Genetic parameters for production traits and somatic cell ... - CGIL

GENETIC PARAMETERS FOR PRODUCTION TRAITS
AND SOMATIC CELL SCORE OF CANADIAN HOLSTEINS
WITH MULTIPLE TRAIT RANDOM REGRESSION MODEL
J.Jamrozik, L.R.Schaeffer and F.Grignola
Centre for Genetic Improvement of Livestock
Department of Animal and Poultrv Science
Universitv . of Guelph, Guelph. ON. Can&la. N 1G 2W 1
SUMMARY
Multiple trait random regression model was applied to test day records of milk. fat, protein
and somatic cell score in tlte first three lactations of Canadian Holsteins. Linear model for
each of 12 simuhaneously analysed traits included herd-test date (fixed), permanent
efivironment (random) and fixed and random regressions. with three covariates. Gibbs
sampling method was used to generate samples from marginal posterior distributions of 864
(co)variance components. Production traits and somatic cell score in first three lactations
were characterised in terms of genetic and environmental correlations on 3054 basis.
Examples of estimated genetic covariance functions for selected combinations of traits are
presented.
9
Keywords: test day e yields, random regression model. genetic parameters
INTRODUCTION
Random regression (RR) models have been suggested for genetic analysis of test day (TD)
yields (24h measurements) by Schaeffer and Dekkers (1994) because of their ability to model
a separate lactation curve for every animal. Single trait RR models were applied to first
lactation milk, fat and protein TD data with different functions for fixed and random
regressions (Jamrozik and Schaeffer 1997. Jamrozik et nl. 1997a. 1997b). In the simulation
study of Kistemaker (1997) RR models were significantly better than an analysis of 305d
gelds in terms of correlation between estimated and true breeding values.
changes occurring in Canadian milk recording systems will require an application of
multiple trait test day model in genetic evaluations for milk, fat, protein and somatic cell
score (SCS) TD records. In addition. analysing data from Werent lactations as separate traits
wit1 account for selection and culling on correlated traits both within and between lactations.
The objectives of this study were to estimate variance and covariance components of the
multiple lactation, multipIe trait RR model and to character& genetic aspects of dairy
production in the first three lactations of Canadian Holsteins.
MATERIAL AND METHODS
Data consisted of TD records on milk (kg), fat (kg), protein (kg) and SCS (on the lo& scale)
from the first three lactations of Canadian Holsteins from Ontario and Quebec. Two disjoint
subsamples of data were created by random selection of herds with at least 300 TD records.
All four traits were required to be recorded on each test day between 5 and 305 days in milk
(DIM). Cows had to have at least one first lactation TD record with their first calving before
January 1, 1993. Age at calving 3pas restricted to 18 - 68 months. Cows were assigned to one
of four subclasses for age at calving within lactations and td one of two seasons of calving
(September - February, March-August). Combined with region (Ontario, Quebec) this gave
48 region-age-season subclasses within lactation. A summary of the data is given in Table 1.

,
Tahlel. Characteristics of two subsets of Holstein data
Cows with records
Sires
Animals
TD records
Lact 1
Lact 2
Lact 3
Total
Herd-test date subclasses
Lact 1
Lact 2
Lact 3
Data I Data II
3297
884
10.876
27.196 25.785
20.149 17.337
13.466 11.648
60.8 I 1 54.770
3032 - 4703
3384 4627
3278 4063
Data was analysed by a multiple trait model in which TD milk. fat, and protein yields and
SCS in merent lactations were considered as different traits. The model equation was
assumed to be the Same for each parity - trait combination. For trait h in lactation n it was
yhtijkl = HTbi + &h&171 + Cahj&t, + Phnj + 4mtijll? wherf?
yhtbu is record. 1 on cow j made on day t within herd-test day effect i, for a cow belonging to
subclass k for region, age, and season of calving, Hm”i is fixed herd-test day effect, bhn)n are
fixed regression coefficients specific to subclass k, ah+ are random regression coefficients
specific to cow j, bj is random permanent environmental (PE) effect, ki~u is residual effect
for each observation? zt, are covariates. I assumed to be the same for both fixed and random
regressions.
Wilmink’s function (1987) was chosen to describe the shape of lactation curves. The function
is W(t) = wgto + wlztl + w2zt2 where ztO = 1, ztl = t, zt2 = exp(-O.O5t).
Let pj represent the 12 by 1 vector of PE effect for cow j with covariance matrix P. PE effect
was assumed to be constant for all DIM during lactation. The PE covariance matrix for all
animals was IQPP. For aj, the vector of 36 by 1 random regression coefficients for animal j, the
covariance matrix was G. AQPG was the genetic covariance matrix for all animals with A
being the additive relationship matrixThe residual covariance matrix between traits on the
same TD was I&. Different residual covariances were allowed for different lactations (n) and
time periods within lactation (t), defined as 5 to 45 DIM, 45 to 115 DIM, 116 to 265 DIM,
and 266 to 305 DIM. Residual effects on different DIM were uncorrelated both within and
between cows.
There were 666 different genetic (co)variances, 78 PE (co)variances and 120 residual
(co)variances to be estimated for the model. A Bayesian approach using Gibbs sampling was
taken to obtain the means of the marginal posterior distributions for all parameters of the
model and selected functions of these parameters. The method used was the generalisation of
Jamrozik and Schaeffer’s (1997) approach for the single trait case. Blocked sampling with
multivariate normal and inverted, Wishart distributions was used. A chain of 2 1,000 samples
was generated for each data set. The first 1000 samples were discarded as the burn-in period.
The mean effective sample size over all single chain (co)variances for the thinned samples
was 490 with a range from 30 to 6400 (average values for two data sets). The mean relative

