Universidad Nacional de Chimborazo
NOVASINERGIA 2020, Vol. 3, No. 1, diciembre-mayo (6-16)
ISSN: 2631-2654
https://doi.org/10.37135/ns.01.05.01
Research Article
http://novasinergia.unach.edu.ec
Further consideration on mating systems for the tropics
Una revisión de los sistemas de apareamiento para el trópico
Jorge A Ordóñez V
Programa de Economía Agrícola, Universidad Nacional Experimental de los Llanos Occidentales “Ezequiel
Zamora” UNELLEZ, Barinas, Venezuela, 5201
* Correspondence: jaordonezv@gmail.com
Recibido 05 mayo 2020; Aceptado 15 mayo 2020; Publicado 01 junio 2020
Abstract:
Beef cattle production systems on pasture differ in terms of the use of resources,
degree of intensification, cultural roles, among others. In relation to the efficiency
and productivity of Beef Cattle Production Systems on Pasture, significant
progress could be made in terms of adopting improved management procedures.
Bibliographic research about Mating Systems in beef cattle production systems
and their application in the American Tropics, with emphasis on Venezuela, was
performed. It reviews the conditions and management practices required to
achieve the expression of genetic potentials, the requirements, advantages, and
disadvantages of alternatives to the rotational system to compare them and
recommend accordingly. Composites and Modified [F1] mating systems have
similarities. However, some differences were highlighted: The use of F1 sires
impedes loss of heterosis due to renewed inbreeding, expands heterosis retention,
does not interfere with selection for additive traits, and capitalizes genetic progress
in the parental breeds. In conclusion, F1 sires able to thrive on adverse conditions,
on a crossbreed population of cows in successive generations, might be a feasible
way to overcome the limitations of other mating systems, combine adaptability
with improved performance in small herds while keeping management simple,
capacity for adjustment, and adaptation to new restrictions and opportunities
generated by the changing environment.
Keywords:
Beef cattle, composites, crossbreeding, heterosis, Venezuela.
Resumen:
Los sistemas de producción de ganado de carne a pastoreo difieren en materia de
utilización de recursos, grado de intensificación, roles culturales, entre otros. En
relación con la eficiencia y la productividad de los sistemas de producción de
ganado bovino de carne a pastoreo, se podría hacer grandes progresos en lo
relativo a la adopción de procedimientos de manejo mejorados. Se realizó una
investigación bibliográfica sobre los Sistemas de Apareamiento en los sistemas de
producción de ganado bovino de carne y su aplicación en el Trópico Americano,
con énfasis en Venezuela. En ella se revisan las condiciones y prácticas de manejo
requeridas para lograr la expresión de los potenciales genéticos, los
requerimientos, ventajas y desventajas de las alternativas al sistema rotativo para
compararlos y recomendar en consecuencia. El sistema de apareamiento intersé
para la generación de Compuestos y el [F1] modificado tienen similitudes, pero
se han evidenciado algunas diferencias: El uso de sementales F1 impide la
pérdida de heterosis debido a la renovación de la consanguinidad, amplía la
retención de la heterosis, no interfiere con la selección de caracteres aditivos y
capitaliza el progreso genético en las razas progenitoras. En conclusión, unos
toros F1 capaces de prosperar en condiciones adversas, sobre una población de
vacas cruzadas, en generaciones sucesivas, podrían ser una forma viable de
superar las limitaciones de otros sistemas de apareamiento, combinar la
adaptabilidad con un mayor desempeño en rebaños pequeños, manteniendo al
mismo tiempo un manejo sencillo, capacidad de ajuste y adaptación a las nuevas
restricciones y oportunidades generadas por el entorno cambiante.
Palabras clave:
Compuestos, cruzamientos, heterosis, ,vacunos de carne, Venezuela.
http://novasinergia.unach.edu.ec 7
1 Introduction
The sustainability of beef cattle production systems in
relation to concerns about climate change and the
quality of the services provided to society has become
a fundamental issue for public debate. However, beef
cattle production systems on pasture differ in terms of
the use of resources, degree of intensification, cultural
roles, among others. At least 50% of Latin America
and the Caribbean is either too dry, too wet, too steep,
too shallow, too infertile, or too fragile to sustain
cultivation or to support forests. Analyzing
sustainability at the farm level for gaining an
understanding of the reproducibility of pastoral
systems should involve the management of animals
and grazing resources, their economic performance,
and environmental implications.
