Modelling repeated competition records in genetic evaluations of Danish sport horses

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1 J. Anim. Breed. Genet. ISSN ORIGINAL ARTICLE Modelling repeated competition records in genetic evaluations of Danish sport horses L. J onsson 1,2, P. Madsen 3 & T. Mark 1 1 Department of Clinical Veterinary and Animal Sciences, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark 2 Danish Warmblood Association, Maarslet, Denmark 3 Department of Molecular Biology and Genetics, Center for Quantitative Genetics and Genomics, Aarhus University, Aarhus, Denmark Keywords Genetic analysis; competition results; rider effect; judge effect; pseudo-phenotypes. Correspondence L. J onsson, Department of Veterinary Clinical and Animal Sciences, University of Copenhagen, Grønnegardsvej 3, 2. Sal, 1870 Frederiksberg C, Copenhagen, Denmark. Tel: ; Fax: ; Lina.Jonsson@sund.ku.dk Received: 3 June 2015; accepted: 15 September 2015 Summary Genetic evaluations of sport performance typically consider competition records of ranking points in each competition, accumulated lifetime points or annual earnings. Repeated observations have the advantage of allowing for adjustment of effects associated with each competition such as rider experience, judge and competing horses, but also demands more computer capacity than single-trait records, which could prohibit multiple-trait evaluations. The aim of the study was to compare CPU times, estimated breeding values (EBVs), reliabilities and model prediction abilities when modelling repeated competition ranking points (run A), mean ranking points (runs B and C), mean ranking points precorrected for effects associated with each competition (run D) and accumulated lifetime points (run E) for Danish Warmblood horses. CPU times for run A were times (show jumping) and times (dressage) as high as for runs B E. EBVs of run D were perfectly correlated (1.00) with those of run A. Reliabilities were highest in runs E and A. Best model prediction ability and least bias were found in run C (dressage) and run E (show jumping), but the best choice in each discipline was not preferable for the other. Run D was the second best in both disciplines (D), and is expected to increase in performance over time as omission of a relatively large amount of historic data becomes less important. Introduction Records based on achievements in dressage and show jumping competitions form a central part of sport horse breeding evaluations, together with young horse evaluations of talent and conformation (Koenen et al. 2004; Thoren Hellsten et al. 2006). The former is the breeding goal traits, whereas the latter are important indicators being available earlier in life. Somewhat different types of registrations of competition results have been included in the breeding evaluations between studbooks (Thoren Hellsten et al. 2006; Ruhlmann et al. 2009). The most commonly used competition results are accumulated lifetime points, repeated observations of points in each competition, and mean points. In the routine single-trait breeding evaluation of competition success in the Danish Warmblood (DWB), repeated observations of ranking points in each competition have been employed (Boelling 2011), to account for non-genetic factors present at each competition such as rider, judge, competition date and venue, and other participating horses. Multitrait evaluations including both competition results and young horse information are advantageous in breeding of sport horses because preselection is better accounted for. Further, young horse trait heritabilities are comparably higher due to lower environmental influences of 2015 Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015) 1 12 doi: /jbg.12190

2 Modelling repeated competition records L. J onsson et al. training (Luehrs-Behnke et al. 2002; Viklund et al. 2010). Heritabilities of young horse talent traits of the DWB have been estimated at (Thoren Hellsten et al. 2009; J onsson et al. 2014). In multitrait evaluations, restrictions on computer capacity become more important, where repeated observations require higher computer capacity to evaluate than single observations. Furthermore, specification of covariances between single and repeated observations is problematic. Thus, prior to a development of a multitrait evaluation, it was desirable to investigate less computer capacity demanding competition trait records. The use of mean or sum of competition performances could be possible alternatives, however presenting a drawback of not being able to simultaneously correct for non-genetic effects in separate performances. In dairy cattle, two-step approaches have been successfully used to reduce computational demands in multitrait evaluations (Schaeffer 1994; Jairath et al. 1998; Tarres et al. 2006; Lassen et al. 2007b). In the first step, phenotypes are typically precorrected for nongenetic effects, and in some cases, multiple records per animal are summarized. In the second step, several precorrected phenotypes are analysed simultaneously. It was hypothesized that a similar approach may be applicable in horse breeding evaluations, where the sum of the estimated breeding value (EBV) and mean residual [EBV + mean(residual)] from a repeatability model of competition results was used as dependent variable in subsequent evaluations. To the author s knowledge, a similar approach has not been previously applied to genetic analysis of horses. The aim of this study was to compare EBVs for dressage and jumping ability, their reliabilities, model predictive abilities, and computer capacity requirements between evaluations of repeated observations and less