A Profit
Function
By
Fairfull,
R.W.
for White
A.J.
Animal
Leghorn
Layer
Selection
McAllister I, and R.S.
Research
Agriculture
Gowe 2
Centre
Canada
Ottawa, Ontario
KIA 0C6
INTRODUCTION
Selection
index
theory
the index by its economic
The estimation
even though
introduced
value
of relative
economic
there has been much
and some for specific
(Smith,
species.
the concept
of weighting
1936; Hazel,
weights
1943;
continues
each
to have many
research
on the general
However,
there
of indices
published
work
deriving economic weights for indices of egg type chickens.
Possibly
of the complexities
associated with the i0 or more traits of economic
importance,
the use of 3- and 4-way
gene
for egg production,
action
Relative
as a linear
economic
concept.
economic
objectives
economic
model
functions
as selection
quadratic
models
criteria
are adequate
are known.
The properties
established.
Economic
fact
that the ideal bird
different
economic
parts
niches.
for all types
values
layers
While
Therefore,
has a serious
and it is costly
the profit
basically
indices
components.
have
problem
egg layer
to breed
function
an
that
properties
clearly
that stems
is quite
from
unique
the
in
for each of these
in different
IPresent address:
Dept. of Animal Science, 404 W.P. Garrlgus Bldg.,
University
of Kentucky, Lexington, Kentucky 40546-0215,
U.S.A.
2Present address:
Adjunct Professor, Centre for Genetic Improvement of
Livestock, Dept. of Animal and Poultry Science, University of Guelph,
Ontario, Canada NIG 2WI
36
(1970,
profit
their
not been
birds
may vary
and
Harris
into non-linear
it is not clear
models
or the more economical
of the world
effects.
created
quadratic
of non-linearity,
economic
because
er al. (1986) published
quadratic
for layers.
were
on
of non-additive
and sex-linked
indices
Akbar
of breeding
of other
evaluation'in
maternal
(1968) developed
that included
the substitution
the importance
and selection
et al.
and, more recently,
for broilers
1972) suggested
and major
weights
Wilton
crosses,
in
1963).
problems
principles
is little
trait
Henderson,
markets
around
the world
different
prices
prices
in U.S.
eggs by grades
has a different
grades.
Also,
and over time.
and grades
dollars
This
in several
for Canada,
of steps
FIGURE
i.
determined
change
EGG
by weight
price
IN
U.S.
the
i shows
egg
all of which
ranges.
relationships
in all markets
PRICES
with
Figure
and the U.S.A.,
and different
over time prices
illustrated
major markets.
the U.K.,
and these are mainly
number
is clearly
and from
sell
Each country
among
the
time to time
DOLLARS
1.0
Canada
,
°.o....o°°°o°°Do°.o°o°o.°,
U_
.........
USA
Brown
-
USA
White
0.8
_..o°°.°°°.°°.°°._
_..°..°°.°...°..°.-
0.6
.................
VALUE
;............
$
'
e
D°°°°°°.°°°°°°°°°_
0.4
.
,
,
,
'---
!
I
------J
0
•2
=.-. -_..
_
50
60
EGG WEIGHT
the number
of steps changes.
characteristics
other
The price
than weight
(g)
is variably
(grade).
37
70
influenced
For example,
by quality
in Canada,
shipments
of eggs with
sample
Haugh unit
scores
therefore,
earn a uniform
by weight,
egg size.
but the price per unit weight
Intrinsic
assessments
surprises.
"progress"
to the economic
are made
There
of weight.
is higher
evaluation
In Japan,
to selection
(i.e. milk or meat)
and,
are sold
mid-range
is the problem
that holds
will not necessarily
programmes
eggs
for a narrow
process
for a future
is a great deal of discussion
units
than 65 are sent to breakers
objectives should be such
(except those where there
if this progress
applied
production
regardless
in the present
Thus, economic
for most traits
optimum) even
situations.
weights
price
lower
of
that
at least
some
that they will result
is an intermediate
be optimal
in the literature
in enterprises
and the breeding
in
for all
about
economic
that are mainly
programme
is only part
of the overall business.
This situation applies to many livestock enterprises
where the sale of breeding stock is not the greatest source of return.
In
such cases,
breeding
many
factors
programme
is the primary
come
of a major
source
into play
poultry
of income
that are of little
breeder
where
in the
the sale of breeding
and the sale of product
by-product
of that programme.