Grasslands are too often neglected in national land
resource inventories and are given pejoratives as
"uncultivated, idle or underutilized land," but, in
Venezuela, savannahs and grasslands occupy 57% of
the total agricultural land (cropland and forest
included). If it were possible to measure the energy
consumed by the grazing herd in the equivalent of
grain production, the result would be staggering. In
fact, 13+ million heads of cattle consumed in 2007,
only for maintenance, the equivalent of 12,3 million
MT of yellow corn: 5,1 times more than the record
corn harvest of 2007 (INE, 2007). It is about the proper
use of this resource what matters.
On the efficiency and productivity of Beef Cattle
Production Systems on Pasture significant progress
could be made in terms of adoption of improved
management procedures: Individual identification of
the animal to permit proper record-keeping;
Generalized use of the breeding season, allowing
better synchronization of nutritive resources and herd
requirements (Arriaga, 2010); The systematic
weaning and the consequent segregation of the herd by
sex, age, and production status will allow the use of a
limited supplement of younger animals; Development
of applied techniques of forage conservation where
tame pasture grass is available, as well as range
improvement and soil conservation practices, (Tejos,
2014); General improvement of communication and
transportation; more extensive use of mineral
supplementation (Depablos, Ordóñez, Godoy, &
Chicco, 2009), vaccination, dipping and a higher level
of sanitary control (Pierre & Camaripano, 2009;
Camaripano, Reina, & Plasse, 2011). All the above-
mentioned practices are currently being used in
experimental stations and elite herds (Verde, Medina,
& Borges, 2007; Depablos, Ojeda, Martínez, &
Colmenares, 2010). Their use has accounted for an
almost doubling of the production over the
commercial producer's normal level (Plasse, 2000).
Dr. Gordon E. Dickerson was a visionary and
productive scientist whose many scientific
contributions built the scaffolding of the systems
approach to the genetic improvement of the economic
efficiency of beef production (Tess & Davis, 2002). G.
Dickerson's contributions to understanding heterosis
and epistasis rank among his most important works
(Dickerson, 1969; Dickerson, 1973). These studies
demonstrated that economic efficiency was most
improved in systems that exploited both individual
and maternal heterosis.
Hybrid vigor or heterosis is the superiority of the
crosses over the average of the parent breeds.
Bunning, Wall, Chagunda, Banos, & Simm, (2019)
performed a meta-analysis of heterosis in tropical
cattle, concluding: Heterosis was found to be
beneficial for a range of economically important traits,
including those related to fitness such as fertility and
longevity, which are particularly important in low
input systems prevalent in the tropics. The greatest
heterosis was expressed in crosses of breeds adapted
to different environments; they allow the combination
of complementary production and fitness traits,
meaning that there is great potential to utilize heterosis
to increase profitability.
To assess the magnitude of heterosis in each
environment, it is necessary to compare F1 crosses
with the average of both pure parents (Plasse, 2000).
Some estimates of the effects of heterosis in Criollo -
Bos indicus crosses have been published in
Venezuela. Ordóñez et al. (1974) reported for age (-
72.0 days) and weight (35.2 kg) at puberty of heifers,
while Plasse (1983) summarized the available average
values (variation range between experiments in
parentheses) for the different characteristics:
pregnancy percentage, 14 % (9-16 %); weaning
weight, 11 % (9-13 %); post-weaning weight 16 %
(12-19 %). In crosses among Zebu and Bos taurus
breeds other than Criollo, due to lack of adaptation in
pure form only Ordóñez (1985) estimated heterosis for
birth weight (-0.5 kg), weaning weight (3.0 kg) and 18
months weight (16.1 kg) in crosses Brahman X
Charolais to conclude that: (1) The low adaptability of
the Charolais cow in pure breeding prevented the
expression of the crossbred genotypes in pre-weaning
traits, while the post-weaning poor adaptation of the
Charolais progeny, increased the heterosis in post-
weaning gain; (2) Heterosis is not a parameter
determined by the genotypes that intervene in the
crossing, but its expression is conditioned by the
environment; (3) The equations applied to estimate
performance using mean breed effects and expected
http://novasinergia.unach.edu.ec 8
heterosis might be inadequate when environmental
limitations or lack of adaptability prevent the
expression of genetic potentials; (4) Although the
superiority of the crosses over the average of the
parent breeds is explained in genetic terms as the
increased heterozygosity in the hybrid, the phenotypic
expression of the superiority observed in hybrids
relative to their parents, for some traits, is the result of
production potentials that are only reached in an
adequate environment, both must be considered for
the definition of genetic programs.