computer demanding genetic evaluation models. For comparison, also results from a model of accumulated lifetime points were considered. Material and methods Official competition data of DWB horses from regional level or higher were provided from the period From 1986 to 1997, only placings (i.e. best performing horses) were recorded, and from 1998 also starts without placings were included. Repeated observations of points based on ranking in each entered competition class were provided where each record was transformed as: Ranking point ¼ p 11 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðoriginal rankingþð6 level of competitionþ5þ where the part within the square root was the adjustment of ranking points based on level of competition (level 1 = lowest level to level 6 = highest level) so that a 1st placing on level 4 was equal to the ranking points for a 6th placing on level 5, or a 11th placing on level 6. For best normalization (Boelling 2011), 11 the square root of the adjusted ranking points was used, resulting in a skewness of and a kurtosis of for dressage, and and for show jumping, respectively (data in run A). The modifications were executed to assure rankings on high level to be more valuable than rankings on low level, and to ensure better accordance with normal distribution, all in accordance with DWB current breeding evaluation practice (Boelling 2011). Each record was accompanied by information of place, date, discipline and level of the competition class, age and gender of the horse, and rider. For dressage, the raw data included horses, with a total sum of competition results. The average number of competition records per horse was 17 (SD = 24, Min = 1, Max = 350). Each horse had an average of 1.5 riders (SD = 0.92, Min = 1, Max = 10), and each rider on average competed with 2.7 horses (SD = 4.4, Min = 1, Max = 99). For show jumping, the raw competition data included horses with a total sum of competition results. The average number of competition records per horse was 33 (SD = 51, Min = 1, Max = 612). Each horse had an average of 2.0 riders (SD = 1.4, Min = 1, Max = 15), and each rider on average had competed with 4.3 horses (SD = 11.8, Min = 1, Max = 244). Analyses Competition results were analysed in five alternative ways, including four alternatives of repeated observations (A D) and one based on accumulated lifetime points (E) as described in Table 1 as well as in more detail below: Run A: Repeated observations of ranking points in separate competitions Fixed class effects of competition class, age-gender and rider level were included in the model (1) as found most appropriate by AIC values (J onsson et al. 2014) Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015) 1 12

3 L. J onsson et al. Modelling repeated competition records Table 1 Description of runs conducted and descriptive statistics of included competition records Run Dependent variable Explanatory variables in model 1 Weight Dressage Show jumping Years 2 No. 3 Mean 4 SD 4 Years 2 No. 3 Mean 4 SD 4 A B C D E Repeated obs. of ranking points competition level F + age-gender F + rider level F + animal (PE) R Unweighted birth year F + gender F Unweighted Mean ranking points (data as run A) Mean ranking points birth year F + gender F Unweighted (all records) EBV+mean(e) from birth year F + gender F No. obs run A 2 Accumulated lifetime birth year F + gender F Unweighted points F, Fixed effect; R, Random effect. 1 Additive genetic animal model including phantom parent, and residual random effects were also included in all models, but are not mentioned. 2 Recording period reduced for dressage data in alternative (a), (b) and (e) as number of records in earlier years was smaller than stated limits in dataediting procedures. 3 Number of included horses. 4 Based on transformed records. y ijkl ¼ lþcompetition class F i þage-gender F j þrider level F k þanimalðpeþ l þanimal l þe ijkl ð1þ where y ijkl was repeated ranking scores of the lth horse, l was the population mean, competition class F i was the fixed effect of what competition class entry the ranking was a result of representing a combined effects of date, place, class and judge, age-gender F j was the fixed effect of a combination of age and gender, rider level F k was the fixed effect of rider experience, animal(pe) l was the permanent environmental effect of animal N 0; Ir 2 pe, animal l was the random genetic effect N 0; Ar 2 a, and eijkl was the random residual effect N 0; Ir 2 pe, where A was the relationship matrix and I was an incidence matrix. The A matrix included 31 phantom parent groups as random effects for both sires and dams, based on the offspring birth year. The individual effect of rider was not included as it was partly confounded with and therefore difficult to separate from the animal effects which lead to convergence problems. Also, the individual rider effect does not account for the fact that riders often improve during their careers. Instead, a fixed class effect of rider level was included. Three rider level categories were created as follows: rider level low = competition level 1 2, rider level intermediate = competition level 3 5 and rider level high = competition level 6 7. Only three rider levels were used as little difference was expected between riders of pooled competition levels, and riders commonly jump back and forth between these levels. Rider level was defined as the highest level the rider had competed at until time of each competition start. This allowed riders to improve in level over time. To ensure sufficient group sizes of fixed effects, horses with at least 10 competition results and competition classes with at least 10 