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Genetic correlations between horse show jumping competition traits in five European countries
Livestock Science 122 (2009) 234–240
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Livestock Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / l i v s c i
Genetic correlations between horse show jumping competition traits in five European countries C. Ruhlmann a, S. Janssens b, J. Philipsson c, E. Thorén-Hellsten c, H. Crolly d, K. Quinn e, E. Manfredi a, A. Ricard a,⁎ a b c d e
Station d’amélioration génétique des animaux, Institut National de la Recherche Agronomique, BP 52627, F-31326 Castanet Tolosan, France Department of Biosystems, Katholieke Universiteit Leuven, Kasteelpark Arenberg 30, B-3001 Heverlee, Belgium Department of Animal Breeding and Genetics, Swedish University of Agricultural Sciences, Box 7023, S-750 07 Uppsala, Sweden Department of Genetics and Biotechnology, Research Centre Foulum, Postbox 50, DK-8830 Tjele, Denmark Irish Horse Board, Block B, Maynooth Business Campus, Maynooth, Co. Kildare, Ireland
a r t i c l e
i n f o
Article history: Received 24 July 2008 Received in revised form 8 September 2008 Accepted 8 September 2008 Keywords: Horse Genetic correlation Show jumping Multiple trait across-country evaluation
a b s t r a c t Genetic correlations were computed for show jumping competition traits from national estimated breeding values (EBV) of stallions of five countries: Belgium, Denmark, France, Ireland and Sweden. Data involved 24,390 horses, i.e. 8993 stallions with EBV and their ancestors. There were 617 stallions with several EBVs in more than one country. Method involved MACE (Multi-Trait Across Country Evaluation) methodology based on deregressed proofs adapted to the existence of own performance for stallions and to missing EBVs for some ancestors. ASREML was used to estimate covariance with an equivalent multiple trait model described as a random regression model. Within country sire variances were considered as known. The estimated genetic correlations were high (0.86 to 0.88) especially for reliable estimates between Belgium, France, Sweden and between Sweden and Denmark, and relatively high (0.70 to 0.91) for other pairs. These results open perspectives for the international evaluation of sporthorses. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The market of sport horses for show jumping competition has become more and more international and even if estimated breeding values (EBV) are provided by most countries, comparison between these values are difficult. Therefore a working group was founded (Interstallion, 2008) to 1) describe breeding objectives, testing procedures and genetic evaluation methods of warmblood breeding organisations; 2) recommend improvements of national genetic evaluation systems and 3) study methods of comparing genetic evaluations across countries. A first pilot project studied the comparison of genetic evaluations based on traits measured in young horse tests (Thorén Hellsten et al., 2008,
⁎ Corresponding author. Tel.: +33 5 61 28 51 83; fax: +33 5 61 28 53 53. E-mail address: [email protected] (A. Ricard). 1871-1413/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.livsci.2008.09.006
in press). The present study, was conducted in pilot project II, and focussed on competition traits measured in jumping events. The connectedness between countries was previously checked and acceptable to compute genetic correlations (Ruhlmann et al., in press). The aim of this study was to calculate genetic correlations for show jumping competition traits recorded in five European countries: Belgium, Denmark, France, Ireland and Sweden. 2. Materials and methods 2.1. Materials Sires EBVs were provided by 5 European countries: Belgium, Denmark, France, Ireland, Sweden. Requirements were that the files should include EBV's and reliabilities of all stallions bred for show jumping competition, i.e. with own
C. Ruhlmann et al. / Livestock Science 122 (2009) 234–240 Table 1 Number of stallions and ancestors provided by each of the five countries.
Belgium Denmark France Ireland Sweden
Stallions with EBV
Sires without EBV
Mares without EBV
Total horses in pedigree file
926 563 5290 854 2153
1500 1010 102 1365 932
3439 1614 5624 1903 1925
5865 3187 11016 4122 5010
Table 2 Number of common stallions with estimated breeding value (above diagonal) and number of common ancestors (below diagonal) between countries. Belgium Belgium Denmark France Ireland Sweden
Denmark
France
3 778 1242 476 733
135 23
442 329 976
614 711
Ireland 7 5 54
Sweden 99 207 272 85
471
performances or progeny with performances in jumping competition, and their complete pedigree up to 3 generations. The files provided contained from 563 to 5290 stallions with EBV and from 3187 to 11,016 horses (Table 1). Some countries (Belgium, Denmark, Ireland) provided EBV of only a subset of stallions (in reproductive activity or approved) and not for all ancestors and some (France, Sweden) provided EBV of near all stallions included in pedigree. So, according to the completeness of EBVs for stallions in pedigree, the deepness of pedigree varied between countries. For countries which gave EBV of only a subset of stallions, 41% to 92% of ancestors of these stallions at the third generation were known. For countries which provided almost all EBV of stallions, 12% to 44% of ancestors of these stallions at the third generation were known as even founders stallions had EBV. After checking the identity of the horses, the final files contained 24,390 different horses. Among them, 8993 stallions have at least one EBV in one country, 617 in two countries, 79 in
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three and 6 in four. Common stallions between two countries varied from 3 to 272 (Table 2). Birth year was not always provided: from 23% to 95% of the horses had a known birth year. In order to include genetic groups defined by birth year of founders, birth year was estimated with the following rules. Four years were subtracted from the birth year of a horse to estimate the (unknown) birth year of its parents. The minimum value over all progeny was retained. This procedure was applied recursively. For horses without any information, a standard birth year was assigned depending on the mean number of generations between the individual and stallions with an EBV in the file. When three generations take place between the stallions with EBV and the horse without birth year, the birth year 1956 was attributed, when two, the year 1966 was attributed, when one 1976 and when the horse was a stallion with EBV the year 1986 was attributed. The breed of the horse was not always provided, especially in the Swedish and Danish data. When missing, the breed code was inferred from the original identification number or a search was conducted in other databases (for example www. allbreedpedigree.com). Finally, except for Thoroughbreds which were considered as one international breed, the different breeds in the same country of birth were pooled together and breed was confounded with country of birth. Additional countries of birth were added for horses identified in Germany or The Netherlands. The number of founders (horses without parents in the file) was 9699: 6744 mares, 2461 sires and 494 stallions with EBV but without sire or mare progeny in the file. Finally, founders were assigned to a breed and a period of birth. About the same proportion of founders (30% to 26%) was born before 1960, between 1960 and 1969 and between 1970 and 1979. A lower proportion was born more recently (17%). Before 1960, founders were mostly identified as French horses (27%), Thoroughbred (22%), Danish (12%), and German (11%). The more recent founders were Swedish (34%), Irish (24%) or belonged to other countries from the panel (14%). Table 3 summarizes the characteristics of the national genetic evaluations used in the countries involved in pilot
Table 3 Traits and genetic parameters used in national breeding evaluations for show jumping. Competition traits Country
Trait
Heritability
Repeatability
Genetic correlations
Belgium Denmark France Ireland Sweden
Rank low/high level Rank Rank/annual earning Rank low/medium/high level Cumulated life points
0.11/0.10 0.10 0.16/0.27 0.08/0.05/0.09 0.28
0.29/0.23 0.20 0.29/0.47 0.16/0.18/0.18 –
0.63 0.90 0.85/0.94/0.98 0.66/0.62/0.72/0.70 b
Indirect traits Country
Sweden (RHQT) a
a b
Trait
(1) (2) (3) (4)
RHQT=Riding Horse Quality Test. With indirect traits (1) to (4).
