Effect of Different Mating Systems on
Population Structure and Genetic Progress
of a Simulated Small Flock
Assis Rubens Montenegro1, Luciano Pinheiro da Silva1 and Raimundo Nonato Braga Lôbo1,2
1Departamento de Zootecnia, Universidade Federal do Ceará, Brazil
2Embrapa Caprinos e Ovinos, Estrada Sobral/Groaíras, Brazil
Submission: July 25, 2019; Published: August 12, 2019
*Corresponding author: Raimundo Nonato Braga Lôbo, Departamento de Zootecnia, Universidade Federal do Ceará, Embrapa Caprinos e Ovinos, Estrada Sobral/Groaíras, km 04, Caixa postal 71, Sobral 62010-970, CE, Brazil
How to cite this article: Assis Rubens Montenegro, Luciano Pinheiro da Silva, Raimundo Nonato Braga Lôbo. Effect of Different Mating Systems on Population Structure and Genetic Progress of a Simulated Small Flock. Int J Environ Sci Nat Res. 2019; 21(1): 556051. DOI:10.19080/IJESNR.2019.21.556051
Strategies to promote genetic progress or preserve genetic diversity in small populations may change due to population size. Higher inbreeding coefficients are associated to the use of breeding values predicted by mixed model methodology, which tends to score better animals within the best families. The reduced effective population size makes herds more susceptible to genetic drift and inbred matings. We compared three methodologies/software on simulated data that reproduced small-closed populations: Mate Selection (evolutionary differential), Gencont (Lagrange Multipliers) and SGRmate (linear programming). Algorithms optimized the objective function in order to achieve the higher genetic progress, but with an inbreeding coefficient of less than 10%, selecting the necessary number of sires and forming the reproductive pairs, except for Gencont, whose objective function was only to minimize the coancestry. All software generated populations with similar genetic progress. Mate Selection generated populations with the highest levels of inbreeding coefficients, similar to RANDOM, which presented best controlled mating between relatives. Gencont produced populations with intermediate levels of inbreeding. SGRmate maintained lowest levels of inbreeding due to higher number of sires selected and equal proportionality in combination of the pairs. Use of linear programming (SGRmate) was more efficient in maintaining the genetic diversity of small-closed populations.
One of the first steps in defining strategies used in a breeding program is to determine the purpose of production and criteria to select and evaluate animals, and after, assign breeding pairs. However, it is a complex operation due to correlation among mating values, i.e., all breeding pairs must be planned simultaneously within each generation.
Genetic progress is directly related to the intensity of selection, that is, the smaller the number of animals selected the greater the response to selection, which can also result in higher levels of inbreeding. Therefore, the number of animals selected for reproduction and the intensity of use should be weighted by inbreeding coefficient (F) and genetic gain. Populations under intense selection process show a systematic increase of F, which has detrimental effects on performance, reproductive, conformation and survival traits . The use of a mating management software could be a useful tool to mitigate the negative impact that the selection process can generate.
Mating selection software select the best animals and to form breeding pairs within a pre-established limit of inbreeding .
There are several methodologies available for directed mating, such as linear programming , the theory of optimal genetic contribution with the Lagrange multipliers  and genetic algorithms . In some production systems, random mating seems to be the most practiced , and it has been reported in some simulation studies that this strategy presents poorer results than the directed mating system [6,7].
Mc Parland et al.  described that linear programming was more efficient than random mating in maintaining genetic variability and promoted greater genetic gain. According to these authors, linear programming can be used in small populations, if the breeder uses semen from animals evaluated in national breeding programs. On the other hand, Kinghorn  applied a genetic algorithm developed by Price & Storn , entitled Evolutionary Differential, which uses evolution processes in the treatment of vector solutions as a tool to target mating and to promote genetic gain within the limit of inbreeding allowed.
The theory of optimal genetic contribution consists in defining the intensity of use of sires and dams in the composition of the future progeny. It has already been evaluated in simulation
studies , in pig farming , milk-cattle raising  and, more
recently, in poultry farming , and presented positive results.
Optimal genetic contribution can be used both for software’s that
have genetic progress as their central objective, as for genetic resources
conservation scenarios .
The objective of this study was to evaluate the use of different
software with simulated data, over ten generations, namely Mate
Selection available on Pedigree Viewer (evolutionary differential),
Gencont (Lagrange Multipliers) and SGRmate (linear programming),
compared to a random mating scenario.