horses ( competition classes for dressage and for show jumping) were included in the genetic analysis. Thus, dressage competition results of 7814 horses and show jumping competition results of horses were kept. Run B: Mean of the same repeated observations as included in run A Mean of repeated observations of each horse was used as phenotype. The number of horses included was the same as in run A to enable a fair comparison. The model (2) of run B was: y ijk ¼ l þ birth year F i þ gender F j þ animal k þ e ijk ð2þ where y ijk was the mean ranking score of the kth horse, l was the population mean, birth year F i was the fixed effect of birth year, gender F j was the fixed effect of gender, animal k was the random genetic effect N 0; Ar 2 a, and eijk was the random residual effect N 0; Ir 2 pe, where A was the relationship matrix and I was an incidence matrix. Phantom parent groups were included as in run A. It was not possible to correct for rider and competition levels as these 2015 Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015)

4 Modelling repeated competition records L. J onsson et al. varied across observations within horse. Observations were analysed in an unweighted analysis. Run C: Mean of repeated observations of all horses with competition results The model was the same as in run B, except more data were considered (dressage: N = ; show jumping: N = ). This was possible because group sizes of included non-genetic effects of gender and birth year were large, generating a smaller reduction in data compared to, for example, run A. This run was performed to quantify the advantages of being able to use more of the data (i.e. runs B versus C). Run D: Using EBV+mean(residual) from run A as dependent variable in a two-step analyses Results of model (1) were used where the mean(residual) was calculated within horse, so that each horse had only one observation. The model (3) used in the 2nd step of run D was as follows: y ijk ¼ l þ birth year F i þ gender F j þ animal k þ e ijk ð3þ where y ijk was the EBV+mean(residual) from run A of the kth horse, l was the population mean, birth year F i was the fixed effect of birth year, gender F j was the fixed effect of gender, animal k was the random genetic effect N 0; Ar 2 a, and eijk was the random residual effect N 0; Ir 2 pe, where A was the relationship matrix and I was an incidence matrix. Phantom parent groups were included as in run A. The observations in this 2nd step analysis were weighted with number of observations per horse in the 1st step analysis (i.e. run A). Note that the dependent variable is equivalent to the mean phenotype with all nongenetic effects subtracted except the mean(residual) [i.e. pseudo-phenotypes (Tarres et al. 2006; Lassen et al. 2007b)]. The motivation for this approach was that rider experience and competition level could be accounted for while being easier to extent to multiple-trait models than run A. Fixed effects of birth year and gender were included in the 2nd model although also being accounted for in the 1st model. This is because they were still significant and other studies have found it advantageous to include key nongenetic effects in both steps (Tarres et al. 2006; Lassen et al. 2007a) Run E: Accumulated lifetime points For comparison, accumulated lifetime points which are based on a similar but slightly different scoring system were also studied as sum of points during the career. Points were given for placings, where higher points were received for placings on higher level of competition compared to the same placing on lower level. This run was similar to run C, except that points were summed rather than averaged within horse. The raw data included horses with dressage lifetime points, born between 1969 and 2008, including (66%) males and 7554 (34%) females. For show jumping, the raw data included horses, born between 1970 and 2008, including 6060 (58%) males and 4340 (42%) females. Number of horses with a record and known identity, birth year and gender that could be included in the analyses (dressage: N = ; show jumping: N = ) was slightly smaller than in run C. The difference was due to horses that only had a registered competition result in run C from a low level competition or low ranking, which did not qualify for a lifetime point in run E. The accumulated lifetime points were transformed with 10-logarithm, similar to previous studies of the trait in the Swedish warmblood (Viklund et al. 2010). The model (4) used in run E was as follows: y ijk ¼ l þ birth year F i þ gender F j þ animal k þ e ijk ð4þ where y ijk was the log-transformed summed lifetime points of the kth horse, l was the population mean, birth year F i was the fixed effect of birth year, gender F j was the fixed effect of gender, animal k was the random genetic effect N 0; Ar 2 a, and eijk was the random residual effect N 0; Ir 2 pe, where A was the relationship matrix and I was an incidence matrix. Phantom parent groups were included as in run A. The pedigree was traced back seven generations from individuals with competition results, comprising horses for runs (A, B and D) and horses for alternatives (C and E). All genetic analyses were performed using single-trait models and average information restricted maximum likelihood (AI- REML; Jensen et al. (1997)) as implemented in the DMU software (Madsen & Jensen 2013). Estimated heritability and used CPU time were studied for each run, together with average reliability of EBVs among horses with own competition records. Reliabilities were calculated as follows: ria 2 ¼ 1 PEV genetic variance where PEV was the exact prediction error variance under the assumption of a correct model including correct variance components. Reliabilities of run D were expected to be inflated due to disregarding uncertainty associated with precorrection of nongenetic effects. To reveal what non-genetic effects Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015) 1 12

