origin. The results will be used for implementation
of conservation strategies of the evaluated breeds.
MATERIAL AND METHODS
The pedigree information on the Hucul, Shagya
Arabian, and Lipizzan horses was available from the
Central Register of Breeding Horses in Slovakia and
the National Stud Farm Topoľčianky. The National
Stud Farm founded in 1921 plays an important role
in horse breeding, management of closed herd
books by breeds, etc. The data on the Slovak Sport
Pony were obtained from the open stud book of the
Slovak Sport Pony Association. A total of 4879 animals (3177 out of them females) were registered.
The analysed reference populations consisted of
533 animals registered in the stud books of the
individual breeds within the years 2002–2007. The
analysis covered living mares and stallions as well
as frozen genetic materials of stallions deposited in
the Reproduction Centre of the National Stud Farm
at Topoľčianky. Population sizes differentiated by
sex, reference populations and totals for the four
assessed breeds are given in Table 1. Populations of
the Lipizzan and Shagya Arabian were the largest.
The animals were bred in the Topoľčianky stud as
well as in other small private studs in Slovakia. An
organized exchange of genetic materials among all
the studs was assured. The genealogical information was completed to maximise the number of
the ancestral generations used in the analysis. The
pedigree information was used to calculate the parameters associated with the completeness of the
pedigrees and genetic variability.
The quality level of the pedigree information was
characterized by computing:
(1) The number of fully traced generations was defined as the number separating the offspring
from the furthest generation in which the ancestors of an individual are known. Ancestors
with unknown parents are considered as founders (generation 0).
(2) The maximum number of generations traced is
the number of generations separating an individual from its furthest ancestors.
(3) The equivalent complete generations are computed as the sum over all known ancestors of the
terms computed as the sum of (1/2)n, where n
is the number of generations separating the individual from each known ancestor (Maignel et
al., 1996). This is calculated using the equation:
1
N nj
1 t = ––– ∑∑––– (1)
N j=1 i=1 2gij
where:
nj
= number of ancestors of individual j in the evaluated
population
gij = number of generations between the individuals and
ancestor i N = number of animals in the reference population
(4) The index of completeness describes the completeness of each ancestor in the pedigree of
the parental generation (MacCluer et al., 1983)
and is calculated separately for paternal and
maternal lines according to the equation:
a
id
par
= 1/d∑ ai (2)
j=1
where:
ai
= proportion of known ancestors in generation i
d = number of generations found
Table 1. Description of the Slovak horse breeds analysed
Sex HK LK SAK SSP
RP
n 158 162 171 42
sex M F M F M F M F
n 20 138 19 143 28 143 6 36
WP
n 656 2052 1951 220
sex M F M F M F M F
n 195 461 733 1319 689 1262 85 135
HK = Hucul horse, LK = Lipizzan horse, SAK = Shagya Arabian horse, SSP = Slovak Sport Pony, RP = reference population,
WP = whole population, M = male, F = female
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Original Paper Czech J. Anim. Sci., 57, 2012 (2): 54–64
The pedigree completeness index for each individual is calculated as the harmonic mean of paternal and maternal lines according to the equation:
Id = 4Id
par
+ dmat / id
par
+ Idmat (3)
Generation interval
The generation interval was defined as the average age of the parents at the birth of the offspring
used to replace them.
Genetic variability
To characterize the genetic variability of the
population, two types of parameters were analysed
based on the probability of the identity by descent
(1–4) and gene origin (5–6),
estimated as follows:
(1) The individual inbreeding coefficient (Fi
) is defined as the probability that an individual has
two identical genes by descent (Wright, 1922),
calculated according to equation based on the
algorithm described by Meuwissen and Luo
(1992):
Fx = ∑0.5n1 + n2 + 1(1 + FA) (4)
(2) The increase of inbreeding for each individual
(∆Fi
) was computed as follows:
∆Fi
= 1 – t–1√1 – Fi (5)
where:
Fi = individual inbreeding coefficient of individual i
t = equivalent complete generations of ancestors for a given
individual (Gutiérrez et al., 2009)
(3) The effective population size, referred to as the
realized effective size by Cervantes et al.
(2008a,
2011), was calculated in real populations of pedigrees as the individual increase of inbreeding
based on the method of Gutiérrez et al. (2009)
according to the equation:
N
–
e
= 1/2 ∆–
F
–
i (6)
(4) The average relatedness coefficient for each
individual (AR coefficient) is defined as the
probability that a random allele selected from
the whole pedigree of the population belongs
to each individual (Dunner et al., 1998) and was
calculated according to the equation:
c, = (1/n) l, A (7)
where:
c’ = row vector where ci
is the average of the coefficients in
the row of individual i in the numerator relationship
matrix, A, of the dimension n
A = relationship matrix of size n × n
(5) The effective number of founders, f
e
(Lacy, 1989;
Boichard et al., 1997), is defined as the number
of equally contributing founders that would be
expected to produce the same genetic diversity
as in the population under study and was calculated according to the equation:
f
f
e
= 1/∑ q2
k (8)
k=1
where:
qk = expected contribution of the founders to the gene pool
of the present population, i.e., the probability that a
randomly selected gene in this population comes from
founder k. All of the founders contribute to the completeness of the assessed popuation without surplus,
and the sum of all founders equals to 1
(6) The effective number of ancestors (Boichard et al., 1997) is the minimum number of
ancestors explaining the genetic diversity in
a population. This is calculated according to
the equation:
f
f
a = 1/∑ p2
k (9)
k=1
where:
p2
k = marginal contribution, which is derived on the basis of
expected contributions, with redundant contributions
being eliminated
Boichard et al. (1997) identified two types of surplus contributions. In the first case,
n – 1 selected
ancestors may be the ancestors of individual k.
Therefore, the marginal contribution is adjusted
for the expected genetic contributions (ai
) of the
n – 1 selected ancestors to individual k. This is
calculated according to the equation:
n–1
p2
k
= qk (1– ∑ai) (10)
i=1
In the second case of surplus contributions,
n – 1
selected ancestors may move away from individual
k. When their contributions were included, they
should not be imputed to individual k. Therefore,
all important ancestors in its pedigree are deleted
and become pseudo-founders.
57
Czech J. Anim. Sci., 57, 2012 (2): 54–64 Original Paper
The above parameters were calculated using
the program Endog v.4.8 (Gutiérrez and Goyache,
2005).
RESULTS
Demographic analysis
Figure 1 and Table 2 show the pedigree completeness. Except for the Hucul and the Slovak Sport
Pony, the first 4 generations of pedigrees are virtually complete in the Lipizzan and Shagya Arabian
and from then differences among the breeds increase.
Proportion of the known ancestors dropped
to less than 50% after 11 generations in the Lipizzan,
10 in the Shagya Arabian and 7 in the Hucul. The
Slovak Sport pony is a young breed which originated in the year 1982. It is perhaps the reason for
the existing gap in the pedigree recording after the
4 generations and the shortening of the pedigrees to
the maximum of 7 generations. The most complete
pedigrees were found in the Lipizzan and Shagya
Arabian. The pedigree data were used to calculate
the other pedigree completeness parameters. The
average values of the maximum number of genera0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
(%)
Parental generation
Hucul
Lipizzan
Shagya Arabian
Slovak Sport Pony
Figure 1. Ratio of known ancestors per parental generation
Table 2. Average values of parameters of the pedigree completeness
