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A stochastic model for the derivation of economicvalues and their standard deviations for productionand functional traits in dairy cattleH. M. Nielsen a , A. F. Groen b , S. Østergaard c & P. Berg aa Department of Genetics and Biotechnology , Danish Institute of Agricultural Sciences,Research Centre Foulum , Tjele, Denmarkb Animal Breeding and Genetics group , Wageningen Institute of Animal Sciences,Wageningen University , Wageningen, The Netherlandsc Department of Animal Health , Welfare and Nutrition, Danish Institute of AgriculturalSciences, Research Centre Foulum , Tjele, DenmarkPublished online: 01 Feb 2007.
To cite this article: H. M. Nielsen , A. F. Groen , S. Østergaard & P. Berg (2006) A stochastic model for the derivationof economic values and their standard deviations for production and functional traits in dairy cattle, Acta AgriculturaeScandinavica, Section A — Animal Science, 56:1, 16-32, DOI: 10.1080/09064700600836786
To link to this article: http://dx.doi.org/10.1080/09064700600836786
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ORIGINAL ARTICLE
A stochastic model for the derivation of economic values and theirstandard deviations for production and functional traits in dairy cattle
H. M. NIELSEN1, A. F. GROEN2, S. ØSTERGAARD3 & P. BERG1
1Department of Genetics and Biotechnology, Danish Institute of Agricultural Sciences, Research Centre Foulum, Tjele,
Denmark, 2Animal Breeding and Genetics group, Wageningen Institute of Animal Sciences, Wageningen University,
Wageningen, The Netherlands, and 3Department of Animal Health, Welfare and Nutrition, Danish Institute of Agricultural
Sciences, Research Centre Foulum, Tjele, Denmark
AbstractThe objective of this paper was to present a model of a dairy cattle production system for the derivation of economic valuesand their standard deviations for both production and functional traits under Danish production circumstances. Thestochastic model used is dynamic, and simulates production and health in a dairy herd. Because of indirect effects betweentraits, the phenotypic levels of (related) traits can change as a result of genetic changes. Economic values for milk productionand body weight were 0.28 and �/0.76 t/kg per cow-year respectively. For incidence of milk fever, mastitis, retainedplacenta and laminitis economic values were �/402.1, �/162.5, �/79.0 and �/210.2 t/incidence per cow-year. The eco-nomic values for involuntary culling rate, stillbirth and conception rate were �6.66, �/1.63, and 1.98 t/% per cow-year,respectively and the economic value for days from calving to first heat was �/0.94 t/day per cow-year. Standard deviations ofeconomic values expressing variation in realised profit of a farm before and after a genetic change were computed using alinear Taylor series expansion. Expressed as coefficient of variation, standard deviations of economic values based on 1000replicates ranged between 0.07 (milk production) to 16 (retained placenta).
Keywords: Milk production, health traits, breeding objective.
Introduction
Modern dairy cattle breeding has increased produc-
tion levels successfully. However, the upward trend
in milk production per cow has been associated with
undesirable side-effects, such as an increase in
production diseases and reproductive problems
(Rauw et al., 1998). In order to avoid this deteriora-
tion of functional traits, a balanced improvement of
production and functional traits is required. In
Denmark, selection for functional traits has been
practised for several years. A total merit index is
used, and includes milk yield and several functional
traits, such as calving ease, fertility, diseases, and
longevity (Principles of Danish Cattle Breeding,
2001). However, economic values applied in the
breeding goal are not well documented. In addition,
reports of economic values for disease traits are
scarce and breeding goal definition is still of ongoing
interest (Groen et al., 1997).
Derivation of economic values for production
traits in dairy cattle has been thoroughly discussed
in the literature (e.g., Groen, 1989a). Including
functional traits in breeding goals complicates the
derivation of economic values, as many of these traits
are difficult to define and model in an appropriate
way. Also, there is growing public concern about
welfare and ethical issues related to farm animals
(Olesen et al., 2000). Objective methods are being
considered as the most appropriate method to derive
economic values when the production system can be
accurately described. Objective methods are based
on modelling, where equations along with defini-
tions, descriptions and assumptions represent the
behaviour of a production system (Groen et al.,
1997). Using a bio-economic model to derive
Correspondence: H. M. Nielsen, Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Box 5003, NO-1432 As, Norway.
E-mail: [email protected]
Acta Agriculturae Scand Section A, 2006; 56: 16�32
ISSN 0906-4702 print/ISSN 1651-1972 online # 2006 Taylor & Francis
DOI: 10.1080/09064700600836786
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economic values it is possible to examine the effect
of different prices, levels and sizes of the prod-
uction system (Groen et al., 1997). In addition, a
bio-economic model is an efficient tool to model
relationships between functional traits (e.g., repro-
duction and culling). Traditionally, deterministic
bio-economic models have been used to derive
economic values (e.g., Groen, 1989a).
Economic values are derived from the change in
profit of the farm brought about by a genetic change
in a given trait without changing the genetic level of
other traits (Groen et al., 1997). When economic
values are derived as the partial derivative of the
profit equation, genetic levels of other traits in the
breeding objective will not change. However, when
economic values are derived using a bio-economic
model as in this study, interactions between genetic
levels of traits must be zero in order to avoid changes
in genetic levels of other breeding goal traits.
According to Hazel (1943) the economic value of
a trait depends upon the amount by which profit
may be expected to increase for a unit of genetic
improvement in that trait. Profit is a function of
genetic and environmental factors. In earlier studies
concerning derivation of economic values, little
differentiation was made between genetic and phe-
notypic potential of individual animals. This as-
sumes that there is a one-to-one relationship
between genetic change and phenotypic expression,
which may not be the case (Vargas et al., 2002;
Quinton, 2005). Economic values should be derived
under optimal management (Goddard, 1983). En-
vironmental factors can be classified into permanent
(e.g., parity) or temporary effects (e.g., stage of
lactation and health status). Both permanent and
temporary effects interact with the genotype of the
animal and affect feed intake and feed apportioning.
Consequently, phenotypic expressions of traits are
influenced by environmental factors (Bryant et al.,
2005). For example, milk production capacity of a
cow can only be fully expressed at the phenotypic
level as long as the level of feed intake capacity is
high enough to secure sufficient energy to meet
potential milk yield (Vargas et al., 2002). Recently,
Quinton et al. (2006) found that the economic value
for survival depended on the phenotypic level of
litter size in pigs due to a non-linear interaction
between litter size and perinatal survival. Therefore,
the phenotypic expression of survival after a genetic
change was dependent on the phenotypic level of
litter size and a genetic change in survival did not
necessarily result in the same magnitude of change at
the phenotypic level. Therefore, it is important to
consider the level of related traits when deriving
economic values.
The objective of this paper is to present a
stochastic model for the derivation of economic
values and their standard deviations under Danish
production circumstances. This study builds on
a model (Sørensen et al., 1992; Østergaard et al.,
2000, 2003), which previously has been used
for decision support to study management effects
in a herd. However, this dynamic model simulates a
dairy cattle production system and health traits in
detail. In addition, by using a stochastic simulation
model, uncertainty of economic values expressing
variation in realized profit of a farm before and after
a genetic change due to variation in performance of
cows can be obtained.
Material and methods
The derivation of economic values was based mainly
on the existing SimHerd model (Sørensen et al.,
1992; Østergaard et al., 2000, 2003). A module
(SimProfit) was added to derive economic values
and to model breeding goal traits, which could not
be modelled in SimHerd. A description of the overall
model is given in this paper. However, results
presented are limited to traits modelled in SimHerd.
First, an overall description of the model and the
assumed farm characteristics are presented and the
applied profit equations are given subsequently.
Secondly, details on different traits in the profit
equations are given and the method used to derive
economic values is described.