5 L. J onsson et al. Modelling repeated competition records caused most of the inflation, and to investigate ways to adjust inflated reliabilities, effects of mean standard error and mean SD of non-genetic effects in run A were evaluated in GLMSELECT (SAS Insitute Inc 2015), together with number of offspring, during modelling of the expected reliability (from run A) using the inflated reliability (from run D). Model predictive ability and evaluation of bias of EBVs in runs A E were studied according to Reverter et al. (1994), using Pearson correlations (r EBVfull, EBVred) and regression coefficients (b EBVfull EBVred ) studied as EBVs based on reduced data (EBV red ) regressed on EBVs for the full data (EBV full), as EBV full = b 9 EBV red, that is no intercept included. In the reduced data, results of horses born were excluded. Pearson correlations of EBVs between runs A E were estimated, based on horses with own competition results. Spearman rank correlations were estimated between stallions with at least 15 offspring in the competition statistics. The 20 highest ranked stallions of each discipline in run A were also studied in detail for ranking in runs B E, accompanied by mean ranking, SD, Min and Max ranking number. Further, the mean EBV for run A [EBV(A)] of top 20 horses in runs B E were studied to indicate consequences of model choice on potential genetic progress, both for the group of stallions that had at least 15 offspring in run A and for stallions where it was enough to have at least 15 offspring in alternative B E, respectively. Results A comparison of CPU times, heritability, reliability and model predictive ability of runs A-E is found in Table 2 (dressage) and 3 (show jumping). Run A used times and as much CPU time as the other studied runs for show jumping and dressage, respectively. Heritability estimates ranged from 0.16 to 0.33 for dressage and from 0.05 to 0.33 for show jumping. The mean reliability among horses with competition results was higher when using repeated observations (run A) rather than mean observation (run B) as dependent variable. This was the case for both dressage (r 2 IA: 0.45 versus 0.42) and show jumping (r 2 IA: 0.43 versus 0.33). Among horses with observations in run A, the mean reliability of run E was slightly higher than in run A for dressage (r 2 IA: 0.46) and equal to run A for show jumping (r 2 IA: 0.43). When considering all horses of run E (approximately 2 3 times as many as in runs A), mean reliability decreased slightly for dressage (r 2 IA: 0.44) and show jumping (r 2 IA: 0.42). Reliabilities of run C were generally lower than run A, both when considering the same horses as run A, and all horses, especially in show jumping (r 2 IA: 0.30 and 0.28, respectively). Inflated reliabilities of run D were adjusted based on effects and estimates presented in Table 4 to approach those expected (i.e. run A reliabilities), where number of offspring together with mean SE of age-gender had the largest influence on the inflation. Scatter plots of original and adjusted reliabilities of run D (r 2 IA, RunD ) compared to reliabilities if run A (r 2 IA, RunA ) are provided in Fig. 1. Model predictive ability Comparing EBVs for the same horses between runs A-E indicated that EBVs from run C were least biased for dressage (b = 0.98), followed by run D (b = 0.97) and run B (b = 0.95). For show jumping, run E showed least signs of bias (b = 0.97), followed by run D(b = 0.96) and run A (b = 0.90). Out of investigated alternatives, cross-validation correlations (r EBVfull, EBVred) were highest in run C for dressage (r = 0.78), followed by run D (r = 0.74) and run E (r = 0.73). For show jumping, the best results were found in run E (r = 0.80), followed by run D (r = 0.74) and run C (r = 0.66). Consequences of using alternative models for prediction of breeding values The two-step model, using pseudo-phenotypes (run D), produced essentially the same EBVs as the currently used repeatability model (run A). Pearson correlations between EBVs from the two runs A and D (Table 5) as well as Spearman rank correlations were >0.99 for both dressage and show jumping. Substantial differences in EBVs were found among the remaining runs, especially for mean show jumping results (B and C), compared to other alternatives (A, D and E) with Pearson correlations between EBVs ranging between 0.42 and 0.62 (results not shown for Spearman rank correlations because they were similar to EBV correlations). A more detailed description of changes in top 20 stallion rankings (A E) is found in Table 6. Out of the 20 top ranked dressage stallions for run A, 17 were also found in the top 20 for B, 8 in C, 19 in D and 10 in E. The lowest ranking of the top 20 stallions in A, in other alternatives (B E) was 129 in C. Out of the 20 top ranked show jumping stallions for A, 14 were also found in the top 20 for B, 5 in C, 20 in D and 5 in E. The lowest ranking of the top 20 stallions in A, in other alternatives (B E) was 204 in C. Highest mean EBV from run A [EBV(A)] of top Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015)

