Test-day fat to protein ratio as an indicator trait for sub-clinical ...

Test-day fat to protein ratio as an indicator trait
for sub-clinical mastitis in Canadian Holsteins
J. Jamrozik and L.R. Schaeffer
Centre for Genetic Improvement of Livestock
University of Guelph
INTRODUCTION
Mastitis is one of the most frequent and costly diseases in dairy cattle. Data on
health status of cows are not routinely collected in dairy populations and indirect
selection against mastitis utilizes mainly somatic cell scores (SCS) as a correlated trait.
Other indicator traits for mastitis used in selection indices for udder health are mammary
system conformation traits and milking speed. Test-day (TD) records from cows with
clinical signs of mastitis are not usually collected, thus genetic evaluation data for
production traits (including SCS) originates only from healthy cows and cows with subclinical
forms of this disease.
Bacterial infection of the mammary gland results in an increase of the
concentration of somatic cells in cow’s milk. De Haas et al. (2004) showed that cases of
clinical mastitis were significantly associated with an increase in SCS. High producing
cows are genetically more prone to udder infections (Carlen et al. 2004) and mammary
infection is associated with reduced milk yield on a TD basis (Windig et al. 2005, Lukas
et al. 2009).
Fat to protein ratio (F:P) may serve as a measure of cow’s energy balance
(Buttchereit et al. 2010). Cows in an extreme state of energy deficit in early lactation are
metabolically more stressed and show greater incidence of diseases such as mastitis.
Heuer et al. (1999) indicated that F:P was a risk factor for many diseases, including
mastitis. Windig et al. (2005) documented that both increased and decreased F:P resulted
in the increased risk of mastitis. The same authors showed that cows with short and
intensive peaks of SCS related to infections with environmental pathogens exhibited an
increase in F:P, whereas infections caused by contagious pathogens resulted in decrease
of F:P. Thus, patterns of changes in TD milk yield, F:P and SCS during lactation can
potentially be used to detect cases of mastitis in dairy cows.
Traits recorded on cows infected with mastitis (IM+) and those from healthy
cows (IM-) may exhibit different distributions. Detilleux and Leroy (2000) proposed a
finite mixture model for analysis of SCS in the absence of information regarding
infection status. In the mixture model, observations are assigned to two (healthy versus
infected cows) or more groups, based on probabilities estimated from the data. Mixture
models have been applied to analysis of SCS of US Holsteins (Boettcher et al. 2007) and
Danish Holsteins (Madsen et al. 2008). Mixture models could be more powerful when
more than one trait are used for assigning group membership. Jamrozik and Schaeffer
(2010) used a two-trait finite mixture model for a joint analysis of TD milk yield and SCS
in first lactation Canadian Holsteins.
Frequency of mastitis changes during lactation, with the largest proportion of
mammary infection cases occurring early after calving (Heringstad et al. 2003). Joint
1

distributions of milk yield, F:P and SCS may therefore also be different in different parts
of lactation.
The objectives of this research were to analyze first lactation TD milk yield, F:P
and SCS of Canadian Holsteins cows with a three-trait normal mixture random regression
model, allowing for heterogeneity of distributions in different parts of lactation. Genetic
parameters were estimated on lactational and daily bases, and distributions of data from
IM- and IM+ categories were characterized.
MATERIAL AND METHODS
Data
Canadian Holstein first lactation TD data with calving years from 1988 to 2007
were obtained from the Canadian Dairy Network. A small data set was selected by
random sampling of herds with minimum of 50 cows each, and with minimum of 7 TD
records per cow. This resulted in 214,813 TD milk (kg), F:P and SCS records on 25,950
cows. Each cow had all three traits recorded on a given TD. Days in milk (DIM) were
from 5 to 305. Daily averages with corresponding variances are plotted in Figures 1 - 3
for milk, F:P and SCS, respectively. The number of herd – test-day (HTD) classes was
23,984 and there were 80 levels of region – age – season of calving (RAS). Pedigree
data included 66,244 animals. The same edited data set was previously used by Jamrozik
and Schaeffer (2010) for fitting a two-trait mixture model.
DIM were split into 30 disjoint intervals: 5 – 15 DIM, and 29 intervals each of
length of 10 DIM for days from 16 to 305. Records were relatively well distributed across
DIM intervals as well as days in lactation. Number of TD records in the first DIM
interval was equal to 6731; the remaining intervals included from 5890 to 7610 records.
The 5 th and 305 th DIM had 503 and 508 TD records, respectively; the largest number of
records (805) was for the 228 th day of lactation.
Model
The finite mixture model assigns records of milk, F:P and SCS on a given TD into
one of the two components, depending on the unknown health status of the cows. Group
membership (healthy or infected) of the j-th record in the i-th DIM interval was defined
by a binary vector zi where zij = 0 (1) indicated a record from an IM- (IM+) cow. The
equation for the mixture model can be written following Ødegård et al. (2003) as:
yi = X0i 0 + Mzi X1i 1i + Zi a + Wi p + ei,
where yi = vector of observations (milk, F:P and SCS) in the i-th DIM interval, 0 =
vector of fixed effects common to all records in all DIM intervals, 1i = vector of fixed
effect corresponding to data from infected cows, a = vector of random animal additive
genetic effects, p = vector of random permanent environmental (PE) effects, ei = vector
of random residuals, Mzi = matrix with diagonal elements of zij, and X0i, X1i, Zi, Wi =
known incidence matrices. The fixed effects in 0 were HTD effects and regression on
DIM within RAS levels, and elements of 1i included mean differences between ‘sick’
and ‘healthy’ components for milk, F:P and SCS. Additive genetic and PE effects were
regressions on DIM; all regressions (fixed and random) were modeled with orthogonal
Legendre polynomials of order 4. Residuals of records on different TD were
uncorrelated. The conditional distribution of yi was assumed to be:
yi | 0, 1i, a, p, Ri, zi ~ N[ X0i 0 + Mz X1i 1i + Zi a + Wi p, Ri],
2

