CHANGES IN THE RELATIVE IMPORTANCE OF
ADDITIVE AND NONADDITIVE GROUP GENETIC EFFECTS FOR WEIGHTS AND MACROMINERALS
FOR PREWEANING GROWTH
C. Manrique, M. A. Elzo, W. O. Odenya, L.
R. McDowell, and D. L. Wakeman
Department of Animal Science, University
of Florida, Gainesville 32611
Animal Breeding
Mimeo Series, No. 13, Animal Science Dept., University of Florida, Gainesville,
pp 1-30.
Introduction
Crossbreeding has been used in beef
cattle production in order to optimize the use of additive and nonadditive
genetic effects for growth traits and traits related to them (Alenda et al.,
1980). Because macrominerals have
biochemical and physiological links to growth (Littledike and Goff, 1987;
Arnaud and Sanchez, 1990), they are a possible set of traits that could be used
to help evaluate animals for growth traits.
Estimation of additive and nonadditive genetic effects for growth traits
and macrominerals can help design effective crossbreeding schemes or determine
the optimum breed composition of composite populations. Estimates of additive and nonadditive
genetic effects for weight at birth, weaning, yearling, and 18 mo of age,
determined from the crossbreeding of Brahman and Angus, have been reported
(Franke, 1980; Wyatt and Franke, 1986; Elzo et al., 1990). These studies involved additive and
nonadditive (intralocus) group genetic effects. Odenya et al. (1992a) reported estimates of these genetic effects
for macrominerals at weaning in an Angus H Brahman multibreed herd. These estimates followed closely those for
weaning weight. This genetic
information aids in selection and culling decisions at weaning. For instance, the selection of bulls whithin
a herd to produce calves for the following year occurs prior to breeding time,
when calves of these bulls are between two to four months old. Having evaluations of these bulls at earlier
ages can help with selection decisions to optimize crossbreeding production
systems. In addition, earlier
evaluations can help to improve our understanding of the process of growth and
development. Consequently, the
objectives of this study were 1) to obtain estimates of additive and
nonadditive group genetic effects for weight and amount of macrominerals in the
serum at 30, 60, 90, 120, 150, and 205 d of age, and 2) to investigate how the
relative importance of these genetic effects changes across these ages.
Materials and Methods
Description of data
Weight and serum macrominerals were
measured on 380 calves, born in 1989 and 1990, from the multibreed research
herd formed by Angus (A), Brahman (B), and several A H
B crosses at the Pine Acres Research station of the University of Florida,
Citra. These calves were produced by
the mating of six sire breed groups consisting of A, .75A .25B, .5A .5B, .25A
.75B, B and Brangus (.625A .375B) and five dam breed groups (.25A .75B were
unavailable). Table 1 shows the number
of sires and dams by breed group composition.
A total of 28 sires were used.
The number of sires per breed group per year ranged from two (.75a .25B
in 1989) to five (Brangus in 1990).
Between one (.5A .5B) and three (A) sires per breed group were
represented in both 1989 and 1990. This
ensured connectedness in the data set.
The total number of dams was 243.
There was a minimum of 14 dams (.75A .25B in 1990) and a maximum of 65
dams (A in 1989) per breed group per year.
Table 2 shows the number of calves produced by mating subclass in both
years. This number ranged from three
(.5A .5B sires mated to .75A .25B dams) to forty (B sires mated to B dams).
The data included measurements of birth
weight (BW) and weights (WT) and serum calcium (Ca), serum phosphorus (P), and
serum magnesium (Mg) at intervals of approximately 5 weeks up to weaning. Age at first sampling ranged from 1 to 85 d
(97% of calves were sampled within 70 d of birth). Age at weaning ranged from 151 to 275 d (91% of calves were
weaned between 210 and 270 d of age).
Amounts of macrominerals were computed as the product of the
concentration of each macromineral in serum times the estimated serum volume
for each calf (Odenya et al., 1992a).
Weights were adjusted to 30, 60, 90, 120,
150 and 205 d, using the standards proposed by the Beef Improvement Federation
(BIF, 1990). Similar standards were
used to adjust amounts of macrominerals at those ages. Due to the lack of data on serum macrominerals
at birth, the amounts of macrominerals and weight from the first sampling were
used instead in the BIF adjustment formulas.
Genetic Analysis
Regression methods for group genetic
effects, as described by Elzo and Famula (1985) and Elzo (1990), were used to
compute best linear unbiased estimates (BLUE) of additive and nonadditive
direct and maternal group genetic effects.
Sire and dam additive effects were expressed as Angus (A) allele effects
deviated from Brahman (B) allele effects.
Sire H dam nonadditive direct and maternal
effects were expressed as intra- and interlocus interaction effects of A and B
alleles deviated from the interaction effects of pure A and pure B alleles at
one and two loci. One advantage of
including both intra- and interlocus interactions over one locus models was
that the proportion of the variability in the data explained by the model (the
coefficient of determination, R2) increased in all the traits that
were analyzed and also the error mean square of those models decreased. Also, because more effects were involved in
these interactions, a better knowledge of the specific combining ability of
alleles of different breeds can be obtained.
The following definitions of intra- and
interlocus interactions apply to both direct and maternal effects. These definitions assume that 1) intrabreed
nonadditive effects are the same for all base breeds, and 2) nonadditive
effects at more than two loci are negligible.
The intralocus interbreed interaction at
one locus, expressed as a deviation from the intralocus interactions of
purebreds, was as follows:
i12 = interaction between A alleles from one of the parents and B
alleles from the other parent at one locus, summed over all loci.
The two locus interactions, expressed as
deviations from two-locus allelic interactions of purebreds, were as follows:
i22 = interaction among two A alleles at two loci from one of the
parents and two B alleles at two loci from the other parent, summed over all
two-locus combinations,
i23 = interaction among two alleles of the same breed at two loci
from one of the parents and an A allele at one locus and a B allele at another
locus from the other parent, summed over all two-locus combinations,
i24 = interaction among an A allele at one locus and a B allele at
another locus from one of the parents and an A allele at one locus and a B
allele at another locus from the other parent, summed over all two-locus
combinations.