When developing breeding systems applicable to the
tropics, some conditions must be accomplished. To be
useful, the system must: (1) Allow female
replacements to be generated throughout the herd; (2)
Effectively exploit heterosis; (3) Do not interfere with
selection for additive traits; (4) Both females and
males must be fully adapted to the conditions under
which they will have to work.
Rotational crossbreeding seems to be the only mating
system that fulfills these conditions. In a previous
paper, (Ordóñez, 1975) pointed out the shortcomings
of rotation: (1) Complicated handling (more than half
the herds keep one or at most two bulls) and (2)
Divergent genetic composition between successive
generations. This work aims to evaluate and compare
the advantages of alternative mating systems
proposed: (A) Composites or the development of new
breeds;(B) Modified Absorption system where the
bulls used on private holdings are F1.
2 Methodology
This work was based on bibliographic research about
Mating Systems in beef cattle production systems and
their application in the American Tropics, with
emphasis on Venezuela. It reviews the theoretical
basis of hybrid vigor or heterosis (Cartwright, 1970;
Dickerson, 1969; Dickerson & Willham, 1983; Lush,
1948; Stonaker, 1973; Willham, 1970) and its
expression in economically important characters (Tess
& Davis, 2002; Willham, 1972) in grazing cattle
production systems (Bunning et al., 2019; Long, 1980;
Neville, Utley, & McCormick 1985; Ordóñez et al.,
1974; Ordóñez, 1985; Plasse, 1983), as well as the
effects of inbreeding (Dickerson, 1973; Lopez-Fanjul,
1974), crossing over and genetic recombination on the
retention of heterosis (Koch, Dickerson, Cundiff, &
Gregory, 1985; Sanders, Key, Riley, & Lunt, 2005),
resulting from experiments mostly performed in a
temperate climate and its application in the tropics
(Madalena, 2001). It reviews the conditions (Verde et
al., 2007; Depablos et al., 2010) and management
practices of proven technical and economic feasibility
(Arriaga, 2010; Camaripano et al., 2011; Depablos et
al., 2009; Ordóñez, 1990; Pierre & Camaripano, 2009;
Tejos, 2014) required to achieve the expression of
genetic potentials. Finally, the requirements,
advantages, and disadvantages of two alternative
crossing systems are formulated (Cartwright &
Fitzhugh, 1972; Cartwright, Fitzhugh, & Long, 1975;
Ordóñez, 1975; Plasse, 2000; Plasse, Bauer, Galdo, &
Verde, 2005a; Plasse, Bauer, Galdo, & Verde, 2005b),
to the rotational system to finally compare them and
recommend accordingly. The sources consulted were
extracted from the mostly American scientific
literature, in printed or electronic journals, memories
of scientific meetings, and theses.
3 Review and discussion
The criteria to compare the advantages or
disadvantages of the alternative mating systems
proposed should consider several aspects: (1)
Expected heterosis and heterosis retention are the
most important; (2) Flexibility to altered management,
or market conditions or unexpected performance of
the cross, resulting in the loss of resources, time, and
efforts; (3) The simplicity of management; (4)
Previous experiences in similar conditions; (5)
Interference with selection for additive traits; (6)
Minimum population size.
3.1 Composites
Composite development may be indicated when
heterosis is essential, if initial unfavorable
recombination effects are negligible, when there are
new objectives or altered management conditions, and
in areas where the simplicity of the breeding program
is essential. Zebu, some exotic breeds, and native
breeds have been used in some instances for
developing Composites in the tropics (Canchin and
Montana in Brazil, Bonsmara in South Africa,
Droughtmaster in Australia, Santa Gertrudis,
Bradford, Brangus, and Charbray in the Southern
United States).
(1) Management: Synthetic breeds will contribute to
more straightforward management requirements.