3years/jumping 3years/jumping 4years/jumping 4years/jumping
Heritability
style temperament style temperament
0.29 0.21 0.25 0.21
Genetic correlations (2)
(3)
(4)
0.91
0.77 0.69
0.70 0.70 0.92
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3. Method
project II. Genetic parameters were published for France (Ricard, 1997) and Ireland (Quinn, 2005) and given by breeding organisations in other cases in agreement with research works (Olsson, 2006; Janssens et al., 2007) for other countries. Most countries used traits that were directly related to show jumping competition whereas Sweden uses also indirect traits, i.e. measured in young horse tests (subjective note). The trait “rank” is the placing obtained in each event, often transformed in normal scores (Belgium, Ireland) or by taking the square root (Denmark) or modelled with an underlying continuous performance (France). In 4 countries out of 5, EBVs were computed using a multiple trait model. In the present analysis, EBVs used were the ones for high level of competition in Belgium and Ireland (which were also officially published), the trait based on ranks in France, and the cumulated life points in show jumping competition in Sweden. For Denmark the EBV from the single trait model was used. The number of progeny and performances used in the deregression process refers to the total number of progeny and performances for Belgium, Ireland and France. This is supported by high genetic correlations between traits so that all progeny contribute equally to the genetic evaluation whatever the trait recorded. In Sweden, only the number of progeny with results in competition was provided which could underestimate the amount of information used to calculate breeding values in the multiple trait model. As reliability was also provided, an equivalent number of progeny was calculated as: n =
Genetic correlations were calculated after deregression of the national EBV's. 3.1. Deregressed proofs The proposals of Sigurdsson and Banos (1995) were followed. Deregressed proofs for dairy bulls were obtained from EBV's using the information matrix of mixed model equations knowing the number of progeny of each bull in a single country. Adaptations were made to account for 1) the presence of own performances of stallions, which do not exist in dairy bulls and 2) the lack of EBVs for some ancestors of the known relationship matrix. The calculation was made for each country separately, with their own relationship matrix and known EBVs. First, the inclusion of own performances may be easily explained starting from an animal model and after some matrix algebra, going to a sire model. Suppose the following model: y = Xb + ZQg + Zu + Zp + e
with b vector of fixed effects, u random vector of animal breeding values, p random vector of permanent environmental effect, g the vector of genetic groups, e residual vector. In fact there were no genetic groups in any of the models used for computation of national EBVs. However, the files provided for this study were not the complete national files used in the different countries, so that the available data should be considered a sample from the animals included in the national evaluation. To avoid problems due to differences in the sampling of data, we added a single genetic group in the model. The corresponding mixed model equations (MME) were:
ð4 − h2 Þðr0
− h2 Þ with one own h2 ð1 − h2 Þð1 − r 0 Þ
stallion performance (life trait) or n =
ð4 − h2 Þr0 h2 ð1 − r 0 Þ
without own
performance, with n the equivalent number of progeny, h2 the heritability of competition trait, and: r 0 =
r − r r sire 4
rsire 4
+ 1−
rsire 2
(Harris and Johnson, 1998) with r the reliability of the EBV of the stallion and rsire the reliability of his sire. The reliability r was the squared correlation between true breeding value and EBV. According to parameters provided by each country, EBVs were standardized to a genetic standard deviation of 1. Statistics on EBVs, the number of progeny and own performances of stallions are given in Table 4. Mean and standard deviations of EBV are not relevant as they mainly depend on the period of time for which EBV's were provided, the birth year of stallions and the definition in each country of founder population (not necessarily provided in our data). Most stallions with EBV had progeny in competition (69% to 99%) with numbers of tested offspring from 16 to 42 and some have own performances (from 12% to 42% except in Denmark where no stallions have own performances recorded).
ð1Þ
2
X0X 6 Z0 X 6 4 0
X0Z Z Z + αA − 1 −αQ 0 A − 1 Z0Z 0
Z0 X
0 −αA − 1 Q αQ 0 A − 1 Q 0
½
3 X0Z bˆ 0 ZZ 7 ˆ + Q gˆ 7 u 5 0 gˆ Z 0 Z + δI ˆ p
with A the relationship matrix, α =
σ 2e σ 2u
and δ =
3 X0y 6 Z0y 7 7 =6 4 0 5
σ 2e , σ 2p
2
Z0y
σ2e the
residual variance, σ2u the variance of additive genetic effects, σ2p the variance of permanent environmental effects. That is, 2 defining heritability: h2 = σ 2 + σσ u2 + σ 2 and repeatability u p e r = σ 2u + σ 2p . ; α = 1 h−2 r and δ = r1−− hr2 σ2 + σ2 + σ2 u
p
e
After absorption of permanent environmental effect and genetic values of horses with performances but no progeny
Table 4 Statistic on EBV, number of progeny and performances.
Belgium Denmark France Ireland Sweden
Number of stallions with EBV
Mean EBV
Standard deviation EBV
% stallions with tested progeny
Mean number of progeny
Mean number of perf./progeny
% stallions with own perf.
Mean number of own perf.
926 563 5290 854 2153
− 0.20 0.05 − 0.43 0.01 0.44
0.70 0.52 0.99 0.21 0.84
69% 88% 72% 90% 99%
26.0 16.1 33.1 15.9 42.3
16.0 26.1 38.0 31.1 1.0
43% 0% 42% 32% 12%
27.6 . 79.2 19.8 1.0
perf.: performances, nbr: number.
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(supposed to be issued from mares without relationship), the MME became: 2
K 4 L0 0
2 3 3 32 0 r bˆ −1 −αA Q 54 u ˆ + Q gˆ 5 = 4 s 5 0 −1 0 αQ A Q gˆ
L M + αA − 1 0 −1 −αQ A
i
k=1
3
k nk + δ
K 6 L0 6 40 0
L 11 M + αA 21 αA 0 11 0 21 −αQ 1 A − αQ 2 A
0 12 αA 22 αA 0 12 0 22 −αQ 1 A − αQ 2 A
2 3 0 6 11 12 −αA Q 1 − αA Q 2 76 u 76 ˆ 1 21 22 −αA Q 1 − αA Q 2 56 ˆ 4u 2 0 −1 αQ A Q
3 2 3 r bˆ 7 6 7 + Q 1 ˆg 7 7=6s7 7 405 ˆ + Q2g 5 0 gˆ
ð2Þ with û1 the vector of stallions with EBV, û2 the vector of relatives without EBV, A
−1
11 = A21 A
A12 : 22 A
Horses without EBV were supposed to have no direct progeny with performances. The values of û1 were known but not û2 nor ĝ. û2 and ĝ were calculated solving: "
A
0 12 −Q 1 A
22
−
21
0 22 Q2A
22
−A Q 1 − A Q 2 0 −1 QA Q
#
2 3 21 ˆ ˆ −A u ˆ 2 + Q 2 ˆg 1 + Q 1g u 5 = 4 0 11 0 21 ˆg ˆ 1 + Q 1gˆ Q1A + Q2A u
where A and Q were known according to relationships. Now, both û1 and û2 were known and back to (Eq. (2) the deregressed proofs could be calculated as: h i h i h i 0 11 ˆ 1 + Q 1 gˆ + αA12 u ˆ 2 + Q 2 gˆ − α A11 Q 1 + A12 Q 2 gˆ u s − L bˆ = M + αA
from a file with parents, number of progeny, number of performances of progeny and number of own performances. From this equation, in order to write the equivalent models used for the calculation of genetic correlations, let define an equivalent performance for each horse in a country:
4
yi =
According to Sigurdsson et al. (1996) genetic correlations were computed using a multiple trait model with one trait per country. For each country t the model may be written: 4
yt = μ t + W t Q ft + W t ut +
+ 4α
mances of horse i, di the number of progeny of stallion i with performance and without progeny. Knowing û and ĝ, the calculation of s − L'bˆ, the deregressed proof, is simple. But since only EBV's on a set of stallions was provided (EBVs of stallions in reproducing activity but generally not of all ancestors), not all û were known. The vector û was decomposed in two parts: horses with known EBV, horses without known EBV (Jairath et al., 1998). So, the equations were rewritten as: 2
the vector Q and ĝ the solution of the only group effect, ûj the corresponding element of û1 or û2 for horse j. 3.2. Genetic correlation
with M a diagonal matrix with elements equal to mii = n δ d α n k+ δ P ni δ k with ni the number of own perforn + δ + n δ i
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2 3 N N X X
1 αaij uˆ j + qj gˆ − α aij qjgˆ 5 pffiffiffiffiffiffiffi 4ðmii + αaii Þ uˆ i + qi gˆ + σ e mii j=1 j=1
with aij the coefficient ij of matrix A− 1, N the number of horses in the complete file, mij as above, qi the coefficient of
et
ð3Þ