The implications
been discussed by Smith et al. (1986).
importance
is usually
of this whole
stock
a
subject
have
In addition, response from application
of a selection index may be
difficult to interpret since genetic and economic evaluation are combined.
This is a practical consideration,
implications
of the index applied.
in that, all "users" may not understand
It is difficult to understand how a
selection program can be properly monitored in such cases and index
not be detected.quickly
even by competent, experienced
geneticists.
Economic
evaluation
is not of secondary
evaluation.
If either
demonstrated
that the method
economic weights,
consideration.
The above
important
represents
them
limited
the other
of derivation
so that, methods
to keep
It represents
are flawed,
importance
loses
and philosophy
some
concerns
in economic
in mind;
however,
this paper
steps
in a long difficult
38
Gibson
a large
deserve
effect
process.
(1989)
on relative
serious
evaluation.
will
may
to genetic
value.
can have
errors
the
It is
not address
them
all.
Strictly
economic
where selection
issues
can be based upon
These must be translated
At the Animal
scheme
methods
employed
Thus,
Research
one of which
traits
profit
and a profit
or a correlated
values
long-term
linear
Culling
project
characters
component
initiated
Trait
selection
evaluation
character.
of the target
(ARC), we have
is the Multiple
in Bob Gowe's
in layer
there is a prediction
Centre
1990) and the other uses best
evaluation
a part-record
into the expected
global assessment of merit.
assessment in layers.
selection
are not the only concern
for
to
a comparison
Levels
(Falrfull
of
(MTCL)
and Gowe,
prediction
(BLUP) for genetic
for economic
evaluation
of the quantitative
function
unbiased
(McAllister et al., 1990).
It is this latter method, especially the
function, that forms the basis of the remainder of this discussion.
METHODS
Overall
Breeding
values
Evaluarion
(BV's) are estimated
using
multiple
trait BLUP.
The
method used is recurslve prediction on a reduced, animal model (Hudson, 1984).
The BV's of the seven traits for each selection candidate are substituted
in
the profit
function.
the population
mean,
The inputs
used are actually
so that the results
the BV
are in the range
(a deviation)
plus
of actual
performance
as required for calculation of the profit function.
The resulting
value represents merit for the traits considered.
The central issue of this
approach
economic
is the idea that the profit
merit.
All
selected
the genetic
assessment
all-or-none
to select
testing
will
which
In this group
and traits
that apparently
assesses
in this manner.
is difficult
We believe
as adequate
are discontinuous
have
relative
methods
traits,
non-llnear
that
for
and
inheritance
the traits.
theory has been published
(Gianola
application
traits
directly
such
and hatchability
(Gowe and Fairfull, 1982; Gowe, 1983; Frankham,
1 lists the different traits under selection and the method
Recently,
traits
of several
are not available.
as, fertility
1990).
Table
employed
traits are not considered
evaluation
traits
function
and Foulley,
require
1983;
extending
have not yet been
Foulley
that leads
et al.,
the theory
accomplished.
39
to BLUP
1983),
of all-or-none
but the practical
to an application
Also,
level
and
for some all-or-none
traits,
llke general
specific
mortality,
in terms of disease
intense
organism
or virulence
of pathogens
little
in the new environment.
worth
which
may have
non-linear
For a discussion
Table
change,
I.
Traits
Selection
Trait
BLUP
Hen-day
with
Residual
Profit
Egg weight
Function
For other
current
(1983) and Frankham
and method
feed consumption
at 340 days
egg in days
body weight
Culling
Hatchability
Levels
Viability
theory
is not adequate.
egg to 497 days
(HDR)
(RFC)
at 340 days
(SGR)
(AFE)
(BWT)
units at 340 days
Fertility
as fertility,
(EWT)
gravity
Multivariate
levels
gains may be of
such
genetic
is
(1990).
rate of lay from first
Egg specific
Haugh
If exposure
selection
traits
as mortality
of evaluation
Age at first
Mature
is futile
and its virulence.
then previous
inheritance,
see Gowe
selection
(HAU)
- Brooding
Rearing
Laying
Blood
spot
incidence
Egg shape
Profi=
The data used
target
traits
were based
and Gowe,
1990),
(Grunder
e_ al.,
The function
to calculate
at which penalization
would be above
shell eggs
accept
with
units
begins.