Kowalsky (2020) described the Venezuelan cattle
herd structure: 94,6 % are smallholdings, 87% own
less than 30 crossbred cows. They are well-served
with just one bull. As in any pure stock, sires of similar
genetic composition are used. Thus, the number of
pastures required will be minimal, particularly
favorable to small ranchers.
(2) Selection for additive traits: Lopez-Fanjul (n.d.)
has shown that when heritabilities have been
estimated in composites, their value was not found to
differ from those in their parental breeds. But,
selection intensity will be limited in the first
generations, if inbreeding is to be kept at minimal
http://novasinergia.unach.edu.ec 9
levels as well as a need for increased numbers as the
breed develops.
(3) The exploitation of heterosis and heterosis
retention: Heterosis, the difference between the
average performance of a cross and the average
performance of the parents, has two main components.
The first and most important is the result of
differences in gene frequencies between the two
parental populations and the degree of dominance
present. Willham (1970) has shown how heterosis at a
single locus in the F1 is equal to
, where
is the difference in the gene frequency between the
two parental populations, and is the degree of
dominance. After the first filial generation F1, the
gene frequencies remain constant according to the
Hardy-Weinberg equilibrium, then the amount of
heterosis remains constant in the successive
generations. As the gene frequencies in the F1
becomes intermediate between the parental gene
frequencies, the degree of heterosis is equal to
; meaning that half the original heterosis is
retained in successive generations. In general, if n
breeds are utilized in the Composite development, 1/n
of the original heterosis is lost, or (n-1)/n is retained.
The second component of heterosis is due to favorable
epistatic combinations of linked genes in the repulsion
phase (inherited separately), which had been fixed by
selection or isolation in the parental breeds. Under
interse mating, successive crossing over and
recombination will tend to destroy those linked
groups. After two or three generations, all these
epistatic effects will probably be lost. When the
epistatic effects are significant, loss of heterosis will
be larger than what is theoretically expected. Koch et
al. (1985) result supports the hypothesis that heterosis
effects of crosses among Bos taurus breeds, for traits
related to growth and size as well as for reproductive
and maternal traits, can be accounted for by the
dominance effects of genes. Nevertheless, strengthen
that large-scale comprehensive experiment is needed
to estimate retention of heterosis in advanced
generations of interse mated composite populations
with contributions by both Bos taurus and Bos indicus
breeds. Indeed, Sanders et al. (2005) present
additional questions regarding the validity of the
dominance model for the prediction of heterosis and
heterosis retention for reproductive and maternal traits
in Bos indicus x Bos taurus females. Heterosis
retention estimates for the traits of interest were found
to be lower than expectations of the dominance model
for some groups and higher than expectations of the
dominance model for other groups. Plasse et al.
(2005a) suggested that line formation was difficult
since crosses among tropical breeds under
conventional management did not exceed the best
parental breed. Madalena, (2001) concluded that in
Bos taurus and Bos indicus crosses for milk, the
performance of the F1s has been much higher than the
other crosses, followed by the rotational crosses, while
the "bimestizos" (in Brazil, daughters of mestizo
parents) have had very poor performance. The relative
economic performance of F1, rotational cross, new
breed (Composite), and Holstein were, respectively,
100, 59, 30, and 21, in privates farms.
(4) Minimum population numbers: Lopez-Fanjul
(1974) states that the primary advantage of increased
heterozygosity can be "squandered" by renewed
inbreeding unless large population numbers are kept.
How large should the experimental herd be to keep
inbreeding at a low level can be estimated with some
approximation.
The rate of inbreeding is a function of effective
population size. Lush (1948) showed how
where is the effective population size and is
the variation in inbreeding per generation. When there
is a different number of males and females,
becomes
, where
Nm =
number of
males and
Nf =
number of females. The rate of
inbreeding per generation can be rewritten as
. As population size becomes larger,
becomes smaller, and the generation with the
smallest number has the most significant effect.