Stochastic simulation was used to simulate a population and
to verify genetic and populational changes over ten generations,
using mating systems based on the following software’s: Gencont
(Optimal Genetic Contribution and Lagrange multipliers, ),
Mate Selection (Evolutionary differential ) and SGRmate (Linear
programming ) and, a reference scenario, using random
mating (RANDOM). The generations were overlapped, resulting in
the use of animals throughout all generations. A single trait with
normal distribution, NID (0, σ2) and expressed in both sexes, with
no dimorphism, was simulated twenty times in each scenario.
The base population built from 200 individuals, divided equally
between males and females, with unknown paternity. These
individuals were then randomly mated through five generations,
summing up 600 animals, considered so as the base population,
by using “simul.pedigree” function from “synbreed” package .
Next, the kinship matrix, here called matrix A, was build using
the functions “makeA” and “symatrix” to adjust results in matrix
structure. True breeding values were initially simulated using the
“mvrnorm” function, from “MASS” package  and assigned as a
vector MVN. The covariance matrix was calculated by multiplying
the A matrix and an arbitrary value of 0.3 units that simulated a
heritability of 30%.
We simulated two scenarios: the first one, the 10 sires and 50
dams (named T10) with the highest breeding values; the later, the
number of sires was set as 17. Males and females that not selected
as breeding stock were automatically discarded. Ten generations
of mating were simulated, using the aforementioned mating systems.
The software output is often a mating list, except for Gencont,
which contains only the genetic proportions that each individual
should contribute to the next generation. In this case, a randomized
sire-dam combination based on those proportions.
The progeny breeding value was estimated by the mean
breeding value of the parents plus Mendelian segregation:
where ap is the estimated breeding value of progeny; as and
ad, the breeding values of sire and dam, respectively; and, sm, the
Mendelian segregation, which is defined as:
where fs and fd are the inbreeding coefficients
of sire and dam, respectively, and 0.3 is the genetic variance.
The population was simulated with a mean litter size of 1.5
offspring/birth, 55% of births were single, 40% twin and 5% triplet.
A progeny sex ratio was set as 1:1. Each round of simulation
was considered as a new generation.
Mate Selection and SGRmate were set up to allow mating between
individuals with up to 0.35 of genetic relationship and an
average inbreeding coefficient of up to 10%.
Gencont software  uses Lagrange multipliers to find the
maximum genetic gain with a restricted level of inbreeding. Thus,
we used Gencont’s tool ‘minimise ΔF’, that search a solution with
the lowest inbreeding coefficient.
The Mate Selection is a tool from Pedigree Viewer software
to direct mating that uses evolutionary differential as a search
algorithm (Kinghorn, 2002). The software was set up with “soft
constraint on coancestry” option, with mating between individuals
limited on genetic relationship (0.35) and in populational inbreeding
coefficient (10%). The operational parameters for performing
the differential algorithm routines range from 1,000 to
7,000 for the number of generations of solution vectors.
The SGRmate  uses the SIMPLEX method to optimize the
objective function, which maximize the genetic gain and minimize
the populational inbreeding in a given population. The SGRmate
was set to allow the maximum populational inbreeding of 10%
and maximum value of 35% of genetic relationship for a given
Inbreeding coefficient was calculated using the “calcInbreeding”
function from “pedigree” package  for each animal. This
package uses the methodology proposed by Wright .
The populational inbreeding coefficient in a given generation
is the mean of every inbreeding coefficient in a given population.
Intergenerational change of the inbreeding coefficient (Δf) is the
ratio of F from two consecutive generations. Effective population
size (Ne) is inversely proportional to two times Δf.
Other variables evaluated were the number of mating between
parents and offspring, between full siblings and half siblings,
and the average relatedness coefficient (AR), described as:
where AR is the average relatedness coefficient; 1’, vector of
1’s; and A, the genetic relationship matrix. Endog 4.8v  was
used to estimate the response variables.
The mean number of offspring per sire, the maximum number
of offspring, the number of sires and the variance of the number of
offspring were calculated. All differences among mating systems
from different software were compared by Tukey test (α=0.05).
Regressions of true breeding values and inbreeding coefficients
over time, during ten generations of directed mating, were
used to compare mating systems. To compare slopes from multiples
mating systems with dummy variables we used 5% confidence
After 10 generations, the T10 truncation selection scenario
promoted oscillations in the inbreeding coefficients (F) and in the
mean breeding values, regardless of the mating system (Figures
1 & 2).
