SelAction: Software to Predict
Selection Response and Rate
of Inbreeding in Livestock
Breeding Programs
M. J. M. Rutten, P. Bijma, J. A.
Woolliams, and J. A. M. van Arendonk
Software was developed to predict selection responses and rates of inbreeding
from livestock breeding programs. Variance components are needed as input for
the program, which subsequently enables the user to evaluate various breeding program designs. Consequently,
breeding program structures with discrete (e.g., fish or poultry breeding) or
overlapping generations (e.g., pig or
cattle breeding) can be evaluated for
selection on multiple traits. For discrete
generations, selection response of multistage selection schemes can be predicted
as well. Rates of inbreeding can be
predicted for breeding programs with
discrete generations and single-stage
selection. With this software program,
BLUP breeding values (animal model)
456 The Journal of Heredity 2002:93(6)
can be used as information sources. It
also accounts for reduction of genetic
variance due to selection (‘‘Bulmer effect’’), and for reduction of selection
intensity due to finite population size
and correlated index values of family
members. Predefined information sources can be either switched on or off,
according to the user’s needs. The
number of traits is limited to a maximum
of 20.
Quantitative genetic research has resulted in a large amount of theory to
predict selection response and rates of
inbreeding of livestock breeding programs. Application of this theory in
practical livestock breeding programs,
however, is hampered by the lack of
computer software that implements the
available theory.
Virtually all methods to predict responses of breeding programs are based
on selection index theory. After the
basics of selection index theory were
developed (Hazel 1943), further developments have aimed at, for example, the
effect of selection on genetic (co)variances (Bulmer 1971), the effect of correlated index values on selection intensity
(Meuwissen 1991), the effect of multistage selection (Tallis 1961; Young 1964),
selection in overlapping generations
(Meuwissen 1989), and prediction of
selection response on BLUP breeding
values (Villanueva et al. 1993; Wray and
Hill 1989). In addition, methods to predict rates of inbreeding in selection
programs have recently been developed
(Bijma et al. 2001; Bijma and Woolliams
2000; Woolliams and Bijma 2000).
In this article, a computer program
called SelAction is presented, which
implements existing theory in order to
provide a tool to predict selection response and rates of inbreeding in livestock breeding programs for a wide range
of population structures and selection
strategies. SelAction requires little computing time, allowing it to be used as an
interactive optimization tool.
Genetic Model, Breeding Goal,
and Selection Index
The infinitesimal model is assumed and
traits are assumed to remain normally
distributed over time. Further, a common
mating structure, where dams are nested
within sires, and random mating of
selected animals are assumed. Inbreeding is ignored when predicting selection
response. The genetic model for each
trait is P 5 G 1 E, where P is a phenotypic
observation, G is the genetic component,
and E is the environmental component.
Optionally the environmental component
E can be partitioned into a component
common to full sibs, C, and an individual
component, E*.
The breeding goal is the sum of
a maximum of 20 traits weighted by their
respective economic values. An index of
information sources is used to predict
the genetic merit of individuals for the
breeding goal. Index traits and breeding
goal traits are allowed to be different
traits, which enables prediction of correlated selection response. Variance components of the traits involved are
required as input for the program.
For each index trait, the index can
contain the following information sources: individual phenotypic performance,
pedigree information (BLUP), and average phenotypic performance of full sibs,
half sibs, and/or progeny. All information
sources can be switched either on or off.
A maximum of 20 distinct full-sib, 20 halfsib, and 20 progeny groups can be used
in the program, and the animals of each
group are correctly treated as different
individuals. Pedigree information consists of the estimated breeding value
(EBV) of the dam, the EBV of the sire,
and the mean EBV of the dams of each
half-sib group. Wray and Hill (1989) and
Villanueva et al. (1993) show that including EBVs as information sources in
the selection index accounts for complete pedigree information (animal model). In the case of BLUP selection, the
user indicates which information sources
have been used to estimate the breeding
values.
Discrete Generations:
Single-Stage Selection
In discrete generations, the selected animals produce offspring and are culled
afterwards, as is often practiced in fish or
poultry breeding. The program creates
selection index equations, and equilibrium genetic parameters (Bulmer 1971) are
obtained by iterating these equations as
described in Villanueva et al. (1993).
Selection intensities are corrected for
finite population size and for correlated
index values of family members (Meuwissen 1991). Correlations between index
values of full sibs and half sibs are
calculated from the selection index equations (see De Boer and van Arendonk
1989, equation 5).
Selection response is predicted for the
equilibrium situation, using the approach
of Villanueva et al. (1993). After that,
long-term genetic contributions of individuals are predicted using the method
of Woolliams et al. (1999). Next, the rate
of inbreeding is predicted from the
expectation of the squared long-term
contribution, using the method of Woolliams and Bijma (2000).
the response after the second stage of
selection, the program also predicts the
response after the first stage of selection,
which is calculated with single-stage
selection index theory using the equilibrium genetic parameters. The program
does not predict rates of inbreeding for
multistage selection. Calculating selection response from three-stage selection
is an analogy of two-stage selection.