Model
The normative approach was chosen because of the
possibilities of detailed modelling of the production
circumstances and the flexibility to investigate effects
of price changes, for example. The overall model to
derive economic values is given in Figure 1. The
SimHerd model is a dynamic (discrete, weekly time-
stepping) model, simulating production and state
changes of a dairy herd with additional young stock.
The SimHerd model was developed and validated
for Danish production circumstances (Sørensen
et al., 1992; Østergaard et al., 2000, 2003). An
animal at any given time is characterized by its age,
lactation stage, lactation number, actual body
weight, milk yield, pregnancy status, and disease
occurrence. All discrete events at the animal level
(e.g., heat detection, conception, diseases and in-
voluntary culling) are stochastic variables randomly
sampled from relevant distributions (see Sørensen
et al., 1992; Østergard et al., 2000), which introduce
variation among phenotypic performance of cows. In
a dynamic model, production of the herd is the
accumulation of state changes and production of
Stochastic model for traits in dairy cattle 17
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individual cows over time (Sørensen et al., 1992).
Genetic effects at the animal level are expressed at
the herd level through the realised phenotypic
expressions given at the herd level.
The number of heifer and bull calves at the farm is
controlled by a probability of birth of a heifer calf
and by the stillbirth rate in the herd. Heifer calves
are raised at the farm to be used as replacements.
The heifer enters the milking herd if the actual
number of cows in the herd is less than the
maximum capacity or if at least one cow has been
selected for culling. Surplus heifers for replacements
are sold at the age of calving. A replacement heifer
will be purchased if no heifers born within the herd
are available at the time of culling of a cow and the
herd size has reached the specified minimum. Herd
dynamics arise from state changes of the animals and
from variation in number of animals due to culling in
the herd. The culling strategy is controlled by herd
size (maximum number of cows in the herd), a
maximum number of days open (specified separately
for low and high yielding cows) and low milk yield
(specified separately for first, second and third parity
cows, respectively).
Genetic levels for milk yield, body weight, repro-
duction, culling, stillbirth and diseases are the basis
for phenotypic performance of cows in the SimHerd
model. Phenotypic performance of a cow is a
combination of genetic effects and environmental
components from the stochastic element of the
model. In addition, traits are related via non-linear
relationships (indirect effects). Change in genetic
level of traits is performed by independent changes
in level of each trait. However, due to the indirect
effects the final phenotypic outcome of (related)
traits can change when genetic changes are per-
formed. For example, genetic level for milk yield
partly determines potential feed intake, which also
influences phenotypic cow performance of body
weight. The phenotypic performance of cows and
input and output of animals from SimHerd are
entered into SimProfit. In SimProfit, calving perfor-
mance, temperament, milking speed and beef pro-
duction of bull calves are simulated deterministically
and these traits are uncorrelated. Input and output
from both SimHerd and SimProfit and economic
parameters are combined to give revenue and costs
per farm per year. Details on modelling of the
different traits are given in later paragraphs.
Farm characteristics and production system
An average Danish farm with regard to production
level, production system and management strategy
was chosen as the basic situation. The simulated
dairy farm represented a loose-house production
system with cubicles and a 6�/2 herringbone milking
parlour. Beef production from bull calves was
evaluated as an integrated part of the dairy cattle
production system, which is common practice in
Denmark. In 2000, the average farm size in Den-
mark was 70 milking cows with additional young
stock. In this study, maximum number of cows in the
herd was 72. Cows were inseminated until day 210
or day 168 after calving for high and low yielding
cows, respectively. After designation for culling, both
high and low yielding cows were latest culled at day
392 after calving. Voluntary culling thresholds of
cows were 25, 32, and 33 kg energy corrected milk
(ECM) per day as an average over weeks 1 to 24 after
TIFORPMISDREHMIS
stiart fo slevel citeneG
esae gnivlaC
tnemarepmeT
deeps gnikliM
)sevlac llub( noitacifissalc ssacraC
)sevlac llub( niag yliaD
scimonocE stsoc dna seuneveR
seulav cimonocE
setats woC
egA
rebmun noitatcaL
egats noitatcaL
sciteneg woC ecnerrucer esaesiD
yticapac dleiy kliM
,revef klim ,sititsam( ksir esaesid cisaB
)atnecalp deniater ,sitinimal
taeh tsrif ot gnivlac morf syaD
noitpecnoc fo ecnahC
thgiew erutaM
gnilluc yratnulovni fo ksiR
etar htribllitS
yticapac ekatni deeF
erocs noitidnoC ygetarts dreH
gnilluc yratnuloV
ygetarts gnideeF
eR p etarts noitcudor yg
cipytonehP
woc
ecnamrofrep
slaitnetop woC
+
tnemnorivnE
)scitsahcotS(
Figure 1. Overview of the model used to derive economic values.
18 H.M. Nielsen et al.
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calving for first, second, and later parities, respec-
tively.
Until 24 weeks after calving all milking cows and
culled cows were fed ad libitum the same total mixed
ration with a fill unit of 0.37 (volume per Scandina-
vian feeding unit). Later, cows were assigned to two
feeding groups according to their current milk yield.
High yielding cows after 24 weeks after calving
(ECM above 23 and 28 for first parity and later
parity cows) were fed a ration with a fill unit of 0.46.
This ration was also used for the dry cows, but these
were fed restrictively. Low yielding cows (ECM
above 18 and 22 for first and later parity cows) after
24 weeks since calving were fed a ration with a fill unit
of 0.55. Feeding rations and feeding groups for cows
might possibly change with increased yield levels of
cows. However, preliminary analysis showed that
the feeding rations and groups described above were
also optimal for cows at higher yield levels. Therefore
the same feeding plan and feeding groups before
and after a genetic change in milk yield were used.
Profit equations
Profit of the farm was calculated as:
P�R�C
where,
R�/revenues of the farm (t/year)
C�/costs of the farm (t/year)
Milk, beef production and sales of surplus heifers
provided the revenues of the farm. Revenue from
beef production came both from fattening of bull
calves and culling of cows. Beef revenue of culled
cows was determined by the live weight of culled
cows and price per kg live weight. Variation in
carcass classification was not considered. However,
differentiation was made for culled cows, which had
a slaughter value, and dead cows, for which the
farmer had to pay a disposal price (Daka, 2001).
Subsidy denotes price compensation paid to the
farmer due to the low market price on beef. This
price compensation was a specific amount per
slaughtered bull calf (SUBSBC) or per slaughtered
cow (SUBS) (Direktoratet for FødevareErhverv,
2000). The number of milking cows on the farm is
given as number of cow-years defined as all feeding
days divided by days in the year:
R�N�[(ECM�PECM)
�NSCOW�(SUBS�(BCOW�PBCOW))
�(NDCOW�PDCOW)
�NBC�(SUBSBC�RBCALV)
�RHEIF�PRHEIF] (1)
where,
N�/number of milking cows on the farm (cow-year)
ECM�/energy corrected milk (kg/cow-year)
PECM�/price per kg of energy corrected milk (t)
NSCOW�/number of slaughtered cows per cow-
year
BCOW�/average live weight per slaughter cow (kg)
PBCOW�/price of slaughter cow (t/kg)
SUBS�/subsidy per slaughtered cow (t)
NDCOW�/number of dead cows per cow-year
PDCOW�/cost per dead cow (t)
NBC�/number of bull calves finished per cow-year
SUBSBC�/subsidy per bull calf (t)
RBCALV�/revenue per bull calf per cow-year (t/
year)
RHEIF�/number of heifers sold per cow-year
PRHEIF�/price of mature heifer (t/heifer)
Farm costs were defined using the approach by
Groen et al. (1997):
C�CVC�CFC�CFF
where
CVC�/variable cow costs
CFC�/fixed cow costs
CFF�/fixed farm costs
CVC�N�(CONC�PCONC�ROUG�PROUG
�Ccalving�Cmastitis�Cmilkfever�Crplacenta
�Claminitis�Ctemper�Cmilking�OTHER
�AICOW�NRHEIF�PRHEIF
�NBC�CBC) (2)
where further,
CONC�/concentrate (Scandinavian feeding unit
(SFU)/cow-year, 1 SFU�/7.89 MJ NE)
PCONC�/price of concentrate (t/SFU)
ROUG�/roughage (SFU/cow-year)
PROUG�/price of roughage (t/SFU)
OTHER�/other costs (t/cow-year)
Cmastitis�/cost of mastitis (t/cow-year)
Cmilkfever�/cost of milk fever (t/cow-year)
Crplacenta�/cost of retained placenta (t/cow-year)
Claminitis�/cost of laminitis (t/cow-year)
Ccalving�/cost of calving ease (t/cow-year)
Cmilking�/cost of milking (t/cow-year)
Ctemper�/cost of temperament (t/cow-year)
AICOW�/insemination costs (t/cow-year)
NRHEIF�/number of replacement heifers per cow-
year
PRHEIF�/cost of replacement heifer (t/heifer)
CBC�/cost per bull calf (t/bull calf)
Variable costs (CVC) included costs of feed, dis-
eases, calving, milking, temperament, insemination,
replacement and costs of producing bull calves.