As the number of animals chosen as breeders (60) was not
enough to meet the 10% coancestry restrictions, in some cases it
was not possible to satisfy all the imposed inequations and when
this happened, Gencont created a solution vector that indicated
the use of few sires, which elevated the F in a few generations.
Therefore, we used the ‘minimise’ option to give more weight on
After 10 generations of mating, SGRmate use produced the
lowest inbreeding coefficient (4.11 ± 0.91), statistically differ
ing (Table 1) from the values obtained for random mating (5.17
± 0.84), directed by Mate Selection (5.15 ± 0.67) and Gencont
(5.12 ± 1.61). SGRmate performed better control of inbreeding for
T10, probably to the constant number of sires in all generations,
while Mate Selection and Gencont changed according to the preset
coancestry, varying from two up to 10 (Figure 3). On average,
Mate Selection selected 5.5 sires per generation. Another possible
advantage of the use of SGRmate in small populations is the selection
of the same number of females per male, that is, all males
will contribute equally to the formation of the future progeny, favoring
the maintenance of levels of inbreeding. Since that using of
equal sex ratio in commercial herds is not economical, the use of
less unequal ratio would be better to maintain genetic variability.
Reducing family size variance with fewer selected animals within
each family would result in lower rate of inbreeding for each unit
of genetic progress .
For variables followed by #, the Mate Selection scenario was not considered in the analysis of variance.
The average individual F value estimated in this study over the
ten generations of directed or random mating was 4.89%, close
to the reference value of 6.25% to avoid inbreeding depression in
livestock . In the seventh generation, 77% of the animals had
individual F higher than 6.25%, and 40% had a value higher than
10%, regardless of sex (Figure 4). This significant portion of population
would probably have already reduced performance due
to inbreeding depression. Hossein-Zadeh  found reduction in
birth weight in sheep only above 10% of inbreeding and recommended
that the control of mating can guarantee the maintenance
of genetic diversity.
SGRmate was more efficient to control inbreeding (20%)
when compared to RANDOM system. Similar results were reported
by studies using linear programming as an optimization tool
[6-8], in which it presented greater results than randomized mating.
Through the measurement of the effective size of the population
(Ne) it is possible to evaluate the changes of the population
structure over time. Ne can be influenced by sexual ratio, fluctuation
of population size in time, selection and mating system.
SGRmate was the software that simulated populations with the
highest absolute value of Ne (22.20 ± 5.06), although it was not
statistically different (p> 0.05) from the Mate Selection and Gencont
softwares, but different (p< 0.05) of the RANDOM, which produced
the lowest Ne (17.60 ± 3.06). Mate Selection was the software
that simulated the least amount of inbreeding mates (Table
1), but it was not enough to compensate for the smaller number
of males used as breeder and the greatest variation in the number
of progeny (Table 2), as it presented Ne (18.80 ± 2.75) statistically
similar to RANDOM. In turn, Gencont used the same number of
sires as SGRmate and RANDOM, but did not direct the matings,
resulting in Ne and F similar to RANDOM. Therefore, it is possible
to infer that the combination between directed mating and use of
the largest number of sires is a good strategy to preserve genetic
diversity in small closed populations.
At the beginning of simulations, all the populations had 600
animals and Ne of 533.33. Over the ten generations, the selection
process, the different reproductive rates and the mating systems
caused a reduction of the Ne to 19.39, far away from the 50 recommended
by FAO 
All the scenarios evaluated in this study had the same level
of coancestry, but Gencont, Mate Selection and SGRmate systems
could vary the number of sires per generation (Figure 3), as well
as the proportion of use. SGRmate used all males that were available,
similar to the RANDOM (Table 2). Gencont indicated almost
all sires, but over the generations there was variation. On the other
hand, Mate Selection presented a great variation in relation to
the number of sires (Table 2), which grew gradually over the generations
until reaching the maximum number allowed. The lower
use of sires in the initial generations occurred to prioritize genetic
gain in the short term, increasing selection intensity. The animals
selected for breeding had a low average kinship coefficient.
However, that even with the use of a few sires, Mate Selection still
maintained the level of individual inbreeding at zero in the first
generations (Figure 1), which characterizes it as the best control
of inbreeding at the beginning in this work. However, over the ten
generations it had F similar to RANDOM.