This point
below
selection
genotypes
1986)
traits
study
was chosen,
and superimposed
study.
for the initial
so that,
lots of eggs
to
(Fairfull
from the selection
on data except
which
selected
cannot
Haugh
point
units
be sold
as
at the end of lay.
of 65 Haugh
increasing
eggs from
relating
e_ al., 1983,
utilizing
is not based
65 (the standard
in Canada)
The standard
decline
(Falrfull
studies
for Haugh
the functions
on data from a long-term
and crosslng
1989)
Function
units
is not high even
age of the hen.
a flock,
the penalty
Haugh
As long as the grading
for producing
40
though
eggs below
units
station
will
the standard
is
not severe
in Canada
above this standard
against
very
eggs very
low Haugh
as genotypes
for much of the first
low in Haugh units
values_
The profit
only
especially
however,
from the quantitative
characters
of important
Two of the most
constant
returns
assumptions
important
are:
selection
functions of specific
shown in appendices.
i.
Gross
profit
2.0
Income
2.1
Egg income
considered
gravity,
- (Income
- (expected
(income
reached.
Haugh
SBvSGR
-
breeding
-- function
breakage)(rate
4.931
for expected
value
-
Typical
are a
values
of the
and body weight
for albumen
are
of
height)
[BvAFE]})(SBvHAU)
egg specific
proportion
- 0.02046(BvSGR )
(;BvSGR) - 0.702,
BvHDR
costs
grade-out)
of egg specific
relating
the restrictions:
then
are a
of diminishing
of lay)(length
period)(adJustment
to the expected
-
program
units
There
of this function.
pullet value)
- (SBvSGR)({BvHDR)([DA ]
where BvSGR
i).
Expenses)
- (egg income + spent
laying
(see Table
2) that a period
egg weight,
against
in that it is composed
i) that the breeding
gains has not been
prejudice
selection
in the construction
and
be
is perplexing.
is restricted
implicit
for a fixed set of traits,
from
form
should
Consumer
seem to require
the exact
shown below
number
laying cycle.
would
function
from most breeders
(;IBvEWT),
gravity,
gravity
of intact
at 340 days
eggs,
195.739(I/BvSGR),
if BvSGR < 70 (1.070)
with
then
and if BvSGR340 > 102 (1.102)
(_BvSGR340) - 0.926,
breeding
value
of hen day rate of lay from first
egg,
DA
-
disposal
age - 497 days of age (whole
BvAFE
-
breeding
value
of age at first
BvHAU
-
breeding
value
of Haugh
_BvHAU
-
function
of Haugh
Haugh units,
-
at 340 days whereby
the number
of eggs is reduced,
18.81791(BvHAU)
708.311
-
breeding
value
then
then
75.51
the
(SBvHAU) -- 0.0,
(;BvHAU) - 1.0,
of egg weight,
41
under
- 0.12481(BvHAU) 2, with
if BvHAU < 72.57
and if _vHAU > 75.51
length),
units,
units
restrictions:
BvEWT
record
egg in days,
JIsvEWT - function
revenue
year
relating
per egg generated
grade
- 0.113326
with
egg weight
distribution
(SIBvEWT) -- 0.0620,
2.2
Spent pullet
-
to the
by the expected
full
at that weight,
+ 0.000118264(svEWT )
the restrictions:
(]'lsvEWT)
at 340 days
2.85977(I/svEWT),
if svEWT < 50.0 then
and if svEWT340 > 69.0
then
0.0801.
value
- (spent pullet
weight)(price/unit
weight)
- (J,vBWT)
(F/BWT),
where svBWT
;svBWT
- breeding
value
of mature
- function
relating
mature
body weight
(365 d),
body weight
to final
body weight,
- 72. 809 + 0.578(svBWT)
P/BWT
3.1
- price
Expenses
per unit body weight.
- cost of feed consumed
- (feed for maintenance
adult
residual
- ({@F/gE}{Egg
aF/gE
- constant
Egg Number
- ({svHDR){[DA]
S_vEWT
per unit
Number}{S_vEWT
{[aF/gBWT][svBWT]
where
+ feed for egg mass +
feed)(cost
} +
+ [svRFC]}{PHD})
(C/U)
for feed per gram of egg lald,
[svAFE]})
- function
relating
egg weight
average
egg weight
expected
- 8.610573
of feed)
at 340 days
over
+ 0.8070588(svEWT),
restrictions:
the full year,
with
if svEWT < 50.0
to the
then
the
(;_vEWT)
- 48.96,
@F/gBWT
- constant
for feed per gram of live body weight,
svBWT
- breeding
value
svRFC
- breeding
value
PHD
- number
of days
of mature
of residual
C/U
feed consumption,
in the laying
- ({DA} - {Housing
day periods
System),
(365 day) body weight,
age})/28,
to correspond
- cost of feed per unit.