squared difference between (co)variance estimates from two data sets was 3%. The resulting
parameters were therefore estimated based ou the samples from two data sets (40,000 samples
in total).
RESULTS AND DISCUSSION
There were 864 different (co)variance components estimated for the multiple trait RR model.
They could be used to describe different characteristics of dairy production traits and ‘SCS
within and between lactations. Traits could be expressed on a 305d basis, as part lactation
yields or as daily yields. Results presented in this paper are restricted to selected aspects of
dairy production during first three lactations..
Coefficients of genetic covariance function, and PE and residual (co)variances for milk yield
(kg) in the first three lactations are shown in Table 2. Estimates of (@variance components
differed between first and later lactations. Residual variances were largest at the beginning
and at the end of 3OSd interval. PE variances did not change significantly from first to later
lactations. (Co)variances for fat, protein and SCS showed similar pattern of behaviour
between and within lactations.
PE efkct was modelled as a constant value for all DIM in lactation. Using a function with
random regression coefficients to model this effect might change the partition of the total
variance into different components. Genetic covariance as we11 as genetic correlation
functions could be plotted for any parity-trait combinations thus allowing the analysis of the
pattern of genetic {co)variabilitv . between traits during the course of lactations. -
Table 2. Estimatei of (co)variances for random regression coefficients, PE effects and
residuals for milk yield (kg) in first three lactations of Canadian Holsteins
Lact 1 Lact 2 Lact 3
a0 a1 a2 a0 a1 a2 a0 a1 a2
ac, 20.55 hle-2 -22.64 40.27 -0.15 -41.83 47.03 -0.18 -52.64
a1 3.17e-4 4.97e-2 8.58e-4 0. I3 I .05e-3 0.16
a2 59.38 93.40 136.89
PE 4.03 5.51 6.45
es-45 5.95 10.55 16.42
%-1 15 3.97 6.62 8.45
el16-265 3.08 4.48 4.86
e266305 4.89 7.51 * 8.13
Table 3 contains the genetic (above diagonal) and PE (below diagonal) correlations between
traits on a 305d basis for milk, fat and protein yields, and on average daily basis for SCS, as
well as average daily genetic variances for all traits (diagonal elements). Mean daily genetic
variances tend to increase with lactation number. Larger diflerences were observed between
first and later lactations than between second and third lactation. Estimates of genetic and
environmental correlations folldwed the general pattern reported in other studies. Milk, fat
and protein were all positively and highly correlated within-lactation on the 305d basis with
the largest correlations between milk and protein yields, Within trait genetic correlations
between lactations were smaller than other reported estimates, especially for SCS (Mrode and

Swanson 1996). Genetic correlation between production traits and SCS were small and
positive (unfavourable) in first and negative in second and third lactations. This could be
explained as an effect of culling in the first parity on the basis of mastitis and production. All
within lactation environmental correlations between production traits and SCS were negative.
Multiple trait model applied in this study could allow for a comprehensive description of
genetic and environmental relationships between production traits and SCS in different
parities.
Estimates of (co)variances obtained in this studs will be used as parameters for multiple trait
random regression model for genetic evaluatioh of Holstein bulls and cows for production
traits and SCS in Canada.
Table3. Correlations (x100) for 305d yield traits and average daily SCS (genetic
correlations above diagonal, PE correlations below diagonal) and average daily genetic
variances for milk (M), fat (F), protein (P) (in kg) and SCS (S) in first (I), second (2) and
third (3) lactations (diagonal elements)
1M IF 1P 1S 2M 2F 2P 2s 3M 3F 3P 3s
1M 7.8 69 92 7 70 45 67 12 63 34 54 12
1F 84 0.009 79 1 42 68 55 IO 38 60 45 5
1P 95 89 0?006 6 62 50 71 14 56 42 60 8
1s -28 -20 -20 0.59 4 -2 2 48 4 2 4 34
2M 53 49 55 -18 13.9 76 94 -20 76 49 67 -4
2F 38 60 49 -10 85 ‘0.02 83 -25 57 75 61 -11
2P 48 51 56 -13 96 91 0.01 -19 73 9 76 -7
2s -12 -14 -12 39 -24 -23 -20 0.84 -15 -17 -14 48
3M 47 39 46 -12 51 38 48 -5 14.2 75 94 -20
3F 34 52 43 -5 43 57 50 -5 84 0.02 82 -25
3P 44 46 51 -8 51 48 57 -4 94 92 0.01 -20
3s -17 -9 -9 31 -21 -11 -14 53 -29 -22 -20 1.09
ACKNOWLEDGMENTS
The authors acknowledge the financial support of the Ontario Ministry of Agriculture, Food ,
and Rural Affairs, the Cattle Breeding Research Council of Canada; and the Natural Science
and Engineering Research Council
REFERENCES
Jamrozik, J., Kistemaker, G.J., Dekkers? J.C.M. and Schaeffer, L.R. (1997a) J. Dairy Sci.
(in print)
Jamrozik, J. and Schaeffer. L.R. (1997) J. Dairv Sci. 80:762-770.
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Kistemaker, G. J. (1997) PhD Thesis, University of GucIph.
Mrode, R.A. and Swanson, G.J.T, (1996) Anim. Breed. Ah. 64:847-857.
Schaeffer, L.R. and Dekkers, J.C.M. (1994) Proc. 5* WCGALP Guelph, Canada, l&443-
446.
Wilmie J.B.M. (1987) Livesf. Prod. Ski. 17:2 1 l-2 17.