These four nonadditive effects cannot be
estimated because intralocus interbreed interactions are confounded with
two-locus interactions. Thus, these
interactions were reparameterized as a combination of the above interactions at
one locus and two loci. Details of the
definition of these nonadditive effects are given in the Appendix.
The resulting interactions were:
D1 = d22 + d12,
D2 = d23 + 2d12,
D3 = d24 + 2d12, for direct effects,
M1 = m22 + m12,
M2 = m23 + 2m12,
M3 = m24 + 2m12, for maternal effects.
The model used to obtain the BLUE of
additive and nonadditive group genetic effects included environmental effects
(year, management group within year, calf age at first sampling and sex of calf
H age of dam subclass), breed group genetic effects ( sire additive,
dam additive, and sire H dam nonadditive) and residual
effects. Management group refers to the
assignment of cows to six replicated forage supplementation and one control (13
herds) in winter (mid-December to March).
There were three sex categories (bulls, heifers and steers) and six age
of dam categories (three, four, five, six, seven and eight or more years of
age). Calf age at first sampling was
defined as a discrete variable using intervals of ten days of age (1 = 1 to 10
d, 2 = 11 to 20 d, etc.). There were
six calf age categories at first sampling.
The sire additive genetic effect represents .5 direct genetic effect and
the dam additive genetic effects represents .5 additive direct genetic effect +
additive maternal genetic effect. All
effects in the model, except the residual, were assumed to be fixed. Residual effects were assumed to be random
with mean zero, common variance and uncorrelated.
The GLM procedure of the SAS system (SAS,
1985) was utilized for the computations.
Results and Discussion
Weights
The BLUE of the additive and nonadditive
direct and maternal genetic effects at 30, 60, 90, 120, 150 and 205 d of age
are presented in Table 3. Among the
additive genetic effects, there was a negative trend for direct effects between
30 d and 205 d. The difference in
weight between A and B changed from !14.45 " 9.57 kg
at 30 d to !19.86 " 6.50 kg
at 205 d (P < .01), indicating that B produced calves with faster growth
than A. Previous studies have also
reported differences in weight between these two breeds at several calf
ages. Wyatt and Franke (1986), in the
analysis of multibreed beef cattle data from the southern region, reported a
significant difference between A and B for birth weight (!7.4
" .25 kg), but no significant difference
for weaning weight (!2.5 " 1.44 kg). Elzo et al. (1990) also found a significant difference between A
and B for birth weight (!2.99 " 1.04 kg),
but no significant difference for weaning weight (!4.8
" 5.15 kg) in an A H
B crossbreeding study. For maternal
effects, the ability of A to produce heavier calves than B increased from 5.92 "
7.06 kg at 30 d to 16.80 " 4.80 kg (P < .01) at 205 d. Wyatt and Franke (1986) found a significant
maternal difference between A and B at birth (6.1 "
.24 kg) and at weaning (3.7 " 1.35 kg). Elzo et al. (1990), found no significant maternal difference
between A and B at birth (2.71 " 1.65 kg) or at weaning (!13.56
" 8.19 kg).
Among the nonadditive genetic effects,
the most significant interaction effect across calf ages, for both direct and
maternal effects, was the interaction among two A alleles from one of the
parents and two B alleles from the other parent at two loci (D1 and
M1, respectively). These
interactions are the only type found in F1 animals. Thus, A H B crossbred
calves and calves from A H B crossbred cows had different growth
with respect to purebred animals. For
direct effects, this interaction increased from 6.03 "
6.12 kg at 30 d to 23.20 " 4.16 kg (P < .01) at 205 d. For maternal effects, this interaction
increased from 25.12 " 6.37 kg (P < .01) at 30 d to 50.02 "
4.33 kg (P < .01) at weaning.
Previous studies, that involved a single locus model, have also reported
significant differences for direct and maternal effects at several calf ages. Wyatt and Franke (1986) reported significant
direct and maternal heterosis effects for both birth weight (2.9 "
.18 kg, and 1.0 " .18 kg, respectively) and weaning weight
(24.2 " 1.4 kg, and 13.0 "
1.06 kg, respectively). Elzo et al.
(1990) also found significant direct and maternal effects for birth weight
(5.98 " 2.08 kg, and !5.70
" 1.91 kg, respectively) and significant
maternal effects at weaning (20.95 " 3.56 kg). The remaining interactions were not important across ages. The interaction among two alleles of the
same breed at two loci from one of the parents and an A allele at one locus and
a B allele at another locus from the other parent increased, for direct effects
(D2), from !18.33 " 10.36 kg
at 30 d to !7.52 " 7.04 kg
at 205 d, while for maternal effects (M2) showed a curvilinear
trend, decreasing from 21.36 " 12.50 kg at 30 d to 6.31 "
4.67 kg at 60 d and then increasing to 22.13 " 8.49 kg
(P < .01) at 205 d. The interaction
among an A allele at one locus and a B allele at another locus from one of the
parents and an A allele at one locus and a B allele at another locus from the
other parent increased, for direct effects (D3), from !44.10
" 26.25 kg at 30 d to !17.88
" 9.81 kg at 60 d, but then decreased to !34.40
" 17.83 at 205 d. For maternal effects, this interaction (M3)
increased from !5.61 " 29.62 kg
at 30 d to 23.01 " 20.13 kg at 205 d.
To see how the importance of the genetic
effects change across ages, the BLUE of the additive and nonadditive genetic
effects relative to the weight mean at each age are presented in Table 4. Relative values are used to avoid scale
effects. The relative additive direct
genetic effects increased from !.2164 at 30 d to !.0924
at 205 d. However, maternal effects
showed an opposite pattern. These
effects decreased from .0887 at 30 d to .0354 at 150 d, and then increased at
205 d (.0782). Thus, the importance of
the difference between A alleles and B alleles for both direct and maternal
effects decreased across ages.