6 Modelling repeated competition records L. J onsson et al. Table 2 Dressage results regarding CPU time used, heritability, mean reliability of breeding values (EBVs) for horses with at least one competition record and model predictive ability for run A E Model predictive ability 3 Reliability of horses with records 2 Of available horses in each run (A E) Of horses included in run A Run CPU time 1 h 2 SE (h 2 ) No. horses r 2 IA SD (r 2 IA) Correlation (r EBVfull, EBVred ) Regr. coeff (b EBVfull EBVred ) Correlation (r EBVfull, EBVred ) Regr. coeff (b EBVfull EBVred ) A. Repeated obs. of 311 m22.3s ranking points B. Mean ranking points 3 m45.8s (data as run A) C. Mean ranking points 4 m3.5s (all records) D. EBV + mean(e) from 3 m17.0s run A 2,4 E. Accumulated lifetime points 5 m18.0s CPU time used for AI-REML estimation of parameters in DMU. 2 Weighted with no. of observations available for each horse. 3 Based on young horses with records in full data but without records in reduced data. In the latter, phenotypic records of horses born were excluded (N A,B and D = 1080, N c = 3485, N E = 2565). 4 Same model estimating ability derived if variances were fixed to results from alt (a) using DMU among horses included in run A (n = 7814) after adjustment as: r 2 IA est(d) = r 2 IA (D) intercept + N offspring N 2 offspring SD of SE rider level SD of SE age-gender mean SE rider level mean SE age-gender among horses included in run A (n = 7814). stallions with at least 15 offspring in runs A E was found for run E because some stallions with high EBVs were excluded in the ranking of A as data were reduced. Comparison among the same stallions, that is those with at least 15 offspring in all runs, found mean EBV(A)s among top 20 dressage stallions in A D to be fairly similar ( ) and those in E to differ most (0.50). For show jumping, runs A, D and E had similar mean EBV(A), whereas mean results (B and C) differed most. Discussion Model predictive abilities The model that produced the most consistent EBVs between full and reduced data (i.e. over time) was different between disciplines (dressage: run C, show jumping: run E), whereas run D was the second best alternative in both disciplines (r EBVfull, EBVred = 0.74). The same trends were also found considering indications of least bias using b EBVfull EBVred (0.96 < b < 0.98). Run E that was most advantageous for show jumping, at the same time produced the most biased dressage EBVs, and model C which was most advantageous for dressage showed among the highest biases among show jumping runs. The fact that runs C and E indicated best model predictability in respective discipline, despite lack of correction for nongenetic effects as rider experience and judge, suggests historic information to be important for horses without own results. Run D was only slightly disadvantageous compared to the best alternative in each discipline, but showed consistently good results for both disciplines. These discipline differences may be due to differences in structure between data sets. In show jumping, generally more horses enter each competition class, and possibly each separate result might be considered slightly more random than for dressage. Thus, the ranking of one particular show jumping horse could differ more between classes than in dressage. On the other hand, show jumping horses generally compete more frequent than dressage horses, with an average of 33 records per horse in the raw data compared to 17 in dressage (see material section). Further, dressage is a subjectively judged competition trait, where the judge is expected to have a larger influence than for show jumping which is more objectively scored. The variance of the competition class effect including judge was distinctly larger Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015) 1 12

7 L. J onsson et al. Modelling repeated competition records Table 3 Show jumping results regarding CPU time used, heritability, mean reliability of breeding values (EBVs) for horses with at least one competition record and model predictive ability for run A E Model predictive ability 3 Reliability of horses with records 2 Of available horses in each run (A E) Of horses included in run A Run CPU time 1 h 2 SE (h 2 ) No. horses r 2 IA SD (r 2 IA) Correlation (r EBVfull, EBVred ) Regr. coeff (b EBVfull EBVred ) Correlation (r EBVfull, EBVred ) Regr. coeff (b EBVfull EBVred ) A. Repeated obs. of 2717m1.6s ranking points B. Mean ranking points 3 m30.5s (data as run A) C. Mean ranking points 4 m22.5s (all records) D. EBV+mean(e) from 3 m28.4s run A 2,4 E. Accumulated lifetime points 3 m54.5s CPU time used for AI-REML estimation of parameters in DMU. 2 Weighted with no. of observations available for each horse. 3 Based on young horses with records in full data but without records in reduced data. In the latter, phenotypic records of horses born were excluded (N A,B and D = 1689, N c = 2696, N E = 1974). 4 Same model estimating ability derived if variances were fixed to results from alt (a) using DMU among horses included in run A (n = ) after adjustment as: r 2 IA est(d) = r 2 IA (D) intercept + N offspring N offspring SD of SE competition class SD of SE age-gender mean SE rider level mean SE competition class mean SE age-gender among horses included in run A (n = ). (0.52) compared to effects of rider level (0.29) and age-gender (0.03), in dressage. In contrast, the competition class effect had a small variance in show jumping (0.07), compared to rider level (0.30) and age-gender (1.94) (not shown in results). Advantages and disadvantages with studied alternatives Each of the studied alternatives had different advantages and disadvantages as summarized in Table 7. A strong incentive of modelling repeated observations (run A/D) rather than summarized (mean or sum) observations is the possibility to correct for experience of the rider and influencing factors associated with the competition class and venue for which the observation was recorded. The opportunity