Mate Selection generated populations with the highest number
of offspring per sire (11.44 ± 0.74), the highest number of offspring
(62.10 ± 10.32), the highest number of breeding animals
in the ten generations (65.00 ± 4.07) and higher variance in the
number of offspring (91.20 ± 19.92) than all the other scenarios
(Table 2). Gencont and SGRmate used the same number of sires
over the ten generations as the RANDOM. Although in this scenario,
the same number of sires was used in equal proportions
per generation. The variance of the number of offspring (37.70 ±
11.11) was caused by the different birth rates (1.5 births on average)
and mainly due to overlapping generations, in which one sire
could be used in several successive generations given that it had
one of the ten highest breeding values. This combination of factors,
in the RANDOM scenario, allowed the same sire to produce
up to 46 offspring over the ten generations. On the other hand,
Mate Selection directed the maximum of up to 94 offspring to the
In the early generations, inbreeding was below the imposed
10% restriction, which allowed Mate Selection to indicate lower
numbers of sires in the first generations. In studies that evaluated
scenarios with increasing levels of inbreeding, the number of sires
increased as restriction increased [12,25,26]. In a way, this corroborates
with the result of this study, since the level of inbreeding
increased over generations (Figure 2). In the same sense, Barreto
Neto , in studying sheep of Santa Inês breed, tested different
directed mating scenarios weighted by levels of coancestry, optimized
by genetic algorithms, and described an increased number
of sires as coancestry restriction increased.
If the restriction to F is small, the best animals would be selected
regardless of the genetic relationship and the results may
not differ from a non-restricted system. On the other hand, at high
levels of F, the results may be similar to a scenario that only seeks
to maintain genetic variability . Therefore, it seems that intermediate
values of F give the greatest benefits.
There is no single recommendation for the use of mating relatives
to the pre-established level of F, it depends on the objectives
of the genetic breeding program and thus can vary widely.
In situations in which breed association has a closed book, and it
is not possible to enter animals with unknown kinship and/or no
relationship with animals of the population, it is more important
to maintain Ne and, consequently, genetic variability. This is also
true for populations with few individuals, such as in zoos and native
breeds conservation program.
Mucha & Komen  performed a study with simulated data
to evaluate different mating strategies for a small population, simulating
animals raised in three zoos. The authors compared a rotational
mating scenario with different intensities of selection, in
which 10%, 20% and 50% of the males were transferred from one
zoo to the other, that is, the females always remained in the place
of birth and the males were exchanged. The other scenario used
the optimal genetic contribution to select males in three different
situations: between all zoos, inside a zoo and with male exchange.
Gencont was set to produce the lowest inbreeding rate possible,
as performed in this study. The scenario that most approached
our study was the one that used Gencont without exchanging
animals with reproductive rate of one male for every five dams.
An inbreeding increase of 1.53 was reported, close to our results
(1.61). The authors suggested that animal exchange is a solid way
of preserving genetic diversity, since optimal genetic contribution
theory needs complete and correct pedigrees and recommended
its use in situations where it is not possible to exchange animals
between zoos. They also reported that between the rotational
mating scenario and Gencont, the level of inbreeding seems more
related to the number of animals selected and that a population
cannot be managed with less than 60 animals, without considerable
loss of genetic diversity.
In turn, in a scenario where animals from other populations
or breeds are accepted, the assignment of mating pairs should
mainly concern on the genetic progress and in the control of mating
among between close relatives, because if Ne needs to be increased,
animals from other populations can be included.
Another parameter used to assess the level of population genetic
similarity is the average relatedness coefficient (AR). Conceptually,
it is the probability of an allele chosen at random in the
population belongs to a particular animal. In other words, the AR
value indicates the allelic sharing of a given animal with the rest
of the population, that is, an animal with a low AR value could be
used more intensively to disseminate its germplasm . Mate
Selection simulated populations with mean AR of 6.79% ± 1.42,
being the highest value among all the scenarios (Table 1). The AR
of the populations simulated from the use of SGRmate did not differ
statistically from RANDOM, which corroborates that the number
of animals selected for reproduction was determinant.
In relation to the mating of closely related individuals, such
as between parents and offspring (MPO), full siblings (MFS) and
half siblings (MHS), it is known to be harmful mainly due to higher
probability of homozigozity of deleterious recessive alleles
in the progeny, which may affect fitness, reducing reproduction
rates and survival. Therefore, restriction on these matings is an
important feature of a software. Note that the parameter imposed
a priori allowed up to 35% of probable genetic similarity between
pairs. In order to make a more correct comparison between SGRmate,
RANDOM and Gencont, the observations from Mate Selection
were taken from the analysis of variance and from the means
comparison test, since the variance of the treatment was null, violating
the assumptions of normality and homoscedasticity.