Changes in nonadditive genetic effects
were not consistent across ages. The
interaction among two A alleles from one of the parents and two B alleles from
the other parent at two loci increased, for direct effects (D1),
from .0903 at 30 d to .1080 at 205 d, but decreased for maternal effects (M1),
from .3762 at 30 d to .2336 at 205 d.
The interaction among two alleles of the same breed at two loci from one
of the parents and an A allele at one locus and a B allele at another locus
from the other parent increased, for direct effects (D2), from !.2745
at 30 d to !.0350 at 205 d, while for maternal
effects (M2) decreased from .3199 at 30 d to .1030 at 205 d. The interaction among an A allele at one
locus and a B allele at another locus from one of the parents and an A allele
at one locus and a B allele at another locus from the other parent increased
for both direct and maternal effects (D3 and M3,
respectively), from !.6605 at 30 d to !.1601
at 205 d (for D3), and from !.0840 at 30 d to .1071 at 205 d (for M3). These results indicate that the A and B
alleles interact differently across ages.
Thus, there exist changes in the importance of nonadditive direct and
maternal effects during the growth of animals.
Perhaps this indicates that there are different sets of alleles that
become active at various calf ages.
Macrominerals
Macrominerals participate in the growth
and development of animals (Littledike and Goff, 1987) and contribute to
increments in weight of growing animals.
There exists a biological part-whole relationship between amounts of
macrominerals and body tissues (e.g., bone, muscle, serum). The genetic effects for amounts of macrominerals
and weights obtained in this study would be expected to be similar because
weights were used here to predict amounts of macrominerals in serum of
calves. This limits the usefulness of
the macromineral trait in this study.
The similarity of these results when compared to results that would be
obtained when direct measurements of serum macrominerals were used can not be
quantified because it was not feasible to measure directly the amount of
macrominerals in serum.
The importance of the additive and
nonadditive genetic effects over time for serum Ca, P, and Mg are presented in
Tables 2-5, 2-6, and 2-7, respectively.
Among additive genetic effects, there was
a negative trend for direct effects for all macrominerals. For Ca, this effect decreased from !215.79
" 89.46 mg (P < .05) at 30 d to !244.61
" 77.08 mg (P < .01) at 205 d (Table
5). For P, from !58.61
" 68.88 mg at 30 d to !182.73
" 68.05 mg (P < .01) at 205 d (Table
6). For Mg, from !18.74
" 21.52 mg at 30 d to !51.28
" 16.83 mg (P < .01) at 205 d (Table
7). Maternal effects increased for Ca,
from 59.22 " 66.04 mg at 30 d to 198.84 "
56.91 mg (P < .01) at 205 d (Table 5), and for Mg, from 11.03 "
15.89 mg at 30 d to 61.86 " 12.42 mg (P < .01) at 205 d (Table
7), and decreased for P, from 40.89 " 50.85 mg at 30 d to !272.73
" 50.24 mg (P < 01) at 205 d (Table
6). Among macrominerals, Ca and Mg
showed a pattern similar to the one found in weight for these additive genetic
effects. For this A-B multibreed herd,
Odenya et al. (1992a), using an intralocus model, reported a nonsignificant
additive direct genetic effect at weaning for Ca (!15.07
" 13.65 mg), P (!11.21
" 12.07 mg), and Mg (!1.23
" 2.99 mg). They also reported nonsignificant additive maternal genetic
effects at weaning for Ca (9.79 " 6.94 mg), for P (!5.72
" 6.14 mg) and Mg (1.64 "
1.52 mg). No other study has reported
estimates of these genetic effects for macrominerals.
Among nonadditive genetic effects, the
interaction among two alleles of the same breed coming from one of the parents
and two alleles of the opposite breed coming from other parent at two loci for
direct effects (D1) increased for all macrominerals. This trend was similar to the one found for
weight. For Ca, this interaction
increased from 37.45 " 57.19 mg at 30 d to 250.03 "
49.27 mg (P < .01) at 205 d (Table 5).
For P, D1 increased from 41.71 " 44.03 mg
at 30 d to 102.28 " 43.50 mg (P < .05) at 205 d (Table
6). For Mg, D1 increased
from 6.77 " 13.76 mg at 30 d to 51.70 "
10.76 mg (P < .01) at 205 d. The
interaction among two alleles of the same breed at two loci from one of the
parents and an A allele at one locus and a B allele at another locus from the
other parent (D2) increased for P, from !152.89
" 74.62 mg (P < .05) at 30 d to 10.54 "
73.72 mg at 205 d (Table 6), and for Mg, from !41.00 "
23.31 mg at 30 d to !9.32 " 18.23 mg
at 205 d (Table 7). This interaction
decreased for Ca, from 178.06 " 96.90 mg at 30 d to !106.84
" 83.50 mg at 205 d (Table 5). Only P and Mg had an increase in the
interaction among an A allele at one locus and a B allele at another locus from
one of the parents and an A allele at one locus and a B allele at another locus
from the other parent (D3), from !394.39 "
188.94 mg (P < .05) at 30 d to !267.47 " 186.66 mg
at 205 d (for P, Table 6), and from !103.75 " 59.03 mg
at 30 d to !52.80 " 46.16 mg
at 205 d (for Mg, Table 7). Serum Ca
had an increase for this interaction (D3) from !438.08
" 245.38 at 30 d to !370.32
" 167.07 mg (P < .01) at 150 d but
decreased to !497.66 " 211.43 mg
(P < .01) at 205 d (Table 5). For
maternal effects, the interaction among two alleles of the same breed coming
from one of the parents and two alleles of the opposite breed coming from the
other parent at two loci for direct effects (M1) increased only for
Ca and Mg, from 262.05 " 59.52 mg (P < .01) at 30 d to 536.07 "
51.29 mg (P < .01) at 205 d for Ca (Table 5), and from 55.72 "
14.32 mg (P < .01) at 30 d to 96.38 " 11.20 mg (P < .01) at 205 d for Mg
(Table 7). For P, M1
decreased from 213.13 " 45.83 mg (P < .01) at 30 d to 134.04 "
45.28 mg (P < .01) at 205 d (Table 6). The interaction among two alleles of
the same breed at two loci from one of the parents and an A allele at one locus
and a B allele at another locus from the other parent (M2) increased
only for Ca, from 200.67 " 116.86 mg at 30 d to 219.60 "
100.69 mg (P <.01 ) at 205 d (Table 5), and decreased for Mg, from 52.27 "
28.11 mg at 30 d to 20.95 " 21.98 mg at 205 d (Table 7). For P, this interaction decreased from
142.89 " 89.98 at 30 d to 99.47 "
68.86 mg at 150 d but increased to 142.34 " 88.89 mg at 205 d (Table 6). The interaction among an A allele at one
locus and a B allele at another locus from one of the parents and an A allele
at one locus and a B allele at another locus from the other parent (M3)
increased for Ca and Mg, from 11.97 " 276.92 mg at 30 d to 426.67 "
238 61 mg at 205 d (for Ca, Table 5), and from !20.64 "
66.62 mg at 30 d to 101.59 " 52.10 mg at 205 d (for Mg, Table
7). Thus, the trends found in these
macrominerals for nonadditive genetic effects followed a pattern similar to the
one found in weight, indicating that A and B alleles may interact differently
for these traits during calf ages.