However, as the population size increases, the
previous inbreeding is not eliminated but remains
where it was before the increase in number because
new inbreeding is reduced. Thus, the first three or four
generations, while the Composite is being tested, are
the most important ones in terms of inbreeding. More
than ten to twelve unrelated bulls and two hundred and
fifty to three hundred cows are required per generation
if less than one percent increase in inbreeding per
generation is desired, assuming random mating, which
is not the case. Even if selection and further assortative
mating are used, the above holds because Lush, (1948)
has shown them to be almost powerless in changing
heterozygosis. Selection will be limited to the extent
that more sires per generation will have to be used,
which will reduce intensity. , where
is the number of males reaching reproductive age and
the proportion saved. If selection intensity
, for
i to be large, must be small, but if is small, Nm will
also be small in the Composite, making large.
Then the advantage of more considerable additive
variance can be neutralized by the requirement of
keeping inbreeding at a low level.
In conclusion, a large population is a condition for full
utilization of heterosis resulting after crossing
different breeds for the development of Composites.
The cost of keeping such a large population can limit
the effectiveness of this proposal.
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(5) Flexibility against risk: The success or failure of
the Composite is determined at the precise moment of
the population closure. Sampling errors, loss of
heterosis due to renewed inbreeding, or
recombination, the variation in prevailing conditions
(environment or market), or unexpected performance
of the Composite may result in the loss of resources,
time, and efforts. If, after three or four generations, the
results are unsatisfactory, everything will have to start
all over. The literature contains just the successful
trails, while many failures stay undisclosed to the
public. This risk factor must be considered before any
breed development is begun. Plasse (2000) concludes,
"The author is not aware of any information in the
current Latin American scientific literature that would
allow him to responsibly recommend this system
(composite) to livestock practice." While Leachman
(2000) proposed "composed populations of several
original breeds, permanently open to new genetic
contributions."
3.2 Modified Absorption
A second alternative to rotation system could be one
that combines the simplicity of the purebred mating,
exploits heterosis in successive generations with the
versatility of totally open herds. Such a mating system
was empirically purposed in previous papers
(Ordóñez, 1975, cited by Ordóñez, 1990) based on
earlier work by Cartwright & Fitzhugh (1972) and
Koger (1973). A schematic representation of the
mating system is depicted in figure 1.
Figure 1: Modified Absorption to [F1].
A proportion of purebred female of Breed A (adapted
to the environment) is mated to sires of Breed B. The
F1 progeny of that mating, bulls, and heifers, are
removed from the purebred herd and incorporated into
the commercial herd. F1 sires are mated to the
commercial cows, originally of Breed A, in successive
generations until all the females in the commercial
herd are of genetic composition like the F1. The
modified F1's is represented within brackets [F1]. The
female progeny from the commercial herd are kept as
replacements, while the males go to market. In any
generation, new unrelated F1 sires are used. It can be
said that the mating system tries to absorb or grade up
to [F1]. The expected composition of successive
generations at equilibrium has been developed with
that of the rotation to allow comparisons.
Rotation: First, let us call
n
Y
the fraction of genes
from the parental breed in the n
th
generation and
n
X
the fraction of genes from the maternal grandsire in
the same generation of any progeny of rotation
mating.
Then:
Or
but
in the purebred population, then in general:
while,
(1)
Table 1 summarizes the application of this general
formula to fill the genetic composition of the herd in
the successive generations of rotational crosses.
Modified [F1]: By analogy in Modified [F1]
is the
fraction of genes from the newly introduced breed
carried by the progeny in generation n; then in general:
(2)
Table 2 summarizes the application of these general
formulas to fill the genetic composition of the herd in
the successive generations of "Modified [F1]".
As can be seen from table 2, the genetic composition
of the population at equilibrium resembles that of the
first generation of interse mating. The properties of
such a population must be studied in more detail.
(1) The simplicity of management: At the commercial
level, the system performs as simply as does any pure
breeding system. Only one breed of sires is used,
allowing for entire herds in the small operations. The
system also provides for their replacement females.
Still, F1 sires must be provided from elite herds
located at accessible areas, where AI increases the
ability to capitalize on genetic progress in the
progenitor breeds, under the prevailing conditions.
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(2) Flexibility: It is one additional advantage of the
proposed system. Change in the exotic breed due to
adjustment of the performance of the products
following changes in environmental conditions, the
market, and the goals is relatively simple and in no
way affects the development of the system, reducing
the risk mentioned above. The flexibility available
through crossbreeding to match performance levels to
specific conditions must also be considered a real
advantage (Long, 1980).