Stochastic model for traits in dairy cattle 19
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Costs of mastitis, milk fever, retained placenta and
laminitis per cow value were calculated as the cost in
t per incidence (Table I) multiplied by the number
of incidences per cow-year. Costs per incidence of
mastitis, milk fever and laminitis included labour,
veterinary treatment (fee and medicine) and dis-
carded milk (Danish Agricultural Advisory Centre,
2002), whereas costs for retained placenta only
included labour and veterinary treatment. Perma-
nent reduced milk yield and reduced feed intake was
not accounted for. Replacement costs included costs
of rearing all heifers born at the farm and cost of
purchased heifers. Bull calves from the milking cows
in the herd were kept and raised at the farm.
Therefore, revenues of selling newborn bull calves
and costs of purchasing newborn bull calves were not
included in the profit equations. Other costs
(OTHER) were mainly veterinary service, which
was not specified in the cost equation and cost of
milking control association (SJFI, 2000). Fixed cow
costs (CFC) included costs of labour, milking
parlour, electricity and housing and were based on
statistics from Economics of Agricultural enterprises
(SJFI, 2000). Prices in EURO (current value No-
vember 10, 2005: 1 t�/1.18 US$) used to derive
economic values are given in Table I. Average market
prices (2001) of milk (Danish Dairy Board, 2001),
beef (Danish Meat Board, 2002) and feed (LK,
2001) were used.
Traits
Data for cow performance were chosen to represent
an average Holstein cow in Denmark and were
supplied from the national cattle database (Bund-
gaard & Hoej, 2000). Economic values were derived
for 10 different traits. The traits were milk yield,
conception rate, days from calving until first heat,
stillbirth, incidence of mastitis, incidence of retained
placenta, incidence of milk fever, incidence of
laminitis, body weight, and involuntary culling rate.
Conformation traits were not included since they are
predictors for functional traits (e.g., leg conforma-
tion as predictor for laminitis). Therefore, most
conformation traits do not have a direct economic
value and should be included in the selection index
instead of in the breeding goal. Genetic levels of milk
yield, stillbirth, days from calving until first heat,
conception rate, involuntary culling rate, and body
weight are in Table I, whereas genetic levels for the
disease traits are in Table II (given as basic disease
risks). However, more traits were modelled to give
Table I. Applied prices (t) and genetic levels of traits before and after genetic change of 20%.
Abbreviation Value
Prices/costs
Price of energy corrected milk (t/kg) PECM 0.34
Price of culled cow (live weight) (t/kg) PBCOW 0.94
Subsidy (t/slaughter cow) SUBS 53
Price per dead cow paid by the farmer PDCOW 100
Price of concentrate (t/SFU) PCONC 0.15
Price of roughage (t/SFU) PROUG 0.13
Price of replacement heifer (t/heifer) PRHEIF 942
Cost of mastitis (t/incidence) COSTmas 131
Cost of milk fever (t/incidence) COSTmf 167
Cost of retained placenta (t/incidence) COSTrpl 48.4
Cost of laminitis (t/incidence) COSTlam 112
Labour price (t/hour) Plabour 15.5
Insemination cost (t/insemination) AI 14.8
Other costs (t/cow-year) OTHER 202
Fixed cow costs (t/cow-year) CFC 471
Fixed farm costs (t/farm/year) CFF 33647
Trait Level in basic situation Level after genetic change
Energy corrected milk (kg/cow-year)1 8340 10008
Stillbirth (%), first lactation 12 10
Stillbirth (%), later lactations 8 6
Days from calving to first heat2 35 28
Conception rate (%)2 60 72
Involuntary culling rate3 24 19
Body weight (kg/cow)4 630 756
1Milk yield per year for a cow in third lactation.2Average of all lactations.3% of involuntary culling in the herd per year.4Mature body weight for a cow in third lactation adjusted for foetus weight.
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performance of cows, heifers and bull calves to be
included in the profit equations (Equations 1 and 2).
A detailed description of all traits is given in the
following paragraphs.
Milk yield, body weight and feed intake capacity. Milk
yield of the cow was described by milk yield capacity,
milk yield potential and actual phenotypic milk yield
as described by Sørensen et al. (1992). Milk yield
potential at a certain stage of lactation was modelled
using an incomplete Gamma function (Wood,
1967). Milk yield capacity described the aver-
age predicted yield in energy corrected milk 1 to
24 weeks after calving for a third parity cow not
diseased. Average daily level of milk yield capacity
for a third parity cow was set to 33.4 kg, correspond-
ing to a lactation yield of 8340 kg ECM per cow-year
(see also Table I). For each individual cow, milk yield
capacity assigned at the time of birth was sampled
from a normal distribution with a mean correspond-
ing to the average genetic milk yield capacity in the
herd and a standard deviation of 2. Additionally, at
each calving a random deviation was sampled from a
normal distribution and added to the milk yield
capacity of the cow to create variation in milk yield
between lactations of the same cow.
Change in genetic level of body weight was
modelled by increasing mature weight (defined as
the weight of a mature cow with a body condition
score of 2). Mature weight of the cow was 630 kg.
Variation in actual expressed (phenotypic) body
weight for the cow was created through variation in
milk yield capacity and disease occurrence. Growth
potential was modelled using a Gompertz growth
function (Sørensen et al., 1992). Potential body
condition score (BCS) was simulated from a Gom-
pertz weight curve with body condition score of
3 (scored from 1 to 5) (Østergaard et al., 2003).
Actual BCS of the cow was calculated from simu-
lated actual body weight corrected for foetus weight
and from potential BCS. Feed intake capacity of the
cow was modelled using equations corrected for
parity, stage of lactation and weight at calving.
Potential feed intake was then calculated from feed
intake capacity and milk yield capacity as described
by Sørensen et al. (1992). From potential feed
intake, actual energy intake was calculated depen-
dent on feed composition. Next, energy require-
ments based on milk yield potential and growth
potential were calculated. Finally, actual energy
intake was compared with requirements based on
growth potential and potential milk yield to give
actual (phenotypic) milk yield and change in body
weight. In situations where available energy was
insufficient to meet milk yield potential and potential
growth, a rule for distribution between milk produc-
tion and growth was used to calculate actual
phenotypic milk yield and body weight. Details
regarding equations for distribution rules between
milk production and growth are described in Sør-
ensen et al. (1992).
Table II. Risk factors and effects of diseases.