with y⁎t the vector of the y⁎t defined previously for each country, missing for horses without information in that pffiffiffiffiffi m country, Wt a matrix with elements wii = σ ii with m ii e defined previously for each country and f t the vector of new genetic groups defined as follows, Q the matrix that assigns horses to phantom parent groups. The variance of residuals was V(ε t) = I by construction of this equivalent model with Eq. (1) (except for the genetic groups). Defining ε = (ε1,…, ε5) the complete vector of residuals, V(ε) = I, assuming zero correlation between residuals between countries. The vector u t now included all horses and defining u = (u1,…, u5) the complete vector of genetic values of all horses in each of the five countries, V(u) = G⊗A with G the genetic variance–covariance matrix between countries and A the complete relationship matrix between all horses. This model is a multiple trait model with slope of random regression defined by the terms w ii for each trait. The diagonal of the matrix G was fixed, assuming that genetic variance in each country was known (according to genetic parameters given in Table 3). Genetic covariances were computed using ASREML (Gilmour et al., 2002). The genetic groups were difficult to estimate for all traits because, in each country, a majority of founders were born in this same country. Therefore, we chose to define 18 genetic groups based on to residual errors obtained for the genetic group estimates. For founders born before 1960, nine groups were defined according to the 5 countries involved in the project, adding Germany, The Netherlands, the thoroughbred breed and a group of “other countries”. For founders born after 1960, we combined 3 periods of time (1960/1969, 1970/ 1979, N = 1980) with 3 major breeds: German, Thoroughbred and “other countries”. 4. Results It was not possible to obtain convergence with the 5 countries simultaneously, especially due to the estimation of correlation between Belgium and Denmark, Belgium and Ireland, Denmark and Ireland. These correlations, when computed by pairs, were estimated near 1 (0.99, 0.99, 0.92) due to a lack of information.. So, a first group was formed including Belgium, Denmark, France and Sweden and a second with France, Ireland and Sweden (the two estimates of genetic correlation France⁎Sweden are given in the tables). Table 5 gives the correlations without genetic groups and with genetic groups. For the genetic correlations which were the most reliable, i.e. for the pairs Belgium⁎France, Belgium⁎Sweden, Denmark⁎Sweden, France⁎Sweden, the addition of genetic
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Table 5 Genetic correlation (standard error in brackets) without genetic groups above diagonal and with genetic groups below diagonal. Belgium Belgium Denmark France Ireland Sweden a b
Denmark 0.91 (0.19)
0.74 (0.22) a 0.88 (0.06) a 0.86 (0.08) a
France a
Ireland a
0.76 (0.06) 0.74 (0.15) a
0.70 (0.16) a 0.86 (0.07) a
0.45 (0.16) b 0.73 (0.16) b 0.88 (0.05) a 0.88 (0.05) b
Sweden 0.54 (0.09) a 0.57 (0.09) a 0.86 (0.05) a 0.83 (0.05) b 0.36 (0.16) b
0.91 (0.14) b
Analysis with Belgium, Denmark, France, Sweden together. Analysis with France, Ireland, Sweden together.
groups increased genetic correlations to values between 0.86 and 0.88. 5. Discussion 5.1. Data Checking the identity of the horses in the five files was a time consuming work and this step must be validated by the respective countries before any international breeding evaluation is made. The lack of information on birth year and breed (or country of birth) for a number of horses made the definition of genetic groups difficult. The definition of genetic groups have impact on genetic correlations. But the number of horses with uncertainty about their genetic group was relatively small so that they probably did not have a great impact on present genetic correlation estimates. This problem should also be solved for future official breeding evaluation. The effect of heterogeneity of the sets of stallions provided by each country was limited by the addition of a single genetic group in the deregression process. With the addition of such an effect, the distance between the set of stallions in the study and the founder population in the national breeding evaluation was evaluated and corrected for. 5.2. Connectedness and genetic correlations It is well known (Mark et al., 2005) that in weakly linked populations, the estimation of genetic correlations is imprecise. The connectedness between countries for show jumping competition evaluation was calculated in a previous study (Ruhlmann et al., in press) in which Germany and The Netherlands were included. The conclusion was that connectedness was sufficiently high, especially between Germany, The Netherlands, France, Belgium and Sweden. The absence of Germany and, to a lesser extent, The Netherlands in this study, decreased the degree of connectedness as most stallions with progeny and sires progeny in several countries have a German origin. But, on the other hand, the sample provided by Sweden was more complete (compared to Ruhlmann et al., in press) and this increased the connectedness between Sweden and all other countries and provided a fructuous link with Denmark. The standard error of estimates of the genetic correlations (0.05 to 0.08) indicates that the connectedness was sufficient for the pairs Belgium/France, Belgium/Sweden, Denmark/Sweden, France/Sweden and to a lesser extent for the other correlations (standard deviation between 0.14 and 0.22). These standard errors would have been higher if sire variances were not considered as fixed. As a test, the values were respectively 0.06 to 0.11 for the first
group of countries and 0.20 to 0.25 for the second one with joint estimation of variances and covariances. But these standard errors remained in the same range and the hypothesis of known variances in each country, according to the total mount of information used in each country to estimate them, was reasonable. 5.3. Strategy of estimation of genetic correlations Some choices were made in the process of estimation of the genetic correlations. The first one was fixing the genetic variance within countries. In horses, heritabilities are mostly estimated with an animal model in which own performances are included. These selection scheme relies more on relationship information between all horses (also mares) rather than only on stallions. So, we assumed that the estimation of sire variances from the data would have been less reliable than the national estimates performed in each country. The second choice was the use of only one trait by country, even if a multiple trait was used for national breeding evaluation. The use of multiple trait MACE (MT-MACE, Schaeffer, 2001; Liu et al., 2004) would have been possible, especially because ASREML allows all possible configuration of residual variances. The total number of traits would have reached 8 if restricting ourselves to competition traits (2 for Belgium, 3 for Ireland, 2 for France and one for Denmark and Sweden) or 12 when including the young horse tests (4 more traits for Sweden). Eight traits remained manageable but a set of 12 traits would perhaps require strategies such as structural covariance matrices (Leclerc et al., 2006) or principal component analysis as dimension reduction techniques (Tarres et al., 2008) to ensure coherences for inside and between countries correlations. Moreover, the superiority of MT-MACE compared to ST-MACE was only modest when high genetic correlations existed between traits within country (Sullivan et al., 2005) and the advantage of MT-MACE was restricted to sires for which some EBVs was missing (Mark and Sullivan, 2006). This was not the case in our data. However, MT-MACE could be considered as an alternative for an international evaluation of horses. The third issue was the choice of ASREML (Gilmour et al., 2002) to estimate genetic correlations. ASREML is reliable and easy to use. It allows for random regression, needed for MACE as there are different weighing factors for different sires, it may use different structures of residual variances, and one can restrict variance components if required. Several methods to estimate (co)variance components across countries were developed (Sigurdsson et al., 1996; Klei and Weigel, 1998; Madsen et al., 2000) with the main purpose to manage a large