(3) The adaptability of the parents: As has been
indicated, a primary consideration for crossbreeding is
the possibility of combining useful traits quickly in an
individual. The main objective of using crossbreed
bulls is to combine in an animal the adaptability of the
tropical breed and the improved performance of the
exotic, hoping to obtain an animal able to work in
adverse conditions, but that simultaneously transmits
to his progeny desired genes for beef production. F1
Zebu x European bulls have proven to be suitable as
mentioned by Neville et al. (1985) on "the comparison
of SB (purebred) and F1 bulls for reproductive and
progeny performance… there were no differences
(P>.05) among the four sire groups for the proportion
of cows exposed that had a calf, had a live calf or
weaned a calf." The adaptability of the female, on the
other hand, is guaranteed if their genetic potential for
mature size and particularly for milk production, is
maintained within limits coupled with the level of
nutrition (Plasse, 2000). As stated by Willham (1972),
"If low-quality roughage that can be harvested only by
the cow is considered, milk production in excess of
growth demands by the calf seems of little economic
value." The cow adaptability depends, to a large
extent, on the exotic breed, which is chosen to be
incorporated in the population.
Table 1: Genetic Composition in Successive Generations of Rotational Crosses.
Generation
Genetic composition of Females of
Herd A*
Genetic composition of Females of
Herd B*
0
1
0
1B:0A
1A:0B
1
1B:1A
1A:1B
2
3B:1A
3A:1B
…
…
…
…
…
n
…
…
…
…
…
ꝏ
* A and B are breeds of sires mated to those females.
Table 2: Genetic Composition in Successive Generations of "Modified [F1]".
Generation
n
Y
n
X
Genetic composition of females
Genetic composition of
sires
0
0
1
1A:0B
( ) ( )
1 2 A : 1 2 B
1
14
34
3A:1B
( ) ( )
1 2 A : 1 2 B
2
38
58
3B:1A
( ) ( )
1 2 A : 1 2 B
…
…
…
…
…
n
1
21
2
n
n+
−
1
n
Y−
A : B
nn
XY
( ) ( )
1 2 A : 1 2 B
…
…
…
…
…
ꝏ
12
12
( ) ( )
1 2 A : 1 2 B
( ) ( )
1 2 A : 1 2 B
Table 3: Some comparisons between the main systems.
Mating
System
% Crossbreed
% Heterosis of
individual
Sire
adaptability
Sire
value
Management
simplicity
Calf
Cow
Calf
Cow
Sire
Purebred
0
0
0
0
0
1
1
1
Rotation
100
100
67
67
0
<1
>1
<1
F1 x [F1]
88
83
50
50
100
1
1
1
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(4) The efficiency - the ability to produce an output
without waste: As indicated by Cartwright (1970),
rather than individual performance, the whole system
performance must be considered when comparisons
between systems must be made. Following the scheme
indicated by Cartwright et al. (1975), some
comparisons between the main alternatives made in a
previous paper, are included here because of their
importance. Although the rotational cross seems to be
more useful for exploiting hybrid vigor, the last four
columns of table 3 can make a difference in the
profitability of the proposed system.
(5) The exploitation of Heterosis: Following
Willham's (1970) approach to genetic consequences
of crossbreeding, some properties of such a population
can be estimated. Considering a single locus with two
alleles L1 and L2 and two breeds A and B, that have
gene frequencies p:q and p+Δp:q-Δp.
( )
2
AA
p q a pqd
= − +
( )
2
22
BB AA
pa p d
= + −
( )
2
AB AA
pa p d
= + −
; where µ
AB
is mid parent
value,
1F AB BA AA
pa
= = = +
where µ
F1
is the mean of the reciprocal crosses µ
A.B
and µ
B.A;
a is the average effect of a gene substitution,
and d is the dominance deviation from the
homozygote average.
Then, heterosis is defined as the difference between
the mean of the cross and the average of the parents
and is equal to:
( )
( )
1
= 2
= 2
F AB
AA AA
h
pa pa p d
pd
=−
+ − − +
(3)
For this locus to show heterosis, it is required both a
difference in allele frequencies between the
populations (Δp ≠ 0) and positive dominance (d > 0).