These differences have also been found by Odenya et al. (1992a) who
reported significant intralocus nonadditive direct and maternal genetic effects
for Ca (242.21 " 51.56 mg and 373.63 "
38.44 mg, respectively) and Mg (52.16 " 11.27 mg and 69.90 "
8.41 mg, respectively). These authors
also found that only nonadditive maternal effects were important (P < .01)
for P (93.96 " 34.02 mg).
The results found in this study indicate
that these macrominerals followed a pattern similar to the one shown for
weight. It is known (Littledike and
Goff, 1987; Arnaud and Sanchez, 1990) that there are biochemical and
physiological relationships between Ca, P and Mg, and growth. Thus, the similarity in behavior of these
macrominerals and growth during preweaning are probably, in part, due to the
biochemical and physiological links that exist between Ca, P and Mg, and
growth. Also, because predictions of
amounts of macrominerals in serum used the weights of the animals, the genetic
effects of these estimated amounts of macrominerals are more similar to the
genetic effects of weight than those that would have been obtained between
direct measurements of serum macrominerals and weight.
The BLUE of the additive and nonadditive
genetic effects, relative to the average amount of macrominerals in serum at
each age, are presented in Tables 2-8, 2-9, and 2-10. Only Ca and Mg had similar trends for the relative additive
direct genetic effect to the one found for weight. For Ca, this effect increased from !.3315 at 30 d
to !.1188 at 205 d (Table 8).
For Mg, the importance of direct genetic effect increased from !.1581
at 30 d to !.1238 at 205 d (Table 10). For P, this effect decreased from .0872 at
30 d to !.1320 at 205 d (Table 9). The relative importance of additive maternal
effects decreased for P, from .0872 at 30 d to !.1970 at 205 d
(Table 9), but increased for Ca, from .0910 at 30 d to .0966 at 205 d (Table
8), and for Mg, from .0930 at 30 d to .1493 at 205 d (Table 10).
Among nonadditive direct genetic effects,
the interaction among two A alleles from one of the parents and two B alleles
from the other parent at two loci (D1) and the interaction among
alleles from both breeds A and B coming from both parents at two loci (D3)
increased for Ca and Mg, following a similar trend for weight. For Ca, D1 increased from .0575
at 30 d to .1215 at 205 d (Table 8) and D3 increased from !.6730
at 30 d to !.2418 at 205 d (Table 8). For Mg, D1 increased from .0571
at 30 d to .1248 at 205 d (Table 10), and D3 increased from !.8751
at 30 d to !.1274 at 205 d (Table 10). The interaction among two alleles of the
same breed at two loci from one of the parents and an A allele at one locus and
a B allele at another locus from the other parent (D2) increased for
P, from !.3260 at 30 d to .0076 at 205 d (Table
9), and for Mg, from !.3458 at 30 d to !.0225
at 205 d (Table 10). For Ca, this
interaction decreased from .2736 at 30 d to !.0519 at 205 d
(Table 8). These results indicates that
the importance of the combining ability of A and B change across ages.
Among the nonadditive maternal genetic
effects, the interaction among two A alleles from one of the parents and two B
alleles from the other parent at two loci (M1) and the interaction
among two alleles of the same breed at two loci from one of the parents and an
A allele at one locus and a B allele at another locus from the other parent (M2)
decreased across ages for all macrominerals.
For Ca, M1 decreased from .4026 at 30 d to .2604 at 205 d,
and M2 decreased from .3083 at 30 d to .1067 at 205 d (Table
8). For P, M1 decreased from
.4544 at 30 d to .0968 at 205 d, and M2 decreased from .3046 at 30 d
to .1028 at 205 d (Table 9). For Mg, M1
decreased from .4700 at 30 d to .2326 at 205 d, and M2 decreased
from .4409 at 30 d to .0506 at 205 d (Table 10). The interaction among alleles from both breeds A and B coming
from both parents at two loci (M3) increased for Ca, from .0184 at
30 d to .2073 at 205 d (Table 8), and for Mg, from !.1741
at 30 d to .2452 at 205 d (Table 10), while decreased for P, from .1996 at 30 d
to !.1266 at 205 d (Table 9).
The trends found for these macrominerals, especially for Ca and Mg,
showed patterns closest to the ones found in weight. As explained before, this is probably due, in part, to the links
that exist between weights and serum macrominerals.