Discrete Generations: Two- or
Three-Stage Selection
Overlapping Generations
In two-stage selection, animals are first
selected on index 1. Next, the remaining
animals are selected on index 2. The
second index consists of index 1 plus
additional information sources. Eventually the selected animals (index 2) produce offspring and are culled afterwards.
Equilibrium genetic parameters (Bulmer 1971) are obtained by iterating on
index 2, as if it concerned single-stage
selection (this results in a minor underprediction of selection response). In the
equilibrium situation, indexes 1 and 2
follow a bivariate normal distribution
with correlation q12 5 q1/q2, where
q1(q2) is the accuracy of selection of
index 1 (index 2). Truncation points of
this bivariate normal distribution are
calculated using Dutt’s (1973) method
(see Ducrocq and Colleau 1986), based
on the selected proportions and q12. The
total selection response after stage 1 and
stage 2 is calculated from the momentgenerating function of the truncated bivariate normal distribution, as given by
Tallis (1961; Ducrocq and Colleau 1986).
Since the total selection response after
stage 2 is not expressed per trait, this is
calculated by a regression of the individual traits on the selection response in the
breeding goal:
R2j ¼ ½ R1
2
r
R2 I1
r2I1
r2I1
r2I2
1 "
0
b1 g1; j
0
b2 g2; j
#
;
where R1 and R2 represent total selection
responses in economic units after stage 1
and 2, respectively, {\sigma _{{\it I}1}^2
and {\sigma _{{\it I}2}^2
represent
variances of index 1 and 2, b1 and b2
represent vectors of index weights, and
g1j and g2j represent vectors of covariances between information sources of
index 1 or 2 with breeding values for trait
j. As with discrete generations, selection
intensities are calculated using the
method of Meuwissen (1991). Besides
In overlapping generations, animals are
assigned to different age classes and can
be selected to produce offspring more
than once (e.g., pig or cattle breeding).
After one selection round, the animals
of a particular age class move up to the
next age class. Culling due to age is
random so that it does not affect genetic
(co)variances.
From the selection index equations,
selection differentials and (co)variances
after selection are calculated for each age
class separately. Selection differentials
are calculated using the method of
Meuwissen (1991). When all age classes
are processed, selection response in the
breeding goal is calculated by weighing
the selection differentials of each age
class by the contribution of that age class
to the next generation and dividing by
the generation interval. Next, (co)variances are updated by weighting (co)
variances of each age class by the
contribution of that age class to the
next generation and adding a term to
account for differences in genetic means
between age classes (Bijma et al. 2001;
Meuwissen 1989). Equilibrium parameters
are obtained by iteration.
SelAction has two options to determine the number of selected animals
from each age class; the user can either
enter fixed numbers, or the number
selected from each age class is determined by truncation selection on indexes
across age classes (Ducrocq and Quaas
1988). When truncation selection is
chosen, it is still possible to exclude certain age classes from selection.
Output
The information specified by the user
is printed in the output file for convenience. In addition to that, equilibrium
parameters are presented. Selection response is presented partitioned over
sires and dams, and for the total popula-
tion. The response is expressed in three
ways: in trait units, in economic units,
and as a percentage of the total selection
response. Correlated responses for nonbreeding goal traits, index variances, and
the accuracy of indexes are also presented. In case of truncation selection in
overlapping generations, the number of
animals selected from each age class are
presented. The selection response is expressed as a response in economic units
per generation (discrete gen.) and per
age class interval (overl. gen.).
Features
In SelAction, once a breeding program
design and accompanying trait parameters are entered, an input file is generated; this can be saved so that it can be
loaded again for later sessions. Other
features include printing and saving of
output and the optional adding of comment lines to the output. An extensive
manual with several examples is also
available. SelAction was programmed in
Borland Delphi 5.0 and runs under Microsoft Windows 95/98/NT. For noncommercial use, it is free of charge (www.zod.
wau.nl/abg/).
From the Animal Breeding and Genetics Group,
Wageningen Institute of Animal Sciences (WIAS),
Wageningen University, P.O. Box 338, 6700 AH
Wageningen, The Netherlands (Rutten, Bijma, and
van Arendonk), and Roslin Institute (Edinburgh),
Roslin, Midlothian, EH25 9PS, United Kingdom (Woolliams). This research was supported by the Netherlands Technology Foundation (STW) and was
coordinated by the Earth and Life Sciences Foundation (ALW). V. Ducrocq and T. H. E. Meuwissen are
acknowledged for providing subroutines. J. A. Woolliams acknowledges financial support from the Ministry of Agriculture, Fisheries and Food (United
Kingdom). Address correspondence to M. J. M. Rutten
at the address above, or e-mail: marc.rutten@wur.nl.
Ó 2002 The American Genetic Association
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Received April 15, 2002
Accepted September 30, 2002
Corresponding Editor: Sudhir Kumar
458 The Journal of Heredity 2002:93(6)