Then, the genetic array of the crossbreed F1 sire is
12
22
pp
p L q L
+ + −
and the mean of the first-generation crossing A
females and F1 males can be developed
( ) ( )
( )
1
22
22
2
22
1
2
2
1
2
FA
AA
pp
a p p q q
pp
d pq q p
a p q dpq p a d p q
pd
= + − +
+ + −
= − + + + −
= +
then, heterosis:
( )
( )
( ) ( )
11
1
2
2
2
1
2
2
F A F AB
AA AB
h
pa pa p d
pd
p a p d
=−
= + − − +
=
= − +
We have estimated
n
Y
as the fraction of genes from the
newly introduced breed in the progeny of generation
n. This same fraction remains of the difference
between gene frequencies at the locus level. Then in
general, means and heterosis from the mating of F1
sires with the crossbred females of generation n can be
calculated as follows:
Genetic array:
Males:
11
12
22
p p L q p L
+ + +
Females:
( ) ( )
12
nn
p Y p L q Y p L+ + −
Genotypic array
( )
2
2
11
11
22
nn
L L p p p Y p p Y p= + + +
( )
( )
2
2
11
1 2 2
22
1
2
1
2
n
nn
n
L L pq q p p p Y q p
Y p p Y p
Yp
= + − +
− −
−
( )
2
2
11
22
22
nn
L L q q p Y q p Y p= − − +
Heterosis:
( )
( )
( ) ( )
2
11
2
2
1
2
1
1 1
2
AB AA n n
FF
AA
nn
Y pa Y p d
pa p d
pa Y p d Y
− = + + −
− − +
= + + + −
( )( )
2
11
1
1
2
nn
FF
h Y pa Y p d
= − + −
(4)
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The level of heterosis depends on the fraction of the
squared difference in gene frequency remaining and
the degree of dominance minus the additive
component of the differences.
By analogy, table 4 summarizes the application of
these general formulas to fill the gene frequencies and
expected heterosis of the herd in the successive
generations of "Modified [F1]" cross.
The expected heterosis from the system in equilibrium
is equal to that of an interse mating. However, it is
necessary to indicate that while synthetics reach their
maximum level of heterosis in the first generation of
crosses, Modified Absorption to [F1] behaves in the
opposite direction, the level of heterosis increases in
successive generations as the coefficient of Δp
increases. That can be a disadvantage if maximum
production potential is desired rapidly, but it could be
an advantage if the selection is applied
simultaneously. It also gives time to the breeder to
provide the appropriate environment required to
match the new genotype tested. On the other hand,
when epistatic effects are essential components of
heterosis, F1 sires can make partial use of this
advantage. If recombination is low enough and
selection is applied, the initial disequilibrium between
repulsion and the coupling phases may persist for
several generations with the additional heterotic
advantage. Furthermore, as heterosis in sire
reproductive performance is important, it could
represent an additional advantage of this system over
the rotation.
(6) Loss of heterosis due to renewed inbreeding: As
the population is maintained open, unrelated sires can
be used to generate F1 sires, in every generation.
Then, the probability of heterosis losses due to
renewed inbreeding is small if nonexistent.
(7) Selection for the additive traits: As said before, F1
sires must be provided from elite herds where AI is
available, capitalizing on the genetic progress in the
progenitor breeds. Then, selection among the
purebred herd that generates the F1 sires will have
similar results that they would have under purebred
mating. Willham (1970), discussed how selection
response in crossbreds is lower than that obtained
when selecting among purebreds or advanced
generations of interse mating. However, the
heritability of a trait is a ratio between the additive and
total phenotypic variances. Although the dominance
and epistatic components of variance are increased in
the crossbred, the additive component is also
increased. Stonaker (1973) has found that
heritabilities are somewhat higher in crossbreds rather
than in purebreds.
Table 4: Expected heterosis of the herd in successive generations of "Modified [F1]".
Generation
Gene frequency of females
Gene frequency of sires
Expected heterosis
0
:pq
11
22
:p p q p+ −
( )
2
1
2
pa p d− +
1
11
44
:p p q p+ −
11
22
:p p q p+ −
( )
2
3
1
44
pa p d− +
2
33
88
:p p q p+ −
11
22
:p p q p+ −
( )
2
5
1
88
pa p d− +
…
…
…
…
n
:
nn
p Y p q Y p+ −
11
22
:p p q p+ −
( ) ( )( )
2
1
2
1
nn
Y pa Y p d− + + −
…
…
…
…
ꝏ
11
22
:p p q p+ −
11
22
:p p q p+ −
( )
2
1
2
pa p d− +
Since crosses are generally less variable, this higher
heritability is probably the result of a smaller
environmental and a more significant genetic
contribution to the difference. Additionally, Sires in
Breed B might be selected mainly on additive merit
based on their progeny from cows of Breed A.
