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

56

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