where Ri= (Ii - Mzi) Ri0 + Mzi Ri1; Ri0 and Ri1 are residual co-variance matrices for
IM- and IM+ records, respectively.
Proper normal distributions (mean = 0 and variance = 10,000) were assumed for
all fixed effects. Random effects were also a priori normally distributed, conditionally on
genetic and PE co-variance components. Elements of zi were assumed to be independent
and following the same Bernoulli distribution, Br(Pi), where Pi was the proportion of
IM+ records (stage-specific mixing proportion). Priors for co-variance components were
independent inverted Wishart distributions with minimal numbers of degrees of freedom,
and prior distributions for Pi were beta distribution with both hyper-parameters equal to
2.
Methods
Gibbs sampling scheme for the single-trait two-component mixture model
(Ødegård et al. 2003) was generalized for the multiple-trait scenario and a heterogeneous
data structure. All fully conditional distributions were: multivariate normal for location
parameters, inverted Wishart for co-variance components, Bernoulli for the group
memberships, and beta distributions for the mixing proportions. Single chain of 120,000
samples was generated; convergence of Gibbs chains was determined by visual
inspection of trace plots for selected parameters. All posterior inferences were based on
100,000 samples after burn-in.
Heritabilities, genetic and environmental correlations were estimated for the first
regression coefficient of the lactation curve. This coefficient determines the overall level
of lactation curves and is equivalent to the cumulative (or average daily) yield for a trait
across lactation (Jamrozik et al. 2002). Heritability of the regression coefficient was
defined as a ratio of genetic and the sum of genetic and PE variances, following the
Bayesian hierarchical TD model approach (Jamrozik et al. 2001). Heritabilities, genetic
and PE correlations between traits were also estimated for every day of lactation, as time
dependant parameters. In this case, the total daily phenotypic variance included a residual
component. Heritability of a Gaussian trait does not depend on a mean value of the trait.
For a trait following a mixture distribution, heritability depends on component-specific
variances, mixing proportions (P) and on mean values of mixture components. Residual
variances for the mixture (within each DIM interval) were therefore estimated following
Gianola et al. (2006) as:
2 e = PIM- 2 IM- + PIM+ 2 IM+ + b0PIM-PIM+,
where b0 was the estimate of mean difference between IM- and IM+ groups, PIM- ( 2 IM-)
and PIM+ ( 2 IM+) were proportion of records (residual variance) for healthy and infected
records, respectively. Genetic and PE components of variance were assumed
homogeneous across mixture components.
Results
Average lactation curves for milk and SCS followed typical shapes for these traits
(Figures 1 and 3). Lactation curve for F:P (Figure 2) was of a similar shape to SCS curve:
largest values on DIM immediately after calving, decrease towards the peak of lactation
for milk yield, and steady but slow increase with the progression of lactation. Daily
variation of F:P was more uniform than patterns of variances for the other two traits.
3