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number of countries and to accelerate convergence due to the weakness of ties between countries. The present size of the data allowed to use ASREML and the convergence was obtained quickly for the subsets of 4 connected countries. The fourth choice was the calculation of weighting factor used for the deregression. According to the importance of diverse relationship in horse breeding, the parameter of choice would have been to use the reliability provided by each country. But as pointed out by Fikse and Sullivan (1999), the way each country computes reliabilities may introduce errors in an international genetic evaluation. So we preferred (except for the special case of Sweden) to combine number of progeny, number of records by progeny and number of own performance, which was an adaptation of what was suggested by Fikse and Banos (2001). The main difficulty was the lack of EBV's for horses in the pedigree data and we suggest that this information should be provided when an international evaluation is made. Compared to studies in dairy cattle, all stallions were used to compute genetic correlations and no subsets strategies were developed, except the 2 groups of countries. Subsetting has been introduced for various reasons: system size, bias due to weakly ties between countries (Mark et al., 2005) or changes in sire variances by time (Van Doormaal et al., 1999; Miglior et al., 2001). There was not really a problem of system size in our context, so full data could be analysed. For biases due to connectedness, the solution proposed is the use of well connected and well balanced (number of daughter across countries) subsets (Jorjani et al., 2005). For biases due to different variances, the use of only a recent subset of bulls (5 years) was proposed (Miglior et al., 2001). However, when older data were excluded, Sigurdsson et al. (1996) showed that within country sire variances were underestimated and that when imported bulls were discarded, genetic correlations were underestimated. Moreover, Klei and Weigel (1998) showed that genetic correlation based on a selected subset was biased downwards with low heritability and upward with high heritability. They developed an algorithm to allow the use of information of all bulls. In order to avoid problems due to heterogeneous variances of sire over time, Van Doormaal et al. (1999) proposed an algorithm to take into account genetic groups and sire variance within birth year. In our case, we showed the importance of pedigree information in connectedness (Ruhlmann et al., in press) compared to dairy bull as selection is largely based on own performance rather than on progeny tests. So, it was not possible to suppress older stallions. We tried to take into account heterogeneity in variances and differences in historical bases by genetic groups and the use of fixed variances to estimate correlation. The proposed strategy should be verified with more complete data, possibly including data from Germany and the Netherlands. 5.4. Level of genetic correlations Genetic correlations between traits for sport horses between Sweden and Denmark were estimated by Thorén Hellsten et al. (in press) on data of smaller size (28 stallions with EBV in both countries and 151 male ancestors). They performed multiple single trait MACE models for 19 pairs of traits concerning conformation, jumping traits and dressage
239
related traits, measured in Riding Horse Quality Test (RHQT) for Sweden and different young horse tests in Denmark. Genetic correlations were low for several conformation traits, especially those related to hind legs (0.10) or front part (0.38) but higher for type related traits (0.69 and 0.76). Genetic correlations were very high for traits related to performances: more than 0.99 for jumping traits (as jumping technique) and from 0.88 to 0.97 for dressage traits (such as rideability). Between country genetic correlations were reported for Icelandic horses for various test traits (conformation, gaits, temperament…) tested in Iceland and Sweden (Arnason and Sigurdsson, 1997). Except for gallop (0.26), all genetic correlations were very high, from 0.71 to 1.00, and nine correlations were higher than 0.80 for the fourteen traits concerned. Therefore, an international evaluation of Icelandic Toelter horse was set up across countries, combining the performances recorded in different countries into the same trait (Arnason and Sigurdsson, 2004; Arnason et al., 2006). This is also in agreement with the international unique breeding goal and standard form of evaluating conformation and riding ability used by International Federation of Icelandic Horse Association (FEIF). Compared to genetic correlations used in international evaluation of dairy bulls (Interbull, 2008), our estimates are of the same magnitude and cover the same range. The genetic correlation for Holstein for milk traits range from 0.75 to 0.94 with most values between 0.85 and 0.90. In Brown Swiss, which is probably more comparable to horse populations in terms of the number of bulls, correlations ranged from 0.76 to .93. Estimates of the genetic correlations between countries obtained in our study are in agreement with results in other horse populations and cattle populations. Genetic correlations were high in spite of large differences between countries with regard to data recording and genetic evaluation procedures. No differences in genetic correlations according to the trait used to measure jumping success in competition were found. Genetic correlations were as higher for Sweden, which used a cumulative life time trait as for Belgium, Ireland, Denmark or France which used the rank in each event. Over the years there have hardly been initiatives for international standardisations in horse breeding. It is therefore promising to see that the estimated correlation are not so much lower than those found for milk production in cattle. So we conclude from our results that the horse data could be used in a joint international evaluation. 5.5. Towards an International evaluation? The estimated genetic correlations encourage the continuation of this work towards an international genetic evaluation. To assure this objective, more work must be done to obtain representative and comparable samples from each country, especially when international EBVs of stallions will be computed. Obtaining EBV's of both stallions and ancestors from each country is needed. But even then, the homogeneity of the sample will not be perfect as the history of EBV-computation is very different between countries However, we cannot restrict ourselves to only young and active stallions because connectedness is provided mostly by older ancestors. More work needs to be done to evaluate the influence of the sample, the differences in genetic progress
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and heterogeneity of sire variances and reliabilities, and the estimation of sire variance on the magnitude of the genetic correlations. There are lot of advantages of across-country evaluations for practical horse breeding. These are not only improved international comparability but also improved reliability by adding performance information on exported horses. 6. Conclusion The objective of pilot project II of Interstallion was to verify connectedness among European countries for show jumping competition traits and to measure genetic correlations. The objective is achieved for 5 countries and genetic correlations are high (0.86 to 0.88) between Belgium, France, Sweden and between Sweden and Denmark, and relatively high (0.70 to 0.91) between Denmark and France or Belgium, and between Ireland and France and Sweden. The choice of particular traits to measure success in competition had no apparent effect on the genetic correlations, The future challenge is to prepare for an international evaluation requiring more complete data (EBV's on all animals, breed and birth year of all stallions and ancestors) and necessitating a study of the influence of heterogeneity of genetic variance over time, genetic trends and sire variance estimation and a subsetting strategy. References Arnason, T., Sigurdsson, A., 1997. Genetic analysis of performance test traits in Icelandic toelter horses in Iceland and Sweden. 48th Ann. Meet. EAAP, Vienna, Austria, 25–28 August 1997. Arnason, T., Sigurdsson, A., 2004. International genetic evaluations of the Icelandic horse. 55th Ann. Meet. EAAP, Bled, Slovenia, 5–9 September 2004. Arnason, T., Sigurdsson, A., Lorange, J.B., 2006. Global genetic evaluations of the Icelandic horse and genetic connectedness between countries. 8th World Congress on Genetics Applied to Livestock Production, Belo Horizonte, Brasil, 13–18 August 2006. Fikse, F., Sullivan, P.G., 1999. Use of national reliability figures to re-engineer effective number of records for application in international genetic evaluations. Interbull Bulletin 22, 44–48. Fikse, W.F., Banos, G., 2001. Weighting factors of sire daughter information in international genetic evaluations. J. Dairy Sci. 84, 1759–1767. Gilmour, A.R., Thompson, R., Cullis, B.R., Welham, S.J., 2002. Asreml Manual. New south Wales, Department of Agriculture, Orange, 2800, Australia. Harris, B., Johnson, D., 1998. Approximate reliability of genetic evaluations under an animal model. J. Dairy Sci. 81, 2723–2728. Interbull, 2008. Genetic evaluations, Production, Appendix I. http://wwwinterbull.slu.se/eval/framesida-prod.htm (Accessed June 23, 2008). Interstallion, 2008. http://www.biw.kuleuven.be/genlog/livgen/chgs_interstallion.html (accessed July 5, 2008).