Mastitis Milk fever Retained placenta Laminitis
Risk factors
Base risk1 (level in basic situation) 0.259 0.075 0.112 0.067
Base risk (level after genetic change�/�/20% from basic situation) 0.207 0.060 0.090 0.054
Parity 1 vs. parity 3, OR2 0.8 0.01 0.60 0.50
Parity 2 vs. parity 3, OR 0.9 0.25 0.85 0.75
Parity 4 vs. parity 3, OR 1.0 1.8 1.15 1.25
Same disease in previous lactation, OR 1.5 4.0 2.0 1.2
Threshold for high or low BCS3 4.0
High risk BCS vs. normal risk BCS, OR4 4.3
Milk yield potential, OR per kg above herd average 1.04 1.04
Milk fever in current lactation, OR 1.1 2.0
Lactation stage, a-parameter in gamma-distribution. 0.60
Lactation stage, b-parameter in gamma-distribution 86
Effects of diseases
Death, risk (%) 1 8 1
Risk of removal (%)5 4 2
1Base risk is defined as the risk for a cow in third lactation with average yield capacity and without any previous cases of diseases.2OR�/odds ratio, an OR of 0.8 means that the relationship between diseased and not diseased first parity cows is 0.8 times the relationship
between diseased and not diseased third parity cows.3BCS (body condition score) threshold used for grouping cows into high or low risk BCS.4The risk of a cow with BCS above the BCS threshold vs. the risk of a cow below the BCS threshold.5Risk of removal in the week where the cow fell ill given that the cow did not die from the disease.
Stochastic model for traits in dairy cattle 21
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Health, fertility, calving and survival traits. Health
traits were modelled using disease risks represented
by a logistic regression model as described by
Østergaard et al. (2000). Starting point is the
definition of a standard cow defined as a cow in
third lactation with average yield capacity and with-
out any previous case of diseases. Disease risk for the
standard cow is called the basic disease risk, the
basic risk being the intercept in the regression model.
For cows deviating from the standard cow (e.g.,
cows in second lactation and cows with milk yield
above average herd level), other risks were added to
the basic disease risk to give a total risk of each
disease. Other risks of diseases were dependent on
the trait under consideration (Table II) and were
modelled by odds ratios (OR). The total disease risk
is calculated as 1/[1�/((1/basic risk�/1)/PORixi)],
the ORi being the OR for each risk factor and xi a
value for each risk factor. Total disease risk for
mastitis for a first parity cow with milk yield capacity
2 kg above herd average is thus 1/[1�/((1/0.259�/1)/
(0.8*1.042))]�/0.232. If the total disease risk is
higher than a random number from a uniform
distribution, the disease is triggered. Parity as a risk
factor of laminitis was based on literature estimates
(Groehn et al., 1992). Milk fever was a risk factor for
both mastitis and retained placenta. Therefore, a
cow suffering from milk fever would have an
increased risk of developing both mastitis and
retained placenta. Indirect effects of diseases were
also increased risk of dying and risk of culling in the
week where the cow fell ill, given that the cow did
not die from the disease. Disease traits in the
breeding goal were defined as disease incidence,
but genetic changes were obtained by changing the
relevant basic disease risk (Table II).
Fertility traits included conception rate and days
from calving to first heat. Chance of conception and
showing heat were triggered stochastically from
average herd rate and occurrence for each cow
sampled from a distribution. Conception rate was
60% and number of days from calving until first heat
was 35. In addition to the farmers’ culling strategy
and the culling and death due to diseases, culling of
cows was controlled by a risk of involuntary culling
expressed as percentage of involuntary culling at the
farm per year. Involuntary culling in the herd did not
depend on voluntary culling in the herd or on
maximum herd size allowed. The trait involuntary
culling rate was modelled by varying the risk of
involuntary culling in the herd with a starting value
of 24%.
Different frequencies of stillbirth for first and later
parities were used. Stillbirth was modelled through
an average herd rate and occurrence for each cow
was sampled from a distribution. Stillbirths of cows
in first and later parities were 12% and 8%,
respectively. When performing the genetic change,
stillbirth rate for both first parity cows and later
parity cows was changed. Cost of calving ease
(Ccalving) was calculated treating calving ease as a
categorical trait with four classes (see Meijering,
1986) as given in Equation 3.
Ccalving�(F(t2�m)�F(t1�m))�cewh
�(F(t3�m)�F(t2�m))�cdifficult
�(1�F(t3�m))�cvethelp) (3)
where,
F(ti)�/cumulative distribution function of a stan-
dard normal distribution N(0,1) with thresholds ti,
i�/1,2,3
m�/mean
cewh�/cost of class ‘easy with help’
cdifficult�/cost of class ‘difficult’
cvethelp�/cost of category ‘difficult with veterinary
assistance’
Costs of calving differed according to degree of
farmer labour and veterinary assistance. Percentage
of cows was 75, 21.4, 2.3, and 1.3 (Bundgaard &
Hoej, 2000) and costs were 0, 4, 15.5 and 178t for
classes easy, easy with help, difficult and difficult
with veterinary assistance, respectively.
Workability traits. Two different workability traits
were considered, milking speed and temperament.
Costs were mainly derived from assumed labour
requirements associated with handling the cow.
Assuming an optimized system the milking costs
were derived based on the number of cows, the
handling time per cow and the milking time of the
cows. The milking time of the cow was dependent on
the milk production and the milk flow rate. Milking
speed as an average over lactation and parities was
2.3 l/min and the handling time per cow per milking
was assumed to be 0.5 min.
MILKCOST�PLABOUR
��
HTIME��
1�KGMILK
FLOWRATE
��
where,
MILKCOST�/milking costs (t/cow-year)
PLABOUR�/labour price (t/min)
HTIME�/handling time (min/cow)
KGMILK�/milk yield (l/cow)
FLOWRATE�/milk flow rate (l/min)
The cost of temperament (Ctemper) was modelled
using a threshold model with two classes of tempera-
ment (1�/nervous, 2�/normal). Handling costs of a
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cow in class ‘nervous’ were assumed to correspond
to 94 t/cow-year, whereas handling of cow in class
‘normal’ was assumed not to include costs. Percen-
tages of cows in temperament class 1 and 2 were 4.7
and 95.3, respectively (Bundgaard & Hoej, 2000).
Ctemper�(F(t1�m))�cnervous�(1�F(t1�m))
�cnormal
where,
F(t1)�/cumulative distribution function of a stan-
dard normal distribution with threshold t1cnervous, cnormal�/labour costs (t/cow-year) of tem-
perament class ‘‘nervous’’ and ‘‘normal’’ respectively
derived as labour time (hour/cow-year) times labour
price (t/hour)
Beef production from bull calves
Gain and classification represented beef production
characteristics for bull calves. Cost per produced
bull calf (CBC) was calculated as:
CBC�(1�MORTBC)
�((CFEED�CNONFEED)�FEEDDAYS)
CFEED�FEEDgain�PFEED
where,
MORTBC�/mortality of bull calves (%)
CFEED�/total feed costs (t/day)
PFEED�/price of feed (t/SFU)
CNONFEED�/non-feed costs (t/day)
FEEDgain�/feed requirements for gain (SFU/kg
gain)
Non-feed costs included veterinary treatment, la-
bour and miscellaneous (SJFI, 2000). Parameters
used to calculate cost of beef production are given in
Table III.
The number of days (FEEDDAYS) to feed the
calf was calculated as
FEEDDAYS�WSL � BWEIGHT
DAYGAIN
where,
WSL�/live weight at slaughter (kg)
BWEIGHT�/birth weight (kg)
DAYGAIN�/average daily gain (kg/day)
In Denmark, carcass classification of bulls is based
on the European classification system (EUROP)
(EEC, 1981). Carcasses are scored for form using
a 5-point scale (E,U,R,O,P) and 3 subclasses
(�/,0,�/) giving 15 different classes. However, owing
to very low frequency of animals in some classes, the
15 classes were merged into five classes. Average
revenue from beef production (RBCALV) depen-
dent on classification was calculated with a threshold
model with five classes of classification.
