R .A. Mrode et al. Livestock Production Science 65 2000 119 –130
121 Table 1
over all dairy breeds despite the lack of conformation
The probability of survival from lactation i to i 11 in the different
data. Secondly to estimate the association between
breeds
LS and SCC in some dairy breeds with a view to
Breed Probability of survival from lactation i to
proposing improvements to the National Index and
i 11
finally to report the application of the algorithm
1–2 2–3
3–4 4–5
.5
proposed by Ducrocq and Besbes 1993 to speed up the production of LS evaluations on a large national
Holstein Friesian 0.78
0.77 0.76
0.73 0.73
Ayrshire 0.76
0.76 0.73
0.71 0.71
data set.
Jersey 0.78
0.78 0.76
0.73 0.73
Guernsey 0.77
0.77 0.74
0.74 0.74
Shorthorn 0.76
0.75 0.73
0.72 0.72
2. Materials and method
range of LS for the HF breed, for instance, was from 2.1. Genetic correlations between LS and
1 lactation completed first lactation and then culled conformation traits using AYR data
. to 7.703 lactations completed 5th lactation and still
alive. To examine the relationship between LS and
Records for conformation traits obtained during conformation traits in the AYR breed, lactation
the first lactation were available on 8087 AYR cows records of heifers calving between 1976 and August
out of 120 063 with LS calculated from survival to 1990 were extracted from the files of Milk Recording
the 4th lactation. The analysis of this data set was Organisations MRO. The latter date was chosen to
therefore restricted to these 8087 cows with LS ensure all cows had the opportunity to complete four
calculated from actual survival and the conformation lactations. The actual number of lactations a cow has
traits. These were the daughters of 893 sires. The completed was determined by searching the MRO
structure of the data in terms of number of calvings files. A cow was deemed to have completed lactation
per year, number of herds and sires is given in Table n if her lactation n and all previous lactation records
2. A pedigree of three generations consisting of were found in the files Brotherstone and Hill, 1991.
18 875 animals was utilised in the multivariate Any cow which did not complete a qualifying
analyses. A total of 15 conformation traits were minimum 200 day lactation or transferred into a
available together with LS. It was not possible to non-milk recording herd, was considered not to have
carry out a single animal model multivariate analysis survived. The percentage of cows not completing a
on them all. Therefore four separate animal model qualifying minimum 200 day lactation is about 3
multivariate analyses, always including LS together within a lactation Pander, 1992.
with groups of closely associated conformation traits, LS, which represents the number of lactations
were carried out. The groupings were LS and body each animal had survived or was expected to survive,
given that the animal had completed a first lactation,
Table 2
was calculated for each cow on the basis of prob-
Distribution of cows, herds and sires per year of calving for the
ability of survival Brotherstone et al., 1997. The
Ayrshire data used to estimate genetic correlations between
probabilities of survival from lactations i to i 1 1 up
Lifespan and type traits
to the fifth lactation, estimated from completed
Year of calving No. of cows
No. of herds No. of sires
lactations for the AYR breed and other breeds
1982 49
17 29
considered later in the study, are given in Table 1.
1983 698
61 212
For instance, if a cow has completed n lactations but
1984 1283
91 318
has not had time to complete n 11 lactations, the LS
1985 1027
85 273
was calculated Brotherstone et al., 1997 as:
1986 1230
89 309
1987 1054
92 271
LS 5 n 1 p 1 p p 1 p p
p 1 ? ? ?
n n
n 11 n
n 11 n 12
1988 1182
95 275
1989 1302
97 261
Where p is the probability of survival to lactation
n
1990 262
71 102
n 11 of a cow that has completed lactation n. The
122 R
.A. Mrode et al. Livestock Production Science 65 2000 119 –130
traits stature, chest width, body depth and angulari- effects with age at first calving as a covariate for
ty, LS and rump, feet and leg traits rump angle, both traits. First lactation milk yield deviated from
rump width, rear legs side and foot angle, LS and the mean of contemporaries was fitted as a covariate
udder traits fore-udder attachment, rear udder at- only for LS. The number of records for LS and SCC
tachment, udder cleft and udder depth and LS and and number of sires represented are shown in Table
teat traits teat placement rear, teat placement side 3. A sire pedigree of three generations was utilised in
and teat length. the bivariate analysis for each breed.
The fixed effects for LS consisted of herd–year HY and month of first calving. Age at first calving
2.3. Prediction of breeding value for LS linear and quadratic and first lactation milk yield
deviated from the herd–year mean linear were Breeding values for LS were predicted in a
fitted as co-variables. The importance of adjusting bivariate best linear unbiased prediction BLUP
for milk yield is to ensure that the LS trait reflects analysis of 1 839 878 Holstein Friesian cows born
involuntary culling Dekkers, 1993. For the con- from 1986 to 1994. In the AYR, JER, Guernsey and
formation traits, the fixed effects were herd–classifi- Shorthorn breeds 156 639, 87 939, 56 886 and
cation visit HV and month of first calving. Age at 22 905 cows with observations respectively were
first calving and stage of lactation were fitted as analysed Table 4. The traits were LS and a
linear and quadratic co-variables. The multivariate phenotypic index INDEX of fore-udder attachment,
analyses were carried out using the VCE software foot angle, udder depth and teat length, which were
Groeneveld, 1993. most highly correlated with herd life Brotherstone et
al., 1998. The INDEX of four conformation traits 2.2. Genetic correlations between LS and somatic
was constructed by applying economic weights to the cell count
phenotypic linear information. Cows with conforma- tion information but lacking the opportunity to
Lactation records of heifers calving between 1986 complete a second lactation were included in the
and 1991 for HF and 1976 and 1991 for AYR and analysis but their LS designated as missing observa-
JER were extracted from MRO files. The last year tions. The total number of cows with observations on
for data extract was chosen to ensure all cows had both traits and those that had observations on only
the opportunity to complete four lactations. LS was one of the two traits are given in Table 4.