In summary, the importance of direct and
maternal additive and nonadditive genetic effects for weight and macrominerals
changed across ages, the largest changes being for nonadditive genetic effects,
emphasizing the need to include these effects in the evaluation of animals for
weight and macrominerals. More detailed
studies need to be conducted with larger data sets to understand the biological
and physiological basis of the differences in amounts of macrominerals in serum
and their relationship with growth and development of animals.
Implications
The genetic effects (additive and
nonadditive) that affect growth traits (weight, serum macrominerals) showed
important changes during preweaning growth.
This indicates that A and B alleles interact differently during the
growth and development of the animals.
The similarity of the genetic effects for serum macrominerals and weight
is likely due to the way amount of macrominerals was calculated, directly from
weight itself.
Literature Cited
Alenda, R., T. G. Martin, J. F. Lasley
and M. R. Ellersieck. 1980. Estimation of genetic and maternal effects
in crossbred cattle of Angus, Charolais and Hereford parentage. I. Birth and weaning weights. J. Anim. Sci. 50:226.
Arnaud, C. D. and S. D.Sanchez. 1990.
Calcium and phosphorus. In: M.
L.Brown (Ed.). Present Knowledge in
Nutrition. p 212. Int. Life Sci. Inst., Washington, DC.
BIF.
1990. Guidelines for uniform
beef improvement programs. North Carolina State Univ., Raleigh.
Elzo, M. A. 1990. Covariances among
sire by breed group of dam interaction effects in multibreed sire evaluation
procedures. J. Anim. Sci. 68:4079.
Elzo, M. A., T. A. Olson, W. T. Butts,
Jr. and M. Koger. 1990. Direct and
maternal genetic effects due to the introduction of Bos taurus alleles into
Brahman cattle in Florida. J. Anim.
Sci. 68:324.
Franke, D. E. 1980. Breed and heterosis
effects of American Zebu cattle. J.
Anim. Sci. 50:1206.
Littledike, E. T. and J. Goff. 1987.
Interactions of calcium, phosphorus,
magnesium and vitamin D that influence their status in domestic meat
animals. J. Anim. Sci. 65:1727.
Odenya, W. O., M. A. Elzo, C. Manrique,
L. R. McDowell, and D. L. Wakeman.
1992a. Genetic and environmental
factors affecting serum macrominerals and weights in an Angus-Brahman
multibreed herd: I. Additive and nonadditive group genetic effects of serum
calcium, phosphorus, and magnesium and weight at weaning. J. Anim. Sci. 70:2065.
SAS.
1985. SAS User's Guide:
Statistics. SAS Inst., Cary, NC.
Wyatt, W. E. and D. E. Franke. 1986.
Estimation of direct and maternal additive and heterotic effects for
preweaning growth traits in cattle traits in cattle breeds represented in the
southern region. Southern Cooperative
Series Bull. 310. p 35.
|
Table 1. NUMBER OF SIRES AND DAMS BY BREED GROUP COMPOSITION AND
YEAR
|
|
|
Sires
|
|
Dams
|
|
Breed Groupa
|
Total
|
1989
|
1990
|
1989 &
1990b
|
|
Total
|
1989
|
1990
|
1989 &
1990c
|
|
A
.75A.25B
.5A.5B
.25A.75B
B
BRANGUS
Total
|
5
3
4
4
5
7
28
|
4
2
2
4
3
4
19
|
4
3
3
3
4
5
22
|
3
2
1
3
2
2
13
|
|
65
18
38
0
76
46
243
|
65
18
30
0
52
25
190
|
42
14
33
0
59
40
188
|
42
14
25
0
35
19
135
|
aA = Angus, B = Brahman.
bNumber of sires present in both 1989 and 1990.
cNumber of dams present in both 1989 and 1990.
|
Table 2. NUMBER OF PROGENY BY MATING TYPE
|
|
|
Breed group of sirea
|
|
|
Breed group
of dama
|
A
|
.75A.25B
|
.5A.5B
|
.25A.75B
|
B
|
BRANGUS
|
TOTAL
|
|
A
.75A.25B
.5A.5B
B
BRANGUS
TOTAL
|
26
6
12
14
8
66
|
13
5
9
18
6
51
|
7
3
5
11
5
31
|
17
6
9
15
8
55
|
20
6
16
39
11
92
|
24
6
12
14
29
85
|
107
32
63
111
67
380
|
aA = Angus, B = Brahman.