RBCALV� (F(t1�m))�pO�
�(F(t2�m)�F(t1�m))�pO
�(F(t3�m)�F(t2�m))�pO�
�(F(t4�m)�F(t3�m))�pP�
�(1�F(t4�m))�pP;
where,
F(ti)�/cumulative distribution function of a stan-
dard normal distribution with thresholds ti (I�/
1, . . . ,4)
PO�, PO, PO�, PP�, PP�/price per kg slaughter
weight of calf with classification class O�/, O, O�/,
P�/, P, respectively (Danish Meat Board, 2002)
Frequencies of bull calves in classes O�/, O, O�/,
P�/, P were 2.3, 17.9, 56.8, 20.7, and 2.3% and
prices were 2.22, 2.15, 2.09, 1.9, and 1.76 t/kg
slaughter weight. Slaughter weight was calculated by
multiplying live weight at slaughter (WSL) with the
dressing percentage (DPCT).
Economic values
Economic values were derived with a fixed number
of cows as basis of evaluation (Groen et al., 1997).
Profit was chosen as the interest of selection, because
usually the farmer decides which animals to use.
When deriving economic values, the model was first
run with all 10 traits at their basic levels (Tables I
and II) using 1000 replicates (1 basic situation).
Secondly, the model was run after changing the level
of each of the 10 traits one at a time by 20% from the
level in the basic situation. This gave 10 alternative
situations, which were each run using 1000 repli-
cates. Economic values for the 10 traits were derived
by comparing farm profit before (basic situation)
and after changing the genetic level of each trait
Table III. Biological parameters, prices and cost applied in beef
production from bull calves.
Parameter Abbreviation Value
Biological parameters
Average gain (g/day) (bull calves) DAYGAIN 1236
Live weight at slaughter (kg) WSL 450
Birth weight (kg) BWEIGHT 40
Mortality (%) MORTBC 7
Dressing percentage (%) DPCT 51
Feed requirements for gain (SFU/kg) FEEDgain 5.9
Prices and costs
Feed price (t/SFU) PFEED 0.16
Non-feed costs (t/day) CNONFEED 0.47
Subsidy (t/bull calf) 259
Stochastic model for traits in dairy cattle 23
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(alternative situation) from the basic situation. Each
simulation was run over a 10-year period. However,
to overcome the influence of the initial herd and to
allow the effect of management and production
system to be expressed, results for each simulation
were based on an average of the last five years of 10
years simulated.
Using a fixed number of cows as the basis of
evaluation, change in revenues and costs are gen-
erally due to the difference between marginal rev-
enue and marginal cost of production only, i.e., fixed
cow costs and fixed farm costs do not change (Groen
et al., 1997). The number of cow-years in each
alternative could differ from the number of cow-
years in the basic situation due to the stochastic
element of the model. Consequently, fixed costs per
cow varied as well. To account for the change in the
number of cow-years in the alternative situation, the
level of each trait was adjusted for number of cow-
years in the alternative situation (see Equation 4).
When deriving economic values, change in profit of
the farm was divided by the actual realized pheno-
typic change in the respective traits and not the
genetic change. For the disease traits this means that
the trait level was disease incidence and not basic
disease risk, which was used when performing the
genetic change.
EV�PROFITalt � PROFITbasic
LEVELalt � COWSalt � LEVELbasic � COWSbasic
(4)
where,
EV�/economic value (t/trait unit per cow-year)
PROFITalt�/farm profit (t/year) for the alternative
situation as an average of 1000 replicates
PROFITbasic�/farm profit (t/year) for basic situa-
tion as an average of 1000 replicates
LEVELalt�/level of trait for the alternative situation
as an average of 1000 replicates
LEVELbasic�/level of trait for the basic situation as
an average of 1000 replicates
COWSalt�/number of cow-years for the alternative
situation as an average of 1000 replicates
COWSbasic�/number of cow-years for the basic
situation as an average of 1000 replicates
Standard deviations of economic values were
computed using a linear Taylor series expansion,
where covariances and variances between parameters
in Equation 4 were accounted for. These standard
deviations represent variation in realized profit of the
farm due to variation in expression of cow perfor-
mance traits before and after a genetic change.
Unless specified otherwise, standard deviations are
the variation in economic values between two
randomly chosen replicates and not the inaccuracy
on the estimated economic values (standard errors),
which can be calculated by dividing by the square
root of the number of replicates.
Simulated scenarios
To describe the farm in terms of production para-
meters the model was first run with all traits at their
basic levels (Tables I and II). Secondly, using
incidence of mastitis as an example, economic values
were derived for different marginal changes (change
in basic risk of mastitis (Table II) of 5% to 50%).
Next, economic values were derived for 10 different
traits (milk yield, conception rate, days from calving
until first heat, stillbirth, incidence of mastitis,
incidence of retained placenta, incidence of milk
fever, incidence of laminitis, body weight, and
involuntary culling rate).
Results
Production parameters in the basic situation
After running the model with all traits at their basic
level, average milk yield of cows in the herd was
8519 kg ECM per cow-year, feed intake was 5560
SFU per cow-year and average body weight of
slaughter cows was 566 kg (Table IV). Number of
first incidence of mastitis, retained placenta, milk
fever and laminitis per cow-year were 0.32, 0.17,
0.10 and 0.07, respectively. The average productive
herd life was 961 days.
Marginal changes
With a marginal change of less than 20%, eco-
nomic values for mastitis varied from �/141.1 to
�/375.5 t/incidence per cow-year (see Table V).
However, from 20% change to 50% change the
economic values ranged from �/148.9 to �/168.4
t/incidence per cow-year. Standard deviations de-
creased with increasing marginal changes. With 5%
change and 20% change, standard deviations of the
economic values were 2860 and 682, respectively.
Because economic values for the disease traits were
unstable (the standard errors of the estimates were
high) with a change of less than 20% and because
the standard deviations of the economic values
depended on the size of the change, economic
values for all traits are represented with a 20%
change.
Production parameters after genetic change
After changing the genetic level of diseases by 20%
the simulation model gave a decrease in incidences
of mastitis and retained placenta with 0.07 and 0.03
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incidences per cow-year (see Table VI). For milk
fever and laminitis corresponding numbers were
0.02 and 0.01 incidences per cow-year.
Changing the genetic level for milk yield increased
milk yield in the herd by 1238 kg per cow-year.
Correspondingly, feed intake increased by 516 SFU
per cow-year (Table VI). The result of increased milk
yield was also a weight loss of 16 kg per cow-year.
The weight loss was due to the rule of energy
distribution between milk yield and growth, which
was used in situations where available energy was
insufficient to meet potential milk yield and growth.
By increasing the yield capacity of the cow, relatively
more energy was used for milk production and less
was available for gain. Likewise, increasing the
mature weight of the cow resulted in decreased
milk yield (Figure 2). This effect was seen when
available energy was insufficient to meet potential
milk yield and growth because relatively more energy
was used for gain.
Economic values and standard deviations
Changes in revenues and cost of the farm and
correspondingly economic values are given in Table
VII. The economic value for energy corrected milk is
from increased revenue from milk and increased feed
cost due to increased feed requirements. The in-
crease in genetic level of milk production resulted in
an increase in farm profit corresponding to 24,859 t
per year. The economic value per kg energy cor-
rected milk was 0.28 t per cow-year. Estimated
economic value of body weight was �/0.76 t/kg per
cow-year, and was mainly derived from increased
revenue from beef production of culled cows and
increased feed requirements. Due to indirect effects
Table IV. Simulated cow performance (mean, standard deviations and coefficient of variation) for the basic situation based on 1000
replicates.