to correct for these non-genetic effects suggests, according to theory, that run A/D would be advantageous, provided that complete competition statistics were available and data editing rules did not markedly reduce the data. However, in practice most of the historic data, when only placings (approximately 25% best) were recorded, is dropped in runs A, B and D, which may introduce a risk of selection bias of runs A and D. Less than 1% of included records were documented before 1998 in dressage, and approximately 5% in show jumping in runs A, B and D. The number of included horses was therefore 2 3 times as many in runs C and E. Number of stallions with at least 15 offspring records was also higher in runs C and E, in particular for the older breeding stallions. On the other hand, using merely statistics from a period that includes also starts without placings may have reduced the risk of preselection. In the Belgium warmblood, heritabilities of competition statistics based on placed (25% best) horses was lower than heritabilities based on all competing horses, presumably as a result of preselection (Janssens et al. 1997). Another aspect to consider is computer capacity requirements that were high for repeated records, and would be even much higher in the context of multitrait evaluations. With the suggested run D (pseudo-phenotypes), this issue could be solved. In a single-trait scenario, the two-step approach (run D) would be more computer demanding than the repeatability model (run A) because the latter is required to generate dependent variables for the former. However, as the number of traits in a multiple-trait setting 2015 Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015)

8 Modelling repeated competition records L. J onsson et al. Table 4 Effects of mean SE and standard deviation (SD) of mean SE of non-genetic effects as selected most appropriate to adjust inflated reliability estimates in GLMSELECT (SAS Insitute Inc 2015), accompanied by p-value and proportion of sums of squares Effect Estimate p= Dressage Intercept 4.58 r 2 IA (D) 0.31 < N offspring < N offspring < SD of SE rider level 2.02 < SD of SE age-gender < Mean SE rider level 1.04 < Mean SE age-gender < Show jumping Intercept 0.25 r 2 IA (D) 0.33 < N offspring < N offspring < SD of SE competition 0.09 < class SD of SE age-gender 1.88 < Mean SE rider level 0.59 < Mean SE competition 0.02 < class Mean SE age-gender 1.35 < % of total sums of squares increases, time used to generate the dependent variable becomes less important. This also applies in a scenario of future genomic multiple-trait evaluations. Estimated heritabilities differed substantially among different runs. Heritabilities for runs A and D, which refer to single competition records, are expected to be lower than heritabilities for runs B, C and E, which refer to traits summarized across several records. Differences in estimated heritabilities for runs A and D (h 2 = 0.16 and 0.21 for dressage; 0.07 and 0.05 for show jumping) may be due to differences in separating non-genetic and residual variances in the single- and two-step procedures. Realized reliabilities were more relevant to compare than heritabilities, because the square root of the former is proportional to potential genetic progress. Mean reliability was similar between run A and E when based on the same set of horses, and lower in runs B and C. Estimated reliabilities of run D were inflated with a mean of 0.86 for dressage and 0.68 for show jumping among horses with competition records. This inflation was likely caused by uncertainty associated with pre-adjustments not being incorporated in the two-step BLUP. Further investigations revealed that number of offspring and mean SE of the age-gender effect showed most contribution to the inflation in both disciplines (Table 4). In the routine breeding practice of the DWB, reliabilities are used to decide whether a horse should obtain an officially published EBV or not (if 0.60). The consequence if using run D in the breeding practice would be for the criterion of official EBVs to be based on something else, for example none of recorded offspring, an altered required level of reliability or to adjust reliabilities as illustrated in Fig. 1. A disadvantage of run E was the risk of bias due to censoring as the youngest horses (5 year olds) had not completed their competition career at the cut of data collection, which was most clearly seen for young dressage horses (b EBVfull EBVred = 1.30). Using such a trait introduces a dilemma of either disregarding information on all horses that are still active (i.e. late selection), adopting complicated survival models or accepting selection bias due to censored records. Also, it was not possible to correct for non-genetic effects present during individual starts, as lifetime accomplishments were summed. The later could, however, be achieved in a two-step model similar to run D if recorded. Consequences of using alternative models for selection Substantial changes in top 20 ranked stallions were found, especially between run A versus C and E. This could merely be explained by the fact that more stallions with 15 offspring records were included in the ranking lists of (C and E). For dressage, number of stallions was 106 in A, 305 in C and 297 in E. For show jumping, it was 46 in A, 261 in C and 251 in E. However, changes also occur as (C and E) was based on results from a longer time period compared to A. This could provide a different picture, especially for older stallions, in situations of relatively limited extents of competition data as in the horse industry, where generation intervals are usually long. This was demonstrated with the fact that mean EBV from run A [EBV (A)] of top 20 stallions with at least 15 offspring in run E were higher (dressage: 1.14, show jumping: 0.70) than mean EBV(A) in the top 20 ranking with 15 offspring in A (dressage: 1.07, show jumping: 0.67). Thus, some high EBV(A) stallions had been excluded from the top 20 ranking of run A. When comparing the same stallions between runs (A E), mean EBV(A) of D and A was similar to each other, whereas run E top 20 would give a markedly different selection response than A in dressage. However, in show jumping, E would give a similar selection response to run A and D, which B and C would not Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015) 1 12