Jairath, L., Dekkers, J.C.M., Schaeffer, L.R., Liu, Z., Burnside, E.B., Kolstad, B., 1998. Genetic evaluation for herd life in Canada. J. Dairy Sci. 81, 550–562. Janssens, S., Buys, N., Vandepitte, W., 2007. Sport status and the genetic evaluation for show jumping in Belgian sport horses. 58th Ann. Meet. EAAP, Dublin, Ireland, 26–29 August 2007. Jorjani, H., Emanuelson, U., Fikse, W.F., 2005. Data subsetting strategies for estimation of across-country genetic correlations. J. Dairy Sci. 88, 1214–1224. Klei, L., Weigel, K.A., 1998. A method to estimate correlations among traits in different countries using data on all bulls. Interbull Bulletin 17, 8–14. Leclerc, H., Minery, S., Delaunay, I., Druet, T., Fikse, F., Ducrocq, V., 2006. Estimation of genetic correlations among countries in international dairy sire evaluations with structural models. J. Dairy Sci. 89, 1792–1803. Liu, Z., Reinhardt, F., Reents, R., 2004. A multi-trait MACE model for international bull comparison based on daughter yield deviations. Interbull Bulletin 32, 46–52. Madsen, P., Jensen, J., Mark, T., 2000. Reduced rank estimation of (co)variance components for international evaluation using AI-REML. Interbull Bulletin 25, 46–50. Mark, T., Sullivan, P.G., 2006. Multiple-trait multiple-country genetic evaluations for udder health traits. J. Dairy Sci. 89, 4874–4885. Mark, T., Madsen, P., Jensen, J., Fikse, F., 2005. Difficulties in estimating acrosscountry genetic correlations for weakly linked bull populations. J. Dairy Sci. 88, 3303–3305. Miglior, F., Sullivan, P.G., Van Doormaal, B.J., 2001. Alternative strategies for estimation of country sire variance in international evaluations of dairy bulls. Interbull Bulletin 27, 84–88. Olsson, E., 2006. Multi-trait evaluation of Swedish warmblood stallions at station performance tests including field and competition records. PhD. Thesis. Swedish university of agricultural sciences. Publication 144. Quinn, K.M., 2005. Genetic evaluation of show jumping horses in Ireland. Irish Horse Board, Department of Agriculture and Food, BlockB, Maynooth Business campus, Maynooth, Kildare, Ireland, p. 31. Ricard, A., 1997. Breeding evaluations and breeding programs in France. 48th Ann. Meet. EAAP, Vienna, Austria, 25–28 August 1997. Ruhlmann, C., Bruns, E., Fraehr, E., Philipsson, J., Janssens, S., Quinn, K., Thorén Hellsten, E., Ricard, A., in press. Genetic connectedness between seven European countries for performance in jumping competitions of warmblood riding horses. Livest. Sci. doi:10.1016/j.livsci.2008.04.016. Schaeffer, L.R., 2001. Multiple trait international bull comparisons. Livest. Prod. Sci. 69, 145–153. Sigurdsson, A., Banos, G., 1995. Dependent variables in international sire evaluations. Acta Agric. Scand., A Anim. Sci. 45, 209–217. Sigurdsson, A., Banos, G., Philipsson, J., 1996. Estimation of genetic (co) variance components for international evaluation of dairy bulls. Acta Agric. Scand., A Anim. Sci. 46, 129–136. Sullivan, P.G., Wilton, J.W., Schaeffer, L.R., Jansen, G.J., Robinson, J.A.B., Allen, O.B., 2005. Genetic evaluation strategies for multiple traits and countries. Livest. Prod. Sci. 92, 195–205. Tarres, J., Liu, Z., Ducrocq, V., Reinhardt, F., Reents, R., 2008. Data transformation for rank reduction in multi-trait MACE model for international bull comparison. Genet. Sel. Evol. 40, 295–308. Thorén Hellsten, E., Jorjani, H., Philipsson, J., 2008. Connectedness among five European sport horse populations. Livest. Sci. 118, 147–156. Thorén Hellsten, E., Jorjani, H., Philipsson, J., in press. Genetic correlations between similar traits in the Danish and Swedish Warmblood sport horse populations. Livest. Sci. Van Doormaal, B.J., Kistemaker, G.J., Sullivan, P.G., 1999. Heterogeneous variances of Canadian bull EBVs over time. Interbull Bulletin 22, 141–148.
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Livestock Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / l i v s c i
Genetic correlations between horse show jumping competition traits in five European countries C. Ruhlmann a, S. Janssens b, J. Philipsson c, E. Thorén-Hellsten c, H. Crolly d, K. Quinn e, E. Manfredi a, A. Ricard a,⁎ a b c d e
Station d’amélioration génétique des animaux, Institut National de la Recherche Agronomique, BP 52627, F-31326 Castanet Tolosan, France Department of Biosystems, Katholieke Universiteit Leuven, Kasteelpark Arenberg 30, B-3001 Heverlee, Belgium Department of Animal Breeding and Genetics, Swedish University of Agricultural Sciences, Box 7023, S-750 07 Uppsala, Sweden Department of Genetics and Biotechnology, Research Centre Foulum, Postbox 50, DK-8830 Tjele, Denmark Irish Horse Board, Block B, Maynooth Business Campus, Maynooth, Co. Kildare, Ireland
a r t i c l e
i n f o
Article history: Received 24 July 2008 Received in revised form 8 September 2008 Accepted 8 September 2008 Keywords: Horse Genetic correlation Show jumping Multiple trait across-country evaluation
a b s t r a c t Genetic correlations were computed for show jumping competition traits from national estimated breeding values (EBV) of stallions of five countries: Belgium, Denmark, France, Ireland and Sweden. Data involved 24,390 horses, i.e. 8993 stallions with EBV and their ancestors. There were 617 stallions with several EBVs in more than one country. Method involved MACE (Multi-Trait Across Country Evaluation) methodology based on deregressed proofs adapted to the existence of own performance for stallions and to missing EBVs for some ancestors. ASREML was used to estimate covariance with an equivalent multiple trait model described as a random regression model. Within country sire variances were considered as known. The estimated genetic correlations were high (0.86 to 0.88) especially for reliable estimates between Belgium, France, Sweden and between Sweden and Denmark, and relatively high (0.70 to 0.91) for other pairs. These results open perspectives for the international evaluation of sporthorses. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The market of sport horses for show jumping competition has become more and more international and even if estimated breeding values (EBV) are provided by most countries, comparison between these values are difficult. Therefore a working group was founded (Interstallion, 2008) to 1) describe breeding objectives, testing procedures and genetic evaluation methods of warmblood breeding organisations; 2) recommend improvements of national genetic evaluation systems and 3) study methods of comparing genetic evaluations across countries. A first pilot project studied the comparison of genetic evaluations based on traits measured in young horse tests (Thorén Hellsten et al., 2008,
⁎ Corresponding author. Tel.: +33 5 61 28 51 83; fax: +33 5 61 28 53 53. E-mail address: [email protected] (A. Ricard). 1871-1413/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.livsci.2008.09.006
in press). The present study, was conducted in pilot project II, and focussed on competition traits measured in jumping events. The connectedness between countries was previously checked and acceptable to compute genetic correlations (Ruhlmann et al., in press). The aim of this study was to calculate genetic correlations for show jumping competition traits recorded in five European countries: Belgium, Denmark, France, Ireland and Sweden. 2. Materials and methods 2.1. Materials Sires EBVs were provided by 5 European countries: Belgium, Denmark, France, Ireland, Sweden. Requirements were that the files should include EBV's and reliabilities of all stallions bred for show jumping competition, i.e. with own
C. Ruhlmann et al. / Livestock Science 122 (2009) 234–240 Table 1 Number of stallions and ancestors provided by each of the five countries.
Belgium Denmark France Ireland Sweden
Stallions with EBV
Sires without EBV
Mares without EBV
Total horses in pedigree file
926 563 5290 854 2153
1500 1010 102 1365 932
3439 1614 5624 1903 1925
5865 3187 11016 4122 5010
Table 2 Number of common stallions with estimated breeding value (above diagonal) and number of common ancestors (below diagonal) between countries. Belgium Belgium Denmark France Ireland Sweden
Denmark
France
3 778 1242 476 733
135 23
442 329 976
614 711
Ireland 7 5 54
Sweden 99 207 272 85
471
performances or progeny with performances in jumping competition, and their complete pedigree up to 3 generations. The files provided contained from 563 to 5290 stallions with EBV and from 3187 to 11,016 horses (Table 1). Some countries (Belgium, Denmark, Ireland) provided EBV of only a subset of stallions (in reproductive activity or approved) and not for all ancestors and some (France, Sweden) provided EBV of near all stallions included in pedigree. So, according to the completeness of EBVs for stallions in pedigree, the deepness of pedigree varied between countries. For countries which gave EBV of only a subset of stallions, 41% to 92% of ancestors of these stallions at the third generation were known. For countries which provided almost all EBV of stallions, 12% to 44% of ancestors of these stallions at the third generation were known as even founders stallions had EBV. After checking the identity of the horses, the final files contained 24,390 different horses. Among them, 8993 stallions have at least one EBV in one country, 617 in two countries, 79 in
235
three and 6 in four. Common stallions between two countries varied from 3 to 272 (Table 2). Birth year was not always provided: from 23% to 95% of the horses had a known birth year. In order to include genetic groups defined by birth year of founders, birth year was estimated with the following rules. Four years were subtracted from the birth year of a horse to estimate the (unknown) birth year of its parents. The minimum value over all progeny was retained. This procedure was applied recursively. For horses without any information, a standard birth year was assigned depending on the mean number of generations between the individual and stallions with an EBV in the file. When three generations take place between the stallions with EBV and the horse without birth year, the birth year 1956 was attributed, when two, the year 1966 was attributed, when one 1976 and when the horse was a stallion with EBV the year 1986 was attributed. The breed of the horse was not always provided, especially in the Swedish and Danish data. When missing, the breed code was inferred from the original identification number or a search was conducted in other databases (for example www. allbreedpedigree.com). Finally, except for Thoroughbreds which were considered as one international breed, the different breeds in the same country of birth were pooled together and breed was confounded with country of birth. Additional countries of birth were added for horses identified in Germany or The Netherlands. The number of founders (horses without parents in the file) was 9699: 6744 mares, 2461 sires and 494 stallions with EBV but without sire or mare progeny in the file. Finally, founders were assigned to a breed and a period of birth. About the same proportion of founders (30% to 26%) was born before 1960, between 1960 and 1969 and between 1970 and 1979. A lower proportion was born more recently (17%). Before 1960, founders were mostly identified as French horses (27%), Thoroughbred (22%), Danish (12%), and German (11%). The more recent founders were Swedish (34%), Irish (24%) or belonged to other countries from the panel (14%). Table 3 summarizes the characteristics of the national genetic evaluations used in the countries involved in pilot
Table 3 Traits and genetic parameters used in national breeding evaluations for show jumping. Competition traits Country
Trait
Heritability
Repeatability
Genetic correlations
Belgium Denmark France Ireland Sweden
Rank low/high level Rank Rank/annual earning Rank low/medium/high level Cumulated life points
0.11/0.10 0.10 0.16/0.27 0.08/0.05/0.09 0.28
0.29/0.23 0.20 0.29/0.47 0.16/0.18/0.18 –
0.63 0.90 0.85/0.94/0.98 0.66/0.62/0.72/0.70 b
Indirect traits Country
Sweden (RHQT) a
a b
Trait
(1) (2) (3) (4)
RHQT=Riding Horse Quality Test. With indirect traits (1) to (4).