The RANDOM presented 26.80 ± 8.64 of MPO and Gencont
had a statistically similar value (26.35 ± 12.80), as both scenarios
used matings as random. In turn, SGRmate also did not differ from
RANDOM, with an average of 26.05 ± 8.48. On the other hand,
Mate Selection only formed three MPOs in a single simulation,
showing to be the most efficient software for this characteristic.
Gencont generated the same amount of progeny arising from
mating between full siblings as RANDOM (Table 1). SGRmate assigned
less MFS (4.05 ± 3.03) over the ten generations, which was
42.5% less than RANDOM. Moreover, it did not direct any MFS in
two of the replicates. Mate Selection avoided almost all MFS (0.10
± 0.31), directing only one mating of this type in two of the simulated
Coefficients of inbreeding of progenies from half siblings,
full siblings and parents and offspring are 12.5%, 25% and 25%,
respectively, given that parent’s inbreeding coefficients are null.
Therefore, 10% restriction on populational F was more effective
in the control of inbred matings, compared to 35% restriction on
individual F allowed on the three types of mating evaluated.
Mate Selection assigned 40.40 ± 18.80 half siblings matings,
and the other software’s or RANDOM generated higher values.
SGRmate directed an average of 65.50 ± 28.00 MHS; Gencont,
80.30 ± 29.40; and RANDOM, 75.70 ± 24.50. Mate Selection was
the software that better restricted mating between direct relatives,
but this was not enough to avoid the highest values of F
and Ne. This diverged from other studies that showed that the
exclusion of full sibling’s and half sibling’s matings reduces the
inbreeding coefficient . However, according to Wang , the
exclusion of sibling’s matings reduces inbreeding in the first generations,
but it does not differ from a random selection scenario
in future generations. This corroborates with the results of this
study, since there was no difference between RANDOM and Mate
Selection inbreeding coefficient, even though MFS and MPO were
Another study demonstrated that exclusion of full or half sibs
mating resulted in lower inbreeding rates . However, in this
study, the exclusion of MFS did not result in a lower inbreeding
rate probably because the exclusion of this type of mating has a
greater impact on genetic diversity due to more intensive is the
use of sires .
The selection pressure practiced generated inbreeding rate of
4.88, Ne of 19.39, AR of 5.30 and some animals born achieved an
individual F value of 52%, higher than recommended for livestock
. These values were similar to those reported by Teixeira Neto
et al. , evaluating 53 herds of Santa Inês sheep, summing close
to 13,000 animals. The authors reported F and AR values of 6.92%,
3.87%, respectively. The similarity of parameters of the simulated
and actual parameters confirms the efficiency of stochastic simulation,
providing confidence for practical application of the best
None of the confidence intervals for genetic trends and inbreeding
included the zero, rejecting the null hypothesis, in which
the linear coefficient is similar to zero (Figure 5). Another finding
is the overlap of values between all the intervals, indicating
that the software did not promote greater genetic gains than the
RANDOM (Figure 5a). Regarding to inbreeding trends (Figure 5b),
there is evidence that SGRmate software generated a population
with lower F.
After regression analysis, we made plots with predicted values
and their respective confidence intervals (95%) for genetic
(Figure 6) and inbreeding trends (Figure 7). Comparative analyses
of slopes for genetic trends at T10 in all scenarios were statistically
similar (p> 0.05). On the other hand, inbreeding trend were
statistically different (p≤ 0.001). SGRmate was lower to all other scenarios; Gencont produced a curve with a linear coefficient lower
than Mate Selection and RANDOM; and, finally, Mate Selection
and RANDOM did not differ statistically. These results are consistent
with previously reported population parameters in this study
Preventing increased inbreeding due to selection process in
a population without new animals is the central issue for some
animal breeding programs. This is more important when the population
is composed of large families and reduced effective size,
which can quickly lead to loss of allelic diversity .
For a small population in which 10 sires and 50 dams (T10)
selected and mated over ten generations, SGRmate software promoted
the same genetic progress with higher control of F and Ne,
probably because it used all males available for breeding. SGRmate
assigned the same amount of matings per sire and avoided
more matings between full siblings than RANDOM and Gencont.