9 L. J onsson et al. Modelling repeated competition records (a) Reliabilities for dressage (b) Reliabilities for show jumping r 2 IA,RunD r 2 IA,RunD r 2 IA,RunA r 2 IA,RunA (c) Reliability differences for dressage (d) Reliability differences for show jumping r 2 IA difference r 2 IA difference r 2 IA,RunA r 2 IA,RunA Figure 1 Actual reliabilities from run D ( ) and adjusted reliabilities from run D (Δ) as function of reliabilities from run A for dressage (a) and show jumping (b). Figure (c) (dressage) and (d) (show jumping) show differences between reliabilities from run A and reliabilities from run D. For run D, differences for both actual (x) and adjusted (Δ) reliabilities are shown. Table 5 Pearson correlations between estimated breeding values (EBVs) of runs A E, p < Dressage 1,2 Show jumping 1,3 Run Run B Run C Run D Run E Run B Run C Run D Run E A. Repeated obs. of ranking points B. Mean ranking points (data as run A) C. Mean ranking points (all records) D. EBV + mean(e) from run A E. Accumulated lifetime points 1 Correlations based on EBVs of horses with at least one competition result in respective discipline. 2 N = 7814, except for (C E) correlation of N = N = , except for (C E) correlation of N = C E correlation of horses included in run A (N = 7814) was C E correlation of horses included in run A (N = ) was Weighted with no. of observations available for each horse Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015)

10 Modelling repeated competition records L. J onsson et al. Table 6 Estimated breeding value (EBV) ranking changes between run A of repeated observations and B E, in dressage and show jumping Run No. stallions top 20 ranked in (A) Mean ranking SD of mean ranking Min. Max. Mean EBV(A) in top 20 of A E 1 Mean EBV(A) red in top 20 of A E 2 Dressage A. Repeated obs. of ranking points B. Mean ranking points (data as run A) C. Mean ranking points (all records) D. EBV + mean(e) from run A E. Accumulated lifetime points Show jumping A. Repeated obs. of ranking points B. Mean ranking points (data as run A) C. Mean ranking points (all records) D. EBV + mean(e) from run A E. Accumulated lifetime points The mean EBV from run A of top 20 stallions with at least 15 competing offspring in each of runs A E, respectively. N = stallions for dressage and N = for show jumping. 2 The mean EBV from run A among top 20 stallions with at least 15 competing offspring in all runs (A E). N = 105 for dressage and N = 46 stallions for show jumping. Table 7 Advantages and disadvantages with studied competition records 1 Advantages Disadvantages Correction for rider, judge/event etc. Compared to theory Amount of data included A and D can correct for these effects Theory suggests A to be most correct, provided a perfect data set with enough observations per horse and event to pass the data editing requirements in the majority of recorded data C and E could include 2 3 times more horses; better modelling of historic selection B, C and E cannot correct for these E introduces a higher risk of bias of estimated breeding values (EBVs) due to censoring of young horses that are still competing A, B and D included information of less horses, fewer stallions with reliable breeding values; problem of modelling historic selection may be alleviated by including correlated traits in multiple-trait analysis (runs B and D) Computation requirements B E computationally feasible in multitrait evaluations A is computationally infeasible in multitrait evaluations Reliabilities A and E produces similar reliabilities that are D produces inflated reliability estimates larger than B and C 1 See text or Table 1 for descriptions of runs A E referred to in table. Model choices and study drawbacks Even though time and age differences had been accounted for in the first step (run A), through competition class and age-gender effects, gender and birth year still had a significant effect on pseudo-phenotypes used in the second step model (run D). Similar results have been found by Lassen et al. (2007a) for head-year-season and birth year. Inclusion of birth year in the second step model increased the accuracy of breeding values as possible bias in genetic trend was reduced (Tarres et al. 2006; Lassen et al. 2007a). Three trials of different weights included for pseudophenotypes in the 2nd step of run D was initially tested, that is unweighted, number of observations and 1/[SEP 2 +VAR(e)/n]. All trials produced EBVs with high correlations to EBVs of run A (r > 0.99), whereas a weight representing number of observations was found to produce the least inflated reliabilities. Thus, number of observations was chosen as weight for pseudo-phenotypes. Trials of weighted analyses of runs B and C based on number of observations showed a lower model predictive ability compared to an unweighted model; thus, only results for the latter was shown. Results for horses competing internationally in other countries were not possible to obtain in a satisfactory way similar to other studies of competition Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015) 1 12