3years/jumping 3years/jumping 4years/jumping 4years/jumping
Heritability
style temperament style temperament
0.29 0.21 0.25 0.21
Genetic correlations (2)
(3)
(4)
0.91
0.77 0.69
0.70 0.70 0.92
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3. Method
project II. Genetic parameters were published for France (Ricard, 1997) and Ireland (Quinn, 2005) and given by breeding organisations in other cases in agreement with research works (Olsson, 2006; Janssens et al., 2007) for other countries. Most countries used traits that were directly related to show jumping competition whereas Sweden uses also indirect traits, i.e. measured in young horse tests (subjective note). The trait “rank” is the placing obtained in each event, often transformed in normal scores (Belgium, Ireland) or by taking the square root (Denmark) or modelled with an underlying continuous performance (France). In 4 countries out of 5, EBVs were computed using a multiple trait model. In the present analysis, EBVs used were the ones for high level of competition in Belgium and Ireland (which were also officially published), the trait based on ranks in France, and the cumulated life points in show jumping competition in Sweden. For Denmark the EBV from the single trait model was used. The number of progeny and performances used in the deregression process refers to the total number of progeny and performances for Belgium, Ireland and France. This is supported by high genetic correlations between traits so that all progeny contribute equally to the genetic evaluation whatever the trait recorded. In Sweden, only the number of progeny with results in competition was provided which could underestimate the amount of information used to calculate breeding values in the multiple trait model. As reliability was also provided, an equivalent number of progeny was calculated as: n =
Genetic correlations were calculated after deregression of the national EBV's. 3.1. Deregressed proofs The proposals of Sigurdsson and Banos (1995) were followed. Deregressed proofs for dairy bulls were obtained from EBV's using the information matrix of mixed model equations knowing the number of progeny of each bull in a single country. Adaptations were made to account for 1) the presence of own performances of stallions, which do not exist in dairy bulls and 2) the lack of EBVs for some ancestors of the known relationship matrix. The calculation was made for each country separately, with their own relationship matrix and known EBVs. First, the inclusion of own performances may be easily explained starting from an animal model and after some matrix algebra, going to a sire model. Suppose the following model: y = Xb + ZQg + Zu + Zp + e
with b vector of fixed effects, u random vector of animal breeding values, p random vector of permanent environmental effect, g the vector of genetic groups, e residual vector. In fact there were no genetic groups in any of the models used for computation of national EBVs. However, the files provided for this study were not the complete national files used in the different countries, so that the available data should be considered a sample from the animals included in the national evaluation. To avoid problems due to differences in the sampling of data, we added a single genetic group in the model. The corresponding mixed model equations (MME) were:
ð4 − h2 Þðr0
− h2 Þ with one own h2 ð1 − h2 Þð1 − r 0 Þ
stallion performance (life trait) or n =
ð4 − h2 Þr0 h2 ð1 − r 0 Þ
without own
performance, with n the equivalent number of progeny, h2 the heritability of competition trait, and: r 0 =
r − r r sire 4
rsire 4
+ 1−
rsire 2
(Harris and Johnson, 1998) with r the reliability of the EBV of the stallion and rsire the reliability of his sire. The reliability r was the squared correlation between true breeding value and EBV. According to parameters provided by each country, EBVs were standardized to a genetic standard deviation of 1. Statistics on EBVs, the number of progeny and own performances of stallions are given in Table 4. Mean and standard deviations of EBV are not relevant as they mainly depend on the period of time for which EBV's were provided, the birth year of stallions and the definition in each country of founder population (not necessarily provided in our data). Most stallions with EBV had progeny in competition (69% to 99%) with numbers of tested offspring from 16 to 42 and some have own performances (from 12% to 42% except in Denmark where no stallions have own performances recorded).
ð1Þ
2
X0X 6 Z0 X 6 4 0
X0Z Z Z + αA − 1 −αQ 0 A − 1 Z0Z 0
Z0 X
0 −αA − 1 Q αQ 0 A − 1 Q 0
½
3 X0Z bˆ 0 ZZ 7 ˆ + Q gˆ 7 u 5 0 gˆ Z 0 Z + δI ˆ p
with A the relationship matrix, α =
σ 2e σ 2u
and δ =
3 X0y 6 Z0y 7 7 =6 4 0 5
σ 2e , σ 2p
2
Z0y
σ2e the
residual variance, σ2u the variance of additive genetic effects, σ2p the variance of permanent environmental effects. That is, 2 defining heritability: h2 = σ 2 + σσ u2 + σ 2 and repeatability u p e r = σ 2u + σ 2p . ; α = 1 h−2 r and δ = r1−− hr2 σ2 + σ2 + σ2 u
p
e
After absorption of permanent environmental effect and genetic values of horses with performances but no progeny
Table 4 Statistic on EBV, number of progeny and performances.
Belgium Denmark France Ireland Sweden
Number of stallions with EBV
Mean EBV
Standard deviation EBV
% stallions with tested progeny
Mean number of progeny
Mean number of perf./progeny
% stallions with own perf.
Mean number of own perf.
926 563 5290 854 2153
− 0.20 0.05 − 0.43 0.01 0.44
0.70 0.52 0.99 0.21 0.84
69% 88% 72% 90% 99%
26.0 16.1 33.1 15.9 42.3
16.0 26.1 38.0 31.1 1.0
43% 0% 42% 32% 12%
27.6 . 79.2 19.8 1.0
perf.: performances, nbr: number.