Trait Mean Standard deviation Coefficient of variation
Number of cow-years 70.8 0.2 (0.003)
Energy corrected milk (kg/cow-year) 8519 63.9 (0.007)
Mastitis (incidence/cow-year) 0.32 0.03 (0.09)
Retained placenta (incidence/cow-year) 0.17 0.02 (0.12)
Milk fever (incidence/cow-year) 0.10 0.02 (0.2)
Laminitis (incidence/cow-year) 0.07 0.01 (0.14)
Feed intake (SFU/cow-year) 5560 29.4 (0.005)
Calvings per cow-year 1.2 0.02 (0.02)
Number of slaughter cows (farm/year) 25.1 2.0 (0.08)
Weight of slaughter cows (kg/cow) 566 7.4 (0.01)
Replacement rate (%/farm/year) 39.1 3.1 (0.08)
Dead cows (%/farm/year) 3.3 1.0 (0.3)
Herd life (days) 961 82.8 (0.09)
Stillborn calves (%/farm/year) 9.2 1.4 (0.15)
Number of heifers sold (farm/year) 11.3 2.5 (0.22)
Number of bull calves produced per year 44.1 2.1 (0.05)
Inseminations per cow-year 1.9 0.05 (0.03)
Table V. Economic values and standard deviations (S.D.) for incidence of mastitis with different magnitude of change from the level of
mastitis in the basic situation. Standard errors of estimated economic values (S.E.) based on 1000 replicates are given in parentheses.
Change in level of trait from
basic situation Mastitisalt1 Change in profit
Economic value
(t/incidence per cow-year)
Mean9/S.D. (S.E.)
�/5% 0.309/0.03 4119/2161 �/375.59/2860 (90.4)
�/10% 0.299/0.03 3209/2036 �/141.19/1327 (42.0)
�/15% 0.279/0.02 6029/2133 �/183.09/915 (28.9)
�/20% 0.259/0.02 7349/2125 �/162.59/682 (21.6)
�/25% 0.249/0.02 8879/2074 �/150.89/505 (16.0)
�/30% 0.229/0.02 10409/2081 �/148.99/442 (14.0)
�/35% 0.209/0.02 13649/2088 �/168.49/368 (11.6)
�/40% 0.199/0.02 14319/2102 �/154.69/322 (10.2)
�/45% 0.179/0.02 16299/2080 �/155.79/282 (8.9)
�/50% 0.159/0.02 17719/2098 �/153.79/259 (8.2)
1Level of trait (incidence/cow-year) and standard deviation in the alternative situation; basic situation 0.329/0.03 (0.09).
Stochastic model for traits in dairy cattle 25
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between milk yield, feed intake and body weight,
milk yield and consequently milk revenues were
reduced, when mature body weight was increased
(Figure 2).
Estimated economic value for involuntary culling
was �/6.66 t/% involuntary culling per cow-year.
Increased average herd life means that fewer replace-
ment heifers are needed, i.e., more heifers can be
sold and relatively more cows are in the older age
groups. Therefore, an increase in milk production
was seen. In addition, a small increase in incidence
of milk fever due to the risk factor of parity was seen.
For mastitis, retained placenta, milk fever and
laminitis economic values were �/162.5, �/79.0,
�/402.1 and �/210.2 t per incidence per cow-year,
respectively. The economic values for diseases arise
mainly from decreased costs associated with dis-
eases. However, for milk fever, a small increase in
average herd life was observed.
The economic value of conception rate of 1.98 (t/
% per cow-year) originates from decreased costs of
inseminations per cow and from increased milk
revenues due to increased average herd life (fewer
cows were culled because of failure to get in calf).
The economic value for number of days from
insemination until first heat was �/0.94 t/day per
cow-year. This value was from shorter calving
interval and decreased costs related to culling due
to more cows below the culling threshold of days
open. However, a small increase in insemination
costs was observed, because of lower chance of
conceiving for cows inseminated at an earlier stage
after calving. Reducing the stillbirth rate among
calves means that more heifer calves and bull calves
can be reared. In this model, heifers were reared at
the farm, and at calving they were either sold or
transferred to the milking herd. The price difference
between the revenue of a sold heifer and rearing the
heifer was limited. Hence, the economic value of
stillbirth was mainly determined from the profit in
producing bull calves.
Standard deviations of the economic values ran-
ged between 0.02 (milk production) to 2936 (lami-
nitis). The economic value for production traits had
the lowest standard deviation, whereas the highest
standard deviations were found among the func-
tional traits. The standard deviations of economic
values were from replicates of a farm with about 70
cows and express variation in realized profit due to
variation in expression of traits before and after a
genetic change. These standard deviations are the
variation in economic values between two randomly
chosen replicates and not the inaccuracy in the
estimate of the economic value (standard error).
On average over the 1000 replicates, the genetic
change was realized (e.g., mastitis incidence in theTab
leV
I.C
ow
per
form
an
cele
vel
sfo
rth
ebasi
csi
tuati
on
an
dm
arg
inal
chan
ge
aft
erch
an
gin
ggen
etic
leve
lof
20%
.
Ch
an
ge
inle
vel
of
Tra
itB
asi
cE
CM
Con
cep
tion
rate
D.
f.c.
tofi
rst
hea
tS
tillb
irth
Mast
itis
Ret
ain
ed
pla
cen
taM
ilk
feve
rL
am
init
is
Bod
y
wei
gh
t
Involu
nta
ry
cullin
g
Nu
mb
erof
cow
-yea
rs70.7
70.0
40.0
70.0
30.0
40.0
10.0
10.0
20
00.2
4
En
ergy
corr
ecte
dm
ilk
(kg/c
ow
-yea
r)8519.3
41238.2
512.0
621.2
71.5
42.4
22.0
8.2
82.1
�/2
03.0
744.2
5
Mast
itis
(in
cid
ence
/cow
-yea
r)0.3
2�
/0.0
10
0.0
1�
/0.0
2�
/0.0
70
00
00
Ret
ain
edpla
cen
ta(i
nci
den
ce/c
ow
-yea
r)0.1
70
0.0
10
00
�/0
.03
00
00
Milk
feve
r(i
nci
den
ce/c
ow
-yea
r)0.1
0�
/0.0
10.0
10
00
0�
/0.0
20
00.0
1
Lam
init
is(i
nci
den
ce/c
ow
-yea
r)0.0
70
0.0
10
00
00
�/0
.01
00
Fee
din
take
(SF
U/c
ow
-yea
r)5559.0
2516.2
83.0
39.9
�/0
.66
0.7
70.8
33.3
80.2
225.7
21.9
9
Wei
ght
of
slau
ghte
rco
w(k
g/c
ow
-yea
r)566.1
8�
/16.1
40.3
7�
/0.6
2�
/0.7
1�
/0.5
3�
/0.2
9�
/0.0
7�
/0.4
191.9
26.3
Dea
dco
ws
(%/f
arm
/yea
r)3.3
2�
/0.1
20.1
0.1
1�
/0.0
6�
/0.0
7�
/0.0
4�
/0.1
9�
/0.1
10
0.0
4
Rep
lace
men
tra
te(%
/farm
/yea
r)39.0
7�
/3.5
1�
/3.3
7�
/0.6
50.0
2�
/0.1
�/0
.06
�/0
.3�
/0.0
40.0
8�
/4.4
5
Her
dlife
(day
s)961.0
399.1
294.3
915.2
8�
/1.6
51.7
60.1
96.5
9�
/0.3
8�
/3.1
6127.8
4
Sti
llb
irth
calv
es(%
/farm
/yea
r)9.3
�/0
.11
�/0
.22
�/0
.1�
/1.9
60.0
3�
/0.0
6�
/0.0
6�
/0.0
90.0
4�
/0.2
Inse
min
ati
on
sper
cow
-yea
r1.8
80
�/0
.28
0.0
50
00
00
0�
/0.0
1
26 H.M. Nielsen et al.
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herd lower after the genetic change than in the basic
situation as illustrated in Figure 3a,b). Conse-
quently, average farm profit increased. Genetic
change in some replicates was not realized in the
herd and incidence of mastitis was higher than
average incidence of mastitis in the basic situation.