If nonadditive effects contributed to their ranking on
the EBV, then the Sires selected in Breed B would be
chosen in part for their genetic differences from Breed
A. Thus, the long-term effects of selection in the two
breeds would be for genetic divergences, and hence
the enhancement of heterosis between them.
4 Comparison of alternative
mating systems
4.1 Similarities
Comparing Composites and Modified [F1], it becomes
evident that (1) both mating systems generate female
replacements throughout the herd and (2) effectively
exploit heterosis to a similar extent, given they are
made of the same number of breeds. (3) 100% of the
cowherd as well as of the calves marketed are
crossbreds so, (4) if meticulously designed, females
http://novasinergia.unach.edu.ec 14
and males could be fully adapted to the conditions
under which they will strive. (5) Minimum number of
breeding pastures required is one.
4.2 Differences
However, some differences need to be highlighted:
Modified [F1] overcome three fundamental
requirements: (1) The use of F1 sires impede loss of
heterosis due to renewed inbreeding, expand heterosis
retention, do not interfere with selection for additive
traits, and capitalize genetic progress in the parental
breeds. (2) There is not a minimum herd size, a
valuable attribute for the small rancher. (3) The
flexibility available, through a change in the exotic
breed, to match genetic potential to specific conditions
of the environment, market, and goals.
Finally, a valid criterion to compare the advantages or
disadvantages of the alternative matting systems is
"previous experiences” in similar conditions. There
are no experiences with the Modified [F1], but, as
mentioned before, the literature contains just the
successful trails while many failures stay undisclosed
to the public. Plasse (2000) was very brave to admit,
after several attempts, that he was not aware of any
information that would allow him to recommend
composites to livestock practice. So, in the absence of
previous experience with the Modified [F1] system,
more research on mating systems in beef cattle
production is required.
5 Conclusions
From this review, it can be inferred that significant
progress could be made in terms of adopting improved
management procedures currently being used in
experimental stations and elite herds. However, for the
next several years, the beef cow and their lactating
progeny will be relegated to marginal areas where
environmental limitations or lack of adaptability
prevent the expression of genetic potentials.
The main objective of using crossbreed bulls is to
combine in an animal the adaptability of the tropical
breed and the improved performance, hoping to obtain
an animal able to work in adverse conditions, but that
simultaneously transmits to its progeny desired genes
for beef production and exploit heterosis.
Heterosis, the superiority of the crosses over the
average of the parent breeds, improve economic
efficiency in systems that exploit both individual and
maternal heterosis. However, heterosis is not a
parameter determined by the genotypes that intervene
in the crossing; its effects are conditioned by
environmental limitations or lack of adaptability that
prevent the manifestation of the genetic potentials.
In general, if n breeds are utilized in the development
of the Composite, 1/n of the original heterosis is lost
under interse mating in successive generations.
Additionally, crossing over and recombination will
tend to destroy linked groups, and after two or three
generations, all epistatic effects will be lost. When the
epistatic effects are important, loss of heterosis will be
more significant than what is theoretically expected.
Furthermore, a large population is a condition for full
utilization of heterosis resulting after crossing
different breeds for the development of composites.
For the traits of interest, in Bos indicus x Bos taurus
females, heterosis retention estimates were found to
be lower than expectations of the dominance model
for some groups and higher than expectations of the
dominance model for other groups, which confirm
that more research is needed on mating systems in B
indicus crosses for beef cattle production.
The use of F1 sires able to thrive on adverse
conditions, on a crossbreed population of cows in
successive generations, might be a feasible way to
overcome some of the Composites limitations,
combine adaptability with improved performance in
small herds while keeping management simple,
capacity for adjustment, and adaptation to new
restrictions and opportunities generated by the
changing environment.
Conflict of Interest
The author hereby declares that he has no conflict of
interest of any kind.
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