|
Table 3. BEST LINEAR UNBIASED ESTIMATES OF ADDITIVE
AND NONADDITIVE GENETIC EFFECTS FOR WEIGHT AT SEVERAL CALF AGESa
|
|
|
Age of adjustment, d
|
|
Effect
|
30
|
60
|
90
|
120
|
150
|
205
|
|
Additiveb
Direct
Maternal
Nonadditive
Directc
D1
D2
D3
Maternald
M1
M2
M3
|
!14.45"9.57
5.92"7.06
6.03"6.12
!18.33"10.36
!44.10"26.25
25.12"6.37**
21.36"12.50
!5.61"29.62
|
!10.26"3.58**
7.36"2.64**
7.50"2.29**
!5.36"3.87
!17.88"9.81
17.55"2.38**
6.31"4.67
14.02"11.07
|
!12.85"3.68**
6.90"2.72*
11.22"2.35**
!2.53"3.99
!17.95"10.09
22.06"2.45**
6.78"4.81
12.00"11.39
|
!14.51"4.41**
6.30"3.25
13.81"2.82**
!2.22"4.77
!21.93"12.09
27.09"2.93**
9.61"5.76
10.57"13.64
|
!16.16"5.21**
5.70"3.85
16.41"3.33**
!1.90"5.65
!25.92"14.30
32.13"3.47**
12.44"6.81
9.15"16.14
|
!19.86"6.50**
16.80"4.80**
23.20"4.16**
!7.52"7.04
!34.40"17.83
50.02"4.33**
22.13"8.49**
23.01"20.13
|
a Estimates expressed in kg
b Angus minus Brahman
c D1 = d22 + d12
; D2 = d23 + 2d12 ; D3 = d24
+ 2d12
d M1 = m22 + m12
; M2 = m23 + 2m12 ; M3 = m24
+ 2m12
* P < .05
** P < .01
|
Table 4. RELATIVE ADDITIVE AND NONADDITIVE GENETIC
EFFECTS FOR WEIGHT AT SEVERAL CALF AGES
|
|
|
Age of adjustment, d
|
|
Effect
|
30
|
60
|
90
|
120
|
150
|
205
|
|
Additivea
Direct
Maternal
Nondadditive
Directb
D1
D2
D3
Maternalc
M1
M2
M3
Weight mean, kg
|
!.2164
.0887
.0903
!.2745
!.6605
.3762
.3199
!.0840
66.7647
|
!.1187
.0851
.0868
!.0620
!.2068
.2030
.0730
.1622
86.4423
|
!.1158
.0622
.1011
!.0225
!.1617
.1987
.0611
.1081
111.0002
|
!.1068
.0464
.1016
!.0163
!.11614
.1993
.0707
.0778
135.9111
|
!.1005
.0354
.1020
!.0118
!.1612
.1998
.0774
.0569
160.8219
|
!.0924
.0782
.1080
!.0350
!.1601
.2336
.1030
.1071
214.8693
|
a Angus minus Brahman
b D1 = d22 + d12
; D2 = d23 + 2d12 ; D3 = d24
+ 2d12
c M1 = m22 + m12
; M2 = m23 + 2m12 ; M3 = m24
+ 2m12
|
Table 5. BEST LINEAR UNBIASED ESTIMATES OF
ADDITIVE AND NONADDITIVE GENETIC EFFECTS FOR SERUM Ca AT SEVERAL CALF AGESa
|
|
|
Age of adjustment, d
|
|
Effect
|
30
|
60
|
90
|
120
|
150
|
205
|
|
Additiveb
Direct
Maternal
Nondadditive
Directc
D1
D2
D3
Maternald
M1
M2
M3
|
!215.79"89.46*
59.22"66.04
37.45"57.19
178.06"96.90
!438.08"245.38
262.05"59.52**
200.67"116.86
11.97"276.92
|
!147.16"42.64**
65.76"31.47*
56.66"27.25*
!47.98"46.18
!193.06"116.94
181.63"28.37**
79.15"55.69
137.56"131.98
|
!165.39"45.90**
63.38"33.89
93.59"29.34**
!29.43"49.72
!237.61"125.91
231.14"30.54**
90.72"59.96
143.86"142.09
|
!178.40"52.70**
60.15"38.90
124.29"33.69**
!24.87"57.08
!303.96"144.55*
283.59"35.06**
115.37"68.84
153.46"163.13
|
!191.41"60.91**
56.93"44.97
154.99"38.94**
!20.31"65.98
!370.32"167.07*
336.04"40.53**
140.02"79.56
163.05"188.55
|
!244.61"77.08**
198.84"56.91**
250.03"49.27**
!106.84"83.50
!497.66"211.43*
536.07"51.29**
219.60"100.69*
426.67"238.61
|
a Estimates expressed in mg
b Angus minus Brahman
c D1 = d22 + d12
; D2 = d23 + 2d12 ; D3 = d24
+ 2d12
d M1 = m22 + m12
; M2 = m23 + 2m12 ; M3 = m24
+ 2m12
* P < .05
** P < .01
|
Table 6. BEST LINEAR UNBIASED ESTIMATES OF
ADDITIVE AND NONADDITIVE GENETIC EFFECTS FOR SERUM P AT SEVERAL CALF AGESa
|
|
|
Age of adjustment, d
|
|
Effect
|
30
|
60
|
90
|
120
|
150
|
205
|
|
Additiveb
Direct
Maternal
Nondadditive
Directc
D1
D2
D3
Maternald
M1
M2
M3
|
!58.61"68.88
40.89"50.85
41.71"44.03
!152.89"74.62*
!394.39"188.94*
213.13"45.83**
142.89"89.98
93.64"213.23
|
!66.66"34.29
29.81"25.31
55.04"21.92*
!65.57"37.14
!200.28"94.05*
141.51"22.82**
52.71"44.79
182.91"106.14
|
!82.72"36.36*
!23.33"26.84
71.65"23.24**
!62.44"39.38
!213.19"99.72*
150.37"24.24.19**
56.92"47.49
150.55"112.54
|
!91.98"43.74*
!77.57"32.29*
80.13"27.96**
!77.53"47.28
!254.52"119.98*
163.07"29.10**
78.20"57.14
122.48"135.41
|
!101.23"52.79
!131.81"38.97**
88.62"33.74**
!92.63"57.18
!295.85"144.79*
175.77"35.12**
99.47"68.96
94.42"163.40
|
!182.73"68.05**
!272.73"50.24**
102.28"43.50*
10.54"73.72
!267.47"186.66
134.04"45.28**
142.34"88.89
!175.23"210.66
|
a Estimates expressed in mg
b Angus minus Brahman
c D1 = d22 + d12
; D2 = d23 + 2d12 ; D3 = d24
+ 2d12
