum, and average
inbreeding coefficient were 0.01%, 31.3%, and 3.9%, respectively. Most of the animals
(84%) were classified in the inbreeding level of 0 < F < 6.25.% The number of cows born
from 1990 to 1995 decreased in this level of inbreeding from year to year (Table 1.). In
comparison, the number of inbred animals with inbreeding greater/equal to 6.25%
increased considerably from year to year (from 8.2% in 1990 to 20.5% in 1995, Table 1.).
In a previous investigation on Canadian Holsteins (Miglior and Burnside, 1995) the
percentage of cows with inbreeding greater/equal to 6.25% slightly increased from 3.3%
in the 1971-75 period to 4% in the 1986-90.
Table 1. Distribution of cows by level of inbreeding (F) from 1990 to 1995.
Level of Inbreeding
(%)
1990
%
1991
%
1992
%
1993
%
1994
%
1995
%
All cows
%
F = 0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0 < F < 6.25
91.84
89.33
87.56
84.44
80.64
79.54
84.88
6.25 ≤ F < 12.50
7.84
10.10
11.75
14.77
18.55
19.53
14.41
12.50 ≤ F < 18.75
0.30
0.56
0.67
0.76
0.79
0.90
0.70
18.75 ≤ F < 25.00
0.00
0.00
0.01
0.02
0.01
0.01
0.01
F ≥ 25.00
0.02
0.01
0.02
0.01
0.00
0.02
0.01
38176
41763
45377
39870
222685
Number of cows
25625
31874
Descriptive statistics including mean and standard deviation of cow, sire, and dam
proofs for all the traits analyzed in this study are provided in Table 2. Mean values for
cow and sire LPI were similar and both were considerably higher than dam LPI. Average
cow indexes for production traits were slightly lower than sire proofs, but significantly
higher than dam indexes. This provides evidence of positive genetic progress for
production traits due to the selection of genetically superior sires and dams and planned
mating.
Mean, standard deviation, minimum, and maximum values for the Mendelian
sampling by trait are shown in Table 3.
Fitting the inbreeding coefficient as a classification variable indicated that the
effect of inbreeding depression was linearly proportional to the level of inbreeding.
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Report to the Genetic Evaluation Board - September 2001
Table 4 shows the effects of inbreeding on calculated Mendelian Sampling for all
traits analyzed, per 1% increase in inbreeding coefficient. Inbreeding depressions were
initially computed using a model accounting for inbreeding coefficient as a covariate.
These results were slightly lower for production traits than the results from the model
including classification effect of year of birth, and reliability and inbreeding coefficient
as covariates. The magnitude of inbreeding depression on somatic cell score and milking
speed was not significant (Table 4 & 5).
Values of inbreeding depression may seem low for all traits. However, values are
very close to those estimated in previous studies in Canadian and US Holsteins (Miglior
et al., 1995a; Miglior et al, 1995b; Smith et al., 1998). Those investigations analyzed
inbreeding depressions using animal model and regression of phenotypic values on
inbreeding coefficients. Results across investigation can be compared as % of SD of the
analyzed variable. Magnitude of inbreeding depression in the current study was 2% of
MS standard deviation for production traits, 1-2% for conformation traits and . 1% for
SCS and milking speed, and 2% for herd life. Same magnitude of inbreeding depression
was found in previously mentioned studies.
Results of inbreeding depression were then transformed from Mendelian
Sampling to the Parent Average scales for all traits, dividing the inbreeding depression by
the MS standard deviation and multiplying by the correspondent Parent Average standard
deviation. For example: inbreeding depression for LPI per 1% inbreeding was -5.37, SD
of MS and PA LPI were 265.18 and 444.13, respectively. Thus inbreeding depression on
LPI PA scale is: (-5.37 / 265.18)  444.13 = -9.00.
Table 2. Descriptive statistics for cows, sires, and dams genetic evaluations.