C. Ruhlmann et al. / Livestock Science 122 (2009) 234–240
(supposed to be issued from mares without relationship), the MME became: 2
K 4 L0 0
2 3 3 32 0 r bˆ −1 −αA Q 54 u ˆ + Q gˆ 5 = 4 s 5 0 −1 0 αQ A Q gˆ
L M + αA − 1 0 −1 −αQ A
i
k=1
3
k nk + δ
K 6 L0 6 40 0
L 11 M + αA 21 αA 0 11 0 21 −αQ 1 A − αQ 2 A
0 12 αA 22 αA 0 12 0 22 −αQ 1 A − αQ 2 A
2 3 0 6 11 12 −αA Q 1 − αA Q 2 76 u 76 ˆ 1 21 22 −αA Q 1 − αA Q 2 56 ˆ 4u 2 0 −1 αQ A Q
3 2 3 r bˆ 7 6 7 + Q 1 ˆg 7 7=6s7 7 405 ˆ + Q2g 5 0 gˆ
ð2Þ with û1 the vector of stallions with EBV, û2 the vector of relatives without EBV, A
−1
11 = A21 A
A12 : 22 A
Horses without EBV were supposed to have no direct progeny with performances. The values of û1 were known but not û2 nor ĝ. û2 and ĝ were calculated solving: "
A
0 12 −Q 1 A
22
−
21
0 22 Q2A
22
−A Q 1 − A Q 2 0 −1 QA Q
#
2 3 21 ˆ ˆ −A u ˆ 2 + Q 2 ˆg 1 + Q 1g u 5 = 4 0 11 0 21 ˆg ˆ 1 + Q 1gˆ Q1A + Q2A u
where A and Q were known according to relationships. Now, both û1 and û2 were known and back to (Eq. (2) the deregressed proofs could be calculated as: h i h i h i 0 11 ˆ 1 + Q 1 gˆ + αA12 u ˆ 2 + Q 2 gˆ − α A11 Q 1 + A12 Q 2 gˆ u s − L bˆ = M + αA
from a file with parents, number of progeny, number of performances of progeny and number of own performances. From this equation, in order to write the equivalent models used for the calculation of genetic correlations, let define an equivalent performance for each horse in a country:
4
yi =
According to Sigurdsson et al. (1996) genetic correlations were computed using a multiple trait model with one trait per country. For each country t the model may be written: 4
yt = μ t + W t Q ft + W t ut +
+ 4α
mances of horse i, di the number of progeny of stallion i with performance and without progeny. Knowing û and ĝ, the calculation of s − L'bˆ, the deregressed proof, is simple. But since only EBV's on a set of stallions was provided (EBVs of stallions in reproducing activity but generally not of all ancestors), not all û were known. The vector û was decomposed in two parts: horses with known EBV, horses without known EBV (Jairath et al., 1998). So, the equations were rewritten as: 2
the vector Q and ĝ the solution of the only group effect, ûj the corresponding element of û1 or û2 for horse j. 3.2. Genetic correlation
with M a diagonal matrix with elements equal to mii = n δ d α n k+ δ P ni δ k with ni the number of own perforn + δ + n δ i
237
2 3 N N X X
1 αaij uˆ j + qj gˆ − α aij qjgˆ 5 pffiffiffiffiffiffiffi 4ðmii + αaii Þ uˆ i + qi gˆ + σ e mii j=1 j=1
with aij the coefficient ij of matrix A− 1, N the number of horses in the complete file, mij as above, qi the coefficient of
et
ð3Þ
with y⁎t the vector of the y⁎t defined previously for each country, missing for horses without information in that pffiffiffiffiffi m country, Wt a matrix with elements wii = σ ii with m ii e defined previously for each country and f t the vector of new genetic groups defined as follows, Q the matrix that assigns horses to phantom parent groups. The variance of residuals was V(ε t) = I by construction of this equivalent model with Eq. (1) (except for the genetic groups). Defining ε = (ε1,…, ε5) the complete vector of residuals, V(ε) = I, assuming zero correlation between residuals between countries. The vector u t now included all horses and defining u = (u1,…, u5) the complete vector of genetic values of all horses in each of the five countries, V(u) = G⊗A with G the genetic variance–covariance matrix between countries and A the complete relationship matrix between all horses. This model is a multiple trait model with slope of random regression defined by the terms w ii for each trait. The diagonal of the matrix G was fixed, assuming that genetic variance in each country was known (according to genetic parameters given in Table 3). Genetic covariances were computed using ASREML (Gilmour et al., 2002). The genetic groups were difficult to estimate for all traits because, in each country, a majority of founders were born in this same country. Therefore, we chose to define 18 genetic groups based on to residual errors obtained for the genetic group estimates. For founders born before 1960, nine groups were defined according to the 5 countries involved in the project, adding Germany, The Netherlands, the thoroughbred breed and a group of “other countries”. For founders born after 1960, we combined 3 periods of time (1960/1969, 1970/ 1979, N = 1980) with 3 major breeds: German, Thoroughbred and “other countries”. 4. Results It was not possible to obtain convergence with the 5 countries simultaneously, especially due to the estimation of correlation between Belgium and Denmark, Belgium and Ireland, Denmark and Ireland. These correlations, when computed by pairs, were estimated near 1 (0.99, 0.99, 0.92) due to a lack of information.. So, a first group was formed including Belgium, Denmark, France and Sweden and a second with France, Ireland and Sweden (the two estimates of genetic correlation France⁎Sweden are given in the tables). Table 5 gives the correlations without genetic groups and with genetic groups. For the genetic correlations which were the most reliable, i.e. for the pairs Belgium⁎France, Belgium⁎Sweden, Denmark⁎Sweden, France⁎Sweden, the addition of genetic
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Table 5 Genetic correlation (standard error in brackets) without genetic groups above diagonal and with genetic groups below diagonal. Belgium Belgium Denmark France Ireland Sweden a b
Denmark 0.91 (0.19)
0.74 (0.22) a 0.88 (0.06) a 0.86 (0.08) a
France a
Ireland a
0.76 (0.06) 0.74 (0.15) a
0.70 (0.16) a 0.86 (0.07) a
0.45 (0.16) b 0.73 (0.16) b 0.88 (0.05) a 0.88 (0.05) b
Sweden 0.54 (0.09) a 0.57 (0.09) a 0.86 (0.05) a 0.83 (0.05) b 0.36 (0.16) b
0.91 (0.14) b
Analysis with Belgium, Denmark, France, Sweden together. Analysis with France, Ireland, Sweden together.
groups increased genetic correlations to values between 0.86 and 0.88. 5. Discussion 5.1. Data Checking the identity of the horses in the five files was a time consuming work and this step must be validated by the respective countries before any international breeding evaluation is made. The lack of information on birth year and breed (or country of birth) for a number of horses made the definition of genetic groups difficult. The definition of genetic groups have impact on genetic correlations. But the number of horses with uncertainty about their genetic group was relatively small so that they probably did not have a great impact on present genetic correlation estimates. This problem should also be solved for future official breeding evaluation. The effect of heterogeneity of the sets of stallions provided by each country was limited by the addition of a single genetic group in the deregression process. With the addition of such an effect, the distance between the set of stallions in the study and the founder population in the national breeding evaluation was evaluated and corrected for. 5.2. Connectedness and genetic correlations It is well known (Mark et al., 2005) that in weakly linked populations, the estimation of genetic correlations is imprecise. The connectedness between countries for show jumping competition evaluation was calculated in a previous study (Ruhlmann et al., in press) in which Germany and The Netherlands were included. The conclusion was that connectedness was sufficiently high, especially between Germany, The Netherlands, France, Belgium and Sweden. The absence of Germany and, to a lesser extent, The Netherlands in this study, decreased the degree of connectedness as most stallions with progeny and sires progeny in several countries have a German origin. But, on the other hand, the sample provided by Sweden was more complete (compared to Ruhlmann et al., in press) and this increased the connectedness between Sweden and all other countries and provided a fructuous link with Denmark. The standard error of estimates of the genetic correlations (0.05 to 0.08) indicates that the connectedness was sufficient for the pairs Belgium/France, Belgium/Sweden, Denmark/Sweden, France/Sweden and to a lesser extent for the other correlations (standard deviation between 0.14 and 0.22). These standard errors would have been higher if sire variances were not considered as fixed. As a test, the values were respectively 0.06 to 0.11 for the first
group of countries and 0.20 to 0.25 for the second one with joint estimation of variances and covariances. But these standard errors remained in the same range and the hypothesis of known variances in each country, according to the total mount of information used in each country to estimate them, was reasonable. 5.3. Strategy of estimation of genetic correlations Some choices were made in the process of estimation of the genetic correlations. The first one was fixing the genetic variance within countries. In horses, heritabilities are mostly estimated with an animal model in which own performances are included. These selection scheme relies more on relationship information between all horses (also mares) rather than only on stallions. So, we assumed that the estimation of sire variances from the data would have been less reliable than the national estimates performed in each country. The second choice was the use of only one trait by country, even if a multiple trait was used for national breeding evaluation. The use of multiple trait MACE (MT-MACE, Schaeffer, 2001; Liu et al., 2004) would have been possible, especially because ASREML allows all possible configuration of residual variances. The total number of traits would have reached 8 if restricting ourselves to competition traits (2 for Belgium, 3 for Ireland, 2 for France and one for Denmark and Sweden) or 12 when including the young horse tests (4 more traits for Sweden). Eight traits remained manageable but a set of 12 traits would perhaps require strategies such as structural covariance matrices (Leclerc et al., 2006) or principal component analysis as dimension reduction techniques (Tarres et al., 2008) to ensure coherences for inside and between countries correlations. Moreover, the superiority of MT-MACE compared to ST-MACE was only modest when high genetic correlations existed between traits within country (Sullivan et al., 2005) and the advantage of MT-MACE was restricted to sires for which some EBVs was missing (Mark and Sullivan, 2006). This was not the case in our data. However, MT-MACE could be considered as an alternative for an international evaluation of horses. The third issue was the choice of ASREML (Gilmour et al., 2002) to estimate genetic correlations. ASREML is reliable and easy to use. It allows for random regression, needed for MACE as there are different weighing factors for different sires, it may use different structures of residual variances, and one can restrict variance components if required. Several methods to estimate (co)variance components across countries were developed (Sigurdsson et al., 1996; Klei and Weigel, 1998; Madsen et al., 2000) with the main purpose to manage a large