Proportion of TD records from cows infected with putative, sub-clinical mastitis
was 0.66 in DIM from 5 to 15 (Figure 4), decreasing to 0.19 in DIM from 36 to 45 and
staying relatively constant at this level, dropping to 0.13 at the end of lactation (Figure 4).
Posterior standard deviations for mixing proportions were 0.02 for the first DIM interval
and around 0.01 for the remaining intervals.
Average differences between IM+ and IM- groups and estimates of residual
variances by DIM interval are in Figures 5 – 7 for milk, F:P and SCS, respectively. Cows
infected with mastitis were characterized by smaller daily milk yield (up to 5 kg on DIM
from 5 to 15), larger F:P (up to 0.13 on DIM from 26 to 35) and larger SCS (up to 1.3 on
DIM from 16 to 25). Differences between mean values for mixture distributions were
relatively uniform in DIM intervals for milk and SCS. The effect of putative mastitis on
F:P different parts of lactation followed, in general, the shape of lactation curve for milk
yield.
Estimates of residual variances differed substantially between mixture
components for all traits (Figures 5 – 7). Residual variances for records from healthy
cows were smaller and more uniform across lactation than corresponding values for
mastitic cows. General shapes of the variance curves for IM+ categories were similar to
lactation curves for milk yield. Residual correlations between F:P and SCS in IM-
category were all positive and small (250) was
characterized by slightly negative genetic correlations between F:P and SCS. Daily
correlations for the PE effect among traits were small and mostly negative (Figure 11).
Milk and F:P were slightly positively correlated at the beginning of lactation (DIM

DISCUSSION
Changes in SCS and milk yield are well known indicators of mammary infection
in dairy cattle. Clinical mastitis is relatively easy to detect, as the milk or udder is
abnormal and systemic signs of a disease are present. In contrast, sub-clinical mastitis is
an infection that occurs without obvious clinical signs such as abnormal milk, udder
swelling or tenderness, and fever. Somatic cells consist mainly of immune cells that enter
the udder. When infection of the udder occurs, the number of immune cells increases
rapidly, as the immune system attempts to overcome the infection. Simultaneously, milk
yield decreases as the animal is under the stress of coping with infection. Once the
infection has been cleared, the SCC levels and the milk yield gradually return to normal
levels. Early lactation is associated with an energy deficit in a high producing dairy cow.
Feed intake does not compensate energy losses associated with milk production and a
cow enters a negative energy balance. An energy deficit leads to an increase fat synthesis
in the udder, and inadequate intake of carbohydrates can cause an insufficient protein
synthesis by ruminal bacteria resulting in a decrease of milk protein content (Butthereit et
al. 2010; after Gürtler and Schweigert, 2005). Thus F:P may be an easy tool to
differentiate between cows that can or cannot cope with the challenges of an early
lactation.
The mixture model for milk, F:P and SCS used in this study was an extension of a
two trait specification for milk and SCS applied to the same data by Jamrozik and
Schaeffer (2010). In addition to adding one more trait, the lactation length was split into
more intervals in the current study (30 vs. 4) allowing for more precise inferences,
especially at the beginning of lactation. Estimated mixing proportions were similar
between these studies with the exception of the extreme parts of lactation (the first and
last DIM intervals in the more dense partition). The pattern of distributions for milk and
SCS between mixture components was also in good agreement for both applications.
Sub-clinical mastitis is not a precisely defined trait. Diagnoses are subjective; they
are mostly based on the pre-assumed threshold level of SCS. In addition, an elevated SCS
does not necessarily mean the occurrence of mammary infection. Estimates of incidence
rates of sub-clinical mastitis are therefore rare and not precise. Other applications of
mixture models for SCS in dairy cattle indicated proportions of records from infected
cows ranged from 5% for the US Holsteins (Boettcher et al. 2007) to 30% for the Danish
Holsteins (Madsen et al. 2008). Simulation study of Ødegård et al. (2003) indicated
relatively low sensitivity (probability of correct classification of IM+ records) of the
single-trait two-component mixture model, ranging from 0.53 to 0.94. A little higher
specificity (probability of correct classification of IM- records) varied from 0.87 to 0.98,
depending on the simulation scenario and the assumptions of the fitted model. Boettcher
et al. (2005) verified classification properties of the finite mixture model applied to SCS
of Italian goats with bacteriological information on the mammary gland infection status.
The mixture model was able to classify correctly 60 and 48% of the healthy and infected
records, respectively. This was, as the authors concluded, slightly higher than would be
expected from random classification, but not enough for useful mastitis diagnosis.
Further studies seem to be needed.
Fat to protein ratio has received relatively less attention in genetic studies of dairy
cattle. Estimates of genetic parameters for this trait are scarce. Vos and Groen (1998)
estimated heritability of protein to fat ratio as high as 0.79 for Dutch Holstein Black and
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White cattle. Estimates of Meinert et al. (1989) for this trait were 0.31 for the part of
lactation from 40 to 100 DIM and 0.69 for the entire 305 d lactation for the same
population. Lower heritability of F:P (0.14) was estimated for Austrian Simmentals
(Gredler et al. 2006) and for Spanish Holsteins (0.19) (Peña, 2006). Genetic correlations
between milk yield and protein to fat ratio was 0.19 for the entire 305 d lactation and -
0.15 for DIM from 40 to 100 (Meinert et al. 1989), and 0.18 (Vos and Groen, 1998).
Estimates of phenotypic correlation between these traits ranged from 0.19 (Vos and
Groen, 1998) to 0.88 (Meinert et al. 1989). To our knowledge, estimates of correlation
between F:P and SCS have not been up till now a subject of any published study.
Producer-recorded data collection of clinical mastitis cases started in 2007 in
Canadian dairy herds, with the objective to develop genetic selection tools for resistance
to clinical mastitis. Selection index based on genetic evaluations of SCS and mammary
system conformation will likely continue to complement direct selection against clinical
mastitis. Test-day milk yield and F:P, especially at the beginning of lactation, seem to be
potential traits that could contribute to the accuracy of such an index, with the overall
goal of reducing mastitis incidence in Canadian dairy cattle.
CONCLUSIONS
A mixture model for TD milk, F:P and SCS allowed classification of the data into
two components: healthy and infected with putative, sub-clinical mastitis. Distributions
of data differed in means and variances between mixture components and across different
parts of lactation. Frequency of mastitic records was high immediately after calving and
decreased as lactation progressed. Records from infected cows had lower TD milk yield,
and higher F:P and SCS, as compared with healthy cows. Fat to protein ratio, easily
available, highly heritable and relatively independent from milk and SCS, could serve as
an additional indicator for indirect selection against mastitis in dairy cattle.
REFERENCES
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Boettcher P.J., Moroni P., Pisoni G., Gianola D. (2005) J. Dairy Sci., 88, 2209-2216.
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Livestock Production, August 13-18, 2006, Bello Horizonte, Brasil, Communication No.
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Table 1: Heritability (on diagonal), genetic (above diagonal) and permanent
environmental (below diagonal) correlations for the first regression coefficients (average
level) for milk, fat to protein ratio and SCS; posterior standard deviations are in brackets
Milk Fat : Protein SCS
Milk 0.48 (0.02) -0.30 (0.02) 0.14 (0.05)
Fat : Protein -0.12 (0.03) 0.71 (0.02) 0.04 (0.04)
SCS -0.12 (0.02) -0.13 (0.02) 0.17 (0.01)
Figure 1: Average daily milk yields and their respective variances
kg
35
30
25
20
15
10
1 51 101 151 201 251
10
301
DIM
mean variance
7
45
40
35
30
25
20
15
kg*kg