11 L. J onsson et al. Modelling repeated competition records statistics of warmblood riding horses. This is a drawback that will need to be solved for best outcome of the systems in the future. However, generally horses competing internationally would also be expected to have the highest competition results nationally, to get to international level. Furthermore, it is only a small fraction of horses that compete internationally. Including correlated traits measured on most young horses (i.e. before export) in multivariate analyses could reduce such bias. Closing remarks In conclusion, there are benefits and drawbacks of all alternative genetic evaluation procedures presented in this study (runs A E). It is likely that the slight disadvantage in model predictive ability and bias of run D compared to run C (in dressage) and E (in show jumping) was due to the large reduction in included data when assuring sufficient number of horses in classes of fixed effects. By time, as a larger proportion of competition records include all starts regardless of the result, the reduction of data is expected to be less of a disadvantage. The inclusion of young horse traits in a multiple-trait setting may possibly also have such an effect. Thus, even if different approaches are to recommend for the two disciplines at present (run C and E, respectively), run D of pseudo-phenotypes may be expected to be advantageous for use in both disciplines in the future. Regardless of whether a summed or average type of data is desired, it is possible to first precorrect single competition scores for rider experience and competition class using a less computer capacity demanding two-step approach with pseudo-phenotypes as illustrated in this study (run D) provided that this information is recorded. Acknowledgements This research is part of the GenHors project which is partly funded by the Innovation fund in Denmark and Asta og Jul. P. Justesen s Fund. Data were kindly provided by the Danish Warmblood Association and the horse section at SEGES. References Boelling D. (2011) Description of competition index (in Danish). Word-document from the Danish warmblood association, received 27 September pp. Jairath L., Dekkers J.C., Schaeffer L.R., Liu Z., Burnside E.B., Kolstad B. (1998) Genetic evaluation for herd life in Canada. J. Dairy Sci., 81, Janssens S., Geysen D., Vandepitte W. (1997) Genetic parameters for show jumping in Belgian sporthorses. In: Proceedings of the The 48th Annual Meeting of the European Association for Animal Production (EAAP), August 1997, Vienna, Austria, 5 pp. Jensen J., M antysaari E.A., Madsen P., Thompson R. (1997) Residual maximum likelihood estimation of (co)variance components in multivariate mixed linear models using average information. J. Indian Soc. Agric. Stat., 49, J onsson L., Christiansen K., Holm M., Mark T. (2014) Genetic correlations between young horse and dressage competition results in Danish warmblood horses Vancouver, BC, Canada, August 2014, No 791. Koenen E.P.C., Aldridge L.I., Philipsson J. (2004) An overview of breeding objectives for warmblood sport horses. Livest. Prod. Sci., 88, Lassen J., Sørensen M.K., Madsen P., Ducrocq V. (2007a) An approximate multitrait model for genetic evaluation in dairy cattle with a robust estimation of genetic trends. Genet. Sel. Evol., 39, Lassen J., Sørensen M.K., Madsen P., Ducrocq V. (2007b) A stochastic simulation study on validation of an approximate multitrait model using preadjusted data for prediction of breeding values. J. Dairy Sci., 90, Luehrs-Behnke H., Roehe R., Kalm E. (2002) Genetic associations among traits of the new integrated breeding evaluation method used for selection of German warmblood horses. Vet. Zootec., 18, Madsen P., Jensen J. (2013) An User s Guide to DMU. A package for analysing multivariate mixed models. Version 6, release 5.2. Danish Institute of Agicultural Science, Department of Animal Breeding and Genetics, Research Center Foulum, Tjele, Denmark, pp Reverter A., Golden B.L., Bourdon R.M., Brinks J.S. (1994) Technical note: detection of bias in genetic predictions. J. Anim. Sci., 72, Ruhlmann C., Janssens S., Philipsson J., Thoren-Hellsten E., Crolly H., Quinn K., Manfredi E., Ricard A. (2009) Genetic correlations between horse show jumping competition traits in five European countries. Livest. Sci., 122, SAS Insitute Inc (2015) SAS Online Doc 9.2. SAS Institute Inc, Cary, NC. (accessed 17 March 2015) Schaeffer L.R. (1994) Multiple-country comparisons of dairy sires. J. Dairy Sci., 77, Tarres J., Piedrafita J., Ducrocq V. (2006) Validation of an approximate approach to compute genetic correlations between longevity and linear traits. Genet. Sel. Evol., 38, Thoren Hellsten E., Viklund A., Koenen E.P.C., Ricard A., Bruns E., Philipsson J. (2006) Review of genetic parame Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015)

12 Modelling repeated competition records L. J onsson et al. ters estimated at stallion and young horse performance tests and their correlations with later results in dressage and show-jumping competition. Livest. Sci., 103,1 12. Thoren Hellsten E., Jorjani H., Philipsson J. (2009) Genetic correlations between similar traits in the Danish and Swedish Warmblood sport horse populations. Livest. Sci., 124, Viklund A., Braam A., N asholm A., Strandberg E., Philipsson J. (2010) Genetic variation in competition traits at different ages and time periods and correlations with traits at field tests of 4-year-old Swedish Warmblood horses. Animal, 4, Blackwell Verlag GmbH J. Anim. Breed. Genet. (2015) 1 12