origin. The results will be used for implementation of conservation strategies of the evaluated breeds. MATERIAL AND METHODS The pedigree ...
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
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