Trait
Cow
Sire
Dam
Mean
SD
Mean
SD
Mean
SD
-198.59
-259.89
548.55
639.78
-202.30
-118.11
664.34
784.20
-621.4
-700.93
550.8
638.72
Fat
Protein
-4.79
-7.31
24.39
18.70
1.60
-2.71
29.14
23.53
-19.84
-22.21
24.24
18.79
Conformation
Capacity
1.41
1.28
4.14
4.19
-0.71
-0.53
4.68
5.06
-0.08
0.68
4.31
4.46
Feet & Legs
Mammary System
1.07
0.65
3.66
4.00
-0.41
-0.60
5.00
4.74
0.48
-0.81
3.74
4.19
Udder Depth
SCS
-0.02
3.01
3.79
0.20
0.22
2.99
4.92
0.23
0.13
3.00
3.68
0.19
Herd Life
Milking Speed
3.01
69.30
0.12
3.77
3.00
69.21
0.16
4.93
2.98
69.07
0.12
4.09
LPI
Milk
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Report to the Genetic Evaluation Board - September 2001
Table 3. Descriptive statistics for calculated Mendelian Sampling terms and Parent
averages.
Mendelian Sampling
Trait
Mean
SD
Min
Parent Average
Max
Mean
SD
Min
Max
LPI
12.23
265.18 -1148.50
1526.00
-210.82
444.13 -2207.50
1739.50
Milk
21.98
319.65 -1418.00
1653.50
-281.87
516.72 -2633.50
2110.00
Fat
0.51
12.54
-56.50
81.50
-5.30
19.13
-81.50
86.00
Protein
0.69
8.97
-40.50
49.50
-8.00
15.35
-76.50
67.00
Conformation
0.02
2.12
-13.50
11.00
1.40
3.28
-15.00
13.00
Capacity
0.02
2.25
-13.00
10.50
1.26
3.25
-15.50
15.50
Feet & Legs
0.01
1.55
-8.50
8.50
1.07
3.16
-14.00
12.00
Mammary System
0.04
2.01
-11.50
10.00
0.61
3.17
-14.50
12.00
Udder Depth
0.03
2.15
-13.00
10.50
-0.05
2.86
-14.00
14.50
SCS
0.00
0.11
-0.44
0.58
3.00
0.15
2.40
3.66
Herd Life
0.01
0.08
-0.39
0.42
3.01
0.10
2.53
3.42
Milking Speed
0.11
1.80
-11.50
8.50
69.18
3.02
46.50
79.50
Table 4. Estimates for inbreeding depression when only inbreeding coefficient (covariate)
was in the model.
Dependent Variable
MS_LPI
Inbreeding Depression
Standard Error
t Value
Pr > |t|
-5.21903
0.22552
-23.14
<.0001
MS_Milk
MS_Fat
-7.47488
-0.28470
0.27171
0.01066
-27.51
-26.71
<.0001
<.0001
MS_Protein
MS_Conformation
-0.22072
-0.03224
0.00762
0.00181
-28.96
-17.85
<.0001
<.0001
MS_Capacity
MS_Feet & Legs
-0.04167
-0.02068
0.00191
0.00132
-21.81
-15.69
<.0001
<.0001
MS_Mammary System
MS_Udder Depth
-0.01691
0.01986
0.00171
0.00183
-9.91
10.87
<.0001
<.0001
MS_SCS
MS_Herd Life
0.00007
0.00211
0.00010
0.00007
0.73
29.53
0.4634
<.0001
MS_Milking Speed
-0.00266
0.00153
-1.74
0.0821
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Report to the Genetic Evaluation Board - September 2001
Table 5. Estimates for inbreeding depression when birth year (class effect), reliability
(covariate), and inbreeding coefficient (covariate) were in the model.