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number of countries and to accelerate convergence due to the weakness of ties between countries. The present size of the data allowed to use ASREML and the convergence was obtained quickly for the subsets of 4 connected countries. The fourth choice was the calculation of weighting factor used for the deregression. According to the importance of diverse relationship in horse breeding, the parameter of choice would have been to use the reliability provided by each country. But as pointed out by Fikse and Sullivan (1999), the way each country computes reliabilities may introduce errors in an international genetic evaluation. So we preferred (except for the special case of Sweden) to combine number of progeny, number of records by progeny and number of own performance, which was an adaptation of what was suggested by Fikse and Banos (2001). The main difficulty was the lack of EBV's for horses in the pedigree data and we suggest that this information should be provided when an international evaluation is made. Compared to studies in dairy cattle, all stallions were used to compute genetic correlations and no subsets strategies were developed, except the 2 groups of countries. Subsetting has been introduced for various reasons: system size, bias due to weakly ties between countries (Mark et al., 2005) or changes in sire variances by time (Van Doormaal et al., 1999; Miglior et al., 2001). There was not really a problem of system size in our context, so full data could be analysed. For biases due to connectedness, the solution proposed is the use of well connected and well balanced (number of daughter across countries) subsets (Jorjani et al., 2005). For biases due to different variances, the use of only a recent subset of bulls (5 years) was proposed (Miglior et al., 2001). However, when older data were excluded, Sigurdsson et al. (1996) showed that within country sire variances were underestimated and that when imported bulls were discarded, genetic correlations were underestimated. Moreover, Klei and Weigel (1998) showed that genetic correlation based on a selected subset was biased downwards with low heritability and upward with high heritability. They developed an algorithm to allow the use of information of all bulls. In order to avoid problems due to heterogeneous variances of sire over time, Van Doormaal et al. (1999) proposed an algorithm to take into account genetic groups and sire variance within birth year. In our case, we showed the importance of pedigree information in connectedness (Ruhlmann et al., in press) compared to dairy bull as selection is largely based on own performance rather than on progeny tests. So, it was not possible to suppress older stallions. We tried to take into account heterogeneity in variances and differences in historical bases by genetic groups and the use of fixed variances to estimate correlation. The proposed strategy should be verified with more complete data, possibly including data from Germany and the Netherlands. 5.4. Level of genetic correlations Genetic correlations between traits for sport horses between Sweden and Denmark were estimated by Thorén Hellsten et al. (in press) on data of smaller size (28 stallions with EBV in both countries and 151 male ancestors). They performed multiple single trait MACE models for 19 pairs of traits concerning conformation, jumping traits and dressage
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related traits, measured in Riding Horse Quality Test (RHQT) for Sweden and different young horse tests in Denmark. Genetic correlations were low for several conformation traits, especially those related to hind legs (0.10) or front part (0.38) but higher for type related traits (0.69 and 0.76). Genetic correlations were very high for traits related to performances: more than 0.99 for jumping traits (as jumping technique) and from 0.88 to 0.97 for dressage traits (such as rideability). Between country genetic correlations were reported for Icelandic horses for various test traits (conformation, gaits, temperament…) tested in Iceland and Sweden (Arnason and Sigurdsson, 1997). Except for gallop (0.26), all genetic correlations were very high, from 0.71 to 1.00, and nine correlations were higher than 0.80 for the fourteen traits concerned. Therefore, an international evaluation of Icelandic Toelter horse was set up across countries, combining the performances recorded in different countries into the same trait (Arnason and Sigurdsson, 2004; Arnason et al., 2006). This is also in agreement with the international unique breeding goal and standard form of evaluating conformation and riding ability used by International Federation of Icelandic Horse Association (FEIF). Compared to genetic correlations used in international evaluation of dairy bulls (Interbull, 2008), our estimates are of the same magnitude and cover the same range. The genetic correlation for Holstein for milk traits range from 0.75 to 0.94 with most values between 0.85 and 0.90. In Brown Swiss, which is probably more comparable to horse populations in terms of the number of bulls, correlations ranged from 0.76 to .93. Estimates of the genetic correlations between countries obtained in our study are in agreement with results in other horse populations and cattle populations. Genetic correlations were high in spite of large differences between countries with regard to data recording and genetic evaluation procedures. No differences in genetic correlations according to the trait used to measure jumping success in competition were found. Genetic correlations were as higher for Sweden, which used a cumulative life time trait as for Belgium, Ireland, Denmark or France which used the rank in each event. Over the years there have hardly been initiatives for international standardisations in horse breeding. It is therefore promising to see that the estimated correlation are not so much lower than those found for milk production in cattle. So we conclude from our results that the horse data could be used in a joint international evaluation. 5.5. Towards an International evaluation? The estimated genetic correlations encourage the continuation of this work towards an international genetic evaluation. To assure this objective, more work must be done to obtain representative and comparable samples from each country, especially when international EBVs of stallions will be computed. Obtaining EBV's of both stallions and ancestors from each country is needed. But even then, the homogeneity of the sample will not be perfect as the history of EBV-computation is very different between countries However, we cannot restrict ourselves to only young and active stallions because connectedness is provided mostly by older ancestors. More work needs to be done to evaluate the influence of the sample, the differences in genetic progress
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and heterogeneity of sire variances and reliabilities, and the estimation of sire variance on the magnitude of the genetic correlations. There are lot of advantages of across-country evaluations for practical horse breeding. These are not only improved international comparability but also improved reliability by adding performance information on exported horses. 6. Conclusion The objective of pilot project II of Interstallion was to verify connectedness among European countries for show jumping competition traits and to measure genetic correlations. The objective is achieved for 5 countries and genetic correlations are high (0.86 to 0.88) between Belgium, France, Sweden and between Sweden and Denmark, and relatively high (0.70 to 0.91) between Denmark and France or Belgium, and between Ireland and France and Sweden. The choice of particular traits to measure success in competition had no apparent effect on the genetic correlations, The future challenge is to prepare for an international evaluation requiring more complete data (EBV's on all animals, breed and birth year of all stallions and ancestors) and necessitating a study of the influence of heterogeneity of genetic variance over time, genetic trends and sire variance estimation and a subsetting strategy. References Arnason, T., Sigurdsson, A., 1997. Genetic analysis of performance test traits in Icelandic toelter horses in Iceland and Sweden. 48th Ann. Meet. EAAP, Vienna, Austria, 25–28 August 1997. Arnason, T., Sigurdsson, A., 2004. International genetic evaluations of the Icelandic horse. 55th Ann. Meet. EAAP, Bled, Slovenia, 5–9 September 2004. Arnason, T., Sigurdsson, A., Lorange, J.B., 2006. Global genetic evaluations of the Icelandic horse and genetic connectedness between countries. 8th World Congress on Genetics Applied to Livestock Production, Belo Horizonte, Brasil, 13–18 August 2006. Fikse, F., Sullivan, P.G., 1999. Use of national reliability figures to re-engineer effective number of records for application in international genetic evaluations. Interbull Bulletin 22, 44–48. Fikse, W.F., Banos, G., 2001. Weighting factors of sire daughter information in international genetic evaluations. J. Dairy Sci. 84, 1759–1767. Gilmour, A.R., Thompson, R., Cullis, B.R., Welham, S.J., 2002. Asreml Manual. New south Wales, Department of Agriculture, Orange, 2800, Australia. Harris, B., Johnson, D., 1998. Approximate reliability of genetic evaluations under an animal model. J. Dairy Sci. 81, 2723–2728. Interbull, 2008. Genetic evaluations, Production, Appendix I. http://wwwinterbull.slu.se/eval/framesida-prod.htm (Accessed June 23, 2008). Interstallion, 2008. http://www.biw.kuleuven.be/genlog/livgen/chgs_interstallion.html (accessed July 5, 2008).
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