Figure 2: Average daily fat to protein ratios and their respective variances
ratio
1.35
1.3
1.25
1.2
1.15
1.1
1.05
1 51 101 151 201 251
0.01
301
DIM
mean variance
Figure 3: Average daily somatic cell scores and their respective variances
score
4.5
4
3.5
3
2.5
2
1.5
8
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
1 51 101 151 201 251
0.5
301
DIM
mean variance
3.5
3
2.5
2
1.5
1
ratio*ratio
score*score

Figure 4: Proportion (P) of records from cows infected with putative, sub-clinical
mastitis, by DIM interval
P
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
3
5
7
9
11
13
15
9
17
DIM interval
Figure 5: Differences in means between infected (IM+) and healthy (IM-) groups (Diff),
and residual variances (var) for IM- and IM+ for milk yield, by DIM interval
mean (variance)
25
20
15
10
5
0
-5
-10
1
3
5
7
9
11
13
15
P
17
19
DIM interval
21
19
23
21
25
23
Diff var (IM-) var (IM+)
27
25
29
27
29

Figure 6: Differences in means between infected (IM+) and healthy (IM-) groups (Diff),
and residual variances (var) for IM- and IM+ for fat to protein ratio, by DIM interval
mean (variance)
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
1
3
5
7
9
11
13
15
10
17
DIM interval
19
21
23
Diff var (IM-) var (IM+)
Figure 7: Differences in means between infected (IM+) and healthy (IM-) groups (Diff),
and residual variances (var) for IM- and IM+ for SCS, by DIM interval
mean (variance)
4
3.5
3
2.5
2
1.5
1
0.5
0
1
3
5
7
9
11
13
15
17
DIM interval
19
21
23
Diff var (IM-) var (IM+)
25
25
27
27
29
29

Figure 8: Residual correlation among milk yield (M), fat to protein ratio (F:P) and SCS
for healthy (IM-) group, by DIM interval
correlation
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
1
3
5
7
9
11
13
15
11
17
DIM interval
19
21
23
M-F:P M-SCS F:P-SCS
Figure 9: Daily heritability of milk yield (M), fat to protein ratio (F:P) and SCS, by DIM
interval
heritability
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1 51 101 151 201 251 301
DIM
M F:P SCS
25
27
29

Figure 10: Daily genetic correlations among milk yield (M), fat to protein ratio (F:P) and
SCS
correlation
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
1 51 101 151 201 251 301
12
DIM
M-F:P M-SCS F:P-SCS
Figure 11: Daily permanent environmental correlations among milk yield (M), fat to
protein ratio (F:P) and SCS
correlation
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
1 51 101 151 201 251 301
DIM
M-F:P M-SCS F:P-SCS