As expected, there were also oscillations in inbreeding coefficients
and in the mean breeding values between the replications,
regardless of the system used to assign matings (Figures 8 & 9).
Mate Selection produced, on average, populations with F of
4.21 ± 0.58 (Table 3), statistically higher (p< 0.05) to the RANDOM
(3.48 ± 0.45). SGRmate and Gencont generated populations with
F of 2.75 ± 0.53 and 2.88 ± 0.29, respectively, with no statistical
difference (p> 0.05), however, lower to the two aforementioned
scenarios. AR showed a similar result, in which Mate Selection
presented the highest value (7.06 ± 1.00), followed by RANDOM
(4.09 ± 0.39), and finally SGRmate (3.52 ± 0.54) and Gencont (3.56
± 0.27), which did not differ statistically (p> 0.05). The greater
control of genetic variability of Gencont must have occurred main ly due to the culling of some sires that are related with the dams.
It can be observed (Figure 10) a trend in reducing the number
of sires up to the sixth generation, maintaining this number up
to the tenth generation for Gencont. The use of all males (17 per
generation) for mating in each generation resulted in a lower level
of inbreeding, a strategy used by SGRmate (Table 4), which used
the same number of sires as RANDOM.
Mate Selection was the software that best controlled inbreeding
in the first generations (Figure 8), even though it selected, on
average, 2.35 and 4.45 sires in the second and third generation
(Figure 9), respectively. However, over the ten generations, it generated
populations with the highest value of F and AR (Table 3)
when compared to RANDOM and the other software’s.
The maximum number of offspring per sire can be an indication
of selection intensity. Over ten generations, 740 offspring
were simulated in each iteration. On average, the sires most used
by Mate Selection left 68.40 ± 13.43 offspring, which was higher
(p< 0.05) than all scenarios (Table 4), reaching a maximum value
of 96 offspring for a single sire, which represented approximately
13% of all simulated progeny. The SGRmate attributed a higher
number of offspring per sire (30.05 ± 8.20) when compared to
RANDOM and Gencont. However, it was much lower than Mate Selection,
which directed up to 56 offspring per sire. Gencont, on the
other hand, obtained a similar result to RANDOM, probably due to
the configuration of minimizing the coancestry, which attenuates
the intensity in the use of males. The variance of the number of
offspring per sire had a similar result to the maximum number of
offspring per sire, because softwares that led a higher number of
offspring per sire, simultaneously, would cause a disproportionality
in relation to the progeny size.
In Ethiopia, in a flock of Menz sheep, the use of Mate Selection
generated a similar genetic gain with a smaller increase of inbreeding,
comparing simulated data with real data over ten years , so it was recommended as a tool to maintain genetic diversity
in the long term. For the scenario used in the mating routines
of this study, Mate Selection was the best option to achieve genetic
gains in short term with maintenance of F. Gencont presented
higher genetic gain with a lower inbreeding level when compared
to truncation selection scenario based on breeding value.
For variables followed by #, the Mate Selection scenario was not considered in the analysis of variance.
For T17, 50% of the animals have F higher than 6.25% in
the seventh generation, far below the 77% presented in T10. In
addition, the higher use of sires, in T17, reduced the number of
animals with F higher than 10% from 40% to 7.6% (Figure 11).
The increase in the number of sires, as the less numerous genders,
proved to be efficient in delaying the undesirable effects of selection,
such as the increase in individual inbreeding.
All populations simulated using the different software’s resulted
in the same genetic progress of the RANDOM scenario (p>
0.05), with no statistical difference in the linear coefficient comparison.
It is observed through graphical analysis that there is
overlap of the confidence intervals of the linear coefficients (Figure
12b). It is also possible to observe the projection of the breeding
values predicted by the regression equation for the different
softwares and RANDOM that were in parallel (Figure 13), that is,
the genetic modification by generation was similar for all scenarios.
Genetic progress achieved over ten generations of directed
mating was caused by selection. Mate Selection had an intercept
value (0.51) higher than the RANDOM (0.38), Gencont (0.39) and SGRmate (0.39) scenarios in about 31.9%, probably due to the
higher selection intensity in the first generations, but with a similar
slope, as aforementioned. Mating systems may cause genetic
progress in the early generations, however, over time, this progress
tends to be only maintained .
In other studies, directed mating softwares (algorithms) presented
greater genetic progress when compared to real situations
[26,38] and to random mating .
