ESTIMATION OF GENETIC PARAMETERS FOR NUMBER OF PIGLETS
BORN ALIVE USING RANDOM REGRESSION MODEL
LUKOVIĆ Z.¹, ², GORJANC G.¹, MALOVRH Š.¹, KOVAČ M.¹
¹University of Ljubljana, Biotechnical Faculty, Ljubljana, Slovenia
²University of Zagreb, Faculty of Agriculture, Zagreb, Croatia
Keywords: random regression model, genetic parameters, litter size, pigs
INTRODUCTION
In conventional animal breeding, both repeatability and multitrait (MT) models have
been applied to analyze traits that are measured more than once in lifetime. More
appropriate way of dealing with these traits is to fit a set of random regression (RR)
coefficients describing production over time for each animal to allow individual
variation in the course of trajectory (1). In pigs, RR models were mainly used for
growth and feed intake. Although litter size differs from fattening traits, some authors
suggest that RR models could be applied in selection on this trait (2, 3). Possible genetic
differences in litter size along the trajectory could be identified using RR models and
something like persistency in litter size could be used to select breeding sows (3).
The aim of this paper was to estimate and compare dispersion parameters from MT and
RR models with Legendre (LG) polynomials of different order for number of piglets
born alive (NBA).
MATERIAL AND METHODS
Data from 98,359 litters from first to sixth parity, collected between years 1990 and
2002 at farm Nemščak, were analyzed. The pedigree file contained 28,055 sows with
records and 6,733 ancestors. Fixed part of the models was developed with the SAS
package (4). In MT, model 1 was used for gilts and model 2 for sows after first parity.
Model 3 was used in RR analysis for sows together.
2
y1ijkl    Bi  S j  bI xijkl  x   bII xijkl  x   lik  aikl  eijkl
(1)
y2  6ijklm    Bi  S j  Wk  bI xijkl  x   bII xijkl  x   bIII zijkl  z   lijkl  aijklm  eijklm
2
y ijklmno    Bi  S j  Pk  Wl  bI k x ijklmno  x   bII k x ijklmno  x   bIII z ijklmno  z  
(2)
2
*
   ijklmno
   sm  m  p ijklmno
3
k
(3)
s 1 m  0
where y is NBA, B , S , P and W are fixed effects of breed, mating season, parity and
weaning to conception interval, respectively. For MT models age at farrowing ( x ) was
adjusted by quadratic regression for each trait separately, while it was nested within
parity in RR model. Previous lactation length ( z ) was fitted as linear regression.
Random part of the MT models consisted of direct additive genetic ( a ) and common
litter effect ( l ). RRs described by LG polynomials of standardized parity ( p * ) were
included for direct additive genetic, permanent environmental and common litter effect.
LG polynomials from the first (LG(1)) to third order (LG(3)) were fitted. Estimation of
(co)variance components from MT and RR models was based on REML method using
the VCE5 software package (5). Modul SAS/IML was used for computation of
eigenvalues for covariance matrices of regression coefficients to quantify contribution
of higher order of LG polynomials.
RESULTS AND DISCUSSION
Estimated phenotypic variances and ratios were approximately the same between
models. Eigenvalues of genetic covariance function show that the constant term
accounted for around 93-95% of total genetic variability for NBA. This means that 57 % of variability in our study is covered by different production curves of sows.
Computing time needed for MT analyze was about five times longer than for RR model
with LG3.
Table1. Estimated variance and ratios in multitrait and random regression models
Multitrait model
Random regression with LG3
Parity
Var(ph)
h²
l²
Var(ph)
h²
l²
p²
1
7.85
0.102
0.021
7.87
0.101
0.021
0.054
2
7.38
0.130
0.030
7.39
0.125
0.013
0.070
3
7.99
0.112
0.007
8.03
0.123
0.005
0.079
4
8.19
0.111
0.026
8.20
0.118
0.005
0.091
5
8.25
0.123
0.039
8.27
0.118
0.010
0.099
6
8.54
0.118
0.034
8.56
0.119
0.020
0.099
Table 2. Eigenvalues of estimated covariance matrices of RR coefficients as proportion
(%) in the total variability for random effects
Direct Additive
Perm. Environmental
Common litter
Eigenvalues LG(1) LG(2) LG(3) LG(1) LG(2) LG(3) LG(1) LG(2) LG(3)
0th
95.04 94.61 93.60 91.45 91.13 90.85 65.80 63.25 59.71
1st
4.96
4.45
5.08
8.55
8.86
9.14 34.20 36.75 34.40
nd
2
0.93
1.31
0.01
0.01
0.00
5.88
3rd
0.01
0.00
0.01
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