In some of the replicates, profit was therefore lower
after a genetic change than in the basic situation.
Discussion
The aim of this study was to present a model of a
dairy cattle production system for the derivation of
economic values and their standard deviations. The
model was suitable for the derivation of economic
values and standard deviations for both production
and functional traits in dairy cattle assuming Danish
production circumstances. However, more sensitiv-
ity analyses need to be performed for further
validation of the model. Additionally, this study
only considered one set of production parameters.
Because of uncertainty among future production
circumstances, scenario studies should show sensi-
tivity to change in production circumstances.
Model assumptions
Economic values were derived using a marginal
change of 20%. A change of 20% in trait level was
chosen because of unstable economic values (high
standard errors of the economic values) for disease
traits due to the stochastic element of the model (see
Table V). For other traits such as milk production, a
smaller change (e.g., 1%) was possible. Because
standard deviations and standard errors of the
estimated economic values depended on the size of
the change and to be able to compare standard
deviations between traits, the same change was
performed for all traits. Preferably, smaller changes
would have been performed. This would correspond
more closely to the actual genetic change obtained
after one generation of selection. A change of 20% in
milk yield can be obtained after 10 to 20 years of
selection (Danish Cattle Federation, 2003). Eco-
nomic values obtained in this study correspond to
economic values in the long run. However, for other
traits such as disease traits, genetic improvement is
at a lower rate (Danish Cattle Federation, 2003).
Therefore, economic values might be biased when
derived using a large change; the actual realized
change is small and economic values change with
magnitude of the change. In addition, for some traits
profit is a non-linear function of the trait level
(Dekkers et al., 1995). Performing a large change
for such traits might influence economic values.
Moreover, in practice some traits are restricted to
zero change by using a restricted index. However,
restricting changes in traits to zero change by using a
restricted index reduces selection response com-
pared to when the trait is given an appropriate
economic value derived from using a profit equation
(Gibson & Kennedy, 1990).
In principle, economic values should be derived by
dividing change in profit by genetic change. In earlier
studies, profit was divided by genetic change and the
number of cows before a genetic change (e.g.,
Groen, 1989b). In this study however, profit was
divided by the phenotypic realized changed (see
Equation 4). One of the reasons for dividing by
phenotypic change rather than genetic change was
because the equation used to derive economic values
differed from earlier studies. In this study, correction
500
550
600
650
700
750
800
850
900
950
1000
662 693 725 756 788 819 851 882 914 945
Body weight (kg/cow)
,)woc/g
k( thgie
w ydoB
01/)raey-woc/g
k( kli
M
Pweight Gweight Pmilk
Figure 2. Level of phenotypic milk yield (kg/cow-year), phenotypic weight (kg/cow-year) and genetic body weight (kg per mature third
parity cow) of cows with different changes of the genetic level of body weight.
Stochastic model for traits in dairy cattle 27
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Table VII. Revenues and costs (t/farm per year) for the basic situation and marginal costs and revenues after a change in level of trait by 20% and economic values (EV), standard deviation (SD)
and coefficient of variation (CV) for production and functional traits.
Trait Basic ECM
Conception
rate
D. f. c. to first
heat Stillbirth Mastitis
Retained
placenta Milk fever Laminitis Body weight
Involuntary
culling
Revenues
Milk (ECM) 202858 29622 496 594 146 85 71 273 68 �/4820 1739
Culled cows 14461 �/1720 �/1416 �/326 34 �/5 �/4 �/6 30 2213 �/1628
Bull calves 29369 �/743 112 395 620 58 13 �/31 33 �/69 �/426
Heifers 11056 1849 2610 921 778 �/18 27 163 95 �/52 2013
Total revenues 257744 28999 1809 1591 1574 115 104 385 218 �/2729 1702
Costs
Feed 55502 5381 83 134 23 15 15 55 8 2192 399
Mastitis 2961 �/115 61 70 30 �/593 26 23 21 31 23
Retained placenta 578 �/8 23 6 �/1 �/5 �/116 �/13 �/13 0 16
Milk fever 1195 �/94 114 36 �/16 �/9 �/13 �/252 �/13 30 123
Laminitis 581 �/2 23 6 0 3 �/3 �/1 �/115 �/5 1
Temp. 313 0 0 0 0 0 0 0 0 0 1
Milking 7646 4 7 3 4 1 1 3 1 0 22
Insemination 1967 7 �/286 53 6 2 2 4 3 0 �/5
Calving 393 �/9 1 5 0 0 0 �/1 0 0 �/6
Replacement 37271 �/484 358 493 803 �/82 �/13 �/35 80 �/2 �/978
Other 14287 8 15 6 8 2 2 5 1 1 48
Bull production 22460 �/568 86 302 474 44 10 �/24 25 �/53 �/326
Total var. costs 145153 4120 485 1114 1330 �/624 �/89 �/236 �/1 2194 �/682
Fixed cow costs 33336 20 34 14 18 4 4 12 3 2 112
Fixed farm costs 33647 0 0 0 0 0 0 0 0 0 0
Total farm costs 212136 4139 519 1129 1348 �/619 �/85 �/224 2 2196 �/570
Profit 45608 24859 1290 463 226 734 190 609 216 �/4925 2271
Change in level of trait 1238.25 9.1 �/7 �/1.96 �/0.07 �/0.03 �/0.02 �/0.01 91.92 �/4.90
Change in cow-years 0.04 0.07 0.03 0.04 0.01 0.01 0.02 0 0 0.24
EV1 0.28 1.98 �/0.94 �/1.63 �/162.5 �/79.0 �/402.1 �/210.2 �/0.76 �/6.66
SD 0.02 4.5 6.0 21 682 1249 2012 2936 0.55 6.4
CV 0.07 2.3 6.4 12.9 4.2 15.8 5.0 14.0 0.72 1.0
1t/trait unit per cow-year.
28
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number of cow-years before and after a genetic
change could differ due to the stochastic element
of the model (number of cow-years was multiplied
by trait level). Phenotypic levels of traits were
defined per cow-year, whereas definition of genetic
trait levels differed between traits but was for most
traits defined for an average third parity cow.
Secondly, genetic changes for the disease traits
were performed at the underlying level (basic disease
risk). By using phenotypic outcome of the model in
the equation, the economic values were expressed on
the preferred scale (per disease incidence). In
principle, phenotypic change should correspond
closely to genetic change when using 1000 replicates.
Dividing by phenotypic change rather than genetic
change would then not influence economic values.
However, dividing by phenotypic change rather than
genetic change might have influenced the economic
value for milk yield because the increase in the
phenotypic level of milk yield per cow-year did not
correspond to the increase at the genetic level. This
was due to indirect effects where feed intake capacity
of the cow limited expression of genetic milk yield
capacity of the cow, and to herd effects such as age
structure of cows because genetic level was expressed
as milk yield per third parity cow per year, whereas
phenotypic level of milk in the herd was expressed
per cow-year.
Indirect effects influenced the economic values for
both body weight and milk production where the
economic weight for body weight was more negative
than expected due to feed intake as an indirect effect.
Increasing milk production decreased the average
weight of culled cows, because feed intake capacity
was limiting the phenotypic expression of both
weight and milk yield potential of the cow. This
effect was, however, counterbalanced with the ex-
tended herd life of the cows, which decreased
replacement costs. Prior studies estimating eco-
nomic values for dairy cattle production traits used
models where feed intake was determined only by
nutrient requirements for maintenance and produc-
tion. However, in the model presented by Vargas et
al. (2002), performance of the cow was dependent
on the genetic potential, feed availability and feed
intake capacity. This was also the case for the model
presented in the current study, which had an
influence especially on the economic value for body
weight.