In a study simulating a plant breeding program, it was verified
the superiority on genetic and inbreeding trend of the scenario
that minimized the coancestry of the progeny when compared to
the scenarios of assortative or random mating . The authors
attributed this superiority to the maintenance of genetic variability
throughout the generations, measured from the long-term contribution
of the ancestors and the higher connectivity between
unrelated families of the reproductive pairs.
Combinations of mating pairs caused changes in population
structure. Similar to the genetic progress, it is possible to follow
the changes in the degree of average inbreeding of the population
per unit of time by the inbreeding trend. The confidence intervals
of mean inbreeding trends for simulated populations using different softwares and the RANDOM (Figure 12a) did not show
any overlap of values, which is indicative of statistical difference
between treatments. The different selection intensities on Mate
Selection and Gencont and the differences in sires use influenced
inbreeding during the period of analysis.
Mate Selection generated populations with the highest trends
of inbreeding, followed by the RANDOM and, finally, SGRmate and
Gencont, with similar results (Figure 14). Regression lines presented
intercept values close to zero. We can infer that the base
population and the five initial generations of random mating produced
populations with low level of inbreeding for all software’s.
Sun et al.  reported the superiority of linear programming
to control inbreeding coefficient in relation to random mating,
which corroborates with the results of this study. Older studies,
in dairy cattle, verified the efficiency of linear programming in
directing mating , generating populations with 2.8% less inbreeding
compared to other methods. That same study performed
an economic evaluation of mating, estimating an increase of up
to US $59 when the objective function was maximized for the net
profit of the productive life corrected for inbreeding depression.
For small and enclosed populations, mating of individuals
with high genetic relationships can easily raise the inbreeding
coefficient. This study showed that the selection of mating using
the largest number of sires available is the most efficient strategy
to control inbreeding. The linear programming, implemented
in the SGRmate, provided better control of inbreeding in the long
term, with the same genetic gain of the other softwares. Gencont,
which uses Lagrangian multipliers and is set only to meet the lowest
coancestry possible presented results close to the RANDOM,
which uses all males available in equal proportions. Mate Selection,
which uses the evolutionary algorithm to optimize vector
solutions, provided better control of inbreeding and promoted the
greatest short-term genetic progress (up to the third generation),
probably due to the higher selection intensity in this period. This
may be relevant, since breeding programs may prioritize genetic
gain in the short term due to the low net present value of the
expected genetic gain in future generations . Although Mate
Selection avoided almost all full siblings and parent-offspring
mating, due to the bottleneck effect it generated the highest levels
of inbreeding, AR and lower Ne, as well as increased inbreeding.
Note that the inbreeding depression on breeding values was not
simulated, which could greatly reduce the genetic progress of the
populations generated, mainly by Mate Selection.
All the methodologies evaluated in this study require
well-structured and correct pedigrees. The use of directing software’s
for mating in commercial herds is already a reality, enabled
by research institutions or companies that commercialize
germplasm. The higher the quality of data, the better the results
of the matings, because the software will correctly estimate the
inbreeding coefficient of the animals. The lack of pedigree information
leads to underestimation of inbreeding coefficients, which
may lead to mating with an inbreeding level higher than expected.
Thus, for small-closed herds with little genealogical information,
the safest option, perhaps, would be the equal use of the largest
number of males available [42-46].
SGRmate was the software that provided the best control of
inbreeding for both scenarios (selection of 10 or 17 sires per generation)
over ten generations with the same genetic gain.
For T10, Gencont simulated populations with the same level
of inbreeding as RANDOM. Therefore, only selection, without
mating system, was not an efficient strategy to control inbreeding
in a small population, even though the selection was made to minimize
For a small-closed population, the number of animals used
for reproduction have a greater impact on population parameters
than the exclusion of mating between full siblings and between
parents and offspring.
The authors acknowledge the National Counsel of Technological
and Scientific Development (CNPq) and the Coordination for
the Improvement of Higher Education Personnel (CAPES) for the
scholarship grants to last and first authors of this manuscript, respectively.
Carneiro PLS, Malhado CHM, Euclydes RF, et al. (2007) Endogamy, allele fixation and selection limit in populations selected by traditional methods and associated with molecular markers. Brazilian Journal of Animal Science 36: 369-375.
Pereira Filho J (2005) Effect of Effective Size and Mating Systems on Inbreeding increase in populations under selection, using simulation. Thesis (PhD in Animal Science) - Federal University of Viçosa, Minas Gerais, p.