d M1 = m22 + m12
; M2 = m23 + 2m12 ; M3 = m24
+ 2m12
* P < .05
** P < .01
|
Table 7. BEST LINEAR UNBIASED ESTIMATES OF
ADDITIVE AND NONADDITIVE GENETIC EFFECTS FOR SERUM Mg AT SEVERAL CALF AGESa
|
|
|
Age of adjustment, d
|
|
Effect
|
30
|
60
|
90
|
120
|
150
|
205
|
|
Additiveb
Direct
Maternal
Nondadditive
Directc
D1
D2
D3
Maternald
M1
M2
M3
|
!18.74"21.52
11.03"15.89
6.77"13.76
!41.00"23.31
!103.75"59.03
55.72"14.32**
52.27"28.11
!20.64"66.62
|
!14.04"8.47
18.77"6.25**
11.33"5.42*
!10.04"9.18
!46.20"23.24*
39.06"5.63**
14.64"11.07
40.26"26.23
|
!21.71"9.03*
22.27"6.67**
21.12"5.77**
!3.28"9.78
!48.17"24.77
48.74"6.01**
12.96"11.80
49.76"27.96
|
!27.38"10.84*
25.44"8.00**
28.51"6.93**
1.89"11.74
!58.50"29.74
59.56"7.21**
16.30"14.16
60.53"33.56
|
!33.04"12.90*
28.62"9.53**
35.91"8.25**
!.50"13.98
!68.82"35.41
70.37"8.59**
19.65"16.86
71.30"39.96
|
!51.28"16.83**
61.86"12.42**
51.70"10.76**
!9.32"18.23
!52.80"46.16
96.38"11.20**
20.95"21.98
101.59"52.10
|
a Estimates expressed in mg
b Angus minus Brahman
c D1 = d22 + d12
; D2 = d23 + 2d12 ; D3 = d24
+ 2d12
d M1 = m22 + m12
; M2 = m23 + 2m12 ; M3 = m24
+ 2m12
* P < .05
** P < .01
|
Table 8. RELATIVE ADDITIVE AND NONADDITIVE GENETIC
EFFECTS FOR SERUM Ca AT SEVERAL CALF AGES
|
|
|
Age of adjustment, d
|
|
Effect
|
30
|
60
|
90
|
120
|
150
|
205
|
|
Additivea
Direct
Maternal
Nondadditive
Directb
D1
D2
D3
Maternalc
M1
M2
M3
Amount mean, mg
|
!.3315
.0910
.0575
.2736
!.6730
.4026
.3083
.0184
650.9044
|
!.1760
.0786
.0678
!.0574
!.2309
.2172
.0947
.1645
836.1869
|
!.1548
.0593
.0876
!.0275
!.2223
.2163
.0849
.1346
1068.7260
|
!.1369
.0462
.0954
!.0191
!.2332
.2176
.0885
.1177
1303.2287
|
!.1245
.0370
.1008
!.0132
!.2408
.2185
.0911
.1060
1537.7313
|
!.1188
.0966
.1215
!.0519
!.2418
.2604
.1067
.2073
2058.2890
|
a Angus minus Brahman
b D1 = d22 + d12
; D2 = d23 + 2d12 ; D3 = d24
+ 2d12
c M1 = m22 + m12
; M2 = m23 + 2m12 ; M3 = m24
+ 2m12
|
Table 9. RELATIVE ADDITIVE AND NONADDITIVE GENETIC
EFFECTS FOR SERUM P AT SEVERAL CALF AGES
|
|
|
Age of adjustment, d
|
|
Effect
|
30
|
60
|
90
|
120
|
150
|
205
|
|
Additivea
Direct
Maternal
Nondadditive
Directb
D1
D2
D3
Maternalc
M1
M2
M3
Amount mean, mg
|
!.1250
.0872
.0889
!.3260
!.8408
.4544
.3046
.1996
469.0548
|
!.1101
.0493
.0909
!.1083
!.3309
.2338
.0871
.3022
605.1990
|
!.1069
!.0301
.0926
!.0807
!.2755
.1943
.0735
.1945
773.9077
|
!.0973
!.0821
.0848
!.0820
!.2693
.1725
.0827
.1296
945.1760
|
!.0907
!.1181
.0794
!.0830
!.2650
.1574
.0891
.0846
1116.4443
|
!.1320
!.1970
.0739
.0076
!.1932
.0968
.1028
!.1266
1384.4334
|
a Angus minus Brahman
b D1 = d22 + d12
; D2 = d23 + 2d12 ; D3 = d24
+ 2d12
c M1 = m22 + m12
; M2 = m23 + 2m12 ; M3 = m24
+ 2m12
|
Table 10. RELATIVE ADDITIVE AND NONADDITIVE GENETIC
EFFECTS FOR SERUM Mg AT SEVERAL CALF AGES
|
|
|
Age of adjustment, d
|
|
Effect
|
30
|
60
|
90
|
120
|
150
|
205
|
|
Additivea
Direct
Maternal
Nondadditive
Directb
D1
D2
D3
Maternalc
M1
M2
M3
Amount mean, mg
|
!.1581
.0930
.0571
!.3458
!.8751
.4700
.4409
!.1741
118.5526
|
!.0892
.1193
.0720
!.0638
!.2937
.2517
.0931
.2559
157.3244
|
!.1048
.1075
.1020
!.0158
!.2326
.2353
.0626
.2402
207.1233
|
!.1063
.0987
.1106
.0073
!.2270
.2311
.0633
.2349
257.6754
|
!.1072
.0929
.1165
!.0016
!.2233
.2283
.0638
.2313
308.2275
|
!.1238
.1493
.1248
!.0225
!.1274
.2326
.0506
.2452
414.3045
|
a Angus minus Brahman
b D1 = d22 + d12
; D2 = d23 + 2d12 ; D3 = d24
+ 2d12
c M1 = m22 + m12
; M2 = m23 + 2m12 ; M3 = m24
+ 2m12
Appendix
Reparameterization of Nonadditive Fixed Genetic
Effects
1. Definition
of nonadditive genetic effects at one and two loci
Let
Ps(A) = fraction of Angus in
the sire,
Ps(B) = fraction of Brahman in
the sire,
Pd(A) = fraction of Angus in
the dam,
Pd(B) = fraction of Brahman in
the dam.
Define (Elzo, 1990) the interaction
effects at one locus as:
v11 = interaction between A alleles from both parents,
v12 = interaction between A alleles from one of the parents and B
alleles from the other parent,
v13 = interaction between B alleles from both parents.