42
year
expressed
with ARC's
as number
of 28
Feed Consumption
Comments
At the Animal
selected
using
significant
differences
are in the laying house.
interpretation.
between
the overall
are relatively
and egg weight.
minor
although
However,
There
from parents
2 shows means
are statistically
means
of strains
selected
of genetic
benefits,
selection
programme
phenotypic
values
identification
but there
is easier.
are practical
inspect
and rectification
procedures
to reduce
their
incidence.
in emphasis
more
emphasis
on
destination
may offer
advantages.
the
the BV's and
This has allowed
the
and the establishment
Once sound
by
no
Monitoring
we print
of data errors
the differences
satisfactory
the printout.
using
residual
on egg weight.
evaluation
Each generation,
and visually
slightly
for a similar,
and economic
part,
divergence
a little more emphasis
Apparently,
both methods are headed
slightly different routes.
The separation
modest
for
are no significant
There
i.e. MTCL places
the rate of lay and BLUP places
editing
Table
for the most
they reflect
from the two methods
theoretical
bred
for age at first egg, hen day rate of lay, body weight,
feed consumption
resulting
the third generation
(parents of the third generation).
to complicate
BLUP or MTCL
Centre,
BLUP or MTCL
the 1989 hatch
interactions
Research
editing
of
procedures
are in place, visual inspection is less important, but checking a few high
ranking and low ranking individuals plus a few random ones is a sensible
precaution.
situations
error.
The results
of both parts
that were apparently
The mathematical
processes
of the process
illogical
have,
appear
thus far, resulted
that make up the profit
should be improved.
The function relating egg specific
indicence is based upon only one data set and that data
is possible
changing
that the share of the egg weight
with
selection,
to be recalibrated.
functions
may not predict
however,
they
Finally,
there
function
including
Probably,
egg weight
pure
so that,
Also,
curve
the equations
due to unaccounted
absolute
should be adequate
is heterosis
values
function
across
involving
adequately
is the character
is an intermediate
llne egg weight
optimum
to egg grade
may not be the best method
where
egg weight
economically.
to handle
this
43
may have
of variation,
some
for some purposes;
characters
of rank.
in the profit
and body
this is the greatest
distributions
from data
age of hen is
age at first egg, rate of lay, egg weight
egg weight
and
can and
for the prediction
important
sense
gravity to breakage
set is not ideal.
It
for sources
(more robust)
for several
to make
weight.
concern
as
For this trait, we fitted
of strain
crosses,
but this
Table
2.
Means
populations
prediction
for three strains I of the 2nd generation
(1989 hatch)
(BLUP)
that were selected
and the profit
the three strains I selected
function
by multiple
Trait
Fertility,
Rearing
_
_
mortality,
mortality,
Laying
mortality
Age at first
Hen housed
best
linear unbiased
with
trait culling
_
_
to 497 d
egg, d
egg prod'n
to 497 d
the means
levels
BLUP
Hatchability,
Brooding
using
compared
test
for
(MTCL).
MTCL
89.7
88.1
75.2
77.7
2.6
2.6
0.8
1.0
3.8
2.9
144.7
147.2-*
286
292
**
Hen day rate AFE-497
d
81.9
83.7**
Hen day rate AFE-357
d, _
88.2
89.6**
Mature
body weight,
Residual
feed consumption,
Egg weight
Specific
g
at 340 d, g
gravity
Haugh units
Blood
g
at 340 d
at 340 d
spots at 340 d, %
Egg shape at 340 d
Egg weight
Specific
at 450 d
gravity
at 450 d
Profit=
IOne strain
from each
of three genetic
2Calculated using the overall means
used are outlined in Table I.
**P<0.01.
1668
1742
**
1087
1058
**
62.1
60.2**
85.6
84.8
84.2
83.0
3.2
2.3
3.9
4.0
65.4
63.8**
82.4
81.5
10.57
10.33
bases.
with constant
44
value.
The traits
problem.
In any case, each section
critically
and improved
as better
of the function
ideas
should
be viewed
or data are advanced.
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M.K.,
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1986.
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R.W.,
and R.S.
Gowe.
1990.
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R.W.,
long-term
selected
reciprocal
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R.W.,
heterosis
of White
Frankham,
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1983.
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calving difficulty
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R.D.
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Sheep
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intact
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Harris, D.L.