The indirect effects applied in this study were the
main reason for the high economic value for milk
fever. The model included underlying risks for
getting a disease, where some of those risks were
the risk of having another disease. For example, milk
fever was specified as a major risk factor for mastitis
and retained placenta. Indirect effects of diseases
were also increased risk of dead cows. Therefore,
reducing the incidence of milk fever at the same time
increased average herd life through reduced invo-
luntary culling and death of cows.
In the model, the farmer’s replacement policy was
determined by a threshold for low yield and a
threshold for maximum number of days open. These
voluntary cullings were not changed after changing
the genetic level of milk yield and conception rate in
the herd. A change in genetic level of those traits
might result in a change in the optimum voluntary
replacement rate. Theoretically, the production
system must be optimal in the basic situation and
should be re-optimized after a genetic change.
However, Dekkers (1991) found less than 1% bias
in economic values for milk yield, involuntary culling
and conception rate when the policy optimum for
the level of trait before a genetic change was also
used after a genetic change. Failing to change culling
thresholds might be increasingly important in this
study due to the indirect effects and the large change
performed when deriving the economic values. For
example, increased genetic level of milk yield influ-
enced herd life of cows because voluntary culling of
0.20 0.24 0.28 0.32 0.36 0.40 0.44
(a)
0.15 0.19 0.23 0.27 0.31 0.35
(b)
Figure 3. Distribution of incidence of mastitis in the herd expressed as incidence per cow-year for the basic situation (a) and after a genetic
change (b). The mean level of incidence of mastitis per cow-year was 0.329/0.03 in the basic situation and 0.259/0.02 after the genetic
change.
Stochastic model for traits in dairy cattle 29
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cows was kept at the same level before and after a
genetic change.
Economic values
Among the disease traits milk fever had the highest
absolute economic value. This was as expected due
to the high cost of an incidence of milk fever. The
economic value for body weight estimated in this
study was �/0.76 t/kg per cow-year. In the review by
Koenen et al. (2000), economic values for body
weight were found in the range of �/1.28 to 0.02 t/
kg per cow per year. However, studies differ with
respect to methods used, prices and restrictions on
the production system applied. In most studies the
economic values were based only on marginal feed
costs and marginal return from beef production. In
this study an increase in the mature weight of the
cow was associated with decreased milk production,
because feed intake of the cow was limiting the
expression of milk yield capacity and growth. This
was the main reason why the economic value for
body weight found in this study was at the upper end
of the range of economic values of live weight
reviewed by Koenen et al. (2000).
The level of economic value of conception rate
found in this study (1.98 t/% per cow-year) is in the
range of economic values reported by others. Boi-
chard (1990) found economic values of conception
rate from 1.14 to 2.14 $/cow per year, whereas the
economic value of conception rate estimated by
Vargas et al. (2002) was 2.42 $/cow per year. The
economic value for milk was 0.28 t/kg per cow-year.
This result is in agreement with other studies using a
fixed number of cows as the base of evaluation
(Groen, 1989b; Bekman & van Arendonk, 1993).
The economic value of involuntary culling esti-
mated in this study was high (�/6.66 t/% involun-
tary culling per cow-year) compared to other studies
(Dekkers, 1991; Rogers et al., 1998) and higher than
expected, because some involuntary culling was
accounted for via the diseases. The economic value
was mainly due to reduced replacement costs and
increased milk yield at the farm due to more cows in
later parities, but might also be due to a more
efficient use of the cow barn. With a low rate of
involuntary culling, the farmer will rarely experience
the fact that a cow is involuntarily culled without
having a replacement heifer available. This was
confirmed by the relatively large change in the
number of cows when the rate of involuntary culling
was reduced. The relatively high economic value of
involuntary culling might also partly be explained by
the way that involuntary culling was modelled.
Voluntary culling only covers non-satisfactory repro-
duction relative to the milk production; all other
culling (except culling due to diseases) is performed
via the percentage of involuntary culling in the herd.
Standard deviations of economic values
Estimated standard deviations of economic values
were high, especially for functional traits. No other
studies were found where standard deviations of
economic values were estimated. However, due to
higher standard deviations among cow performance
of functional traits and especially disease traits
(Table IV), standard deviations of their economic
values were expected to be higher than for produc-
tion traits. There was no variation among mature
body weight of the cows in the herd. The variation in
actual expressed body weight for the cow was only
from the indirect effects of milk yield capacity and
disease occurrence, which might have underesti-
mated the standard deviation of the economic value
for body weight.
The standard deviations of the economic values
were from replicates of a farm and express variation
in realized profit due to expression of cow traits
before and after a genetic change. Variances of profit,
number of cow-years at the farm, and expression of
cow traits and their covariances before and after a
genetic change were used to derive the standard
deviations of the economic values and consequently
influenced the size of the standard deviations (Equa-
tion 4). Variation in realized profit of the farm was
from variation in expression of traits due to the
stochastic component of performance of the cows in
the model. On average over the 1000 replicates,
genetic change was realized at the farm (e.g., mastitis
incidence in the herd decreased) and consequently
profit increased, as reflected by the low standard
errors (see Table V). In some replicates genetic
change was not realized and profit decreased.
The variation in profit was from both variation in
expression of the traits for which the economic
values were derived and variation in other traits
due to the indirect effects between traits. In addition,
profit of the farm was a function of all traits in the
stochastic model. Even in replicates with realization
of a genetic change of a given trait, variation in non-
related traits contributed to variation in profit (e.g.,
mastitis incidence decreased after a genetic change
in mastitis but milk yield per cow was lower than in
the basic situation). In a stochastic model as used in
this study, random variation among the traits implies
that a genetic change is not always realized at
phenotypic level and reflected in farm profit. There-
fore, realized farm profit after genetic improvement
in a given trait is uncertain, which correspond to
what farmers are exposed to in the real world.
Results from this paper show that this type of
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uncertainty differs between traits. From a farmer
perspective, variation in profit due to expression of
traits is highly relevant since farm profit is a result of
the realized genetic improvement in the herd. There-
fore, variation in economic values due to expression
of traits could impact relative selection influence,
because the farmer would tend to put less selection
emphasis on traits, which are highly uncertain, such
as the functional traits. As discussed by Dekkers and
Gibson (1998), farmer acceptance of the breeding
goal is important for optimum impact of selection. If
economic values of traits differ with respect to
uncertainty, farmers may be reluctant to adopt the
breeding goal, which influences the relative selection
influence on traits.
Derived economic values were based on para-
meters from an average Danish dairy farm and
consequently also average herd size. This approach
ignores differences between farm sizes when estimat-
ing standard deviations of the economic values.
However, differences in farm size could be ac-
counted for by estimating standard deviations of
the economic values for different groups of farm
sizes. Ideally, uncertainty of economic values should
include both variation between farms, variation in
prices of inputs and outputs and variation in
expression of traits, which all contribute to variation
in profit and economic values. Both uncertainty of
economic values due to variation in prices and
uncertainty due to variation in expression of traits
are expected to differ between traits. Consequently
both types of uncertainties could possibly impact
farmers’ selection emphasis on a given trait. Amer
and Hofer (1994) suggested including the sampling
distribution of the economic values from variation in
prices when deriving selection index weights. They
showed a reduction in selection response when
economic values were uncertain. However, the
potential use of the standard deviations from this
study to account for reduction in selection response
due to uncertain economic values as suggested by
Amer and Hofer (1994) is beyond the scope of this
paper.
Acknowledgements
The authors thank Lars Gjøl Christensen, Jørn
Pedersen and Jan Tind Sørensen for valuable
discussions about the simulation model and com-
ments on the manuscript. H.M. Nielsen acknowl-
edges the EU for the Marie Curie Fellowship while
staying at Wageningen University, The Netherlands.
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