The probabilities for each of the above
interactions are:
t11 = Prob(v11) = Ps(A)*Pd(A),
t12 = Prob(v12) = Ps(A)*Pd(B)
+ Ps(B)*Pd(A),
t13 = Prob(v13) = Ps(B)*Pd(B).
The possible allelic interactions
occurring among alleles at two loci are defined as follows:
v21 = interaction among two A alleles at two loci from both parents,
v22 = interaction among two A alleles at two loci
from one parent and two B alleles at two loci from the other parent,
v23 = interaction effect among two alleles of the same breed at two
loci from one parent and an A allele at one locus and a B allele at another
locus from the other parent,
v24 = interaction effect among an A allele at one locus and a B allele
at another locus from one parent and an A allele at one locus and a B allele at
another locus from the other parent,
v25 = interaction effect among two B alleles at two loci from both
parents.
The probabilities of occurrence of the
above interactions are:
t21 = Prob(v21) = [Ps(A)*Pd(A)]2,
t22 = Prob(v22) = [Ps(A)*Pd(B)]2
+ [Ps(B)*Pd(A)]2,
t23 = Prob(v23) = 2[Ps(A)2*Pd(A)*Pd(B)]
+ 2[Ps(A)*Ps(B)*Pd(A)2] + 2[Ps(B)2*Pd(A)*Pd(B)]
+ 2[Ps(A)*Ps(B)*Pd(B)2],
t24 = Prob(v24) = 4[Ps(A)*Ps(B)*Pd(A)*Pd(B)],
t25 = Prob(v25) = [Ps(B)*Pd(B)]2.
It is known that 
. Thus, there exists
a linear dependency within and among the interaction effects. It is necessary to redefine the above
interactions.
Define
v113 = v11 + v13
t113 = t11 + t13
v215 = v21 + v25
t215 = t21 + t25.
Then,
t113 = 1 - t12 and
t215 = 1 - t22 - t23 - t24.
Thus, the sum of the nonadditive effects
are:
At one locus,
= t113v113 + t12v12
= (1 - t12)v113 + t12v12
= t12(v12
- v113) + v113.
At two loci,
= t215v215 + t22v22
+ t23v23 + t24v24
= (1
- t22 - t23 - t24)v215 + t22v22
+ t23v23 + t24v24
= t22(v22
- v215) + t23(v23 - v215) + t24(v24
- v215) + t25(v25 - v215) + v215.
But t12 = t22 + 2t23 + 2t24 (see Section 2 below).
Replacing t12 in the summation
at one locus gives:
= t12(v12 - v113)
+ v113
= (t22
+ 2t23 + 2t24)(v12 - v113) + v113.
So, the sum of nonadditive effects at one
and two loci is:
= (t22 + 2t23 + 2t24)(v12 - v113)
+ v113 + t22(v22 - v215) + t23(v23
- v215) + t24(v24 - v215) + v215
= t22(v22-v215)
+ t22(v12-v113) + t23(v23-v215)
+ 2t23(v12-v113)
+ t24(v24-v215) + 2t24(v12-v113) + v113
+ v215.
Let d12 = v12-v113,
and d2n = v2n-v215, n=2,..,4.
= t22d22 + t22d12
+ t23d23 + 2t23d12 + t24d24
+ 2t24d12 + v113
+ v215.
Therefore, the BLUE of v2n,
n=2,..,4, are a linear combination of d12 and d2n, the
allelic interaction effects at one and two loci, respectively.
To estimate direct effects, tij
is computed using the fractions of Angus and Brahman in the sire and in the dam
of the calf. To estimate maternal
effects, tij is computed using the fractions of Angus and Brahman in
the sire and in the dam of the dam of the calf.
2. Dependency
between the nonadditive effects at one and two loci
Using the definition of the t2l's
given in the preceding section, t22 + 2t23
+ 2t24 can be expressed as:
t22 + 2t23 + 2t24
=
[Ps(A)*Pd(B)*Ps(A)*Pd(B)]
+ [Ps(B)*Pd(A)*Ps(B)*Pd(A)]
+
[Ps(A)*Pd(B)*Ps(A)*Pd(A)]
+ [Ps(B)*Pd(A)*Ps(A)*Pd(A)]
+
[Ps(A)*Pd(B)*Ps(B)*Pd(B)]
+ [Ps(B)*Pd(A)*Ps(B)*Pd(B)]
+
[Ps(A)*Pd(B)*Ps(B)*Pd(A)]
+ [Ps(B)*Pd(A)*Ps(A)*Pd(B)]
=
Ps(A)*Pd(B)[Ps(A)*Pd(B)+Ps(A)*Pd(A)+Ps(B)*Pd(B)+Ps(B)*Pd(A)]
+
Ps(B)*Pd(A)[Ps(B)*Pd(A)+Ps(A)*Pd(A)+Ps(B)*Pd(B)+Ps(A)*Pd(B)]
=
[Ps(A)*Pd(B)+Ps(B)*Pd(A)]*
[Ps(A)*Pd(B)+Ps(A)*Pd(A)+Ps(B)*Pd(B)+Ps(B)*Pd(A)]
=
[Ps(A)*Pd(B)+Ps(B)*Pd(A)]*[Ps(A){Pd(B)+Pd(A)}+Ps(B){Pd(B)+Pd(A)]
=
[Ps(A)*Pd(B)+Ps(B)*Pd(A)]*[Ps(A)+Ps(B)]
=
Ps(A)*Pd(B)+Ps(B)*Pd(A).
The last two equations are based on the fact that
Ps(A) + Ps(B) = 1 =
Pd(A) + Pd(B)
But t12 =
Ps(A)*Pd(B) + Ps(B)*Pd(A).
Therefore, t12 = t22 + 2t23 + 2t24 (q. e. d.)
Animal Breeding Mimeo,
University of Florida, 1992, pp 1-30.