Mendelian Sampling
Parent
Average
Inbreeding
Depression
Inbreeding
Depression
Standard
Error
t Value
Pr > |t|
LPI
-5.37394
0.22159
-24.25
<.0001
-9.0004
Milk
-7.19020
0.27471
-26.17
<.0001
-11.6231
Fat
-0.27874
0.01086
-25.68
<.0001
-0.4252
Protein
-0.21662
0.00770
-28.14
<.0001
-0.3707
Conformation
-0.03289
0.00184
-17.83
<.0001
-0.0509
Capacity
-0.04270
0.00196
-21.83
<.0001
-0.0617
Feet & Legs
-0.02109
0.00135
-15.62
<.0001
-0.0430
Mammary System
-0.01796
0.00174
-10.29
<.0001
-0.0283
Udder Depth
0.01858
0.00188
9.90
<.0001
0.0247
SCS
0.00011
0.00010
1.09
0.2744
0.0001
Herd Life
0.00157
0.00007
21.49
<.0001
0.0020
Milking Speed
-0.00148
0.00157
-0.94
0.3449
-0.0025
Trait
On the basis of calculated inbreeding depression (Table 5), and 10% inbred
fictitious progeny, an example was generated to translate the results to a more
understandable format (Table 6). In terms of production, progeny performance calculated
from parental proof averages (PA) decreased by –4.3 kg and –3.7 kg for fat and protein
respectively, due to 10% inbreeding in progeny. Parent Average LPI, after being adjusted
for inbreeding depression, was 2114 (2204-90=2114). This was quite similar to the LPI
(2106) when it was computed from the current LPI formula, using the adjusted PA for
each individual trait in the LPI formula.
Table 6. Inbreeding depression on the performance of a 10% inbred fictitious progeny.
Inbreeding
Depression
Sire
Proof
Dam
Proof
Progeny
PA
Fat
-0.4252
70
50
60
-4.252
55.75
Protein
-0.3707
80
70
75
-3.707
71.29
Capacity
-0.0617
12
8
10
-0.617
9.38
Feet & Legs
-0.0430
11
9
10
-0.430
9.57
Mammary System
-0.0283
11
8
9.5
-0.283
9.22
Udder Depth
0.0247
0
0
0
0.247
0.25
Herd Life Rating
0.0020
3.2
2.8
3
0.020
3.02
Trait
Progeny
10% F
PA
adjusted
0.0001
2.8
3.2
3
0.001
3.00
Milking Speed Rating
-0.0025
70
78
74
-0.025
73.98
LPI
-9.0004
2612
1796
2204
-90.004
2114¥
2106§
Somatic Cell Score
¥
§
LPI adjusted (2204-90=2114)
LPI as product of all adjusted PA
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Report to the Genetic Evaluation Board - September 2001
Conclusion
Average inbreeding levels are rapidly increasing in the Canadian Holstein
population. In particular the percentage of cows with inbreeding level greater or equal to
6.25% has almost tripled from 1990 to 1995 (8 to 20%), suggesting that farmers have
increasingly fewer options to select unrelated bulls to mate their cows.
Inbreeding depression on LPI Mendelian Sampling was equal to –9 LPI points for
each 1% of inbreeding. This adjustment could be implemented in the CDN inbreeding
calculator.
References
Miglior, F., and Burnside E. B. 1995. Inbreeding in Canadian Holstein cattle. J. Dairy
Sci. 78: 1163-1167.
Miglior, F., Burnside E. B., and Dekkers J. C. M. 1995a. Non-additive genetic effects and
inbreeding depression for somatic cell counts in Holstein cattle. J. Dairy Sci. 78: 11681173.
Miglior, F., Burnside E. B., and Kennedy B. W. 1995b. Production traits in Holstein
cattle: estimation of non-additive genetic variance components and inbreeding
depression. J. Dairy Sci. 78: 1174-1180.
Smith, L. A., B. G. Cassell, and R. E. Pearson. 1998. The effects of inbreeding on the
lifetime performance of dairy cattle. J. Dairy Sci. 81: 2729-2737.
Weigel, K. A. and S. W. Lin. 2000. Use of computerized mate selection programs to
control inbreeding of Holstein and Jersey cattle in the next generation. J. Dairy Sci. 83:
822-828.
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