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Breeding for efficiency in livestock production:
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basis
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Selection index and expected genetic advance.
pp. 141-163.
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Star. Genet. Plant Breed.
W.D. Hanson and H.F.
Robinson,
Hudson,
Editors.
G.S.F.
prediction
Unbiased
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A.J.,
R.W.
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weights
of a reduced
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Falrfull
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James
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H.F.
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Extension
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C., J.W.
economic
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Eugen.
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McAlllster,
comparison
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Evans,
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for quadratic
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of total
46
model
1990.
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1986.
to recurslve
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and Best Linear
Livest.
Prod.
for plant
L.D.
A preliminary
Levels
Prod.
XVI:69-72.
On the derivation
Anim.
function
and Van Vleck,
Washington.
Scl. 59:1164-1175.
improvement.
merit.
animal
Genet. Appl.
Brascamp.
A dlscriminant
J.W.,
Trait
Council,
1986.
of
43:545-551.
selection.
Selection
24:937-949.
Ann.
indices
APPENDICES
Typical
Values
of Functions
;svSGR340 - 4.931 - 0.02046(svSGR )
195.739(I/svSGR )
- expected proportion of intact eggs
svSCRI
70
78
82
86
90
94
98
102
170
74
[svSCR
0.702
74
0.772
0.826
0.866
0.895
0.915
0.925
0.929
0,925
- 1.070,
- 1.074, etc.
SIsvEWT - 0.113326 + 0.000118264(svEWT ) - 2.85977(I/svEWT)
- expected average return per egg in dollars
svEWT
50.0
54.0
58.0
62.0
64.0
68,0
[lsvEWT
$0.0620
$0.0668
$0.0709
$0.0745
$0.0762
$0,0793
SsvHAU - 18.81791(svHAU)
svHAU
75.50
75.40
75.00
74.60
74.20
73.80
73.40
73.00
72.60
72,57
708.311
[BvHAU
1.000
0.995
0.976
0.917
0.819
0.680
0.502
0.284
0.026
0,004
47
- 0.12481(svHAU) 2
SsvBWT - 72.809 + 0.578(svBWT )
- expected final body weight
svBWT
210
200
190
180
170
160
150
[BvBWT
194
188
183
177
171
165
160
S2svEWT - 8.610573 + 0.8070588(svEWT )
- expected average egg weight
svEWT
50.0
54.0
58.0
62.0
64.0
68,0
[_vEWT
48.96
52.19
55.42
58.65
60.26
63,49
in the full year
Question:
T.
Wing
Do your BLUP
correlations?
Response:
R.W.
We
use
multiple
genetic
J.
Can
and
for
an
Response:
heritabilities
and
genetic
prediction
and
an
animal
model
for
BLUP.
Multiple
trait
BLUP
includes
and covariances
similar
to a classical
index
are
so
that
considered.
heritabilities
and
genetic
Arthur
should
the
intermediate
R.
include
Fairfull
recursive
trait
variances
selection
correlations
Question:
equations
W.
BLUP
index
optimum
for
be
constructed
egg
to
select
weight?
Fairfull
The
profit
function
has
an optimum
for
egg
weight
at
about
69.1 g (a ridge
on the response
surface).
This
is
probably
too
high
on a practical
basis.
The
profit
function
may
not adequately
account
for
the
effects
of
very
large
egg size
on breakage
because
of the egg
size
distribution
of the
flocks
analyzed
(few
birds
in the
flock
laid
eggs
in 69-72
g range
at 340
days
of age).
However,
the egg flats used for transportation
of eggs in
Canada
are not
roomy
enough
for very
large
eggs
and
so
very
large
eggs will
probably
be exposed
to more
severe
insults
than
smaller
eggs,especially
compression
along
both
axes
during
packing
and
transport.
Also,
egg
grading
equipment
is no
longer
set
up to handle
very
large
eggs
although
the
size
of the
egg
that
can
be
handled
without
severe
insult
due
to size
varies
with
market.
We will attempt
to determine
quantitatively
the
detrimental
effects
of very
large
egg
size
and
consult
with
grading
stations
on
the
maximum
size
egg
their
equipment
will
now
handle
safely.
At
present,
this
function
must
be viewed
as the theoretically
optimum
egg
size given
no upper
limit on egg size as discussed
above.
In a practical
programme,
I would
set
a limit
based
on
commercial
acceptance
which
history
has
shown
us can be
different
from
the purely
economic
optimum.
49