calculated for each cow as described in the previous A bivariate animal model BLUP was im-
section. plemented with a full pedigree relationship file with
First lactation geometric means of test day SCC missing ancestors assigned to groups identified by
’000 per ml for heifers calving from 1991 to 1998 date of birth, sex and country of origin. The only
were extracted from the MRO files. In the early random effect was an animal effect. The fixed effects
1990s the number of farmers recording SCC was for LS were as described in the previous section and
limited since it was a new and optional service, those for INDEX are the same as for the individual
consequently only few cows with LS had any SCC conformation traits in the multivariate analyses in
information. The bivariate analysis of SCC and LS Section 2.1. The genetic parameters used for the
was therefore based on a sire model including only sires with at least 20 daughters HF or ten daughters
Table 3
AYR and JER, with records for each of the traits.
Number of records and sires for Lifespan LS and Somatic Cell
For AYR and JER, sires with ten daughters only for
Counts SCC
SCC or LS but with at least one paternal half sib
Breed No. of sires
No. of records
with ten daughters for the other trait were included.
LS SCC
This implies an error covariance of zero in the
Holstein Friesian 526
434 217 216 465
bivariate analysis. The SCC data were transformed to
Ayrshire 337
23 582 3736
log basis to achieve a normal distribution. Herd–
e
Jersey 113
19 775 4046
year and month of first calving were fitted as fixed
R .A. Mrode et al. Livestock Production Science 65 2000 119 –130
123 Table 4
a
Means and standard deviations for Lifespan LS and total number of cows with observations for Lifespan, INDEX and both traits for each breed
Breed Total cows
Cows with observations for Lifespan
with observations LS Only
INDEX Both LS
Mean S.D.
only and INDEX
lactations Holstein
Friesian 1 839 878
1 382 130 253 179
204 569 4.0
2.4 Ayrshire
156 639 136 928
4555 15 156
3.7 2.5
Jersey 87 939
77 550 5043
5341 4.0
2.6 Guernsey
56 886 50 041
3339 3506
3.9 2.6
Shorthorn 22 905
21 669 392
844 3.8
2.5
a
INDEX, index of survival from fore udder attachment, foot angle, udder depth and teat length.
BLUP analyses for all breeds were those reported for missing observation, the missing value for the ith
the HF data S. Brotherstone, personal communica- trait y for the cow was replaced by its expecta-
im
tion. These were heritabilities of 0.06 and 0.36 for tion calculated as:
LS and the INDEX respectively and a genetic
k k
k
ˆ ˆ
correlation of 0.69. For the AYR breed, the conse- y
5 a 1 e
im im
im
quences of using HF parameters was verified by
k
ˆ ˆ
re-calculating the INDEX based on the genetic Where e
5 r r y 2 a , k 5kth round of itera-
im ij
ii jo
jo
ˆ correlations between conformation traits and LS
tion, a 5breeding value for the ith missing trait on
im
ˆ estimated in Section 2.1. The r between this INDEX
the untransformed scale, a 5breeding value for the
g jo
and LS was then estimated from a bivariate analysis jth observed trait on the untransformed scale, y 5
jo
using the same model and data as described in observed record of jth trait adjusted for solutions of
Section 2.1. Breeding values were re-calculated for fixed effects in the kth round of iteration, r , r 5
ii ij
AYR using these parameters and compared with residual variance for trait i and co-variance for traits
those from the HF parameters. i and j.
The adjusted RHS or estimated missing observa- 2.4. Computing strategy
tions if the cow has any missing records were then transformed to a canonical scale and solutions for
The computing strategy adopted involved iterating animals obtained in a univariate manner. As data
on the data such that solutions for all fixed effects were being read, adjusted RHS were accumulated for
and co-variables were obtained using a multivariate minor fixed effects. After all data have been read,
procedure, accounting for missing observations. Ani- solutions for minor fixed effects were obtained using
mal solutions were obtained by applying a canonical the adjusted RHS and the stored inverted coefficient
transformation to adjusted right hand side RHS. matrix. The iteration process was continued for all
The coefficient matrix for all minor fixed effects all fixed and animal effects until convergence was
fixed effects apart from HY and HV and co-vari- achieved.
ables was set up during the first round of iteration, The evaluations were published as predicted trans-
inverted and stored. The solutions for each level of mitting abilities PTAs, deviated from a fixed base.
HY and HV were obtained as each herd’s data was The base chosen was the average PTA of cows born
read in while adjusting for all other effects in the in 1990, the same definition as the current evaluation
model. To obtain solutions for animals, the RHS for system for production traits. The reliabilities of
each cow was adjusted for the current solutions of PTAs for bulls were calculated by the method
fixed effects and co-variables in the kth round of described by Brotherstone et al. 1998 based on
iteration if the record was observed. In the case of a standard selection theory.
124 R
.A. Mrode et al. Livestock Production Science 65 2000 119 –130
3. Results the conformation traits varied from 20.28 TL to
